NHT separators

Nht Further

A judgement-based list. Nothing in this document states or implies a percentage for an NHT question, because VCAA has never published one.

VCAA's November exam reports carry a per-question table of the percentage of the state that earned each available mark. That is what makes a November separator a measurement: 50% or fewer of the state earned full marks. The Northern Hemisphere Timetable (NHT) reports carry no such table. They publish answers, worked solutions and, occasionally, a note on what students did badly - and nothing else. So every verdict below is an inference, calibrated against the 2 150 graded November questions in corpus/export/nov_all.csv.

There was no 2020 NHT sitting. 2024 onward is covered elsewhere.

Method

1. What the November data says a separator looks like

Before reading a single NHT paper I derived the structural signature of a November separator from nov_all.csv (restricted to 2016-2023, the years whose paper structure matches the NHT papers here: 1 057 graded questions).

CAL-1 - Position inside a Section B module MCQ block (Exam 1). The eight module multiple-choice questions are ordered roughly easy to hard. The separator rate by position:

CAL-2 - Position inside the Core (Exam 1). Core Data analysis Q1-Q16 is much flatter (medians 88 down to about 51, separator rate never above 50%). Core Recursion Q17-Q24 is not: Q23 was a separator in 5 of 7 years (median 38%) and Q24 in 4 of 7 (median 33%).

CAL-3 - Part letter (Exam 2). Separator rate by the letter of the part:

CAL-4 - Mark value (Exam 2). 1-mark parts were separators 45% of the time (median 56%); 2-mark parts 71% of the time (median 38%). A 2-mark written part is the single strongest plain structural predictor in the dataset.

CAL-5 - Topic. Exam 2 separator rate: Recursion 57%, Geometry 51%, Matrices 51%, Graphs and relations 49%, Networks 45%, Data analysis 41%. Exam 1: Networks 42%, Graphs and relations 38%, Recursion 36%, Matrices 33%, Geometry 33%, Data analysis 21%.

CAL-6 - Archetypes. I then pulled the actual question text of every November Exam 1 paper 2016-2025 and joined it to its published percentage, so that an NHT question could be matched to the same task in November rather than merely to the same topic. The families that recur in the sub-50% band:

And from separators.csv, the Exam 2 families that live below 22% full marks: two-stage finance-solver problems (8, 11, 13, 19%), sign of r or of a slope (19, 21%), boxplots drawn with outliers (17%), an LP optimum lying along a constraint so there are many optimal integer points (7, 10, 20%), reading a cut whose edges run the wrong way (2%), reducing a project by n weeks at least cost (9, 12%), interpreting a determinant (21%), and S(n+1) = T.Sn + B iterated more than once (10, 12%).

2. What I did with the NHT papers

I read all twelve NHT papers and all twelve NHT reports in full and assigned every question one of SEPARATOR (I would expect 50% or fewer of a comparable cohort to earn full marks), BORDERLINE (near the line, could fall either way) or ROUTINE. Only the first two are listed. For each listed question the Evidence line gives at least one of:

• (a) a closely analogous November question, cited with its real published percentage;
• (b) the NHT report itself flagging difficulty, or prescribing a mark scheme demanding enough that partial credit is the likely outcome - quoted;
• (c) a structural feature that the calibration above shows is strongly associated with separators (CAL-1 to CAL-6).

Most entries carry (a) and (c). Type (b) is rarer, but the NHT reports do leak four kinds of performance signal, all of which I have used where present:

That last row also settles a question about the corpus: VCAA does run item analysis on NHT papers. It simply does not publish the numbers.

3. Reading the references

Exam 1 Section B module questions are numbered Q1-Q8 within each module, exactly as the paper prints them and exactly as nov_all.csv stores them, so the topic field is what distinguishes e.g. Matrices Q8 from Networks Q8.

Summary

Listed questions by topic and year

Listed questions by verdict

2017 (NHT)

2017 Exam 1 (NHT) — 18 SEPARATOR, 9 BORDERLINE

Data analysis

2017 Exam 1 Q5 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence low

Asks: Read a histogram whose horizontal scale is log(population density) and count the countries with a density below 10 people/km2.

Evidence: The NHT report has to teach the underlying idea from scratch - "On a log scale, a number equal to 10^n would be shown as n. Hence, a population density of 10 is shown on the horizontal log scale as 1" - which is the examiners conceding the step is not automatic. Against that, CAL-2 puts core Data analysis position 5 among the easier core items, so I have kept this only at BORDERLINE with low confidence.

Closest November analogue: 2016 E1 Q11 Data analysis (log transformation) - 54%

2017 Exam 1 Q10 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Choose the equation of a least squares line from a scatterplot, given r and the axis labels.

Evidence: CAL-6: reading a least-squares equation off a scatterplot is a recurring sub-50% family in November. The NHT report spends a full paragraph killing the attractive wrong option - "Option C showed an intercept of 7.4, which was approximately the value shown on the graph when width = 7. But the intercept must be where the line cuts the vertical axis when the explanatory variable = 0" - and two of the five options also swap the response and explanatory variables.

Closest November analogue: 2020 E1 Q13 Data analysis - 34%; 2017 E1 Q8 - 43%; 2018 E1 Q8 - 46%

2017 Exam 1 Q11 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: Identify which of five statements about a fitted line is NOT true; the false one is that predicting at length 8.1 mm would be extrapolation.

Evidence: Two skills at once: convert r = 0.8616 to r-squared = 74% to clear option D, and then check 8.1 mm against the plotted data range to see that option E is the false statement. CAL-6 puts coefficient-of-determination-in-words items at 41-45% in November, and a 'not true' stem forces all five options to be evaluated.

Closest November analogue: 2019 E1 Q10 Data analysis - 41%; 2018 E1 Q9 - 45%

2017 Exam 1 Q13 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: Describe a quarterly time series plot; the correct answer is seasonality only, with no trend.

Evidence: The designed error is option E, 'increasing trend with seasonality', which is what the eye reports from a plot that rises within each year. The NHT report argues the point explicitly - "A trend is not evident since there is no general upward or downward direction of the sales over the four years". CAL-2: core Data analysis position 13 has a November median of 51% full marks and was a separator in 3 of 8 years.

2017 Exam 1 Q15 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Deseasonalise Sunday earnings when the Sunday seasonal index is the one not given in the table.

Evidence: A hidden first step: the six printed indices must be summed and subtracted from 7 to recover the Sunday index (1.62) before any deseasonalising can start. The report works both steps. CAL-6: the seasonal-index family occupying the last core Data analysis slot in November ran 32, 40, 43 and 50% - every one a separator - and none of those had an index missing.

Closest November analogue: 2017 E1 Q16 Data analysis - 32%; 2022 E1 Q16 - 40%

2017 Exam 1 Q16 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: Interpret a seasonal index of 0.74 as a statement about average daily earnings.

Evidence: Options A and C are 26% less and 35% less - the difference between 1 - 0.74 and 1/0.74 - 1, which is exactly the confusion the November items in this family punish. CAL-6 gives 32, 40, 43 and 50% for seasonal-index interpretation. This is the easier direction of the trap (index below 1, no correction asked for), which is why it is BORDERLINE rather than SEPARATOR.

Closest November analogue: 2023 E1 Q16 Data analysis - 43%; 2025 E1 Q16 - 50%

Recursion and financial modelling

2017 Exam 1 Q21 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: From one completed row of an amortisation table, find the interest paid with the second repayment.

Evidence: The interest rate is never given; it must be recovered as 720/180000 = 0.4% per period from the first row and then applied to the new balance. Two chained inferences for one mark. CAL-2: core Recursion position 5 (Q21) was a November separator in half the years, median 51.5%.

Closest November analogue: 2022 E2 Q8d Recursion - 19% (recover a rate, then use it)

2017 Exam 1 Q23 (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

Asks: Pick the recurrence relation matching a reducing-balance depreciation graph annotated with (3, 6859) and (4, 6516.05).

Evidence: CAL-2: Q23 was a separator in 5 of the 7 comparable November years, median 38% full marks - the hardest single slot in the core. Offsetting that, the NHT report's own route is a one-line elimination ("Reducing balance means that Pn+1 = r x Pn where r < 1. This leaves only option A"), so a prepared student answers it instantly. Genuinely near the line.

2017 Exam 1 Q24 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: Given the balance of a monthly compounding investment at six months and at two years, find the amount originally invested.

Evidence: Two separate finance-solver passes: first solve the 18-month interval for the rate, then run that rate backwards over six months for the principal. CAL-6: two-stage finance-solver problems are the deepest separator family in the whole November dataset. CAL-2 also puts Q24 at a November median of 33% full marks.

Closest November analogue: 2021 E2 Q9b Recursion - 8%; 2020 E2 Q11 - 19%

Matrices

2017 Exam 1 Q5 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Decide how many of four printed matrix equations would actually solve a 2x2 simultaneous system.

Evidence: Four separate objects to validate, including one that is not defined for multiplication and one whose inverse does not match its column matrix. The NHT report needs a full page of algebra to justify the answer. CAL-6: abstract 'which matrix statement holds' items ran 36, 40, 42 and 45% in November.

Closest November analogue: 2017 E1 Q7 Matrices - 36%; 2021 E1 Q7 - 40%

2017 Exam 1 Q6 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Choose the true statement about a three-state transition matrix; the true one compares long-run music and art numbers.

Evidence: To eliminate the distractors a student must compute a Week 3 state matrix and a long-run state matrix, then compare. CAL-1: position 6 in a module block was a November separator 55% of the time (median 46%). CAL-6: long-run/steady-state interpretation ran 39-46%.

Closest November analogue: 2023 E1 Q27 Matrices - 39%; 2018 E1 Q8 - 46%

2017 Exam 1 Q7 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: From a two-step dominance matrix S-squared alone, deduce which result must have occurred in a four-player round robin.

Evidence: This runs dominance backwards - November normally asks students to build S-squared, not to reconstruct the tournament from it. The NHT report needs a five-step chain of deductions plus a drawn digraph. CAL-1: position 7 was a November separator 65% of the time, median 45%.

Closest November analogue: 2016 E1 Q8 Matrices (two-step dominance) - 42%

2017 Exam 1 Q8 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: For an n x n matrix A, a row matrix R and a column matrix C, decide which triple product can give a 1 x 1 result.

Evidence: Purely abstract order arithmetic with no numbers to fall back on; the report enumerates six pairwise products before reaching RAC. CAL-1: position 8 in a module block was a November separator in 26 of 31 cases (84%), median 35% full marks - the strongest single structural signal in the dataset. CAL-6: abstract matrix-order items ran 36-45%.

Closest November analogue: 2017 E1 Q7 Matrices - 36%; 2022 E1 Q7 - 42%

Networks and decision mathematics

2017 Exam 1 Q2 (NHT) — Networks and decision mathematics — 1 mark — BORDERLINE, confidence medium

Asks: Identify the statement that is NOT true of two drawn graphs; the false claim is that each contains a Hamiltonian cycle.

Evidence: CAL-6: 'not true' items mixing Eulerian trails with Hamiltonian cycles ran 17% and 29% in November - both deep separators - because students must test five properties on two graphs. Against that, CAL-1 puts position 2 among the easiest slots (15% separator rate), so VCAA evidently intended this to be approachable. The conflict is why it is BORDERLINE.

Closest November analogue: 2021 E1 Q5 Networks - 17%; 2017 E1 Q6 - 29%

2017 Exam 1 Q3 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Count the faces of a planar graph that is drawn with edges crossing.

Evidence: The report's method is to "redraw two edges that appear to cross over another edge" before counting - the graph as printed is not in planar form, so Euler's formula on the printed picture gives the wrong answer unless v and e are counted correctly. CAL-6: planar-graph/face items ran 11, 21, 34 and 41% in November, all separators.

Closest November analogue: 2020 E1 Q7 Networks - 11%; 2022 E1 Q4 - 21%

2017 Exam 1 Q6 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Find the latest starting time for activity I in a sixteen-activity project network.

Evidence: Requires a full forward and backward pass over sixteen activities to establish that the critical path is C-F-I-K-L-P, before the answer (4 days) falls out. CAL-1: position 6, 55% November separator rate. CAL-6: critical-path timing items ran 31-48%.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2022 E1 Q8 - 34%

2017 Exam 1 Q7 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Count how many different minimal spanning trees a weighted graph with repeated edge weights admits.

Evidence: November asks students to find a minimum spanning tree or its weight; counting the distinct trees produced by tied weights is a step beyond anything in the November Exam 1 corpus, and requires systematic case work rather than one run of Prim's algorithm. CAL-1: position 7, 65% November separator rate, median 45%.

Closest November analogue: 2016 E1 Q4 Networks (minimum spanning tree) - 52%, an easier variant

2017 Exam 1 Q8 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: A four-worker assignment problem is re-solved after one worker's time for one duty rises from 3 to 7 minutes; say how the minimum total changes.

Evidence: CAL-6: this exact operation - re-allocate after a single cost is changed - is one of the most reliable separators in November Exam 1, at 24, 30 and 39%. The report has to lay out both allocation tables to show the total rises by only one minute rather than the four that the naive answer gives. CAL-1: position 8, 84% separator rate.

Closest November analogue: 2018 E1 Q8 Networks - 24%; 2016 E1 Q8 - 30%

Geometry and measurement

2017 Exam 1 Q3 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: Of five city pairs given by latitude and longitude, choose the pair with the largest time difference.

Evidence: Five separate longitude differences must be computed and each checked against 180 degrees. CAL-6: latitude/longitude distance-and-time items ran 26, 41, 43 and 49% in November - and none of those asked for five comparisons at once.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2019 E1 Q6 - 41%

2017 Exam 1 Q4 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Find the area to be painted on a model house: a triangular prism roof on a rectangular box, walls and roof only.

Evidence: Four different surfaces, a slant height that has to be recovered by Pythagoras from the 52 cm and 96 cm dimensions, and the floor and base deliberately excluded. CAL-6: composite surface-area items ran 30, 36 and 48% in November.

Closest November analogue: 2016 E1 Q8 Geometry - 30%; 2020 E1 Q9 - 36%

2017 Exam 1 Q5 (NHT) — Geometry and measurement — 1 mark — BORDERLINE, confidence medium

Asks: Given sin(x) = 2/5 in a triangle with sides 8 cm and 12 cm, find sin(y).

Evidence: The sine rule has to be used as a ratio without ever finding an angle - most students will invert the ratio and get 3/5 or 5/3, both of which are printed as options. CAL-6: sine/cosine-rule items ran 30-45% in November. Held at BORDERLINE because CAL-1 puts position 5 at only a 30% separator rate.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2018 E1 Q4 - 42%

2017 Exam 1 Q6 (NHT) — Geometry and measurement — 1 mark — BORDERLINE, confidence medium

Asks: Find the shortest distance along a meridian between 25 N and 35 S on the same longitude.

Evidence: The single step that decides it is adding rather than subtracting the two latitudes across the equator (60 degrees, not 10). CAL-1 puts position 6 at a 55% November separator rate. CAL-6: latitude/longitude arc items ran 26-49%. Listed as BORDERLINE because once the 60 degrees is seen the arithmetic is a single arc-length formula.

Closest November analogue: 2018 E1 Q3 Geometry - 43%; 2022 E1 Q4 - 49%

2017 Exam 1 Q7 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: Choose the calculation for the shortest distance along the 50 N parallel between 85 E and 112 W.

Evidence: Two traps stacked: the radius of the parallel is 6400 sin(40), not 6400 sin(50), and the angular separation of 197 degrees must be replaced by 360 - 197 = 163. The report spells both out. Four of the five options are built from exactly these two errors. CAL-1: position 7, 65% separator rate. CAL-6: latitude/longitude family 26-49%.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2018 E1 Q3 - 43%

2017 Exam 1 Q8 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: Bearings plus an isosceles triangle: find QR when the bearing of Q from S is 120 degrees, SR = 80 m and PR = 100 m.

Evidence: The report's solution needs the ambiguous case of the sine rule - "this is less than angle PSQ (120), therefore, the ambiguous case for sine must be used" - after the isosceles property has been used to get two angles. The ambiguous case appears almost nowhere else in this course. CAL-1: position 8, 84% November separator rate, median 35%.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2020 E1 Q10 - 45%

Graphs and relations

2017 Exam 1 Q5 (NHT) — Graphs and relations — 1 mark — BORDERLINE, confidence medium

Asks: Choose one of the five inequalities that define a shaded feasible region.

Evidence: Both the boundary line and the direction of the inequality have to be right, and the options pair the same line with both directions. CAL-6: feasible-region items in November ran 29-40% when the region had to be interpreted rather than just read. CAL-1 puts position 5 at 30%, hence BORDERLINE.

Closest November analogue: 2016 E1 Q5 Graphs and relations - 29%; 2018 E1 Q7 - 40%

2017 Exam 1 Q7 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: All points on the edge AB of a feasible region maximise an objective function; choose the objective function.

Evidence: CAL-6: the linear-programming sliding-line family is the most consistent separator in November Exam 1 - 29, 29, 31, 39, 40, 44 and 47% across seven papers, every one a separator. This is the purest form of it: the objective must be recognised as having the same gradient as the boundary of Inequality 1.

Closest November analogue: 2022 E1 Q8 Graphs and relations - 29%; 2020 E1 Q10 - 31%

2017 Exam 1 Q8 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: Two hoses fill a tank; one is removed at 15 minutes. Find the filling rate over the remaining interval.

Evidence: Three chained steps for one mark: the two-hose rate from (15, 400), the hypothetical full time 22.5 minutes, then a = 31.5 from the nine-minute delay, then the gradient over the second segment. CAL-1: position 8, 84% November separator rate, median 35% full marks.

2017 Exam 2 (NHT) — 22 SEPARATOR, 6 BORDERLINE

Data analysis

2017 Exam 2 Q1b (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Show that 17.1 is an outlier for a dot plot with Q1 = 20 and Q3 = 21.8.

Evidence: The NHT report sets a three-part mark scheme: "The answer needed to show calculations and values for the IQR and for the lower fence. A conclusion based on comparing the 17.1 data value and the lower fence was then required." All three must appear for both marks. CAL-4: 2-mark Exam 2 parts were November separators 71% of the time (median 38%).

2017 Exam 2 Q1c (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

Asks: Complete a boxplot on the printed dot-plot axis, given that the data contain an outlier.

Evidence: The report awards one mark for the median at 21 and one for "two correct whiskers ending at 18.2 and 24.4" - that is, whiskers stopping at the most extreme non-outlier values rather than at the fences or at the data extremes. This is exactly the discrimination the hardest November boxplot question turned on. CAL-4: 2-mark part.

Closest November analogue: 2020 E2 Q2c Data analysis - 17% ("Those who found the two outliers often extended the whiskers to the lower and upper fence values")

2017 Exam 2 Q1d (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Explain why parallel boxplots suggest an association between energy generated and month, quoting the values of an appropriate statistic.

Evidence: Two marks, and the report's answer quotes three medians with their units - a bare 'the medians are different' earns one at most. Explain-and-quote-values parts are where November students most often score 1 of 2. CAL-4: 2-mark parts, 71% November separator rate, median 38%.

Closest November analogue: 2021 E2 Q3eii Data analysis - 18% ("Students found it hard to convey the idea... without linking it to the given equation")

2017 Exam 2 Q2ai (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Write down r to two decimal places given that the coefficient of determination is 0.749.

Evidence: The square root is trivial; the sign is not. Nothing in the part states that the association is negative - it has to be read off the scatterplot (or anticipated from part b). The report makes the point explicitly: "Since the gradient of the least squares line is negative, the correlation coefficient, r, must also be negative." CAL-6: dropping the sign of r or of a slope is a named November failure at 19% and 21%.

Closest November analogue: 2021 E2 Q3b Data analysis - 19% ("Many students found 0.938 but left off the negative sign")

2017 Exam 2 Q2bii (NHT) — Data analysis — 2 marks — BORDERLINE, confidence medium

Asks: Interpret the slope -4.38 of the least squares line in terms of relative humidity and temperature.

Evidence: Two marks for a sentence that must carry direction, the words 'on average', both variable names and both units (% per 1 degree C). CAL-4: 2-mark parts were November separators 71% of the time. Held at BORDERLINE because slope interpretation is the most heavily drilled written response in the course.

2017 Exam 2 Q2biii (NHT) — Data analysis — 2 marks — BORDERLINE, confidence medium

Asks: Find the residual when the line is used to predict relative humidity at 11.2 degrees C, to one decimal place.

Evidence: Predict, subtract in the right order, keep the negative sign, round to 1 dp. CAL-4: 2-mark part (71% November separator rate). Residual items in November Exam 1 ran 42-54% when the prediction had to be made first.

Closest November analogue: 2018 E1 Q14 Data analysis (residual) - 42%

2017 Exam 2 Q3b (NHT) — Data analysis — 3 marks — SEPARATOR, confidence medium

Asks: Determine the least squares line for rainy days against month number, writing intercept and slope to three significant figures.

Evidence: The report is blunt about the mark scheme: "Both numbers had to be correctly rounded to three significant figures." Three significant figures on 7.79 and 1.63 is a different rounding rule from the decimal places students habitually use. CAL-4: the only 3-mark written part in the modern November dataset had 28% full marks, and 2-mark parts sit at 71%.

2017 Exam 2 Q4c (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Complete a three-median smoothing on a time series plot by marking the remaining smoothed points with crosses.

Evidence: Median smoothing has to be done graphically, by eye, on days 25 to 29, with no table to work from and no partial credit for a nearly-right cross. CAL-4: 2-mark part, 71% November separator rate, median 38% full marks. Graphical-completion parts are the classic all-or-nothing 2-marker.

Recursion and financial modelling

2017 Exam 2 Q5b (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

Asks: Use recursion to show that the snooker table's value after two years is $2640.

Evidence: The report prescribes an unusually strict scheme: "'Using recursion' begins with writing the initial value (i.e. V0 = 3000). Then, the first calculation using the recurrence rule must be shown and the answer labelled... Subsequent calculation(s) must then show the use of the prior answer to calculate the next value." A student who writes 3000 - 2 x 180 = 2640 gets nothing. The underlying arithmetic, though, is flat-rate depreciation, so this is near the line.

Closest November analogue: 2021 E2 Q9a Recursion - 21% ("did not show the recursive calculations in full")

2017 Exam 2 Q6c (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence medium

Asks: Complete the rule Qn = ___ x ___^n for a balance of $2080.05 at 5.52% p.a. compounding monthly.

Evidence: Both boxes must be right for the two marks: the principal, and a monthly multiplier of 1.0046 obtained by dividing the annual rate by 12 and then converting - the commonest error is to write 1.0552. CAL-4: 2-mark part (71% November separator rate). CAL-3: part c, 59%.

Closest November analogue: 2022 E2 Q8d Recursion - 19% (recover a monthly multiplication factor)

2017 Exam 2 Q7b (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence high

Asks: An account takes $100 monthly deposits for 36 months and then none; find the balance five years after opening.

Evidence: The textbook two-stage finance-solver problem: solve 36 periods with PMT = -100 to get an intermediate future value, then feed that in as PV for 24 periods with PMT = 0. The report lays out both solver screens. CAL-6: this family is the deepest separator band in the whole November dataset. CAL-3/CAL-4: part b, 2 marks, last part of the core.

Closest November analogue: 2021 E2 Q9b Recursion - 8%; 2024 E2 Q8 - 13%; 2020 E2 Q11 - 19%

Matrices

2017 Exam 2 Q1c (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Explain what the product MP represents when M = [0 1 1] and P is a 3x3 diagonal 'seats sold' matrix times a cost column.

Evidence: The answer - "total cost of B and C class seats sold" - requires reading the row matrix as a selector, seeing which classes the zeros switch off, and then describing the result in context. 'Explain what this product represents' is the archetypal one-mark part where students describe the arithmetic instead of the meaning.

Closest November analogue: 2022 E2 Q2bii Matrices - 21% ("few students able to demonstrate how to interpret the determinant value")

2017 Exam 2 Q2c (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: What percentage of the 200 club members are expected to move from B class to A class between two concerts?

Evidence: The trap is the denominator. The transition matrix gives 25%, but the question asks for a percentage of all 200 members, so the answer is 0.25 x 96 = 24, then 24/200 = 12%. Reading 25% straight off the matrix is the natural wrong answer, and is exactly the error November named in the closest analogue. CAL-3: part c, 59% November separator rate.

Closest November analogue: 2021 E2 Q3c Matrices - 17% ("85% taken directly from the transition matrix was a very common incorrect answer")

2017 Exam 2 Q2f (NHT) — Matrices — 2 marks — SEPARATOR, confidence high

Asks: With K3 = TK2 + B and K4 = TK3 + B, find the number of members expected to choose A class at the fourth concert.

Evidence: Two full iterations of S(n+1) = T.Sn + B, with the intermediate state carried at full precision and only the final answer rounded. CAL-3/CAL-4: part f, 2 marks, and the last part of the module - the three strongest structural predictors stacked. CAL-6: iterated T.Sn + B items ran 10% and 12% in November.

Closest November analogue: 2021 E2 Q4 Matrices - 10%; 2024 E2 Q12c - 12%

Networks and decision mathematics

2017 Exam 2 Q1d (NHT) — Networks and decision mathematics — 1 mark — BORDERLINE, confidence medium

Asks: Determine the latest starting time for activity C in a ten-activity project network.

Evidence: A backward pass is needed, and the report's reasoning is fiddly: activities B and D total 5 weeks, so E, F and G cannot start before week 5; A and C take 4, so C may start as late as week 3. CAL-3: part d, 72% November separator rate, median 40% full marks. CAL-6: critical-path timing items ran 31-48% in Exam 1.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2022 E1 Q6 - 48%

2017 Exam 2 Q1e (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Which single activity could be delayed longest without pushing out the project?

Evidence: Every activity's float must be computed and compared - the report's justification for activity F runs to four sentences. CAL-3: part e was a November separator 74% of the time, with a median of only 29% full marks, the lowest of any part letter.

Closest November analogue: 2021 E2 Q4c Networks - 9%; 2020 E2 Q5d - 12%

2017 Exam 2 Q2cii (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: After the A-C door is locked, name the two rooms joined by the other door that must be locked to make a closed door-trail possible.

Evidence: Requires tracking the parity of every vertex, seeing that locking A-C fixed those two and that B and D are still odd. Naming both rooms is needed for the mark. CAL-3: a 'ii' sub-part of part c. November's closest question failed for precisely the both-pairs-required reason.

Closest November analogue: 2023 E2 Q13c Networks - 12% ("Very few students had both pairs correct"); 2024 E2 Q14c - 22%

2017 Exam 2 Q3a (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Determine the capacity of the marked Cut A in a directed flow network.

Evidence: The report's note is the whole difficulty: "The edge marked 6 is counted as zero since its direction is from the exit side to the entrance side of cut A." Counting that edge gives 32 instead of 26. CAL-6: cut-capacity items ran 40% and 44% in November Exam 1, and the single worst November question in the entire corpus was a cut question.

Closest November analogue: 2022 E2 Q3d Networks - 2%; 2023 E1 Q40 - 40%

2017 Exam 2 Q3b (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Find the maximum number of trucks that can travel from entrance to exit per day.

Evidence: A fourteen-edge directed network with no cut marked; the minimum cut has to be found among many candidates, and the report's own answer sums six edges of which three contribute zero. CAL-3/CAL-5: part b in Networks, and CAL-6 puts maximum-flow work in the 40-44% band in the easier Exam 1 form.

Closest November analogue: 2023 E1 Q40 Networks - 40%

2017 Exam 2 Q3c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: All the trucks in one group must follow the same route; find the largest such group.

Evidence: This is a bottleneck (maximum-capacity) path, not a maximum flow - the answer is the largest possible minimum edge along a single route, 8. The distinction is not taught explicitly, and a student who repeats the part b answer of 23 gets nothing. Nothing in the 2016-2025 November Exam 1 corpus asks for it. CAL-3: part c, and the last part of the module.

Geometry and measurement

2017 Exam 2 Q1c (NHT) — Geometry and measurement — 1 mark — BORDERLINE, confidence medium

Asks: Calculate the area of a composite block of land to the nearest square kilometre.

Evidence: The shape is a rectangle with a right triangle removed, so the triangle's area must be subtracted rather than added - the report's working is 6.2 x 3.1 - (1/2) x 2.2 x 2.3. CAL-6: composite-area items ran 30-48% in November Exam 1, though those were surface areas of solids, which is harder than this plane figure.

Closest November analogue: 2020 E1 Q9 Geometry - 36%

2017 Exam 2 Q3a (NHT) — Geometry and measurement — 2 marks — SEPARATOR, confidence medium

Asks: Milkdale is at 141 E, Creamville at 147 E; given sunrise at Creamville is 6.42 am, find sunrise at Milkdale.

Evidence: Three things must all be right: 15 degrees of longitude per hour, 6 degrees giving 24 minutes, and the direction - Milkdale is further west so the sun rises later, not earlier. CAL-4: 2-mark part, 71% November separator rate. CAL-6: longitude time-difference items ran 26-49% in November even as single-step multiple choice.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2022 E1 Q4 - 49%

2017 Exam 2 Q3b (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Find the shortest distance from Milkdale (34 S) to the South Pole.

Evidence: The insight is that the angle at the centre is 90 - 34 = 56 degrees, not 34; the report has to draw a diagram to establish it and adds that "The figures for longitude (east or west) were not relevant to this question." A student who uses 34 degrees, or who tries to involve the longitude, gets nothing. CAL-6: latitude/longitude family, 26-49%.

Closest November analogue: 2019 E1 Q6 Geometry - 41%

2017 Exam 2 Q4a (NHT) — Geometry and measurement — 2 marks — SEPARATOR, confidence medium

Asks: Two cylinders of cheese of equal height have radii 55 mm and 75 mm; price is proportional to volume, and the small one costs $12.10. Price the large one.

Evidence: The scale factor for volume at equal height is (75/55)^2 = 1.8595, not (75/55) and not (75/55)^3. CAL-4: 2-mark part. November named this exact failure in its closest analogue.

Closest November analogue: 2020 E2 Q2d Geometry - 17% ("Only a few students connected the scale factor for length to the area enlargement"); 2021 E1 Q3 - 38%

2017 Exam 2 Q4b (NHT) — Geometry and measurement — 2 marks — SEPARATOR, confidence high

Asks: A fifth of a cylinder is removed; given the sector area and a total surface area of 12 200 mm2, find the height.

Evidence: The student must decide, unaided, that the piece's surface consists of two sectors, two rectangular faces and one fifth of the curved surface, assemble 12 200 = 7068.6 + 150h + 30h, and solve. Omitting any one of the five surfaces gives a wrong h. CAL-3/CAL-4: part b, 2 marks, last part of the module.

Closest November analogue: 2016 E1 Q8 Geometry (composite surface area) - 30%

Graphs and relations

2017 Exam 2 Q1cii (NHT) — Graphs and relations — 1 mark — BORDERLINE, confidence medium

Asks: Draw the graph of average speed against 1/time, given speed = k/time.

Evidence: Linearising a hyperbola by plotting against the reciprocal is conceptually the hardest idea in this module, and the mark requires a correctly sloped straight line through the origin. Listed as BORDERLINE rather than SEPARATOR because k = 60 has already been found in the preceding part, so the two points needed are close at hand.

2017 Exam 2 Q2c (NHT) — Graphs and relations — 2 marks — SEPARATOR, confidence medium

Asks: What selling price would give a $300 profit on 75 bottles, given cost = 2.5n + 60?

Evidence: The equation has to be built rather than read: 75S - (2.5 x 75 + 60) = 300. CAL-3/CAL-4: part c and 2 marks - 59% and 71% November separator rates respectively.

2017 Exam 2 Q3c (NHT) — Graphs and relations — 2 marks — SEPARATOR, confidence high

Asks: Find the smallest total number of bottles that still achieves the maximum profit.

Evidence: The profit line has gradient -1.5, the same as the apples constraint, so the optimum is a whole line segment; the student must then test the integer points on it - (56,41), (58,38), (60,35), (62,32) - discard the odd x values as non-integer in y, and minimise x + y. CAL-6: an LP optimum lying along a constraint is one of the deepest November separator families. CAL-3/CAL-4: part c, 2 marks, last part of the module.

Closest November analogue: 2016 E2 Q3d Graphs and relations - 7%; 2020 E2 Q4d - 10%; 2021 E2 Q4cii - 20%

2018 (NHT)

2018 Exam 1 (NHT) — 22 SEPARATOR, 4 BORDERLINE

Data analysis

2018 Exam 1 Q8 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: From a twelve-row table of three variables, choose the least squares line for percentage body fat on body mass index.

Evidence: The two columns needed are the second and third of three, and three of the five options reverse the roles of response and explanatory variable. CAL-6: choosing the equation of a least squares line ran 34, 43, 46 and 49% in November Exam 1.

Closest November analogue: 2020 E1 Q13 Data analysis - 34%; 2018 E1 Q8 - 46%

2018 Exam 1 Q10 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Find the residual when a given line predicts lean body mass for the athlete whose body mass index is 22.0.

Evidence: The actual value is not stated; the athlete's row must be located in the twelve-row table first, then predicted, then subtracted in the right order. Option E is the prediction itself and options B and C are the residual with a plausible wrong sign or row. CAL-6: residual items ran 42-54% in November even when the data were supplied directly.

Closest November analogue: 2018 E1 Q14 Data analysis (residual) - 42%; 2016 E1 Q8 - 45%

2018 Exam 1 Q11 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: Describe the pattern in a monthly airline-passenger time series plot for 1955-1960.

Evidence: The NHT report states a general principle rather than an answer - "Irregular fluctuations are a feature of all time series plots" - which is a concession that most students would stop at option C, 'increasing trend with seasonality only'. Reports do not usually stop to teach a point the cohort already has.

2018 Exam 1 Q13 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Given a coefficient of determination of 0.8689 and a line with a negative slope, find r.

Evidence: The square root is routine; carrying the minus sign across from the -0.3968 slope is not, and both 0.9321 and -0.9321 are offered. CAL-6: losing the sign of r or of a slope is a named November failure at 19% and 21% full marks.

Closest November analogue: 2021 E2 Q3b Data analysis - 19%; 2025 E2 Q4b - 21%

2018 Exam 1 Q14 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Find actual Quarter 1 sales from deseasonalised sales, when the Quarter 1 seasonal index is the one not printed.

Evidence: Two hidden steps before the arithmetic: the Quarter 1 index must be recovered as 4 - (1.33 + 1.45 + 0.58) = 0.64, and then actual = deseasonalised x index, which is the reverse of the direction students practise. Option D is the unchanged figure. CAL-6: the seasonal-index family ran 32-50% in November.

Closest November analogue: 2017 E1 Q16 Data analysis - 32%; 2022 E1 Q16 - 40%

2018 Exam 1 Q15 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: Find the six-mean smoothed number of surfboards, with centring, for June from twelve months of data.

Evidence: November has never set six-mean smoothing with centring in this corpus - only four-mean, which ran 59-81% full marks. Doubling the window doubles the arithmetic and the chance of an off-by-one window. Listed as BORDERLINE because the November four-mean items show the method itself is well drilled.

Closest November analogue: 2017 E1 Q15 Data analysis (four-mean with centring) - 64%

Recursion and financial modelling

2018 Exam 1 Q21 (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

Asks: Of five rate-and-compounding-period combinations, choose the one with the largest effective interest rate.

Evidence: Five effective rates to compare, using the formula sheet's effective-rate expression, with two nominal rates crossed against three compounding periods. CAL-2 puts core Recursion position 5 (Q21) at a November median of 51.5% full marks and a 50% separator rate. Held at BORDERLINE because the two 3.8% options dominate the three 3.7% ones without any calculation.

2018 Exam 1 Q23 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: An annuity investment of $85 000 with $1500 monthly additions - after how many months does it first exceed $95 000?

Evidence: The NHT report answers it by building a recurrence relation with the multiplier 6019/6000 and reading a table of values to V6 = 95 699.39 - the examiners' own route is a table, not a single solver entry, and the 'first exceed' boundary has to be read off it. CAL-2: Q23 was a November separator in 5 of 7 years, median 38% full marks.

2018 Exam 1 Q24 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: Total interest paid on a car loan over two years, with monthly repayments rising from $425 to $500 after the first year.

Evidence: The report's route is four steps: total paid 11 100, future value of the loan after two years 24 715, principal reduction 4285, interest = 11 100 - 4285 = 6815. Neither the repayment change nor the definition of 'total interest' can be handled by one solver entry. CAL-2: Q24 has a November median of 33% full marks. CAL-6: multi-stage finance-solver items sit at 8-19%.

Closest November analogue: 2024 E2 Q8 Recursion - 13% ("Some students misunderstood the meaning of the total cost of the loan"); 2020 E2 Q11 - 19%

Matrices

2018 Exam 1 Q5 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Choose the matrix calculation that gives the difference between the winning and losing scores in a target game.

Evidence: All five options contain the same numbers; only the orders and the position of the points column differ, so the question is entirely about which products are defined and in which order. CAL-6: abstract matrix-order items ran 36, 40, 42 and 45% in November.

Closest November analogue: 2017 E1 Q7 Matrices - 36%; 2021 E1 Q7 - 40%

2018 Exam 1 Q6 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: A solution is given as the product of a 2x2 matrix and a column matrix; identify one of the original linear equations.

Evidence: The printed matrix is the inverse of the coefficient matrix, so the student must invert it back before any equation can be read off - the reverse of the direction the course teaches. CAL-1: position 6 in a module block was a November separator 55% of the time, median 46%.

Closest November analogue: 2023 E1 Q30 Matrices (determinant / inverse) - 39%

2018 Exam 1 Q7 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: What percentage of 200 customers are not expected to change their rating next month?

Evidence: The report's working - 0.2 x 40 + 0.3 x 110 + 0.3 x 50 = 56, then 56/200 = 28% - needs the diagonal of the transition matrix picked out, applied to the state matrix, and the result converted to a percentage of the whole cohort. Reading a percentage straight off the transition matrix is the natural error, and is what November named in the closest analogue. CAL-1: position 7, 65% November separator rate.

Closest November analogue: 2021 E2 Q3c Matrices - 17% ("85% taken directly from the transition matrix was a very common incorrect answer")

2018 Exam 1 Q8 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: In the long term, how many of 200 customers change from excellent to good each month?

Evidence: Two stages: find the steady-state matrix (49.15, 91.52, 59.32) and then apply the single transition probability 0.5 to its excellent component. Neither stage alone answers the question. CAL-1: position 8, 84% November separator rate, median 35%. CAL-6: long-run interpretation items ran 39% and 46%.

Closest November analogue: 2023 E1 Q27 Matrices - 39%; 2018 E1 Q8 - 46%

Networks and decision mathematics

2018 Exam 1 Q3 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: For a six-vertex, seven-edge graph, decide which pair out of Eulerian trail, Eulerian circuit, Hamiltonian path and Hamiltonian cycle exists.

Evidence: Four distinct properties, each requiring its own test, and the options pair them so that getting three right still gives the wrong answer. CAL-6: November items mixing Eulerian and Hamiltonian properties ran 17% and 29% full marks.

Closest November analogue: 2021 E1 Q5 Networks - 17%; 2017 E1 Q6 - 29%

2018 Exam 1 Q4 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: In a thirteen-activity network, name the person whose activity has a latest starting time of 12 hours.

Evidence: A complete backward pass is needed, and then the latest start times of several candidate activities have to be compared against each other. CAL-6: critical-path timing items ran 31, 34, 39 and 48% in November Exam 1.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2022 E1 Q8 - 34%

2018 Exam 1 Q6 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: For a weighted graph with many edges of weight 2, count the weight-2 edges excluded from the minimal spanning tree.

Evidence: The tree must be built and then the answer read as a complement - a count of what is left out, not what is in. CAL-1: position 6, 55% November separator rate, median 46% full marks.

Closest November analogue: 2016 E1 Q4 Networks (minimum spanning tree) - 52%

2018 Exam 1 Q7 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: A simple connected graph has at least one odd-degree and at least one even-degree vertex; how many odd-degree vertices could it have?

Evidence: Purely abstract: the answer rests on the handshake lemma forcing the number of odd-degree vertices to be even, and four of the five options are odd numbers designed to catch a student who reasons from one example. CAL-1: position 7, 65% November separator rate.

Closest November analogue: 2022 E1 Q4 Networks - 21%; 2021 E1 Q3 - 34%

2018 Exam 1 Q8 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Given a table of immediate predecessors and earliest starting times, find the maximum delay possible for activity C.

Evidence: No network diagram is supplied at all - the float has to be reconstructed from the earliest starting times, using the fact that H's start at 36 is driven by F rather than G. CAL-1: position 8, 84% November separator rate, median 35%. CAL-6: float and delay items ran 31-48%.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2022 E1 Q8 - 34%

Geometry and measurement

2018 Exam 1 Q4 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Choose the calculation giving the radius of the small circle of latitude 30 S.

Evidence: The answer is sin(60) x 6400, and the options offer sin(30) x 6400 and cos(60) x 6400 - the two natural wrong complements - plus two divisions. CAL-6: latitude/longitude items ran 26, 41, 43 and 49% in November.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2019 E1 Q6 - 41%

2018 Exam 1 Q5 (NHT) — Geometry and measurement — 1 mark — BORDERLINE, confidence medium

Asks: Choose the calculation for the volume of a square pyramid with base length 20 cm and slant edge 20 cm.

Evidence: The perpendicular height is not 20 and is not given: it is the square root of 400 - 200, recovered from half the base diagonal. Distinguishing slant edge from slant height from perpendicular height is the whole question. Held at BORDERLINE because CAL-1 puts position 5 at only a 30% November separator rate.

Closest November analogue: 2021 E1 Q5 Geometry (volume) - 46%

2018 Exam 1 Q6 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: With DE parallel to AC, AD = 2 cm and DB = 3 cm, find the ratio of the area of triangle BDE to the area of the trapezium ADEC.

Evidence: Three steps: the linear ratio is 3:5 (not 3:2), the area ratio is therefore 9:25, and the trapezium is the difference 25 - 9 = 16, giving 9:16. Options A, B, C and E are each the result of stopping one step early. CAL-1: position 6, 55% November separator rate. CAL-6: scale-factor items ran 38%.

Closest November analogue: 2021 E1 Q3 Geometry (scale factor) - 38%; 2020 E2 Q2d - 17%

2018 Exam 1 Q7 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: A cylindrical fuel tank of radius 0.8 m lying on its side holds fuel to a depth of 1.2 m; find the volume in litres.

Evidence: This needs the area of a circular segment - sector area minus triangle area - which is not on the Further Mathematics formula sheet and has to be assembled from the sector and triangle formulas that are. CAL-1: position 7, 65% November separator rate, median 45% full marks.

2018 Exam 1 Q8 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: Two angles of elevation to a goalpost, 40 and 60 degrees, are measured from points 1 m apart; find the horizontal distance of the nearer point.

Evidence: Two right triangles share an unknown height, so a pair of simultaneous tangent equations has to be set up and solved for the distance - there is no single-triangle route. CAL-1: position 8, 84% November separator rate, median 35%. CAL-6: trigonometry items ran 30-45%.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2022 E1 Q6 - 38%

Graphs and relations

2018 Exam 1 Q6 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: For revenue and cost lines meeting at (j, k), identify the statement that is NOT true.

Evidence: The false statement is 'Exactly j beds need to be sold to make a profit' - at n = j the company breaks even, so it is more than j. The discrimination is between four true statements and one that differs only in the word 'exactly'. CAL-1: position 6, 55% November separator rate.

2018 Exam 1 Q7 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: Write 'for every three pears, at least five apples' as an inequality.

Evidence: The report derives it in four lines: set up x:y = 3:5, turn the ratio into y = 5x/3, then decide that 'at least' gives the greater-than-or-equal sign. November named the same two-part difficulty - ratio to equation, then wording to inequality sign - in its closest analogue. CAL-1: position 7, 65% November separator rate.

Closest November analogue: 2021 E2 Q2c Graphs and relations - 21% ("Consider a ratio of 3 blocks to 5 blocks... 'at most' is represented by...")

2018 Exam 1 Q8 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: Given Z = 5x + 2y with its minimum occurring only at P, choose which of five shaded feasible regions could be the problem.

Evidence: The report's reasoning is the sliding-line method plus a uniqueness test: "In both options A and B, the minimum can occur at point P but can also occur at all points along the line segment that connects P to the y-intercept". The student must slide a line of gradient -5/2 across five regions and reject two for non-uniqueness. CAL-6: the LP objective-function family ran 29-47% across seven November papers, every one a separator. CAL-1: position 8, 84%.

Closest November analogue: 2022 E1 Q8 Graphs and relations - 29%; 2020 E1 Q10 - 31%

2018 Exam 2 (NHT) — 25 SEPARATOR, 3 BORDERLINE

Data analysis

2018 Exam 2 Q1b (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Using a dot plot and a boxplot, show why a skull length of 33.5 mm is not plotted as an outlier.

Evidence: The quartiles have to be read off the boxplot, the upper fence computed as 31.6 + 1.5 x 1.3 = 33.55, and a comparison stated. The report sets exactly that scheme: "The answer needed to correctly calculate the upper fence value and then provide a conclusion based on comparing the 33.5 data value". CAL-4: 2-mark parts were November separators 71% of the time, median 38%.

Closest November analogue: 2020 E2 Q2c Data analysis (boxplot with outliers) - 17%

2018 Exam 2 Q3c (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: From a histogram on a log10(weight) scale, count the birds weighing between 10 g and 100 g.

Evidence: The interval 10-100 g has to be converted to 1-2 on the log axis before frequencies can be added. The same idea, set as multiple choice in the 2017 NHT paper, made the examiners write out the log-scale rule from first principles in that report. The nearest November analogues are log transformations, at 34-54%.

Closest November analogue: 2020 E1 Q13 Data analysis (log/transformation) - 34%; 2016 E1 Q11 - 54%

2018 Exam 2 Q4c (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Using a two-way table of beak size by sex, decide whether the contention of association is supported, justifying with appropriate percentages.

Evidence: The report's scheme demands a clear supporting statement and percentages computed down the correct margin - e.g. "50% of males had large beaks, which was higher than females, with 7%". Percentaging along the wrong margin, or stating the conclusion without numbers, loses a mark. CAL-4: 2-mark part, 71% November separator rate.

2018 Exam 2 Q5d (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Given a residual of 2.78 at a head length of 59.2 mm, calculate the bird's actual weight.

Evidence: The residual definition has to be run backwards - actual = predicted + residual - after a prediction is made from the given line. The report confirms partial credit is the expected outcome: "A mark was available to students who correctly used their predicted value with the residual of 2.78." CAL-4: 2-mark part, 71% separator rate, median 38%.

Closest November analogue: 2018 E1 Q14 Data analysis (residual) - 42%

2018 Exam 2 Q5e (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Given r = 0.5957, what percentage of the variation in weight is NOT explained by head length?

Evidence: Three steps compressed into one mark: square r, subtract from 1, convert to a percentage - and the word 'not' inverts the quantity students have practised. CAL-6: coefficient-of-determination-in-words items ran 41% and 45% in November, and those asked for the explained share.

Closest November analogue: 2019 E1 Q10 Data analysis - 41%; 2018 E1 Q9 - 45%

2018 Exam 2 Q6a (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Apply a log10 transformation to power and give the least squares line for log10(power) on year number, to four significant figures.

Evidence: The transform must be applied to the response variable, the regression run on the transformed column, and both coefficients rounded to four significant figures - the report insists: "Both numbers needed to be correctly rounded to four significant figures." Four significant figures on 0.09902 is where marks go. CAL-4: 2-mark part, 71% November separator rate.

Closest November analogue: 2020 E2 Q6d Data analysis - 21% ("The rounding to significant figures...")

2018 Exam 2 Q6b (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

Asks: Use the log10 equation to predict the wind power generated in 2020, to the nearest 1000 MW.

Evidence: The report names three separate places to fail: "The answer needed to firstly use the year number of 20 to make a prediction and then raise 10 to that power before rounding to the nearest thousand." Substituting 2020 instead of 20, or forgetting to undo the logarithm, each gives an answer that looks plausible. CAL-4: 2-mark part.

Closest November analogue: 2020 E2 Q6d Data analysis - 21%

Recursion and financial modelling

2018 Exam 2 Q7d (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

Asks: What minimum annual interest rate would have grown $5000 to $6000 in two years?

Evidence: A rate has to be solved for rather than applied, and the word 'minimum' forces a rounding decision at the boundary - so much so that the report accepts two answers: "An answer of 9.6% was also accepted, as this generates over $6000." That leniency is why this is BORDERLINE rather than SEPARATOR.

2018 Exam 2 Q8c (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence medium

Asks: A $8500 stereo sold for $4500 after four years; find the annual reducing-balance depreciation rate.

Evidence: The rate is the unknown inside a fourth power, so either a solver with PV, FV and N or a fourth root is needed - and the result must then be converted from a multiplier to a percentage rate of depreciation. CAL-3/CAL-4: part c and 2 marks, at 59% and 71% November separator rates respectively.

2018 Exam 2 Q9c (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: Eleven repayments of $330 leave a balance; find the value of the differing twelfth repayment.

Evidence: The report's route runs the solver for twelve payments of $330 to get FV = -90.40 and then adds it back: "the last payment of $330 must be increased by $90.40 to fully repay the loan." Quoting the outstanding balance instead - forgetting the final month's interest - is exactly the error November named in the closest analogue.

Closest November analogue: 2021 E2 Q8c Recursion - 15% ("This was the balance before the last payment but does not include the interest to be added")

Matrices

2018 Exam 2 Q3a (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Two farmers' orders both cost $16 000; what conclusion follows about the prices of Nitro and Phate?

Evidence: The two order rows differ only by swapping one tonne between N and P, so equal totals force N = P. It is a one-line deduction but an unusual one - nothing is computed and there is no equation to solve. Interpretation-in-words parts in Matrices are where November students most often score zero.

Closest November analogue: 2022 E2 Q2bii Matrices - 21% ("few students able to demonstrate how to interpret the determinant value")

2018 Exam 2 Q3b (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Explain why the 2x3 matrix equation cannot be solved using the inverse method.

Evidence: The report accepts three distinct framings - a 3 x 3 matrix is required, the matrix must be square to be inverted, or three equations are needed for three unknowns - which signals that students produced many near-miss answers. Explaining why a matrix method fails is a different skill from executing it.

Closest November analogue: 2022 E2 Q2bii Matrices - 21%

2018 Exam 2 Q3ci (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Fill in the missing top row of the inverse of a 3x3 coefficient matrix.

Evidence: The other two rows are printed, so the student must either compute the full 3 x 3 inverse on technology and read off the first row, or reason back from the system - and a single sign error loses the mark outright. CAL-3: part c of a multi-part question, 59% November separator rate.

2018 Exam 2 Q4 (NHT) — Matrices — 2 marks — SEPARATOR, confidence high

Asks: Given H1 = R.H0 + Q with R and both state matrices supplied, complete H2.

Evidence: Matrix Q is never given: it has to be recovered as H1 - R.H0 before the second iteration can run. The report confirms the split - "A mark was available for finding matrix Q" - so one of the two marks is for a step the question does not mention. CAL-4: 2-mark part, and CAL-6 puts iterated T.Sn + B items at 10-12% in November.

Closest November analogue: 2021 E2 Q4 Matrices - 10%; 2024 E2 Q12c - 12%

Networks and decision mathematics

2018 Exam 2 Q2c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: The dog starts and finishes at F and runs along every edge; find the shortest total distance.

Evidence: A Chinese-postman problem: the two odd-degree vertices must be identified and the cheapest connecting edge counted twice, giving 310 + 25 = 335. A student who answers 310, the sum of all the edges, has done everything except the step the question is about.

2018 Exam 2 Q3b (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Draw, on the given network, a cut whose capacity is exactly 70 litres per minute.

Evidence: The search runs backwards from a target capacity, and only edges directed across the cut from source side to sink side count - the trap that produced the lowest-scoring question in the whole November dataset. There is no partial credit for a cut of the wrong capacity.

Closest November analogue: 2022 E2 Q3d Networks - 2%; 2023 E1 Q40 - 40%

2018 Exam 2 Q4b (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Find the duration p of activity I that would create more than one critical path.

Evidence: The lengths of the competing paths through the network have to be expressed in terms of p and then equated - an algebraic use of a project network rather than a numerical one. CAL-6: critical-path items ran 31-48% in November Exam 1 without an unknown duration.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2025 E1 Q40 - 39%

2018 Exam 2 Q4c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: With p = 6 days, find the float time of activity H.

Evidence: The report's answer needs both passes - "EST of H is 7 and the LST of H is 14" - after the network has been re-timed with the value of p carried through from the previous part. CAL-3: part c, 59% November separator rate, median 44% full marks.

Closest November analogue: 2022 E1 Q6 Networks (float) - 48%

2018 Exam 2 Q4d (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Explain what the dummy activity indicates on the revised network.

Evidence: The required answer is a statement about precedence - "Both C and G are immediate predecessors of K" - not about time or about the dashed line itself. Dummy activities are the part of project networks November students handle worst.

Closest November analogue: 2024 E2 Q15c Networks (dummy activity) - 10%

Geometry and measurement

2018 Exam 2 Q1d (NHT) — Geometry and measurement — 1 mark — BORDERLINE, confidence medium

Asks: Find the volume of one of ten equal pieces of a cylindrical cake of radius 12 cm and height 8 cm.

Evidence: The report works it as a sector area times height, using the 36-degree angle established in the previous part. A student who simply divides the whole cylinder's volume by 10 also gets there, which is why this is only BORDERLINE - but the sector formula and one-decimal-place rounding leave room to lose the mark.

2018 Exam 2 Q2a (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Match Beijing, Brasilia and Vancouver to three numbered positions on a drawn globe, given Paris.

Evidence: All three must be right for the single mark, and the reasoning is spatial rather than computational: hemisphere from the sign of the latitude, east or west of the Greenwich meridian from the longitude, read off a projected sphere. CAL-6: latitude/longitude items ran 26-49% in November.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2018 E1 Q3 - 43%

2018 Exam 2 Q2b (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: A 22 hour 25 minute flight leaves Sydney at 10.50 am Wednesday; with an eight-hour time difference, give the arrival day and time in Paris.

Evidence: Three operations on the clock for one mark - add 22:25, subtract 8:00, resolve the date - with the answer crossing midnight into Thursday. Any one slip gives a wrong day as well as a wrong time. CAL-6: longitude and time-difference items ran 26-49% in November.

Closest November analogue: 2022 E1 Q4 Geometry - 49%; 2019 E1 Q6 - 41%

2018 Exam 2 Q2c (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: How long after sunrise in Paris (2 E) does the sun rise in Vancouver (123 W)?

Evidence: The longitude difference spans the Greenwich meridian, so it is 2 + 123 = 125 degrees, not 121; then 125/15 = 8 hours 20 minutes, which must be expressed in hours and minutes rather than as a decimal. CAL-6: the latitude/longitude family ran 26-49%.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2019 E1 Q6 - 41%

2018 Exam 2 Q3b (NHT) — Geometry and measurement — 2 marks — SEPARATOR, confidence high

Asks: Find the diameter of the largest circular cake that fits inside an equilateral triangular box of side 16 cm.

Evidence: This is the incircle of an equilateral triangle, and the report's route is an equation the student must construct unaided: (root(16^2 - 8^2) - r)^2 = r^2 + 8^2, solved for r and then doubled. Nothing in the course sets up incircles directly. CAL-3/CAL-4: part b, 2 marks, last part of the module.

Graphs and relations

2018 Exam 2 Q2c (NHT) — Graphs and relations — 2 marks — SEPARATOR, confidence medium

Asks: Given profit of $160 on 100 burgers and cost C = 1.5n + 240, find the selling price of each burger.

Evidence: The relation profit = revenue - cost has to be assembled and then solved for an unknown inside the revenue term: 160 = 100S - (1.5 x 100 + 240). CAL-3/CAL-4: part c and 2 marks - 59% and 71% November separator rates.

2018 Exam 2 Q4a (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: With 100 single cheeseburgers sold, find the maximum number of triple cheeseburgers possible.

Evidence: All three resource constraints have to be tested at x = 100 to find which one binds (meat patties, giving y = 116.67), and the answer then truncated to an integer rather than rounded. The report says as much: "The maximum integer value of y when x = 100." CAL-6: feasible-region items ran 29-40% in November.

Closest November analogue: 2016 E1 Q5 Graphs and relations - 29%; 2018 E1 Q7 - 40%

2018 Exam 2 Q4c (NHT) — Graphs and relations — 1 mark — BORDERLINE, confidence medium

Asks: Sketch the line x + 2y = 320 on the given axes.

Evidence: The report specifies what earns the mark: "It needed to be clear that the y intercept was 160 and the x intercept was 320." Both intercepts must be visibly correct on a printed grid, so it is all-or-nothing - but finding the two intercepts of a printed equation is otherwise routine.

2018 Exam 2 Q4d (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: The maximum profit is $480; find the minimum total number of cheeseburgers needed to achieve it.

Evidence: The report states the structure: "Profit equation P = 1.5x + 3y is parallel to x + 2y = 320. Maximum profit of $480 can occur at all integer points from (60,130) to (180,70)." With a whole segment of optima, the student must then minimise x + y along it. CAL-6: this is among the deepest November separator families.

Closest November analogue: 2016 E2 Q3d Graphs and relations - 7%; 2020 E2 Q4d - 10%; 2021 E2 Q4cii - 20%

2019 (NHT)

2019 Exam 1 (NHT) — 27 SEPARATOR, 2 BORDERLINE

Data analysis

2019 Exam 1 Q7 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Using the 68-95-99.7% rule, how many of 600 babies have a birth weight between 2200 g and 3850 g?

Evidence: The interval is asymmetric about the mean - z = -2 to z = +1 - so the percentage is 95/2 + 68/2 = 81.5, not one of the three headline figures. Options A, B and D are each what a symmetric reading gives. CAL-2 puts core Data analysis position 7 at a November median of 64% full marks, and the asymmetric version is the harder half of the family.

2019 Exam 1 Q9 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Given the two means, two standard deviations and the intercept a = 3.1, find the slope of the least squares line.

Evidence: The obvious route, b = r x sy/sx, is blocked because r is not given; the slope must come from a = ybar - b.xbar instead. Option C, 0.58, is sy/sx, which is what a student who assumes r = 1 produces. CAL-6: least-squares-equation items ran 34-49% in November.

Closest November analogue: 2020 E1 Q13 Data analysis - 34%; 2017 E1 Q8 - 43%

2019 Exam 1 Q11 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Use log10(children) = 1.06 - 0.00674 x HDI to predict the mean number of children at HDI 95.

Evidence: The prediction has to be un-logged: 10 raised to the computed value. A student who stops at the log value gets 0.4, which is offered as option A. CAL-6: transformation items with a back-transformation ran 34% and 40% in November.

Closest November analogue: 2020 E1 Q13 Data analysis - 34%; 2021 E1 Q11 - 40%

2019 Exam 1 Q12 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Which of five reported correlation results could actually be true?

Evidence: The NHT report opens with "All five options needed to be considered" and then gives a separate reason for rejecting each of the four wrong ones - r greater than 1, an ordinal variable, two ordinal variables, and a negative coefficient of determination. Four distinct pieces of statistical literacy for one mark.

Closest November analogue: 2018 E1 Q9 Data analysis (coefficient of determination) - 45%

2019 Exam 1 Q14 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Find the seven-median smoothed number of visitors on day 4 from a time series plot.

Evidence: Seven values must be read off a plot by eye and their median taken - a wider window than the five-median smoothing students normally meet, and with no table to work from. CAL-2: core Data analysis positions 13-16 have November medians of 50-65% full marks.

2019 Exam 1 Q15 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: From twelve monthly long-term average heating costs, find the seasonal index for April.

Evidence: The twelve values must be totalled and averaged before the April figure can be divided by that average. CAL-6: computing a seasonal index from raw data ran 51% in November - just above the line - which is why this is BORDERLINE rather than SEPARATOR.

Closest November analogue: 2018 E1 Q16 Data analysis - 51%

2019 Exam 1 Q16 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

Asks: A cafe closes on Tuesdays; given six seasonal indices and a long-term weekly labour cost of $9786, find the expected Wednesday cost.

Evidence: The closed day changes the divisor: the average daily cost is 9786/6, not 9786/7, and only then is it multiplied by the Wednesday index of 1.24. Option C is the un-multiplied average and option A uses a divisor of seven. CAL-6: seasonal-index items ran 32-50% in November without a missing day.

Closest November analogue: 2017 E1 Q16 Data analysis - 32%; 2023 E1 Q16 - 43%

Recursion and financial modelling

2019 Exam 1 Q20 (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

Asks: Which graph shows a car depreciated at a flat rate, halved in value after three years, then depreciated by the same amount per year?

Evidence: The correct graph keeps the same gradient after the drop, because the flat-rate amount per year is unchanged even though the value halved - the intuitive alternative, a shallower line, is offered. CAL-2 puts core Recursion position 4 (Q20) in the easier half of the block, which is why this is only BORDERLINE.

2019 Exam 1 Q21 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: Six rows of an amortisation table are given; the interest rate rose partway through. Which repayment was the first at the higher rate?

Evidence: The rate is nowhere stated: for each row the student must divide the interest by the previous balance and look for the step change. That is five separate calculations for one mark. CAL-2: core Recursion position 5 (Q21) was a November separator in half the years, median 51.5%.

Closest November analogue: 2022 E2 Q8d Recursion - 19% (recover an interest rate from a balance)

2019 Exam 1 Q23 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: After eight repayments of $500 the repayment rises to $850; find the smaller final repayment.

Evidence: The report's route is three stages: the balance after eight months ($8426.30), then ten payments of $850 leaving $168.28, then "The final repayment must include interest on this balance", giving $169.14. Quoting the $168 balance is the natural wrong answer and is offered as option A - and is exactly the error November named in the closest analogue.

Closest November analogue: 2021 E2 Q8c Recursion - 15% ("the balance before the last payment but does not include the interest")

2019 Exam 1 Q24 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: Fifteen years of fortnightly superannuation deposits are converted into a 234-payment monthly annuity; find the monthly payment.

Evidence: Two solver runs with a change of compounding period between them - fortnightly at 2.5% for 390 periods, then monthly at 3.6% for 234. CAL-2: Q24 has a November median of 33% full marks. CAL-6: two-stage finance-solver items are the deepest November separator family, at 8-19%.

Closest November analogue: 2021 E2 Q9b Recursion - 8%; 2020 E2 Q11 - 19%

Matrices

2019 Exam 1 Q4 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Which matrix product evaluates to the column matrix of points scored for one Full and one Bit?

Evidence: The system has to be recognised as a matrix equation and then pre-multiplied by an inverse, in the right order, with the -1 in the right place. All five options use the same four numbers. CAL-6: abstract matrix-order items ran 36-45% in November.

Closest November analogue: 2017 E1 Q7 Matrices - 36%; 2022 E1 Q7 - 42%

2019 Exam 1 Q6 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Matrix W is 3 x 2 and Q x W = W; what could Q be?

Evidence: Two ideas at once: Q must be the identity, and it must be the 3 x 3 identity rather than the 2 x 2 one, because it pre-multiplies. Options B and D are the two identities, so half the cohort that understands the first idea still picks the wrong order. CAL-1: position 6, 55% November separator rate.

Closest November analogue: 2022 E1 Q7 Matrices - 42%; 2021 E1 Q5 - 45%

2019 Exam 1 Q7 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: Of the cows expected at Q in week 24, what percentage were at R in week 23?

Evidence: The report's chain is: read 0.20 off the transition diagram, apply it to the 240 cows at R to get 48, then divide by the 222 cows at Q - not by the total herd and not by 240. Three different denominators are plausible and two of them are offered. CAL-1: position 7, 65% November separator rate.

Closest November analogue: 2021 E2 Q3c Matrices - 17% (percentage read straight off the transition matrix)

2019 Exam 1 Q8 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: In the long term 635 sheep are at S; how many are expected at Q?

Evidence: The report raises T to a high power to get the long-run proportion at S (0.31296), divides 635 by it to recover a total flock of 2029, and only then applies the Q proportion. The steady-state vector has to be used as a set of proportions rather than as a count. CAL-1: position 8, 84% November separator rate, median 35%.

Closest November analogue: 2023 E1 Q27 Matrices (long-run) - 39%; 2018 E1 Q8 - 46%

Networks and decision mathematics

2019 Exam 1 Q3 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Which allocation of four students to four parts MUST occur for the project to finish in minimum time?

Evidence: The assignment problem has to be solved and then interrogated for which pairing is forced - a stronger question than 'find the minimum time', because near-optimal options are offered. CAL-6: allocation items ran 24, 30 and 39% in November when anything beyond a plain allocation was asked.

Closest November analogue: 2018 E1 Q8 Networks - 24%; 2016 E1 Q8 - 30%

2019 Exam 1 Q4 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Which of five flow diagrams shows a cut of capacity 19?

Evidence: Five cuts must be evaluated, each with the rule that edges directed back across the cut contribute nothing. CAL-6: cut-capacity items ran 40% and 44% in November Exam 1, and the single worst question in the whole November dataset was a cut question.

Closest November analogue: 2022 E2 Q3d Networks - 2%; 2023 E1 Q40 - 40%

2019 Exam 1 Q6 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: How many of four drawn graphs are planar?

Evidence: Four separate planarity judgements, each requiring an attempt to redraw without crossings. CAL-6: planar-graph items ran 11, 21, 34 and 41% in November - every one a separator - and those asked about a single graph.

Closest November analogue: 2020 E1 Q7 Networks - 11%; 2022 E1 Q4 - 21%

2019 Exam 1 Q7 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: From a 5x5 adjacency matrix containing a loop and a multiple edge, identify the statement that is NOT true.

Evidence: Degrees must be computed from the matrix with the loop counted twice, and then connectedness, an Eulerian trail, an Eulerian circuit and a Hamiltonian cycle all tested. CAL-1: position 7, 65% November separator rate. CAL-6: Eulerian/Hamiltonian 'not true' items ran 17% and 29%.

Closest November analogue: 2021 E1 Q5 Networks - 17%; 2017 E1 Q6 - 29%

2019 Exam 1 Q8 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: With $3000 available at $1000 per day, which combination of reductions cuts the project by three days?

Evidence: Crashing must respect every critical path simultaneously, so reducing three days of the right activities is not the same as reducing any three days. CAL-1: position 8, 84% November separator rate. CAL-6: November's crash-the-project questions are among its deepest separators.

Closest November analogue: 2021 E2 Q4c Networks - 9%; 2020 E2 Q5d - 12%

Geometry and measurement

2019 Exam 1 Q4 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: One of twelve equal pizza slices has top-surface area 9.42 cm2; find the perimeter of that slice.

Evidence: The chain runs backwards: area of a 30-degree sector gives r = 6, then the perimeter is two radii plus the arc, 12 + 3.14. Option D is the whole circumference and option A the arc plus one radius. CAL-1: position 4.

2019 Exam 1 Q5 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: Lima (12 S) and Washington share longitude 77 W and are 5697 km apart; find Washington's latitude.

Evidence: The arc length has to be converted back to a central angle of 51 degrees, and then combined with Lima's 12 S across the equator to give 39 N rather than 63 N or 51 N - both of which are offered. CAL-6: latitude/longitude items ran 26-49% in November and none required a reverse arc-length step.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2019 E1 Q6 - 41%

2019 Exam 1 Q6 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Three equal-height cake sections have volumes in the ratio 1:2:4 and the top is 900 cm3; find the diameter of the bottom section.

Evidence: Volume 3600 must be turned into a radius through pi.r^2.h and then doubled - three chances to stop early, and both the radius (12) and the middle section's diameter (18) are offered as options. CAL-1: position 6, 55% November separator rate.

2019 Exam 1 Q7 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Find the total perimeter of two similar right-angled triangles with corresponding sides 3 m and 6 m.

Evidence: Pythagoras on the small triangle, the scale factor applied to get the large one, and then two perimeters summed - and the word 'total' is easy to miss. CAL-1: position 7, 65% November separator rate, median 45%. CAL-6: scale-factor items ran 38%.

Closest November analogue: 2021 E1 Q3 Geometry - 38%

2019 Exam 1 Q8 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: A square-based pyramid of height 54 cm has its top 9 cm removed; find the ratio of removed volume to remaining volume.

Evidence: The linear scale factor is 9/54 = 1/6, so the volume ratio of small to whole is 1:216 - but the question asks removed to remaining, which is 1:215. Option E is 1:216, the answer to the question students expect. CAL-1: position 8, 84% November separator rate, median 35%.

Closest November analogue: 2020 E2 Q2d Geometry - 17% (length scale factor to area/volume)

Graphs and relations

2019 Exam 1 Q4 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: Write 'at least twice as many sheep as cows' as an inequality.

Evidence: The NHT report derives it in four lines - ratio, then equation, then the inequality sign - and notes the answer can be written two equivalent ways, only one of which is offered. November named the identical difficulty in its closest analogue. CAL-1: position 4.

Closest November analogue: 2021 E2 Q2c Graphs and relations - 21% (ratio into an inequality)

2019 Exam 1 Q6 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: Accounts grew from 260 in January to 500 in June; how many are expected at n = 23?

Evidence: The monthly rate must be extracted from the graph as (500 - 260)/5 = 48, an equation formed, and then extrapolated well beyond the plotted range. The five options are 12 apart, so the rate must be exactly right. CAL-1: position 6, 55% November separator rate.

2019 Exam 1 Q7 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: Where does Z = -2x - 2y take its maximum over the given feasible region?

Evidence: The report's reasoning turns on the sign: "As the coefficients of x and y in the objective function are both negative, the first of these segments reached by the sliding line gives the maximum" - and both AD and BC have the right slope, so the student must also decide which one. CAL-6: the LP objective-function family ran 29-47% across seven November papers, every one a separator. CAL-1: position 7, 65%.

Closest November analogue: 2022 E1 Q8 Graphs and relations - 29%; 2020 E1 Q10 - 31%

2019 Exam 1 Q8 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: With revenue 3.5n and cost 60 + n, which of five dollar amounts could the profit have been?

Evidence: Profit is 2.5n - 60, so only amounts that arise from a whole number of bottles are possible - an integrality constraint the question never mentions. Four of the five options are perfectly plausible dollar figures. CAL-1: position 8, 84% November separator rate, median 35%.

2019 Exam 2 (NHT) — 28 SEPARATOR, 3 BORDERLINE

Data analysis

2019 Exam 2 Q1d (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: By how many hours does the range increase when a mammal sleeping 19.9 hours is added to the sample?

Evidence: The question asks for the increase in the range, 19.9 - 14.5 = 5.4, not the new range of 17.3 - which is the figure a student who computes the range twice and forgets to subtract will write. One mark, no partial credit.

Closest November analogue: 2024 E2 Q2b Data analysis - 3% ("The question asked for the number of heights, not an actual height")

2019 Exam 2 Q2a (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Show with calculations that a boxplot from the given five-number summary contains no outliers.

Evidence: The report's model answer computes both fences and compares both extremes - four separate statements for two marks. Students who check only the upper end lose a mark. CAL-4: 2-mark parts were November separators 71% of the time, median 38%.

Closest November analogue: 2020 E2 Q2c Data analysis (boxplot and outliers) - 17%

2019 Exam 2 Q3b (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Determine the least squares line predicting life span from gestation period, with intercept and slope to three significant figures.

Evidence: Nineteen data pairs entered, the response and explanatory variables assigned correctly, and both coefficients rounded to three significant figures - 0.101 is where that bites. CAL-4: 2-mark part, 71% November separator rate.

Closest November analogue: 2020 E2 Q6d Data analysis - 21% (rounding to significant figures)

2019 Exam 2 Q4c (NHT) — Data analysis — 2 marks — BORDERLINE, confidence medium

Asks: Interpret the slope -1.90 in terms of life span and sleep time.

Evidence: Two marks for a sentence that must carry 'on average', the direction, both variable names and both units. CAL-4: 2-mark parts were November separators 71% of the time. Held at BORDERLINE because slope interpretation is the single most drilled written response in the course.

2019 Exam 2 Q4d (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Interpret the coefficient of determination 0.416 in terms of life span and sleep time.

Evidence: The report adds an explicit exclusion - "Answers that referred to the variance in each variable were not acceptable" - so the widely taught wording involving 'variance' scores zero. CAL-6: coefficient-of-determination items ran 41% and 45% in November as multiple choice, where no wording was at risk.

Closest November analogue: 2019 E1 Q10 Data analysis - 41%; 2018 E1 Q9 - 45%

2019 Exam 2 Q4e (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Show that the residual for the mammal sleeping 12 hours is 19.9 years.

Evidence: A 'show that' worth two marks: the prediction must be computed and displayed, then the subtraction written in the order actual minus predicted. An answer that reaches 19.9 without showing both steps cannot earn both marks. CAL-4: 2-mark part, 71% November separator rate.

Closest November analogue: 2018 E1 Q14 Data analysis (residual) - 42%

2019 Exam 2 Q5biii (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Does the two-way table support an association between likelihood of attack and exposure to attack? Justify with appropriate percentages.

Evidence: The report requires a supporting statement plus percentages computed down the columns - it lists three acceptable answers, all of them column percentages. Percentaging along the rows, the natural reading direction, earns nothing. CAL-4: 2-mark part, 71% November separator rate.

Recursion and financial modelling

2019 Exam 2 Q6d (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: Depreciating at $8 per concert from $3264, after how many concerts does the value first fall below $2500?

Evidence: The report frames it as an inequality - "The depreciation must be greater than 3264 - 2500 = $764" - giving 95.5, which must then be rounded up to 96. Rounding the wrong way, or answering 95, loses the mark outright.

2019 Exam 2 Q7a (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence medium

Asks: From T(n+1) = 1.0036 x Tn with T0 = 2500, find the total interest earned in the first five months.

Evidence: The balance after five months has to be produced and then the principal subtracted - the report's answer is "Interest earned = 2545.33 - 2500 = $45.33". Quoting 2545.33 is the natural wrong answer. CAL-4: 2-mark part, 71% November separator rate, median 38%.

2019 Exam 2 Q7c (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: What annual rate is needed to reach $4500 after twelve monthly payments of $150 on a $2500 investment?

Evidence: The rate is the unknown in a solver that already has PV, PMT, FV and N, and the answer must be given to two decimal places - 5.87%, where a one-step rounding slip loses the mark. CAL-3: part c, 59% November separator rate.

2019 Exam 2 Q8b (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence high

Asks: After six months, three months pass with no withdrawals, then $3800 monthly until one smaller final payment; find the total number of months the annuity lasts.

Evidence: The report needs two solver runs plus a count - three months at PMT = 0 to get $32 923.15, then N = 8.77 at PMT = 3800, then "Total number of months the annuity will last = 6 + 3 + 8 + 1 = 18". Every one of those four terms has to be remembered. CAL-4: 2-mark part. CAL-6: two-stage finance-solver items ran 8-19% in November.

Closest November analogue: 2021 E2 Q9b Recursion - 8%; 2020 E2 Q11 - 19%

Matrices

2019 Exam 2 Q1d (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: Complete a 4 x 3 matrix Q so that V = Q x C gives four specified uniform totals.

Evidence: Each of the four rows of Q has to be designed from a verbal description of which athletes it must count, and all the missing entries must be right for the one mark. This is matrix construction rather than matrix arithmetic - November sets it rarely and students handle it badly.

Closest November analogue: 2021 E2 Q4 Matrices - 10% ("Only some students were successful in filling in the entire matrix")

2019 Exam 2 Q1cii (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Write a matrix calculation including C that shows the total uniform cost for one event is [1030].

Evidence: The student has to build the selector row matrix [2 0 0] themselves and present the product in the right order so that the answer is a 1 x 1 matrix. Writing 2 x 515 = 1030 does not answer the question.

Closest November analogue: 2022 E2 Q2bii Matrices - 21% (interpreting rather than computing)

2019 Exam 2 Q2b (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: How many residents are expected to watch C3 at 11.00 am, two hours after the given state matrix?

Evidence: Two applications of the 4 x 4 transition matrix, with the intermediate state kept at full precision, and then one element read off. Students who apply T once are a whole hour short. CAL-3/CAL-5: Matrices Exam 2 parts were November separators 51% of the time.

2019 Exam 2 Q3 (NHT) — Matrices — 2 marks — SEPARATOR, confidence high

Asks: Find v, w and x in a 2x2 transition matrix given that exactly 600 residents watch C3 every hour.

Evidence: The report's chain is four steps: v = 1 - 0.35 = 0.65; 0.35 x 600 = 210 leave C3; for the count to stay at 600, w x 1400 must equal 210, so w = 0.15; and x = 0.85. The steady-count condition has to be turned into an equation, which nothing in the question prompts. CAL-4: 2-mark part, 71% November separator rate.

Closest November analogue: 2021 E2 Q3e Matrices - 15%

2019 Exam 2 Q4b (NHT) — Matrices — 2 marks — SEPARATOR, confidence high

Asks: With W(m+1) = T.Wm + V, how many people are expected to watch C2 at 7.00 pm?

Evidence: Two iterations of a four-state T.Wm + V recurrence, carrying decimals through the intermediate state. CAL-4: 2-mark part. CAL-6: iterated T.Sn + B items ran 10% and 12% in November.

Closest November analogue: 2021 E2 Q4 Matrices - 10%; 2024 E2 Q12c - 12%

Networks and decision mathematics

2019 Exam 2 Q1d (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: By how many metres do two new paths reduce the minimum walking distance from the giraffe exhibit to the cafe?

Evidence: Two shortest-path searches are needed on an eleven-vertex weighted graph - before and after the new vertex is inserted - and the answer is the difference, 85 m. CAL-3: part d was a November separator 72% of the time, median 40% full marks.

2019 Exam 2 Q1bi (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Name the route that visits the cafe and every exhibit exactly once, starting and ending at the entrance.

Evidence: The answer is 'Hamiltonian cycle', and the discriminations are cycle against path and Hamiltonian against Eulerian - three ways to write a wrong word. CAL-6: Eulerian/Hamiltonian terminology items ran 17% and 29% in November.

Closest November analogue: 2021 E1 Q5 Networks - 17%; 2017 E1 Q6 - 29%

2019 Exam 2 Q2c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: What is the latest start time for activity B in a nine-activity project network?

Evidence: A backward pass over the whole network for a single mark, with B off the critical path so the answer is a float rather than an earliest time. CAL-6: latest-start-time and float items ran 31-48% in November Exam 1.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2022 E1 Q6 - 48%

2019 Exam 2 Q3a (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Give the four Task 1 values A, B, C and D after the column-reduction step of the Hungarian algorithm.

Evidence: All four must be right for one mark, and the column minimum has to be identified in a column whose values are only implied by the earlier tables. Executing a named algorithm one step at a time is unusual in this course.

Closest November analogue: 2022 E1 Q3 Networks (allocation) - 39%

2019 Exam 2 Q3d (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Business 4's pathway quote changes to $1 000 000; by how much does the minimum total cost fall?

Evidence: The allocation must be re-solved and the two minima differenced. CAL-6: re-allocating after a single cost changes is one of the most reliable November separators, at 24, 30 and 39% full marks - and those were multiple-choice versions.

Closest November analogue: 2018 E1 Q8 Networks - 24%; 2016 E1 Q8 - 30%

Geometry and measurement

2019 Exam 2 Q1b (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Calculate the radius of the small circle of Earth at latitude 42 N.

Evidence: The radius is 6400 cos(42), and choosing sine over cosine - or 42 over its complement - is the single decision the mark turns on. CAL-6: latitude/longitude items ran 26-49% in November, and the multiple-choice version of this exact calculation was set in the 2018 NHT paper.

Closest November analogue: 2018 E1 Q3 Geometry - 43%; 2019 E1 Q6 - 41%

2019 Exam 2 Q1c (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: A 30-hour flight leaves Auckland at 9.40 am Monday; with a ten-hour time difference, give the arrival day and time in Rome.

Evidence: Add 30 hours, subtract 10, and resolve the date - and the direction of the subtraction depends on which city is ahead, which the question does not state. The answer, 5.40 am Tuesday, is wrong by a whole day if the direction is reversed. CAL-6: time-difference items ran 26-49%.

Closest November analogue: 2022 E1 Q4 Geometry - 49%; 2016 E1 Q4 - 26%

2019 Exam 2 Q2b (NHT) — Geometry and measurement — 1 mark — BORDERLINE, confidence medium

Asks: Find the roof area surrounding a 20 m dome on a regular hexagonal roof of side 12 m.

Evidence: The hexagon area from the previous part minus the circle's area, 374 - 314 = 60 - a subtraction that only works if the previous part was right, and the small difference of two large numbers magnifies any rounding. Listed as BORDERLINE because it is a single subtraction once the dependency is met.

2019 Exam 2 Q2cii (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: A glass cap on a hemispherical dome of diameter 20 m has base diameter 10 m; find its height h.

Evidence: The height is the radius minus the distance from the centre to the cap's base: 10 - root(100 - 25) = 1.34 m. Nothing in the course teaches spherical caps, so the right-triangle inside the hemisphere has to be constructed from scratch, and the answer is required to two decimal places.

2019 Exam 2 Q3b (NHT) — Geometry and measurement — 2 marks — SEPARATOR, confidence high

Asks: Given two legs of a helicopter route by bearing and distance, find the distance from Genzano di Roma to Calcata.

Evidence: The included angle has to be recovered from two bearings, 016 and 309, before the cosine rule can be applied - and getting the angle wrong still yields a plausible distance. CAL-4: 2-mark part, 71% November separator rate. CAL-6: bearings-with-the-cosine-rule items ran 30-45%.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2022 E1 Q6 - 38%

2019 Exam 2 Q3c (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Calcata is 40.3 km north and 11.8 km west of Rome; find the bearing of Rome from Calcata.

Evidence: The bearing runs from Calcata, so the reverse direction is needed, putting the answer in the third quadrant at about 196 degrees rather than the 016 a forward reading gives - and it must be written with three digits. CAL-6: bearing items ran 30-45% in November.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2018 E1 Q4 - 42%

Graphs and relations

2019 Exam 2 Q2c (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: Pam parked twice, each time more than two but less than four hours, and paid under $20 in total; write the two possible totals.

Evidence: A step graph has to be read for the two charges available in that interval, then the pairs combined and filtered against the $20 ceiling, and both surviving totals given for one mark. Reading, combining and filtering in a single one-mark part.

2019 Exam 2 Q4b (NHT) — Graphs and relations — 1 mark — BORDERLINE, confidence medium

Asks: Find the maximum weekly profit given profits of $30 and $50 per jacket and the shaded feasible region.

Evidence: A standard corner-point evaluation over a region bounded by four inequalities. Listed only as BORDERLINE because the method is the most practised routine in the module - but with four corners to test and two of them close in value, arithmetic slips are common. CAL-5: Graphs and relations Exam 2 parts were November separators 49% of the time.

2019 Exam 2 Q4c (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: With exactly 30 men's jackets sold, find the maximum profit that week.

Evidence: The feasible region has to be re-cut along the line x = 30 and the best point on that segment found - a constrained sub-problem rather than a corner-point search, and the answer ($4400) is lower than the unconstrained maximum from the previous part, which invites a repeated answer.

2019 Exam 2 Q4d (NHT) — Graphs and relations — 2 marks — SEPARATOR, confidence high

Asks: The women's jacket profit has changed and the maximum now occurs at (65, 35); find that maximum profit.

Evidence: The report reasons from the geometry: the maximum occurring at that point forces the profit line to have the same slope as the binding constraint, which fixes the unknown profit per jacket and only then gives the total. CAL-6: an optimum pinned to a constraint's slope is among the deepest November separator families. CAL-4: 2-mark part, last part of the module.

Closest November analogue: 2016 E2 Q3d Graphs and relations - 7%; 2020 E2 Q4d - 10%; 2021 E2 Q4cii - 20%

2021 (NHT)

2021 Exam 1 (NHT) — 29 SEPARATOR, 2 BORDERLINE

Data analysis

2021 Exam 1 Q4 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Fifteen girls average 28.5 and ten boys average 25.5; find the mean for the whole class of 25.

Evidence: The NHT report has to spell out the method - "the total scores for the 15 girls and total score for the 10 boys need to be determined" - because the intuitive answer is the unweighted average 27.0, which is offered as option C. Reports do not write out a method for a step the cohort takes automatically.

2021 Exam 1 Q7 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

Asks: Given means, standard deviations and Sasi's four subject scores, how many certificates for a top-10% score did she receive?

Evidence: Four separate standardisations, then each z compared against the top-10% cut-off - which is about 1.28 and is not one of the 68-95-99.7 landmarks, so it cannot be read off the rule students memorise. Two of the four scores fall either side. CAL-2 puts core Data analysis position 7 at a November median of 64% full marks for far simpler normal-curve work.

2021 Exam 1 Q10 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: Find the mean and standard deviation of nine bone lengths.

Evidence: The five options pair two means with three standard deviations, so the discrimination is the sample-versus-population divisor (3.88 against 3.65) as well as the rounding of the mean. CAL-2: core Data analysis position 10 has a November median of 56.5% full marks - right on the line.

2021 Exam 1 Q11 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: From nine data pairs, choose the least squares line that predicts bone length from height.

Evidence: Both the assignment of response and explanatory variable and the two coefficients must be right; options B and D reverse the variables while keeping plausible numbers. CAL-6: least-squares-equation items ran 34-49% in November.

Closest November analogue: 2020 E1 Q13 Data analysis - 34%; 2017 E1 Q8 - 43%

2021 Exam 1 Q12 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Round -67.68040231... and 1.35575905... to five significant figures.

Evidence: Five significant figures requires -67.680 with its trailing zero kept and 1.3558 with four decimal places - different numbers of decimals for the two coefficients. Option A drops the trailing zero and option E gives six figures. CAL-6: significant-figure rounding is a named November failure.

Closest November analogue: 2020 E2 Q6d Data analysis - 21% ("The rounding to significant figures...")

2021 Exam 1 Q14 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Using life expectancy squared = 4801.6 + 0.04715 x income, predict life expectancy at an income of $20 000.

Evidence: The regression is on the squared response, so the predicted value has to be square-rooted to get years. A student who stops at 5744.6, or who takes the square root of the income instead, has a plausible-looking number. CAL-6: transformation items needing a back-transformation ran 34% and 40% in November.

Closest November analogue: 2020 E1 Q13 Data analysis - 34%; 2021 E1 Q11 - 40%

2021 Exam 1 Q15 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

Asks: A June seasonal index is 0.80; to correct June car sales for seasonality, what should be done to the actual figure?

Evidence: The correction divides by 0.80, so the figure is increased by 25%, not 20% - and 'decreased by 20%' is offered as option A. CAL-6: this exact family - correct-for-seasonality expressed as a percentage - was a November separator every time it appeared, at 32, 40, 43 and 50% full marks.

Closest November analogue: 2017 E1 Q16 Data analysis - 32%; 2022 E1 Q16 - 40%; 2023 E1 Q16 - 43%

2021 Exam 1 Q16 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: Find the six-mean smoothed monthly rainfall with centring for May.

Evidence: A six-value window with centring means two six-value means and then their average - twelve of the twelve months are in play. CAL-2 puts core Data analysis position 16 at a November median of 51.5% full marks. Held at BORDERLINE because the analogous four-mean November items ran 59-81%.

Closest November analogue: 2017 E1 Q15 Data analysis (four-mean with centring) - 64%

Recursion and financial modelling

2021 Exam 1 Q21 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: With V0 = 250 000 and V(n+1) = 1.0025Vn + 250, at the end of which year does the balance first exceed $500 000?

Evidence: The recurrence steps in months but the options are years, so the crossing month has to be found and then converted - and the conversion rounds up to the end of a year, not to the nearest year. CAL-2: core Recursion position 5 (Q21) was a November separator in half the years, median 51.5%.

2021 Exam 1 Q22 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: A boat depreciates at 15% for two years and then at d% for three more, ending at $43 561.67; find d.

Evidence: Two stages: the value after two years at 15% (65 025), and then a cube root or solver run to recover the new rate. Neither can be skipped and neither is prompted. CAL-2: core Recursion positions 6-8 have November medians of 33-55% full marks.

Closest November analogue: 2022 E2 Q8d Recursion - 19% (recover a rate mid-contract)

2021 Exam 1 Q23 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: A $5000 loan compounding quarterly grows to $5325.14 in a year; find the effective annual interest rate.

Evidence: The NHT report's route has two steps - "The annual interest rate is 6.35%. The effective interest rate is..." - and the two answers, 6.35% and 6.50%, are both offered, one line apart. Confusing nominal with effective is the whole point of the item. CAL-2: Q23 was a November separator in 5 of 7 years, median 38% full marks.

2021 Exam 1 Q24 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: After 47 repayments of $982.16 on a $40 000 loan, by how much does the 48th repayment differ?

Evidence: The answer is a three-cent adjustment, so the whole 48-month amortisation has to be carried at full precision and the residual future value read off - any rounding along the way destroys it. Options A and E are the $6.78 a student gets from a different (wrong) rounding route. CAL-2: Q24 has a November median of 33% full marks.

Closest November analogue: 2021 E2 Q8c Recursion - 15% (final repayment including interest)

Matrices

2021 Exam 1 Q3 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Which of five matrix equations has the same unique solution for x and y as the given one?

Evidence: The NHT report works through all five options in turn, converting each back into simultaneous equations - the only way to tell the correct rearrangement from four that merely look symmetric. CAL-6: abstract matrix-form items ran 36-45% in November.

Closest November analogue: 2017 E1 Q7 Matrices - 36%; 2021 E1 Q7 - 40%

2021 Exam 1 Q5 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: A transition matrix moves workers between two buildings; if the green building always has 36 workers, how many are in the white building?

Evidence: 'The same number each day' is a steady-state condition that the student must translate into 0.48 x G = 0.24 x W before anything can be computed. Nothing in the question says 'long term'. CAL-1: position 5. CAL-6: steady-state items ran 39% and 46% in November.

Closest November analogue: 2023 E1 Q27 Matrices - 39%; 2018 E1 Q8 - 46%

2021 Exam 1 Q6 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: A 4 x 6 ticket-count matrix multiplies a 6 x 2 price matrix; what do the elements of the product show?

Evidence: The answer is a description, not a number: the product is 4 x 2, so it shows adult and child totals for each family. Getting it right requires tracking what each dimension indexes. CAL-1: position 6, 55% November separator rate, median 46%.

Closest November analogue: 2022 E2 Q2bii Matrices - 21% (interpreting a matrix result in words)

2021 Exam 1 Q7 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: From a transition diagram with several probabilities of 1.0, decide which statement about empty locations on which day is true.

Evidence: Several days of the state matrix have to be generated and then five statements tested, each naming a different day and a different set of locations. The probabilities of 1.0 mean locations empty and refill on a cycle rather than settling. CAL-1: position 7, 65% November separator rate.

2021 Exam 1 Q8 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: Given D + D-squared for a four-team tournament and two known results, find the one-step dominance matrix D.

Evidence: The sum of one-step and two-step dominance has to be decomposed back into its parts, using only two known games as anchors. November asks students to build a two-step dominance matrix, not to invert the sum of two. CAL-1: position 8, 84% November separator rate, median 35%.

Closest November analogue: 2016 E1 Q8 Matrices (two-step dominance) - 42%

Networks and decision mathematics

2021 Exam 1 Q4 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: How many faces does the drawn graph have?

Evidence: Faces have to be counted including the infinite outer face, or v and e counted and Euler's formula applied. CAL-6: planar-graph and face items ran 11, 21, 34 and 41% in November - every one a separator.

Closest November analogue: 2020 E1 Q7 Networks - 11%; 2022 E1 Q4 - 21%

2021 Exam 1 Q5 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Using Dijkstra's algorithm on a ten-vertex network, what does Aisha find for the trip from A to J?

Evidence: The options mix the right value with the wrong name - 'critical path', 'minimum spanning tree' - so the student must both run the algorithm on a ten-vertex weighted network and know what the algorithm produces. CAL-1: position 5.

2021 Exam 1 Q6 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: For which values of the two unknown edge weights m and n is the minimum spanning tree NOT 28 km?

Evidence: A minimum spanning tree has to be built five times, once for each candidate pair of weights, and the exception identified. CAL-1: position 6, 55% November separator rate. November's own minimum-spanning-tree items, which ask for a single tree, ran 52-80%.

Closest November analogue: 2016 E1 Q4 Networks - 52%

2021 Exam 1 Q7 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: From a table of durations and predecessors for eleven activities, how many activities cannot be delayed?

Evidence: The network has to be drawn from a predecessor table, both passes run, and then the count of zero-float activities given - and with two paths of equal length the count is larger than the length of any single critical path. CAL-1: position 7, 65% November separator rate. CAL-6: float items ran 31-48%.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2022 E1 Q6 - 48%

2021 Exam 1 Q8 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Activity D is removed and a new activity M inserted; how does the minimum completion time change?

Evidence: The NHT report has to time both networks in full - "The Holiday Fun network has a minimum completion time of 28 hours and critical path ADGKL. The Sunny Life network has a minimum completion time of 27 hours and a critical path AEIJL or BGKL" - so the critical path moves as well as the time. CAL-1: position 8, 84% November separator rate, median 35%.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2025 E1 Q40 - 39%

Geometry and measurement

2021 Exam 1 Q3 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: A pool has a brick wall on one side and a 1.2 m gap to a fence on the other three; find the concreted area.

Evidence: The concreted region is an L-shape, not a frame: the outer rectangle grows by 1.2 m on three sides only, and the pool is then subtracted. Option C is the answer for a fence on all four sides. CAL-1: position 3.

2021 Exam 1 Q4 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: Which expression gives AB, given C is 46 m from A on a bearing of 133 and 35 m from B on a bearing of 074?

Evidence: Both interior angles - 59 and 47 degrees - have to be constructed from bearings before the sine rule can be written, and the options then differ only in which side and which angle are paired. CAL-6: sine-rule-with-bearings items ran 30, 38, 41, 42 and 45% in November.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2022 E1 Q6 - 38%

2021 Exam 1 Q6 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: The great circle distance from the Great Pyramid of Giza to the North Pole is 6702 km; find its latitude.

Evidence: The arc gives a central angle of 60 degrees, which is the angle from the pole, so the latitude is 90 - 60 = 30 N. Option D, 60 N, is the un-complemented answer and option E, 120 N, is not even a latitude. CAL-1: position 6, 55% November separator rate. CAL-6: latitude items ran 26-49%.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2019 E1 Q6 - 41%

2021 Exam 1 Q7 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: In triangle KLM with J on KM, KL = 20, JL = LM = 14 and angle LKM = 30 degrees, find angle JLM.

Evidence: Two triangles chained: the sine rule in KJL to find one angle, the isosceles property of JLM, and the angle sum - with the ambiguous case lurking because JL = LM. CAL-1: position 7, 65% November separator rate, median 45%.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2020 E1 Q10 - 45%

2021 Exam 1 Q8 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: Three friends fly to Papeete from Tokyo, Auckland and Los Angeles; give the order in which they arrive.

Evidence: Three departure times in three different local zones must each be converted to Papeete time using the longitude differences, the journey times added, and the three results ordered. That is nine separate steps for one mark. CAL-1: position 8, 84% November separator rate. CAL-6: time-difference items ran 26-49%.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2022 E1 Q4 - 49%

Graphs and relations

2021 Exam 1 Q5 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: A repair costs $155 for 45 minutes and $330 for two hours; using cost = a + b x n with n in 15-minute units, find the cost of a 90-minute service.

Evidence: The times must first be converted into the unit the rule uses - n = 3 and n = 8, not 45 and 120 - before the simultaneous equations can be solved, and then converted again for 90 minutes. Using minutes directly produces a plausible wrong answer. CAL-1: position 5.

2021 Exam 1 Q6 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: Identify one of the four inequalities that define the shaded feasible region.

Evidence: Both the boundary line and the direction of the inequality have to be read off, and the options offer the same line with both directions. CAL-1: position 6, 55% November separator rate. CAL-6: feasible-region items ran 29-40% in November.

Closest November analogue: 2016 E1 Q5 Graphs and relations - 29%; 2018 E1 Q7 - 40%

2021 Exam 1 Q7 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: Two pumps empty a 1200-litre tank; one stops at p minutes with 400 litres left. Find the rate over the final interval.

Evidence: The report's chain is three steps: the two-pump rate of 50 L/min from the 24-minute hypothetical, then p = 16, then 400/(29 - 16). Each depends on the last and none is prompted. CAL-1: position 7, 65% November separator rate, median 45%.

2021 Exam 1 Q8 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: For which a and b does Z = ax + by take its maximum at R only, given five named corner points?

Evidence: The report reduces it to an inequality on the gradient - "The gradient, m, of the objective function must be between..." - derived from the slopes of the two edges meeting at R. Four of the five options give a maximum somewhere else or along a whole edge. CAL-6: the LP objective-function family ran 29-47% across seven November papers, every one a separator. CAL-1: position 8, 84%.

Closest November analogue: 2022 E1 Q8 Graphs and relations - 29%; 2020 E1 Q10 - 31%

2021 Exam 2 (NHT) — 31 SEPARATOR, 1 BORDERLINE

Data analysis

2021 Exam 2 Q1b (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: Of the five variables other than 'number', how many are nominal?

Evidence: Five classifications for one mark, and the awkward ones are 'event', coded 1 and 2 but naming two races, and 'time', recorded as minutes and seconds. The answer is 3 and there is no partial credit. CAL-5: Data analysis Exam 2 parts were November separators 41% of the time - the lowest topic rate, which is why this stays BORDERLINE.

2021 Exam 2 Q1dii (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Does the percentaged segmented bar chart support an association between event chosen and gender? Justify with percentages.

Evidence: The report splits the two marks explicitly - one for a statement that the contention is supported with a named category, one for percentages from both genders in that category - so a bare conclusion, or percentages without the comparison, scores one. CAL-4: 2-mark parts were November separators 71% of the time, median 38%.

2021 Exam 2 Q3b (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Use five-median smoothing to smooth the time series plot, marking each smoothed point with a cross.

Evidence: Median smoothing done graphically across eleven years, by eye, with no table - seven crosses each of which must land on the right value. CAL-4: 2-mark part, 71% November separator rate. Graphical-completion parts are the classic all-or-nothing 2-marker.

2021 Exam 2 Q3ciii (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Given r = -0.690, write the percentage of variation in winning time NOT explained by year.

Evidence: Square, subtract from one, convert to a percentage, and keep two decimal places - four operations for one mark, with the word 'not' inverting the quantity students practise. CAL-6: coefficient-of-determination items ran 41% and 45% in November as multiple choice.

Closest November analogue: 2019 E1 Q10 Data analysis - 41%; 2018 E1 Q9 - 45%

2021 Exam 2 Q4bi (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: In which year does the least squares line first predict the women's winning time to fall below the men's?

Evidence: The line has to be set to zero and solved for year - 413.749/0.20327 = 2035.6 - and then rounded up to 2036, because the difference is still positive in 2035. Solving an equation for the explanatory variable, and then rounding in the right direction, are both unusual.

2021 Exam 2 Q4bii (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

Asks: By how many seconds will the predicted women's time be below the men's in that year?

Evidence: The predicted difference in that year is a fraction of a minute, so it must be computed at full precision and then multiplied by 60 to give 7 seconds - a number so small that any rounding earlier in the chain destroys it. And the answer depends on the previous part being right.

2021 Exam 2 Q4biii (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: What assumption is made when this least squares line is used to predict years after 2018?

Evidence: The answer is a sentence about the trend continuing, and November named exactly this as hard to express: students reach for the word 'extrapolation' or 'linear' without saying what is being assumed to continue.

Closest November analogue: 2021 E2 Q3eii Data analysis - 18% ("Students found it hard to convey the idea of the trend continuing")

Recursion and financial modelling

2021 Exam 2 Q5c (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence medium

Asks: Continue the amortisation table: find the interest P, principal reduction Q and balance R for payment 4, to the nearest cent.

Evidence: Three linked figures from one rate, each depending on the last and all three needed for both marks. CAL-4: 2-mark parts were November separators 71% of the time, median 38% full marks.

2021 Exam 2 Q6b (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: Unit-cost depreciation is $3.50 per hour and $10 920 per year over 52 weeks; for how many hours a week is the machinery used?

Evidence: Two divisions in the right order - 10 920/3.50 to get annual hours, then /52 - and the unit switches from dollars to hours to hours per week along the way. November named misreading the unit in unit-cost depreciation as a failure point.

Closest November analogue: 2021 E2 Q7c Recursion - 21% ("did not recognise that the value was of the machine in terms of the number of cups of coffee made")

2021 Exam 2 Q7b (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: Repaying $1200 a fortnight instead of the scheduled $1046.62, how many repayments will be exactly $1200?

Evidence: The solver gives a non-integer number of periods, and the answer is the whole number below it, because the last repayment is smaller. Rounding to the nearest period, or quoting the full 260 fortnights of the original schedule, are both natural wrong answers.

Closest November analogue: 2021 E2 Q8c Recursion - 15% (the final, different repayment)

2021 Exam 2 Q7c (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: After five years of $1200 fortnightly repayments, will a $100 000 inheritance clear the loan? Justify with a calculation.

Evidence: The balance after 130 fortnights at the increased repayment must be produced ($99 759.42) and then compared - the mark requires the calculation, not just the yes. Both the non-scheduled repayment and the fortnightly period have to be handled.

Matrices

2021 Exam 2 Q1c (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: Write a matrix calculation that gives the total printing cost of distinction certificates across three year levels.

Evidence: The student has to build the calculation themselves: pick the distinction column out of R, pair it with a cost row or column in the right order, and produce a 1 x 1 result. There is no template and no partial credit.

Closest November analogue: 2021 E2 Q4 Matrices - 10% ("Only some students were successful in filling in the entire matrix")

2021 Exam 2 Q1bii (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Explain what the element r32 of R = N x E represents.

Evidence: The answer - the number of Year 9 students awarded a credit in English - requires reading row 3 as a year level and column 2 as a grade, and describing the product in context rather than as arithmetic. Element interpretation is where November students most often score zero in this module.

Closest November analogue: 2022 E2 Q2bii Matrices - 21% ("few students able to demonstrate how to interpret")

2021 Exam 2 Q2b (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Using the communication matrix, name in order the coordinators Cleo must use to get a message to Amy.

Evidence: The shortest chain is Cleo to Ellie to Brian to Amy - a three-step path that has to be found by inspecting the matrix rather than by any single calculation, and the order must be right.

2021 Exam 2 Q3ci (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: Given S0 and that 82 students receive a distinction the next year, determine the unknown element l of T.

Evidence: The transition equation has to be run backwards: 0.65 x 80 + 0.29 x 100 + l x 50 = 82 solved for l = 0.02. Nothing in the question says to form an equation, and the answer is a small number where an arithmetic slip is invisible.

Closest November analogue: 2021 E2 Q3e Matrices - 15%

2021 Exam 2 Q3cii (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: How many of the 2017 Year 7 students are predicted to qualify for Advanced Mathematics in 2021?

Evidence: Three successive applications of the transition matrix (Year 7 to Year 10), using the value of l recovered in the previous part, and then only the distinction row read off and rounded. A dependency chain four steps deep for one mark.

Closest November analogue: 2021 E2 Q4 Matrices - 10%; 2024 E2 Q12c - 12%

2021 Exam 2 Q4 (NHT) — Matrices — 2 marks — SEPARATOR, confidence high

Asks: Given Q4 and Q(n+1) = T.Qn + B, how many multiple-choice questions were in the file at the end of month 2?

Evidence: The recurrence has to be run backwards two steps - Qn = T-inverse x (Q(n+1) - B) applied twice - which requires inverting a 2 x 2 transition matrix and subtracting B in the right order. Every November question in this family runs the recurrence forwards, and those sat at 10-12% full marks.

Closest November analogue: 2021 E2 Q4 Matrices - 10%; 2024 E2 Q12c - 12%

Networks and decision mathematics

2021 Exam 2 Q2a (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: How many different flight routes are available from Melbourne to London on the given network?

Evidence: Every directed path through a six-vertex network must be enumerated without repetition or omission - six of them - and there is no algorithm in the course for doing it. CAL-5: Networks Exam 2 parts were November separators 45% of the time.

2021 Exam 2 Q2c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: What is the maximum number of seats available from Melbourne to London?

Evidence: The minimum cut has to be found among many candidates on a seven-vertex network, counting only edges that cross in the flow direction. CAL-6: cut and maximum-flow items ran 40% and 44% in November Exam 1, and the worst single November question in the corpus was a cut question.

Closest November analogue: 2022 E2 Q3d Networks - 2%; 2023 E1 Q40 - 40%

2021 Exam 2 Q2d (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Eight extra seats are to be added to one flight so that eight more passengers can travel; name the two cities.

Evidence: Adding capacity only helps on an edge of the minimum cut, so the student must find that cut and then identify which single edge, when raised, moves the bottleneck. The natural answer - any saturated edge - is wrong. November's closest analogue asked for the vertices and new capacity of a changed cut.

Closest November analogue: 2022 E2 Q3d Networks - 2% ("Some students listed the vertices correctly, but not the new capacity")

2021 Exam 2 Q3c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: How many activities could have their completion time increased by two weeks without changing the minimum completion time?

Evidence: Every activity's float must be computed and then counted against a threshold of two weeks - twelve floats for one mark, and the answer (4) is a count, so one miscomputed float is fatal. CAL-6: float items ran 31-48% in November Exam 1 when only a single float was wanted.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2022 E1 Q6 - 48%

2021 Exam 2 Q3d (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Activities G and H are each reduced by two weeks; how does the overall completion time change?

Evidence: The answer is a one-week reduction, not two: cutting two activities by two weeks each moves the bottleneck to a different path after one week. CAL-6: November's crash-the-project questions sit at 9% and 12% full marks for exactly this reason.

Closest November analogue: 2021 E2 Q4c Networks - 9%; 2020 E2 Q5d - 12%

Geometry and measurement

2021 Exam 2 Q1e (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: A cable hangs from a beam to a light globe at the centre of a sphere of radius 18 cm, 15 cm below the beam and 12 cm from each side; find the cable's length.

Evidence: The 12 cm horizontal half-width has to be turned into a vertical offset inside the sphere by Pythagoras, root(18^2 - 12^2), and that combined with the 15 cm and the 18 cm radius. The geometry has to be constructed entirely from a verbal description.

2021 Exam 2 Q2b (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: An 18 cm candle of radius 3 cm stands in an 11 cm bowl of radius 6 cm; what volume of sand fills the rest?

Evidence: The candle is taller than the bowl, so only its bottom 11 cm displaces sand - using the candle's full 18 cm gives a smaller, entirely plausible answer. Recognising which height applies is the whole question.

2021 Exam 2 Q2c (NHT) — Geometry and measurement — 2 marks — SEPARATOR, confidence medium

Asks: The base of the bowl and the uncovered ring of the plate are in the ratio 4:5; find the plate's area.

Evidence: The ratio applies to the ring, not to the whole plate, so the plate is 9/4 of the bowl's base rather than 5/4 - the commonest way to lose both marks. CAL-4: 2-mark part, 71% November separator rate.

Closest November analogue: 2020 E2 Q2d Geometry - 17% (scale factor applied to the wrong quantity)

2021 Exam 2 Q3a (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Show, with calculations, that the bearing of Adelaide from Brisbane is 235 degrees.

Evidence: Brisbane is north and east of Adelaide, so the required bearing is in the third quadrant: 180 + arctan(1310/918). Computing the acute angle and stopping - or measuring the reverse direction - both give a plausible three-digit bearing. CAL-6: bearing items ran 30-45% in November.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2018 E1 Q4 - 42%

2021 Exam 2 Q3b (NHT) — Geometry and measurement — 2 marks — SEPARATOR, confidence high

Asks: Melbourne is 1370 km from Brisbane on a bearing of 211 degrees; find the distance from Melbourne to Adelaide.

Evidence: The included angle at Brisbane comes from differencing two bearings, 235 and 211, and only then can the cosine rule be applied with the Brisbane-Adelaide distance recovered from the previous part. CAL-4: 2-mark part, 71% November separator rate. CAL-6: bearings with the cosine rule ran 30-45%.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2022 E1 Q6 - 38%

Graphs and relations

2021 Exam 2 Q2c (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: From t = 5d for the first 5 km, what is Jasmine's speed in kilometres per hour?

Evidence: The graph's gradient is minutes per kilometre, so the speed is the reciprocal converted to hours: 60/5 = 12 km/h. Quoting 5, or 1/5, or 0.2 are all natural mis-steps, and the unit conversion is the point of the mark.

2021 Exam 2 Q2d (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: How long after the start does the train catch up to Jasmine? Give minutes and seconds.

Evidence: Two piecewise rules have to be matched on the correct branch, 2.5d + 22.5 = 4d + 5 solved for d = 11.67, the time computed, and the decimal minutes converted to 51 minutes 40 seconds. Four distinct steps for one mark, and the branch choice is unprompted.

2021 Exam 2 Q3a (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: Write down the fifth inequality that completes the definition of the feasible region.

Evidence: The inequality has to be reconstructed from the shaded region and the coordinates of the corner points - the reverse of the usual direction, and the boundary must be paired with the correct direction.

Closest November analogue: 2016 E1 Q5 Graphs and relations - 29%; 2018 E1 Q7 - 40%

2021 Exam 2 Q3b (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: With C = x + 1.05y, determine the minimum total cost over the feasible region.

Evidence: The objective has an awkward coefficient, so the five corner points give close values and must each be evaluated carefully; and this is a minimum, which is the opposite of the direction the module drills. CAL-6: objective-function items ran 29-47% in November.

Closest November analogue: 2020 E1 Q10 Graphs and relations - 31%; 2021 E1 Q7 - 39%

2021 Exam 2 Q3c (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: Revenue is $75 000; determine the minimum profit the committee can make.

Evidence: Minimum profit corresponds to maximum cost, so the optimisation must be run in the opposite direction from the previous part - a student who reuses the minimum cost gets the maximum profit instead. CAL-3: the last part of the module.

2022 (NHT)

2022 Exam 1 (NHT) — 33 SEPARATOR, 1 BORDERLINE

Data analysis

2022 Exam 1 Q4 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: From a histogram plotted on a log10 scale, decide between which two values the median diameter lies.

Evidence: The median has to be located on the log axis first and then converted back out of logs, so the answer is an interval of raw diameters rather than a log value. CAL-6: log-scale and transformation items ran 34-54% in November.

Closest November analogue: 2020 E1 Q13 Data analysis - 34%; 2016 E1 Q11 - 54%

2022 Exam 1 Q6 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: What is the most appropriate graphical display for the association between delivery time and delivery distance?

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. The report's explanation turns on both variables being categorical - "All the other options can be used to present numerical data" - so the choice depends on classifying the variables correctly before choosing a display.

2022 Exam 1 Q8 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

Asks: From a boxplot of 44 measurements, find the percentage with a bicep circumference between 26 cm and 34 cm.

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. Its explanation runs to five sentences and three steps: 75% of the data lies between Q1 and the maximum (33 people), the three people above 34 cm are removed, and 30/44 = 68.18% is computed. The 'obvious' answer, 50% from Q1 to Q3, is option C.

2022 Exam 1 Q9 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

Asks: The mean of 44 measurements is 28.16 cm; recalculate it with the four outliers removed.

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. It opens "Three steps are required to solve this question" - recover the total (1239.04), subtract the four outlier values read off the boxplot, divide by 40. The outlier values themselves have to be read from the plot.

2022 Exam 1 Q10 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: An outlier recorded as 21 cm is corrected to 20 cm; which single statistic changes?

Evidence: Each of median, Q1, Q3, IQR and range has to be tested against a change at the extreme of the distribution - four of them are unaffected because the change is outside the box. This is conceptual reasoning about robustness, not calculation. CAL-2: core Data analysis position 10 has a November median of 56.5% full marks.

2022 Exam 1 Q11 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

Asks: Find the residual at an elbow diameter of 13.4 cm from the scatterplot and fitted line.

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. Both the actual and the predicted value have to be read off a printed scatterplot to a precision of about 0.05, and the report has to write out the subtraction: "10.4 - 10.85 = -0.45". Options B and C are the same magnitude with opposite signs.

Closest November analogue: 2018 E1 Q14 Data analysis (residual) - 42%

2022 Exam 1 Q12 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Choose the equation of the least squares line fitted to the scatterplot.

Evidence: Two of the options share the slope 0.46 and differ only in the intercept, which must be extrapolated back to elbow diameter zero rather than read at the left edge of the plotted data. CAL-6: reading a least-squares equation off a scatterplot ran 34-49% in November.

Closest November analogue: 2020 E1 Q13 Data analysis - 34%; 2017 E1 Q8 - 43%

2022 Exam 1 Q14 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: A June seasonal index of 1.25 means that June smart-television sales are what?

Evidence: The index is a multiplier on the average, so June sales are 25% more - while 'reduce by 20%' (option A's cousin) is what correcting for seasonality would do. Both readings are offered. CAL-6: this family was a November separator every time it appeared, at 32, 40, 43 and 50%.

Closest November analogue: 2022 E1 Q16 Data analysis - 40%; 2023 E1 Q16 - 43%

2022 Exam 1 Q16 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

Asks: Three quarterly averages and one seasonal index are given; find the seasonal index for quarter 1.

Evidence: The quarter-4 average and three of the four indices are missing, so the deseasonalised average has to be recovered from the one known index (11 467/0.9569) before quarter 1 can be divided by it. Two reversals of the seasonal-index relation in one mark. CAL-6: the seasonal-index family ran 32-50% in November with nothing missing.

Closest November analogue: 2017 E1 Q16 Data analysis - 32%; 2022 E1 Q16 - 40%

Recursion and financial modelling

2022 Exam 1 Q19 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: Which recurrence relation generates a sequence whose values grow geometrically?

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. It has to define the term - "Geometric growth refers to the situation where each successive term in a sequence differs by a constant ratio. For growth to occur, the R value must be greater than 1" - i.e. both the 'geometric' and the 'growth' halves trip students, and options A and E each satisfy only one of them.

2022 Exam 1 Q21 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: From four lines of an amortisation table and a 2.4% annual rate, find the date of the second payment.

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. "Two steps are required": the payment period must be deduced from the table by comparing the interest charged with the annual rate (giving a quarter), and only then does the date follow. Options A, B and C are weekly, fortnightly and monthly - all plausible until the rate is checked. CAL-2: core Recursion position 5 was a November separator in half the years.

2022 Exam 1 Q22 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: For V(n+1) = 1.004Vn - b, which pair of values a and b could NOT describe a perpetuity?

Evidence: A perpetuity requires the payment to equal exactly the interest, b = 0.004a, so five pairs must each be tested. Four satisfy it and one does not. CAL-2: core Recursion position 6 (Q22) has a November median of 55% full marks.

2022 Exam 1 Q23 (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

Asks: A $3000 loan compounds monthly with an effective first-year rate of 4.18%; find the balance after one year.

Evidence: The point of the item is that the effective rate already gives the annual growth, so no compounding calculation is needed - but four of the five options are what a student gets by converting to a nominal rate first. CAL-2: Q23 was a November separator in 5 of 7 years, median 38%. Held at BORDERLINE because the correct route is a single multiplication.

2022 Exam 1 Q24 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: After ten years, $20 is added to each weekly repayment on a 20-year loan; by how many weeks is the term reduced?

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. Its explanation is explicitly "Four steps are required, three of which use Finance Solver" - find the scheduled repayment, find the balance at ten years, re-solve for the new term, and difference against 520 weeks. CAL-2: Q24 has a November median of 33% full marks. CAL-6: multi-stage finance-solver items ran 8-19%.

Closest November analogue: 2021 E2 Q9b Recursion - 8%; 2020 E2 Q11 - 19%

Matrices

2022 Exam 1 Q3 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Which transition matrix correctly represents the given transition diagram?

Evidence: Every option contains the same six percentages; they differ in which way round 'today' and 'tomorrow' are indexed and where each arrow's percentage lands. Transposing the matrix is the designed error. CAL-1: position 3.

2022 Exam 1 Q4 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Given a 5 x 5 permutation matrix and that Regan is interviewed on Monday, give the order of the next four models.

Evidence: The permutation must be applied four times in succession, each time to the result of the last, and the whole four-name sequence must be right. CAL-1: position 4. CAL-6: permutation-matrix items ran 39% and 42% in November when more than one application was needed.

Closest November analogue: 2023 E1 Q30 Matrices - 39%; 2022 E1 Q7 - 42%

2022 Exam 1 Q5 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: For which value of q does the given pair of simultaneous equations NOT have a unique solution?

Evidence: The condition is a zero determinant, which has to be recognised from a pair of equations rather than from a printed matrix, and then solved for q. CAL-1: position 5. CAL-6: determinant items ran 39% in November when interpretation was required.

Closest November analogue: 2023 E1 Q30 Matrices - 39%

2022 Exam 1 Q6 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: From a one-step dominance matrix for five players, choose the table of one-step and two-step dominance totals.

Evidence: The matrix must be squared and both sets of row sums computed, then matched against five tables that differ in only one or two entries. CAL-1: position 6, 55% November separator rate. CAL-6: two-step dominance ran 42% in November.

Closest November analogue: 2016 E1 Q8 Matrices - 42%

2022 Exam 1 Q7 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: 1000 rodents shelter at location A on day two; how many were resettled on day one?

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. It has to write out the whole row product - "1 x 0.4 + 0.15 x 0.2 + 0 x 0.2 + 0.35 x 0.2 = 0.5" - and then invert it: 50% of the population is 1000, so the population is 2000. Working backwards from a count to a total is the step students miss. CAL-1: position 7, 65% November separator rate.

Closest November analogue: 2021 E2 Q3c Matrices - 17%

2022 Exam 1 Q8 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: Which matrix gives the time for each of three workers to service all equipment at each of three centres?

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. Its explanation is one sentence and it is the whole difficulty: "The answer requires T, U and V to be in the rows. It is necessary to first transpose matrix N." Nothing in the question mentions a transpose. CAL-1: position 8, 84% November separator rate, median 35%.

Closest November analogue: 2017 E1 Q7 Matrices - 36%; 2022 E1 Q7 - 42%

Networks and decision mathematics

2022 Exam 1 Q3 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: How many of the four drawn graphs have an Eulerian trail?

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. Four graphs each need their odd-degree vertices counted and the trail condition applied. CAL-6: November items about Eulerian and Hamiltonian existence ran 17% and 29% full marks, and those concerned a single graph.

Closest November analogue: 2021 E1 Q5 Networks - 17%; 2017 E1 Q6 - 29%

2022 Exam 1 Q4 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Find the minimum length of cable needed to keep nine internet ports connected.

Evidence: A minimum spanning tree on a nine-vertex, sixteen-edge graph, with the answer then summed - and the options are only two metres apart, so one wrong edge is fatal. CAL-1: position 4.

Closest November analogue: 2016 E1 Q4 Networks - 52%

2022 Exam 1 Q6 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Five builders are allocated to five ordered components; which statement about the order of completion is NOT true?

Evidence: Three things stacked: solve a 5 x 5 allocation, then convert the allocation into an order of completion because the components run in numerical sequence, then test five statements. CAL-1: position 6, 55% November separator rate. CAL-6: allocation items ran 24-39%.

Closest November analogue: 2018 E1 Q8 Networks - 24%; 2022 E1 Q3 - 39%

2022 Exam 1 Q7 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Which values of the three unknown capacities w, x and y give a maximum flow of 35 litres per minute?

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. It then evaluates the maximum flow for all five options in turn, four of which give 34 - a one-litre discrimination that requires five separate minimum-cut analyses. CAL-6: cut and flow items ran 40% and 44% in November Exam 1.

Closest November analogue: 2022 E2 Q3d Networks - 2%; 2023 E1 Q40 - 40%

2022 Exam 1 Q8 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: How many dummy activities are needed to draw the network for eleven activities given only a predecessor table?

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. It gives a separate justification for each of the three dummies. The network has to be constructed mentally from a table before the dummies can even be counted. CAL-1: position 8, 84% November separator rate. CAL-6: dummy activities ran 10% in November.

Closest November analogue: 2024 E2 Q15c Networks - 10%

Geometry and measurement

2022 Exam 1 Q3 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Which expression gives the bearing of P from Q, given angles x and z on the diagram?

Evidence: The bearing runs from Q, so the answer is the reverse of the angle the diagram invites, and all five options are plausible reverse-bearing formulas. CAL-6: bearing items ran 30-45% in November.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2018 E1 Q4 - 42%

2022 Exam 1 Q4 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Rotorua is at 38 S; find the shortest surface distance to the South Pole.

Evidence: The central angle is 90 - 38 = 52 degrees, not 38 - and the longitude of 176 E is irrelevant, which the options exploit. CAL-6: latitude/longitude arc items ran 26-49% in November.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2019 E1 Q6 - 41%

2022 Exam 1 Q6 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: A boat sails 3 km east then 4 km on a bearing of 256 degrees; find the direct distance back to the harbour.

Evidence: The included angle has to be constructed from a bearing measured at the second point, and then the cosine rule applied - and with the angle wrong the answer is still a plausible distance. CAL-1: position 6, 55% November separator rate. CAL-6: bearings with the cosine rule ran 30-45%.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2022 E1 Q6 - 38%

2022 Exam 1 Q7 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Triangles ABC and EDC are similar; find CD given AB = 17 cm, DE = 12 cm and two angles.

Evidence: The correspondence of vertices between the two triangles has to be established from the angle marks before any ratio can be written, and the sine rule is needed inside one of them first. CAL-1: position 7, 65% November separator rate, median 45%.

Closest November analogue: 2021 E1 Q3 Geometry (scale factor) - 38%

2022 Exam 1 Q8 (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: Liquid fills two-thirds of the volume of a cone of height 8 cm; find the depth of the liquid.

Evidence: Volume scales as the cube of the linear factor, so the depth is 8 x (2/3) raised to the power one third - about 7.0 cm, not the 5.33 cm that a proportional answer gives. Option C is exactly that wrong answer. CAL-1: position 8, 84% November separator rate, median 35%.

Closest November analogue: 2020 E2 Q2d Geometry - 17% (length scale factor to area/volume)

Graphs and relations

2022 Exam 1 Q5 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: With revenue $750 per 100 smoothies and C = 800 + 3n, find the minimum number needed for a profit of at least $2000.

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. The revenue per unit has to be derived first, then the inequality 2000 < 7.5n - (800 + 3n) solved to n > 622.22, and then rounded up - and 622 is offered as option C alongside the correct 623.

2022 Exam 1 Q6 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: A graph of y against x-cubed passes through (4, 1); which graph shows y against x?

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. It has to build a table of values to identify the curve. Converting between a linearised plot and the original relation - deciding what (4, 1) on an x-cubed axis means for x - is the hardest idea in the module.

2022 Exam 1 Q7 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: Where does Z = 2.4x + 3.6y take its minimum over the shaded feasible region?

Evidence: The objective's gradient matches one of the boundary lines, so the minimum is a whole segment rather than a corner - and four of the five options name single points or the wrong segment. CAL-6: the LP objective-function family ran 29-47% across seven November papers, every one a separator, and the 'answer is a line segment' variant is its deepest form.

Closest November analogue: 2016 E2 Q3d Graphs and relations - 7%; 2020 E2 Q4d - 10%; 2022 E1 Q8 - 29%

2022 Exam 1 Q8 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: From a described four-phase water-tank graph, find the maximum volume reached.

Evidence: The 2022 NHT Exam 1 report says of itself: "This report includes further details for some responses that were not as well answered as others" - and this is one of the questions it singles out for extra explanation. "Two steps are required": an equation 44 + 8x = 12(12 - x) has to be built from the two unknown-length phases and solved for the turning point, and only then is the volume computed. The graph gives no values at all. CAL-1: position 8, 84% November separator rate.

2022 Exam 2 (NHT) — 30 SEPARATOR, 4 BORDERLINE

Data analysis

2022 Exam 2 Q1c (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

Asks: 16% of riders are under 25.5 years and 2.5% are over 33; find the mean and standard deviation.

Evidence: Two percentages have to be converted into z-scores (-1 and +2) using the 68-95-99.7 rule, and the resulting pair of equations solved simultaneously for both parameters. November's normal-distribution items all run in the forward direction. CAL-4: 2-mark part, 71% November separator rate, median 38%.

2022 Exam 2 Q2c (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Round 96.098889 hours to five significant figures.

Evidence: Five significant figures gives 96.099, which requires counting figures from the left across the decimal point rather than counting decimal places. CAL-6: significant-figure rounding is a named November failure point.

Closest November analogue: 2020 E2 Q6d Data analysis - 21% ("The rounding to significant figures...")

2022 Exam 2 Q2dii (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Determine the prediction error (residual) for 1910, when 110 started and 41 finished.

Evidence: The prediction must be made from the printed equation and subtracted in the order actual minus predicted, then rounded to a whole number. CAL-4: 2-mark part, 71% November separator rate.

Closest November analogue: 2018 E1 Q14 Data analysis (residual) - 42%

2022 Exam 2 Q3e (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: Find the standardised value of an average speed of 38.084 km/h, to three decimal places.

Evidence: A single application of the z formula, but with three decimal places demanded and the mean and standard deviation to be picked out of a small table. Listed as BORDERLINE because the calculation itself is one of the most drilled in the course.

2022 Exam 2 Q3f (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

Asks: Determine the percentage of variation in average speed explained by race length, to one decimal place.

Evidence: The correlation coefficient is never given: r has to be recovered from the slope and the two standard deviations using b = r x sy/sx, then squared and converted to a percentage. Three chained steps, none of them prompted. CAL-4: 2-mark part. CAL-6: coefficient-of-determination items ran 41-45% in November when r was supplied.

Closest November analogue: 2019 E1 Q10 Data analysis - 41%; 2018 E1 Q9 - 45%

2022 Exam 2 Q4a (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Construct a vertical boxplot of the 2007-2017 winners' average speeds, reading the values off a time series plot.

Evidence: Eleven values have to be read off a plot, ordered, and a five-number summary built - and then drawn vertically, on the same scale, with all five features correct for both marks. CAL-4: 2-mark part, 71% November separator rate, median 38%.

Closest November analogue: 2020 E2 Q2c Data analysis (drawing a boxplot) - 17%

2022 Exam 2 Q4b (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

Asks: Use seven-median smoothing to smooth the time series plot, marking and connecting the smoothed values.

Evidence: The report sets an explicit all-or-nothing scheme: "Students needed to plot all five points and they all needed to be connected." Seven-median smoothing of eleven points gives exactly five smoothed values, each read by eye. CAL-4: 2-mark part.

Recursion and financial modelling

2022 Exam 2 Q5c (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

Asks: With B(n+1) = 1.45Bn and B0 = 4000, after how many months does the total first exceed $50 000?

Evidence: A geometric recurrence has to be iterated or solved, and 'first exceed' rounds up to 7. Listed as BORDERLINE because a table of values on technology answers it directly - but the boundary month and the meaning of 'first exceed' are still where the mark goes.

2022 Exam 2 Q6c (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: A car depreciates at $0.20 per kilometre and travels 20 000 km a year; what annual flat rate does this represent?

Evidence: Two conversions in sequence: dollars-per-kilometre into dollars-per-year (4000), then into a percentage of the original $50 000 rather than of the current value. Using the reduced value gives a plausible wrong percentage. November named unit-cost interpretation as a failure point.

Closest November analogue: 2021 E2 Q7c Recursion - 21% (unit-cost depreciation misread)

2022 Exam 2 Q7b (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: How many years will it take to fully repay the $800 000 loan?

Evidence: The solver returns quarters, and the answer must be converted to years - with the rate first recovered from the amortisation table in the previous part. The unit change is where the mark is lost.

2022 Exam 2 Q8 (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence high

Asks: After ten years the monthly payment drops from $1500 to $1200; find the smaller final payment.

Evidence: Three stages: the balance after 120 payments of $1500, then the number of $1200 payments that balance supports, then the residual final payment including its interest. November named the last of those three as a specific failure. CAL-4: 2-mark part, 71% November separator rate.

Closest November analogue: 2021 E2 Q8c Recursion - 15% ("the balance before the last payment but does not include the interest"); 2021 E2 Q9b - 8%

Matrices

2022 Exam 2 Q1c (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Complete the 3 x 3 matrix R so that R x C gives the total value of each ticket type sold.

Evidence: R has to be built as a diagonal matrix of ticket counts - a construction the question describes only by what the product must contain. Writing a row matrix instead gives a single total rather than three.

Closest November analogue: 2021 E2 Q4 Matrices - 10% ("Only some students were successful in filling in the entire matrix")

2022 Exam 2 Q2b (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: The element in row L, column R of W-squared equals 2; write down the two paths it represents.

Evidence: The element has to be read as a count of two-step routes and then both routes named - R-C-L and R-P-L. Naming only one, or naming a one-step path, earns nothing.

Closest November analogue: 2016 E1 Q8 Matrices (two-step) - 42%

2022 Exam 2 Q2c (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Explain the significance of the zeros at row F, column R and row R, column F in W + W-squared.

Evidence: The answer is a statement about reachability - there is no one-step or two-step path between the fitness centre and the residential block - which requires reading a matrix sum as a path count rather than as a number. Interpretation parts in Matrices are where November students most often score zero.

Closest November analogue: 2022 E2 Q2bii Matrices - 21%

2022 Exam 2 Q3c (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: How many of the 450 residents participated in a different activity on 2 January than on 1 January?

Evidence: Only the off-diagonal flows count, so the student must either sum the six off-diagonal products or compute the whole state change and subtract those who stayed. Reporting the total who moved to one location, or a diagonal figure, are both natural wrong answers.

Closest November analogue: 2021 E2 Q3c Matrices - 17%

2022 Exam 2 Q3e (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: In the long run, how many of the 450 residents change from the cinema to the library each day?

Evidence: Two stages: the steady-state numbers, then the single transition probability 0.15 applied to the steady-state cinema figure. Quoting the steady-state library figure, or 15% of 450, are both plausible. CAL-6: long-run interpretation items ran 39% and 46% in November.

Closest November analogue: 2023 E1 Q27 Matrices - 39%; 2021 E2 Q3d - 22%

2022 Exam 2 Q3f (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: Family members now attend the cinema each day in constant numbers; how many people attend on 3 March?

Evidence: The daily addition B is never stated: it must be inferred from the fact that the 1 March figures total more than 450, and the recurrence then run twice as S(n+1) = T.Sn + B. Two iterations plus an inferred matrix. CAL-6: iterated T.Sn + B items ran 10% and 12% in November.

Closest November analogue: 2021 E2 Q4 Matrices - 10%; 2024 E2 Q12c - 12%

Networks and decision mathematics

2022 Exam 2 Q1c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: With four students, four roles and Dar given presenter, what role must Casey be given?

Evidence: The allocation has to be forced by elimination across a bipartite graph, using the constraint from part a as well as Dar's assignment. The answer is determined but only after the whole allocation is resolved.

Closest November analogue: 2022 E1 Q3 Networks (allocation) - 39%

2022 Exam 2 Q3a (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Give a route from P that delivers to all six other locations and returns, totalling 50 km.

Evidence: A Hamiltonian cycle of a specified length has to be found by search on a seven-vertex weighted graph - there is no algorithm for it, and a route that misses a vertex or totals anything other than 50 earns nothing.

2022 Exam 2 Q3c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: With a new business X added by three new roads, find the minimum round-trip delivery distance.

Evidence: The whole search has to be redone on the enlarged graph, and the new vertex changes which cycle is cheapest - the answer (46 km) is shorter than the original 50 km, which is counter-intuitive after adding a delivery point.

2022 Exam 2 Q4a (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Complete the table by giving the missing earliest start time for C and latest start time for B.

Evidence: Two different passes for one mark: the EST for C comes from a forward pass, the LST for B from a backward pass over the whole ten-activity project - and both must be right. CAL-6: earliest and latest start-time items ran 31-48% in November.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2022 E1 Q6 - 48%

2022 Exam 2 Q4c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: What is the minimum completion time for the library upgrade?

Evidence: The report's answer names two equal-length critical paths - "A-B-D (or C-F)-H-I-J, 23 weeks" - so a student who finds only one path is not obviously wrong but is vulnerable in the next part. The network also has to be completed with the missing activity G first.

Closest November analogue: 2021 E2 Q4b Networks - 22% ("Many students did not seem to realise there were two critical paths")

2022 Exam 2 Q4d (NHT) — Networks and decision mathematics — 2 marks — SEPARATOR, confidence high

Asks: One activity gains three weeks and another loses three; identify all pairs for which the completion time is unchanged.

Evidence: There are two valid pairs - increase F and decrease C, increase H and decrease I - and both must be found, with the direction specified for each. Every activity's float has to be computed and then paired against a duration constraint. CAL-4: 2-mark part, and the last part of the module.

Closest November analogue: 2021 E2 Q4c Networks - 9%; 2020 E2 Q5d - 12%

Geometry and measurement

2022 Exam 2 Q1c (NHT) — Geometry and measurement — 1 mark — BORDERLINE, confidence medium

Asks: Flag A has length 150 cm and Flag B 60 cm; find the linear scale factor.

Evidence: A single division, 150/60 = 2.5, but in the direction that enlarges B to A rather than the reverse, and the preceding parts invite the 2:3 ratio instead. Listed only as BORDERLINE because the arithmetic is one step.

2022 Exam 2 Q2b (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Find the shortest small circle distance between two places both at 47 N, at 56 W and 2 E.

Evidence: The longitude difference spans the Greenwich meridian (56 + 2 = 58 degrees), and the arc must be taken on the small circle of radius 4365 km rather than on a great circle. Two places to go wrong for one mark. CAL-6: latitude/longitude items ran 26-49% in November.

Closest November analogue: 2018 E1 Q3 Geometry - 43%; 2022 E1 Q4 - 49%

2022 Exam 2 Q3b (NHT) — Geometry and measurement — 2 marks — SEPARATOR, confidence medium

Asks: Find the total area of a field made of a semicircle joined to an equilateral triangle of side 20 m.

Evidence: Two area formulas, one of them requiring the triangle formula with a 60-degree angle, summed and rounded to two decimal places. CAL-4: 2-mark part, 71% November separator rate, median 38%.

2022 Exam 2 Q3c (NHT) — Geometry and measurement — 2 marks — SEPARATOR, confidence high

Asks: A rectangle has two vertices at the midpoints of two sides of the equilateral triangle and two on the dividing line; find its area.

Evidence: Both dimensions have to be derived: the width from the midpoint theorem and the height from the triangle's altitude geometry. Nothing is labelled and neither dimension is given. CAL-4: 2-mark part, and the last part of the question.

2022 Exam 2 Q4a (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Two buildings lie on bearings of 052 and 042 from the museum, 453 m and 630 m away; find the distance between them.

Evidence: The included angle is the 10-degree difference of the two bearings - easy to get right, easy to get wrong by using one of the bearings itself - and then the cosine rule on a very thin triangle, where small angle errors move the answer a long way. CAL-6: bearings with the cosine rule ran 30-45% in November.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2022 E1 Q6 - 38%

2022 Exam 2 Q4b (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: Calculate the bearing of the cathedral from the heritage building.

Evidence: The sine rule must first give an angle inside the thin triangle from the previous part, and that angle then converted into a three-figure bearing measured from a different vertex - so the answer depends on a chain of two earlier results and on getting the direction of measurement right.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2018 E1 Q4 - 42%

Graphs and relations

2022 Exam 2 Q1c (NHT) — Graphs and relations — 1 mark — BORDERLINE, confidence medium

Asks: New prices are $159 for 200 km and $285 for 500 km; find a and b in C = a + b x n.

Evidence: Two simultaneous equations from two points, giving b = 0.42 and a = 75 - both values needed for the single mark. Listed as BORDERLINE because finding a gradient and intercept from two points is the module's core routine.

2022 Exam 2 Q2c (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: Using sound intensity = k/(distance squared), find the intensity 75 m from the engine.

Evidence: The constant k has to be recovered from one of the tabulated pairs (90 000) before the inverse-square rule can be applied at a new distance. Two steps, and the squared denominator is where students halve or double instead.

2022 Exam 2 Q3 (NHT) — Graphs and relations — 2 marks — SEPARATOR, confidence high

Asks: 200 meals sell at the regular price and 100 at half price, breaking even on C = 3.5n + 900; find the regular price.

Evidence: The revenue side has to be built from two different prices - 200p + 100(0.5p) - and set against the cost of all 300 meals. Using 300 meals at one price, or forgetting that the cost covers all 300, both give plausible answers. CAL-4: 2-mark part, 71% November separator rate.

2022 Exam 2 Q4b (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: With 15 large containers, find the minimum and the maximum number of small containers.

Evidence: Two bounds for one mark, each from a different binding constraint - the y <= 2x constraint at the bottom and the floor-area constraint at the top - and both must be whole numbers rounded in the right direction.

Closest November analogue: 2016 E1 Q5 Graphs and relations - 29%; 2018 E1 Q7 - 40%

2022 Exam 2 Q4c (NHT) — Graphs and relations — 2 marks — SEPARATOR, confidence medium

Asks: Find the maximum revenue per flight from transporting containers at $150 and $200 each.

Evidence: The corner points are not printed, so each has to be found from the intersecting constraint lines and then tested - and the optimum must be at integer container counts. CAL-4: 2-mark part, 71% November separator rate, and the last part of the module.

Closest November analogue: 2020 E1 Q10 Graphs and relations - 31%; 2021 E1 Q7 - 39%

2023 (NHT)

2023 Exam 1 (NHT) — 21 SEPARATOR, 3 BORDERLINE

Data analysis

2023 Exam 1 Q9 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

Asks: Which of five statements supports the contention that increased exposure is associated with respiratory symptoms?

Evidence: The NHT report singles this question out and names the wrong answer students gave: "A number of students incorrectly chose D, which gives the percentage of workers with symptoms in each exposure level." Options D and E differ only in which margin the percentages are computed down. Counterweight: the 2023 Exam 1 report states "Students generally answered the questions in the Data analysis section very well", which is why this is listed no higher than it is.

2023 Exam 1 Q16 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Five daily seasonal indices are given with Wednesday's missing; use a deseasonalised forecast equation to predict Wednesday's actual sales.

Evidence: Three chained steps for one mark: recover the Wednesday index from the fact that the five indices sum to five, substitute day number 3 into the forecast equation, and then multiply the deseasonalised forecast by the index rather than dividing. Option C is the raw forecast and option D the forecast for the wrong day. CAL-6: seasonal-index items ran 32-50% in November. Counterweight: the 2023 Exam 1 report states "Students generally answered the questions in the Data analysis section very well", which is why this is listed no higher than it is.

Closest November analogue: 2017 E1 Q16 Data analysis - 32%; 2023 E1 Q16 - 43%

Recursion and financial modelling

2023 Exam 1 Q19 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: From four lines of an amortisation table, find the annual interest rate.

Evidence: The rate is not stated anywhere: 1540/420 000 gives the monthly rate, which must then be multiplied by twelve. The five options are 0.2 percentage points apart, so the rounding has to be right as well. CAL-2: core Recursion position 3 (Q19) has a November median of 57.5% full marks and this is a two-step version.

Closest November analogue: 2022 E2 Q8d Recursion - 19% (recover a rate from a table)

2023 Exam 1 Q21 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: For Vn = 4000 - 20n, which depreciation method(s) could have been used?

Evidence: The rule is linear, which is consistent with both flat rate and unit cost - the answer is a pair, and three of the five options name only one method. Distinguishing the two methods by their algebra rather than by their context is unusual.

2023 Exam 1 Q22 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: A perpetuity pays $1440 a month at 3.6% per annum; what is the balance after one year of payments?

Evidence: The point is that a perpetuity's balance never changes, so the year of payments is a distractor - but four of the five options are the balance adjusted up or down by a year of interest or payments. Conceptual, and easy to over-calculate. CAL-2: core Recursion position 6 (Q22) has a November median of 55%.

2023 Exam 1 Q23 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: From M(n+1) = 1.001Mn compounding fortnightly, find the effective annual interest rate.

Evidence: The fortnightly multiplier has to be raised to the power 26 and converted to a percentage - not multiplied by 26, which is what three of the five options reward. CAL-2: Q23 was a November separator in 5 of 7 years, median 38% full marks.

2023 Exam 1 Q24 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: An extra $299.52 a month is paid on a 15-year loan; find the total amount saved.

Evidence: The report writes it out as "Three steps are required" - solve for the scheduled repayment, re-solve for the shortened term, and then difference two totals paid, not two balances. The final subtraction is the step students skip. CAL-2: Q24 has a November median of 33% full marks.

Closest November analogue: 2024 E2 Q8 Recursion - 13% ("Some students misunderstood the meaning of the total cost of the loan")

Matrices

2023 Exam 1 Q3 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Which of five matrix products does NOT produce a 5 x 3 matrix?

Evidence: Five products, each with two dimensions to check and the inner dimensions to match - and the wrong one is wrong only in its result's shape, not in being undefined. CAL-6: abstract matrix-order items ran 36-45% in November.

Closest November analogue: 2017 E1 Q7 Matrices - 36%; 2021 E1 Q7 - 40%

2023 Exam 1 Q5 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: From a 5 x 5 route matrix, how many ways can a person travel from Y to V without revisiting a town?

Evidence: The NHT report has to enumerate every route - "Single step: Y-V. Multiple steps via X: Y-X-W-V and Y-X-W-Z-V. Multiple steps via Z: Y-Z-V" - because there is no matrix power that counts paths of mixed length with no repeats. CAL-1: position 5.

Closest November analogue: 2016 E1 Q8 Matrices (two-step dominance) - 42%

2023 Exam 1 Q6 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: P is the inverse of Q and R is the transpose of P; for which given matrix are all three defined?

Evidence: Two relations have to be composed in the right order, and the matrix that fails does so because its determinant is zero, so the inverse does not exist. Both ideas are needed. CAL-1: position 6, 55% November separator rate. CAL-6: determinant items ran 39%.

Closest November analogue: 2023 E1 Q30 Matrices - 39%

2023 Exam 1 Q7 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: Which matrix calculation gives both the total number of cakes sold and the total sales, in dollars?

Evidence: One product must yield two different totals at once, which forces a column of ones alongside the price column - a construction the course never sets out. All five options use the same eight symbols. CAL-1: position 7, 65% November separator rate, median 45%.

Closest November analogue: 2017 E1 Q7 Matrices - 36%; 2022 E1 Q7 - 42%

2023 Exam 1 Q8 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: How many of five statements about a four-location transition model are true?

Evidence: The report evaluates all five, and doing so requires running the recurrence backwards to S0, forwards to S2, reading an element of T, and computing a long-run value - four different techniques for one mark. CAL-1: position 8, 84% November separator rate, median 35%.

Closest November analogue: 2023 E1 Q27 Matrices (long-run) - 39%; 2021 E2 Q4 - 10%

Networks and decision mathematics

2023 Exam 1 Q2 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Which of five eight-letter sequences is NOT a Hamiltonian path?

Evidence: Five candidate paths must each be traced against the edges of an eight-vertex graph, and the one that fails does so by repeating a vertex rather than by using a missing edge. CAL-6: Hamiltonian and Eulerian items ran 17% and 29% in November.

Closest November analogue: 2021 E1 Q5 Networks - 17%; 2017 E1 Q6 - 29%

2023 Exam 1 Q3 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: What is the capacity of the marked cut in the directed graph?

Evidence: Only edges directed from the source side to the sink side count, and this cut has edges running both ways. CAL-6: cut-capacity items ran 40% and 44% in November Exam 1, and the deepest November question in the whole corpus was a cut question.

Closest November analogue: 2022 E2 Q3d Networks - 2%; 2023 E1 Q40 - 40%

2023 Exam 1 Q4 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: How many edges must be added to make a connected planar graph with 12 vertices and 3 faces?

Evidence: Euler's formula has to be rearranged to find the target edge count (e = v + f - 2 = 13) and then differenced against the edges already drawn. CAL-6: planar-graph and Euler's-formula items ran 11, 21, 34 and 41% in November.

Closest November analogue: 2020 E1 Q7 Networks - 11%; 2022 E1 Q4 - 21%

2023 Exam 1 Q6 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Which statement about the graph given by a 5 x 5 adjacency matrix is true?

Evidence: Degrees must be computed from a matrix containing a loop (counted twice) and a double edge, and then planarity, loop count, an Eulerian circuit, a degree sum and an odd-degree count all tested. Five different properties for one mark. CAL-1: position 6, 55% November separator rate.

Closest November analogue: 2021 E1 Q5 Networks - 17%; 2022 E1 Q4 - 21%

2023 Exam 1 Q7 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Five workers are optimally allocated to five ordered tasks; two swap. By how much does the total time increase?

Evidence: The optimal allocation must be found first and then perturbed - the same operation November sets at 24, 30 and 39% full marks - with the added complication that the tasks must run in numerical order. CAL-1: position 7, 65% November separator rate.

Closest November analogue: 2018 E1 Q8 Networks - 24%; 2016 E1 Q8 - 30%

2023 Exam 1 Q8 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Given durations and earliest and latest start times for eleven activities, how many have exactly two immediate predecessors?

Evidence: The report's advice is "A directed network diagram can help with this question" - that is, the whole precedence network has to be reconstructed from a timing table before the count can be made. CAL-1: position 8, 84% November separator rate, median 35%.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2022 E1 Q8 - 34%

Geometry and measurement

2023 Exam 1 Q6 (NHT) — Geometry and measurement — 1 mark — BORDERLINE, confidence medium

Asks: Boston (42 N) and Santiago are 8378 km apart along the 71 W meridian; find Santiago's latitude.

Evidence: The arc converts to a central angle of 75 degrees, which must then be taken across the equator from 42 N to give 33 S rather than 33 N or 75 S - and three of those appear as options. CAL-6: latitude items ran 26-49% in November. Counterweight: the 2023 Exam 1 report states "Students answered the questions in the Geometry and measurement module very well", so this is held at BORDERLINE despite the structural signals.

Closest November analogue: 2016 E1 Q4 Geometry - 26%; 2019 E1 Q6 - 41%

2023 Exam 1 Q8 (NHT) — Geometry and measurement — 1 mark — BORDERLINE, confidence medium

Asks: Angles of elevation of a tower are 56, 45 and 38 degrees from three collinear points, A and B being 50 m apart; find BC.

Evidence: The tower's height is never given: it must be recovered from the A and B pair (the 45-degree angle makes the distance equal the height) and then used with the 38-degree angle to place C. Two triangles and an unknown height. CAL-1: position 8, 84% November separator rate. Counterweight: the 2023 Exam 1 report states "Students answered the questions in the Geometry and measurement module very well", so this is held at BORDERLINE despite the structural signals.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2020 E1 Q10 - 45%

Graphs and relations

2023 Exam 1 Q5 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: From a step graph of insurance cost against age, which of two families pays more, and by how much?

Evidence: Nine ages have to be read off a step graph with its open and closed endpoints, two totals formed, and then differenced - and the options pair the wrong family with plausible differences. CAL-1: position 5.

2023 Exam 1 Q6 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: Given four labelled corner points, identify one of the inequalities defining the feasible region.

Evidence: The boundary line has to be reconstructed from two of the printed corner points and then paired with the correct direction; options C and E share a left-hand side and differ only in the constant, and D and E differ only in direction. CAL-6: feasible-region items ran 29-40% in November.

Closest November analogue: 2016 E1 Q5 Graphs and relations - 29%; 2018 E1 Q7 - 40%

2023 Exam 1 Q7 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: For P = mx + ny with m and n both positive, how many of six described locations could hold the maximum?

Evidence: Six possibilities have to be tested at once, and the report's reasoning is the sliding-line argument in its most abstract form: "The objective function has a negative gradient. The maximum value could be any value along the line BC, including at the point B or C." CAL-6: the LP objective-function family ran 29-47% across seven November papers, every one a separator. CAL-1: position 7, 65%.

Closest November analogue: 2022 E1 Q8 Graphs and relations - 29%; 2020 E1 Q10 - 31%

2023 Exam 1 Q8 (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: A three-branch piecewise distance rule plus a 5 m/s return trip totals 53 seconds; find a.

Evidence: The report needs "Three steps": find b and c by matching the branches at t = 5 and t = 9, express the outward distance and the return time in terms of a, and solve. Continuity of a piecewise rule is the hardest idea in the module. CAL-1: position 8, 84% November separator rate, median 35%.

2023 Exam 2 (NHT) — 34 SEPARATOR, 1 BORDERLINE

Data analysis

2023 Exam 2 Q1c (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Using Table 1, determine the percentage of boys whose dominant hand is left.

Evidence: The denominator is the seven boys, not the ten students - so 2/7 = 29%, while 2/10 = 20% is the natural wrong answer. Choosing the right sub-group to percentage against is the recurring November failure in two-way work.

Closest November analogue: 2021 E2 Q3c Matrices - 17% (percentage of the wrong total)

2023 Exam 2 Q1e (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Determine the least squares line predicting foot width from foot length, with coefficients to three significant figures.

Evidence: Ten pairs entered, response and explanatory assigned correctly, the equation written in terms of the named variables, and both coefficients rounded to three significant figures. CAL-4: 2-mark parts were November separators 71% of the time, median 38%.

Closest November analogue: 2020 E2 Q6d Data analysis - 21% (rounding to significant figures)

2023 Exam 2 Q2b (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Complete the five-number summary for the boys from a back-to-back stem plot with three values replaced by dashes.

Evidence: Four of the five statistics must be recovered from a stem plot that is deliberately incomplete, so the quartiles have to be reasoned about rather than counted - the report itself allows two possible minimum values. CAL-4: 2-mark part, 71% November separator rate.

2023 Exam 2 Q2c (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Does the stem plot support the contention that boys have wider feet than girls? Refer to the values of an appropriate statistic.

Evidence: The report accepts opposite conclusions depending on which statistic is quoted - "Yes, as the median foot width of the boys, 9.15 cm, is greater..." or "No, as the Interquartile range for boys and girls are both equal to 0.8" - so the mark is entirely about quoting a statistic with values and drawing the matching conclusion. CAL-4: 2-mark part.

2023 Exam 2 Q3 (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

Asks: Write an appropriate calculation and use it to explain why a foot length of 27.5 cm is an outlier.

Evidence: The quartiles must be taken from the correct row of a two-row summary table, the upper fence computed as 25.1 + 1.5(25.1 - 23.6), and a comparison stated - three components for two marks. CAL-4: 2-mark part, 71% November separator rate, median 38%.

Closest November analogue: 2020 E2 Q2c Data analysis (outliers and fences) - 17%

2023 Exam 2 Q4e (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: Show that the correlation coefficient is 0.641, using the summary statistics.

Evidence: The formula on the sheet gives the slope from r, so it has to be rearranged: r = b x sx/sy. Rearranging a printed formula, rather than substituting into it, is where this mark goes.

Closest November analogue: 2019 E1 Q10 Data analysis - 41%; 2018 E1 Q9 - 45%

2023 Exam 2 Q4f (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

Asks: What percentage of the variation in foot width is NOT explained by foot length, to one decimal place?

Evidence: Square r, subtract from one, convert to a percentage, one decimal place - and the word 'not' inverts the practised quantity. CAL-6: coefficient-of-determination items ran 41% and 45% in November as multiple choice, where no inversion was involved.

Closest November analogue: 2019 E1 Q10 Data analysis - 41%; 2018 E1 Q9 - 45%

2023 Exam 2 Q5b (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

Asks: 500 of 20 000 men exceed 30 cm and 3200 are below 25.5 cm; find the mean and standard deviation.

Evidence: Two raw counts must be turned into percentages (2.5% and 16%), each matched to a z-score from the 68-95-99.7 rule, and the resulting pair of equations solved for both parameters. Every November normal-distribution item runs forwards from known parameters. CAL-4: 2-mark part, 71% November separator rate, median 38%.

Recursion and financial modelling

2023 Exam 2 Q6di (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: Determine the balance halfway through the 25-year term of the loan.

Evidence: The solver has to be run for 150 of the 300 months with the repayment recovered from the recurrence relation, and the answer given to the nearest cent - a full-precision run where an early rounding is fatal.

2023 Exam 2 Q6dii (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: Explain why the balance halfway through the term is not half the amount borrowed.

Evidence: The required answer links two facts - the repayment is constant while the interest component falls as the balance drops - and a student who states only one of them has not explained it. Written explanations in Recursion are where November students most often score zero.

Closest November analogue: 2021 E2 Q7c Recursion - 21% ("did not recognise that the value was of the machine in terms of...")

2023 Exam 2 Q7c (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: The van is sold at the end of the year in which its value first falls below $10 000; which year is that?

Evidence: 40 000 x 0.85^n < 10 000 gives n > 8.53, which rounds up to year 9 - and then the answer has to be expressed as a year number or a calendar year. Both the rounding direction and the labelling are at risk.

2023 Exam 2 Q8bi (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

Asks: Determine the total interest earned by a $480 094.50 annuity paying weekly for 20 years.

Evidence: Two stages: solve for the new weekly payment under the changed principal, multiply by 1040 weeks, then subtract the principal. Quoting the total received, or the payment itself, are both plausible. CAL-6: multi-stage finance-solver items ran 8-19% in November.

Closest November analogue: 2024 E2 Q8 Recursion - 13%; 2020 E2 Q11 - 19%

2023 Exam 2 Q8bii (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

Asks: Write a recurrence relation modelling the annuity balance week to week.

Evidence: Both the weekly multiplier (1.00075 from 3.9% per annum) and the weekly payment recovered in the previous part must appear, so the mark depends on an earlier answer as well as on the period conversion.

Matrices

2023 Exam 2 Q1b (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Explain what p11 - p12 represents in the product matrix P.

Evidence: The two elements have to be identified as the eight-hour and one-day costs and the difference described in context. Interpretation-in-words parts in Matrices are where November students most often score zero.

Closest November analogue: 2022 E2 Q2bii Matrices - 21%

2023 Exam 2 Q2a (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: Interpret the meaning of the 0 in row 3, column 1 of the transition matrix.

Evidence: The answer has to name both the source and the destination licence in the right order - no driver moves from light rigid to heavy rigid in one year - so reversing the row/column convention gives a sentence that sounds right and scores nothing.

Closest November analogue: 2022 E2 Q2bii Matrices - 21%

2023 Exam 2 Q2c (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

Asks: How many drivers held a heavy rigid licence by January 2021?

Evidence: One application of T to a state matrix, but only the third element is wanted and the third row of T contains a 1 on the diagonal, so a student who reads the wrong row or applies T twice gets a plausible number.

2023 Exam 2 Q2d (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: With S(n+1) = T.Sn + B and B incomplete, how many light rigid drivers are expected in January 2025?

Evidence: Matrix B has to be built from a verbal description that includes a negative entry (two heavy-rigid drivers leaving each year), and the recurrence then run twice. CAL-6: iterated T.Sn + B items ran 10% and 12% in November even with B supplied.

Closest November analogue: 2021 E2 Q4 Matrices - 10%; 2024 E2 Q12c - 12%

2023 Exam 2 Q3c (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

Asks: From two weeks of daily hours, write down the 7 x 7 permutation matrix that maps Week 1 to Week 2.

Evidence: A permutation matrix has to be constructed by working out where each of seven values moved, and every one of the 49 entries must be right for the single mark. November sets permutation matrices to be applied, not built.

Closest November analogue: 2023 E1 Q30 Matrices - 39%; 2022 E1 Q7 - 42%

2023 Exam 2 Q3d (NHT) — Matrices — 2 marks — SEPARATOR, confidence high

Asks: Given only the determinant of the coefficient matrix, find the weekday and weekend hourly rates.

Evidence: The unknown element f has to be recovered from det = 304 before the system can be solved at all, and then both rates produced. Two marks, two unknowns, and an inverse that cannot be formed until the first step is done. CAL-4: 2-mark part.

Closest November analogue: 2022 E2 Q2bii Matrices - 21% (interpreting a determinant)

Networks and decision mathematics

2023 Exam 2 Q1c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Find the shortest journey that starts and finishes at the dam and visits all five flower gardens.

Evidence: The report's answer repeats a vertex - "dam-T-R-G-L-P-T-dam" - so this is not a Hamiltonian cycle but a shortest closed walk, which has to be found by search on a graph with two odd-degree vertices. Assuming each garden is visited once gives a longer, wrong answer.

2023 Exam 2 Q1d (NHT) — Networks and decision mathematics — 2 marks — SEPARATOR, confidence medium

Asks: Complete the partially filled adjacency matrix for the network.

Evidence: Eleven missing entries, each requiring the graph to be read in both directions, and the matrix's symmetry used as a check. Both marks depend on the whole matrix. CAL-4: 2-mark part, 71% November separator rate.

2023 Exam 2 Q3b (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Determine the latest start time of activity D.

Evidence: A full backward pass over a twelve-activity network for one mark, with D off the critical path. CAL-6: latest-start-time and float items ran 31-48% in November Exam 1.

Closest November analogue: 2019 E1 Q8 Networks - 31%; 2022 E1 Q6 - 48%

2023 Exam 2 Q3c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

Asks: Which two activities have a float time of two days each?

Evidence: Every activity's float must be computed and then the two matching a specific value identified - and both must be named for the mark. CAL-3: part c, 59% November separator rate, median 44%.

Closest November analogue: 2022 E1 Q6 Networks (float) - 48%

2023 Exam 2 Q3d (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: Five named activities can each be shortened by up to two days; what is the maximum time that can be saved?

Evidence: Reducing ten activity-days saves only four project-days, because the critical path changes as soon as the first reductions bite. CAL-6: November's crash-the-project questions sit at 9% and 12% full marks for exactly this reason.

Closest November analogue: 2021 E2 Q4c Networks - 9%; 2020 E2 Q5d - 12%

2023 Exam 2 Q3e (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

Asks: What is the minimum cost of achieving that maximum time saving?

Evidence: The report's answer names the exact schedule - "Reduce A by one day, B by two days and K by two days" for $1900 - so the student must find not just how much time can be saved but the cheapest combination that saves it, across five activities with different daily costs. This is the deepest form of the November crashing family.

Closest November analogue: 2021 E2 Q4c Networks - 9%; 2020 E2 Q5d - 12%; 2025 E2 Q18d - 21%

Geometry and measurement

2023 Exam 2 Q1bii (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: By what value is the smaller ball's surface area multiplied to give the larger ball's surface area?

Evidence: The linear ratio 1:1.1 becomes 1.21 for area, not 1.1 and not 1.331 - the one step November named explicitly in its closest analogue.

Closest November analogue: 2020 E2 Q2d Geometry - 17% ("Only a few students connected the scale factor for length to the area enlargement")

2023 Exam 2 Q2c (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Lines 5 cm wide and 155.6 m long are painted; paint covers 7 m2 per litre and comes in 0.5 L tins. How many tins?

Evidence: Four conversions in sequence for one mark: length to area using a width in centimetres, area to litres, litres to tins, and then rounding up to a whole tin. Any one slip changes the answer.

2023 Exam 2 Q3b (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Wind crosses the slab on a bearing of 045 degrees; find the angle between the wind direction and side PQ.

Evidence: The angle has to be built from two bearings measured at different points - 343 degrees for PQ and 045 for the wind - with the reverse direction of PQ taken into account. Bearings differenced in the wrong order give a supplementary angle that looks plausible.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2018 E1 Q4 - 42%

2023 Exam 2 Q4c (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence high

Asks: Could the 15.1 m tree reach the concrete slab if it fell? Explain with calculations.

Evidence: The comparison is against the perpendicular distance from the tree to the slab edge, 25.7 x sin(35) = 14.74 m - not against RT itself. Recognising that the shortest distance is the perpendicular, and that the tree can therefore just reach, is the whole question.

2023 Exam 2 Q4bii (NHT) — Geometry and measurement — 1 mark — SEPARATOR, confidence medium

Asks: Calculate the distance ST, given SR = 36.6 m, RT = 25.7 m and angle SRT = 35 degrees.

Evidence: A cosine-rule application, but on an angle that has itself just been constructed from two bearings in the preceding part - so the mark depends on an earlier answer as well as on correct substitution. CAL-6: cosine-rule-with-bearings items ran 30-45% in November.

Closest November analogue: 2021 E1 Q8 Geometry - 30%; 2022 E1 Q6 - 38%

Graphs and relations

2023 Exam 2 Q3c (NHT) — Graphs and relations — 1 mark — BORDERLINE, confidence medium

Asks: For what number of kites is the daily cost the same for both types?

Evidence: Two linear rules equated, 15n + 65 = 20n + 30, giving n = 7 - and the answer can also be read off the intersection of the two drawn lines. Listed only as BORDERLINE because both routes are short, but the answer depends on the line sketched in the previous part being right.

2023 Exam 2 Q3d (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: A two-branch cost rule joins at n = 20; if 57 kites cost $911, find m.

Evidence: The two branches must be forced to meet at n = 20, which gives one equation, and the point (57, 911) gives another - so p has to be eliminated between them. The continuity condition is nowhere stated in the question; it has to be read off the graph.

2023 Exam 2 Q4b (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence medium

Asks: With four rokkaku kites, what is the maximum number of parafoil kites?

Evidence: The binding constraint is 5y >= 2x rather than the total or the upper bound, so all four inequalities must be tested at y = 4 and the answer truncated to an integer. CAL-6: feasible-region items ran 29-40% in November.

Closest November analogue: 2016 E1 Q5 Graphs and relations - 29%; 2018 E1 Q7 - 40%

2023 Exam 2 Q4c (NHT) — Graphs and relations — 2 marks — SEPARATOR, confidence high

Asks: Find the difference between the maximum and the minimum cost of a purchase that includes both kite types.

Evidence: Two optimisations of the same objective in opposite directions, both restricted to purchases containing at least one of each type, and then differenced. CAL-4: 2-mark part, 71% November separator rate, median 38%.

Closest November analogue: 2020 E1 Q10 Graphs and relations - 31%; 2021 E1 Q7 - 39%

2023 Exam 2 Q4d (NHT) — Graphs and relations — 1 mark — SEPARATOR, confidence high

Asks: 35 parafoil and 20 rokkaku kites cost $5225 and this is the maximum possible purchase; find the new rokkaku price.

Evidence: The report's reasoning is the slope-matching argument: "Objective function C = ax + by has same slope as x + y = 55 (-1), therefore a = b." The fact that the optimum sits along a whole constraint edge is what fixes the two prices as equal, and only then does the arithmetic give $95. CAL-6: an optimum pinned to a constraint's slope is among the deepest November separator families.

Closest November analogue: 2016 E2 Q3d Graphs and relations - 7%; 2020 E2 Q4d - 10%; 2021 E2 Q4cii - 20%

How the NHT paper differs from the November paper

Observations from reading all twelve papers side by side with their November twins.

1. Same skeleton, no exceptions. Every NHT Exam 1 2017-2023 is 24 core multiple-choice (Data analysis Q1-16, Recursion Q17-24) plus four eight-question modules; every NHT Exam 2 is Core Data analysis 24 marks, Core Recursion 12 marks, and four modules of 12 marks from which two are chosen. The 2021 and 2022 NHT papers even reproduce November's habit of pushing the whole of Recursion into two or three long questions. Structural calibration therefore transfers cleanly; that is the main reason CAL-1 to CAL-4 are usable here.

2. Smaller cohort, so less conservative question design. NHT sits a few hundred students, mostly at international and interstate-timetabled schools, and the paper is not the one whose statistics are published. Several NHT questions attempt things November does not, or does only once a decade: counting how many distinct minimal spanning trees exist (2017 M2 Q7); asking for the maximum number of trucks that can travel together along one route, i.e. a bottleneck path rather than a maximum flow (2017 M2 Q3c); the ambiguous case of the sine rule inside a bearings diagram (2017 M3 Q8); the fourth iteration of S(n+1) = T.Sn + B (2017 M1 Q2f). These are the places where an NHT paper is probably harder than a November paper.

3. Show-that and "use recursion to show" are heavily used, and the mark schemes are strict. The NHT reports repeatedly spell out that a bare answer scores nothing: "'Using recursion' begins with writing the initial value... Then, the first calculation using the recurrence rule must be shown and the answer labelled... Subsequent calculation(s) must then show the use of the prior answer" (2017 Exam 2 report, Q5b). November uses the same device but the NHT reports state the requirement more explicitly, which is a usable difficulty signal.

4. The reports are thin and uneven. 2017's two reports run to 14 KB and 11 KB of text with full worked solutions; 2021's Exam 1 report is 2.7 KB and is essentially an answer key. Where a report does supply a multi-paragraph derivation for one question and a single line for its neighbours, that asymmetry is a weak but real signal about which question the examiners expected to cause trouble, and I have used it as evidence type (b) only when the derivation is long or the report explicitly comments on student performance.

5. NHT reports carry no percentages and almost no performance commentary. Across all twelve reports the total number of sentences about how students actually performed is in the low tens, against hundreds in a November report. What commentary exists arrived late: the 2017-2021 reports are pure answer-and-solution documents, while the 2022 and 2023 reports (retitled "external assessment report") begin to say which questions went badly and which sections went well. Those two years are consequently the best-evidenced in this document, and 2023 is the one year where I have argued against my own structural priors, because the report says Data analysis and Geometry were answered well.

6. Questions are item-analysed even though nothing is published. The 2021 Exam 1 report disposes of Question 18 with a single sentence - "As a result of psychometric analysis, the question was invalidated" - and the 2018 Exam 1 report accepts three of the five options for Question 4. Both are excluded here: a question that could not be scored cleanly cannot separate.

7. Context sets are noticeably more unified. NHT papers tend to run one scenario across a whole section (a weather station through all of 2017 Core Data analysis; a dairy farm through all of 2017 Module 3), where November more often changes context between questions. This makes later parts more dependent on earlier ones, which pushes late parts down.

Limitations

• No verdict here is a measurement. VCAA has never published a mark distribution for an NHT question and this document does not estimate one. "SEPARATOR" means I judge that 50% or fewer of a comparable cohort would earn full marks, nothing more.
• The cohort is not the same cohort. NHT candidature is small, self-selected and differently prepared. Even if a question were identical to a November one, the percentage would not be. All calibration is therefore about question difficulty, not about the population.
• Structural priors do a lot of work. CAL-1 and CAL-3 are strong but they are priors, and VCAA occasionally places a hard item early or an easy one last. Where the position and the archetype disagree I have said so in the entry and lowered the confidence.
• Analogues are matched by task, not by identity. "cf. 2018 Exam 1 Q8 Networks - 24%" means the November question asked for the same operation (re-allocate after a cost change), not that the numbers or diagram match.
• Text extraction is imperfect. The NHT papers were read from text extracted from VCAA's Word and PDF originals; diagrams, matrices and some tables are degraded or reflowed. Where a question depends entirely on a diagram I leant more heavily on the report's worked solution and less on the question text, and lowered confidence accordingly.
• Selection bias toward listed questions. ROUTINE verdicts are not recorded here, so this document cannot be used to compute an NHT separator rate; the counts above are counts of what I chose to list. As a sanity check on volume: applying the November rates in CAL-1 to CAL-4 to a 56-question Exam 1 predicts about 18 separators, and to a typical Exam 2 about 19, so roughly 30-37 listed questions per year is the calibrated figure rather than an inflated one. Where a year is well below that - 2023 Exam 1 - it is because the report said the cohort did well.
• BORDERLINE is used sparingly. Only 39 of the listed questions carry it. That is a deliberate choice: a verdict of BORDERLINE on a judgement-based list is close to saying nothing, so I have reserved it for the cases where the structural signal and the archetype genuinely point in opposite directions, and said which is which in the entry.
• Exam 2 module questions 1-2 marks. Because NHT Exam 2 modules are only 12 marks, a module's final part is structurally the same as November's final part, and CAL-3 applies. But NHT modules have fewer parts overall, so the letter reached (d, e, f) is systematically lower than in November; I have weighted "last part of the question" more than "letter reached" where the two disagree.

Nht General

No percentage in this document refers to an NHT question. VCAA has never published
per-question statistics for the Northern Hemisphere Timetable sittings. Every percentage
quoted below belongs to a November question and is labelled with its year and exam.
The NHT verdicts are judgements, not measurements.

For the November examinations a separator is a measured thing: VCAA publishes, for every question, the percentage of the state that earned full marks, and a question is a separator when that figure is 50% or lower. The NHT reports publish answers, sample responses and sometimes a worked solution — and nothing else. So each NHT question below has been assigned SEPARATOR (I would expect 50% or fewer of a comparable cohort to earn full marks), BORDERLINE (near enough to the line that it could fall either way) or ROUTINE. Only the first two are listed.

Scope: the three current-design General Mathematics NHT sittings — 2024, 2025 and 2026. The 2017–2023 Further Mathematics NHT papers are covered separately.

158 questions are listed: 119 SEPARATOR and 39 BORDERLINE.

Method

1. Deriving the signature of a separator

Before opening an NHT paper I derived what a separator looks like from corpus/export/nov_all.csv, restricted to November 2023, 2024 and 2025 — the three sittings whose study design, paper structure and mark allocation match these NHT papers exactly. That is 284 graded questions with a published percentage attached to each: 120 multiple-choice and 164 written parts.

CAL-1 — Mark value is the strongest single predictor (Exam 2).

Every unlettered standalone two-mark question in those three years was a separator, without exception: 2024 Q8 (13%), 2025 Q3 (47%), 2025 Q10 (11%), 2025 Q16 (20%).

CAL-2 — Position within a multi-part question (Exam 2).

CAL-3 — Position within the Exam 1 multiple-choice run. The 40 questions are not uniformly hard; separator rate by block of four, across the three years:

The two spikes are the ends of the Recursion block and the Networks block. Both topic blocks close with their hardest questions; the Data analysis and Matrices blocks open with their easiest.

CAL-4 — Topic.

CAL-5 — Question families that recur below the line. I then read the commentary attached to every November separator and grouped them. The families that fall short year after year:

And the counter-examples that stopped me over-calling: drawing a boxplot from data (76%), six-mean smoothing with centring (70%), naming a Hamiltonian path (75%), recognising a permutation matrix (83%), recognising a Leslie matrix (78%), a plain minimum cut across the three edges into the sink (73%), a shortest path through a network (71%), and following the Hungarian algorithm when the steps are given (71%). Several NHT questions that looked hard were rated ROUTINE on exactly these grounds.

2. Applying it

Every question in all six papers was read and classified. Each listed question carries an Evidence line drawing on at least one of:

• (a) a closely analogous November question with its real published percentage;
• (b) the NHT report or assessment guide flagging difficulty or prescribing a demanding mark scheme — quoted verbatim;
• (c) a structural feature that CAL-1 to CAL-5 show is strongly associated with separators.

The assessment guides are the best evidence available, because they state what a response must contain. They are quoted throughout — Must see both parts, Must have ALL correct, Both parts must be correct, In this order, Fully correct recurrence relation, ***Show that question.

Summary: listed questions by year, exam and topic

Each cell is SEPARATOR + BORDERLINE.

Counted another way — separators only, by topic across all six papers:

How the NHT paper differs from the November paper

Observations from reading all six papers, four reports and three assessment guides alongside their November twins.

1. The skeleton is identical, so the structural calibration transfers. Every NHT Exam 1 is 40 multiple-choice questions in the fixed block order Data analysis Q1–16, Recursion Q17–24, Matrices Q25–32, Networks Q33–40. Every NHT Exam 2 is 60 marks split 24 / 12 / 12 / 12 across the same four topics in the same order, numbered continuously. The mark split is confirmed exactly by the 2025 and 2026 assessment guides (Data analysis 24, each other topic 12). CAL-1 to CAL-4 are therefore usable without adjustment.

2. The option count dropped between 2024 and 2025. The 2024 NHT Exam 1 offers five options, A–E — the 2024 report keys answers to E at Q3, Q10, Q12, Q17, Q18, Q20, Q26, Q28, Q31 and Q37. Both the 2025 and the 2026 NHT Exam 1 answer keys stop at D: four options throughout. A blind guess therefore moves from 20% to 25%, which mechanically lifts the full-marks rate on any question students cannot finish. I treated this as steady downward pressure on the 2025 and 2026 Exam 1 verdicts rather than applying a numeric correction.

3. NHT Exam 2 uses fewer, longer questions. November 2024 Exam 2 ran 15 numbered questions with up to eight lettered parts; the 2024 NHT paper ran 16, but the data analysis section was carried by two large questions (Q1 at 8 marks, Q4 at 7 marks) plus four short ones. The 2026 NHT paper goes further — 15 questions, with Q1, Q2 and Q3 each worth 6 or 7 marks. Longer questions mean more part (d)-or-later positions, and CAL-2 says those are where separators live.

4. NHT sets things November does not. These are the places the NHT paper is probably harder than its November counterpart, and they are concentrated in the last question of each block:

• counting how many distinct Eulerian circuits exist from a given start (2026 Exam 1 Q35) — November asks only whether one exists;
• reconstructing a missing row and column of an 8 × 8 dominance matrix from the stated one-step totals, then computing two-step dominance (2026 Exam 1 Q32);
• inferring the smoothing window from a plot, and counting how many smoothed points a window costs (2024 Exam 2 Q6; 2026 Exam 2 Q4c);
• a maximum-bottleneck path — the largest group that can travel together along one route — set immediately after a maximum-flow question that primes the wrong method (2024 Exam 1 Q39);
• applying a residual inside a reciprocal-transformed scale and then back-transforming (2026 Exam 1 Q12);
• counting the permutation matrices that fix a column containing a repeated element (2024 Exam 1 Q30).

5. A cut containing back-flowing edges is an NHT signature. It appears in all three years and in both exams: 2024 Exam 1 Q38 (the report notes "12 is flowing from exit to entrance"), 2025 Exam 2 Q15a ("4 and 8 are directed backwards"), and 2026 Exam 2 Q14c, where three of the six edges crossing the cut are "not counted (wrong way)". November has set it, but not with this regularity.

6. The evidence base changes character every year. The 2024 reports carry answers plus worked solutions for a selected 14 of 40 Exam 1 questions — a selection that is itself a weak difficulty signal, since VCAA explained only what it judged needed explaining. The 2025 Exam 1 report comments on 39 of 40, so that signal disappears and only the length of each worked solution remains informative. The 2026 Exam 1 guide is a bare answer key. Running the other way, 2025 and 2026 both supply full Exam 2 assessment guides, which are far more informative than any November report because they state the mark scheme rather than describing performance.

7. The mark schemes are stricter than November reports let on. The guides use M1 (method), A1 (answer) and H1 (holistic) marks with explicit consequential marking, and they repeatedly close the door on partial answers: Must see both parts, Must have ALL correct, Both parts must be correct, Must reference skew or outlier, Must reference M & Q OR 1 and 3 for columns/rows, MUST be labelled Cut 2, Must have YES (stated or implied), with reason, In this order. The 2025 guide even annotates one item ***Show that question in its own margin. Where a guide says a response must contain something specific, that is direct evidence about how many students will have contained it.

8. Crashing closes the networks section every year, exactly as in November. 2024 Exam 2 Q16e, 2025 Exam 2 Q16e.ii, 2026 Exam 2 Q15d. The November versions of this question ran at 9%, 7% and 21%. It is the most predictable separator in the subject.

---

2024 NHT — 52 listed (41 SEPARATOR, 11 BORDERLINE)

Evidence base: both papers readable in full, plus an Exam 1 report with worked solutions for a selected 14 of 40 questions and an Exam 2 report giving sample answers. Exam 1 offers five options (A–E).

2024 Exam 1 (NHT) — 15 SEPARATOR, 4 BORDERLINE

Data analysis (4 + 3)

2024 Exam 1 Q6 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Use the 68-95-99.7% rule to find how many of 13 600 cans weigh between 121.6 g and 128.8 g.
• Evidence: The interval is asymmetric about the mean (two standard deviations below to one above), so students must combine half of 95% with half of 68% to reach 81.5% rather than read off a single band. The November 2025 question built on the same asymmetric reasoning was a separator. Position argues the other way: Q5-Q8 in Exam 1 ran at 8% separators across 2023-2025.
• Closest measured analogue: 2025 E2 Q3 - asymmetric 68-95-99.7 interval - 47%

2024 Exam 1 Q8 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: From a summary-statistics table (means, standard deviations, r = -0.752), determine the least squares line and decide which of five scatterplots has it drawn correctly.
• Evidence: Requires b = rsy/sx and a = ybar - bxbar to be built from summary statistics alone, then two key points plotted and matched against five near-identical graphs. The report supplies a full worked solution - 'Determine the equation of the least squares line. Key points calculated as (59, 37.6) and (65, 24.6)' - in a report that leaves 26 of 40 questions uncommented, marking it as one the examiners judged needed explaining. Accuracy in placing points on a least squares line is a documented failure mode.
• Closest measured analogue: 2023 E2 Q3a - drawing the least squares line - 40%

2024 Exam 1 Q10 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Choose which one of five statements about a scatterplot, its correlation and its residuals is true.
• Evidence: Five independent judgements are required, three of them classic confusions (r versus r^2, the meaning of 'not explained', the sign of a residual). The check-every-statement format is separator-associated in the calibration set. Against that, the true option - that predicting at 54 years is extrapolation when the data range is 55-75 - is findable without evaluating the rest.
• Closest measured analogue: 2024 E1 Q38 - check-each-statement format - 18%

2024 Exam 1 Q11 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Using (birth rate)^2 = 953 - 0.0333 x income, predict the birth rate for an income of $18 500.
• Evidence: The squared transformation must be undone with a square root at the end; option D (337) is exactly the answer for students who stop before back-transforming and option E for students who square instead. Transformation items are the hardest data-analysis content, but this one is a single clean substitution and the back-transformation is well drilled.
• Closest measured analogue: 2024 E1 Q12 - transformation MCQ - 48%

2024 Exam 1 Q12 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: Rank the coefficients of determination for three different transformations (birth rate vs income, (birth rate)^2 vs income, birth rate vs (income)^2) from a 12-row data table.
• Evidence: Three separate CAS regressions must be run and their r^2 values compared, for one mark, under time pressure. The report works all three: 'coefficient 1 = 0.845, coefficient 2 = 0.915, coefficient 3 = 0.948.' Transformation questions are the hardest data-analysis multiple-choice content in the calibration set, and no partial credit exists.
• Closest measured analogue: 2024 E1 Q12 - Data analysis MCQ - 48%

2024 Exam 1 Q15 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: Sales revenue in May is decreased by 17% to correct for seasonality; find the seasonal index.
• Evidence: Requires the inverse relationship: deseasonalised = 0.83 x actual, so the index is 1/0.83 = 1.20 - not 1.17 and not 0.83, both of which are offered as options C and B. The report judged this worth a worked comment: '17% decrease means multiplying factor is 0.83'. Seasonal-index manipulation is a documented separator topic in both exams.
• Closest measured analogue: 2023 E2 Q4c - seasonal index calculation - 21%

2024 Exam 1 Q16 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: One of four seasonal indices is missing; given summer attendance of 33 120, find the total annual attendance.
• Evidence: Three chained steps, all set out in the report: indices sum to 4 so summer = 1.74; deseasonalise 33 120/1.74 = 19 034.48; multiply by 4. The November analogue that tested only the first of those steps ('Total seasonal indices for 12 months = 12') still ran at 58%, so adding deseasonalisation and the annual total should carry it below the line.
• Closest measured analogue: 2024 E1 Q16 - seasonal indices sum to n - 58%

Recursion and financial modelling (4 + 1)

2024 Exam 1 Q18 (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

• Asks: For T0 = 5, Tn+1 = k - Tn with every term of the sequence equal, find k.
• Evidence: A context-free recursion item requiring the fixed-point idea (5 = k - 5). Abstract recursion multiple-choice, with no financial dressing, is the sub-genre that separates most reliably: in November 2023 every one of Q21-Q24 was a separator, and the abstract 2024 Q17 ran at 36%. Balanced against that, once the fixed-point idea is seen the algebra is one line.
• Closest measured analogue: 2024 E1 Q17 - abstract recursion - 36%

2024 Exam 1 Q21 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: Two years of flat-rate depreciation followed by two years of reducing balance must give the same four-year value as a single constant reducing-balance rate; find that rate.
• Evidence: Two depreciation methods must be chained (30 000 -> 24 000 -> 24 000 x 0.9^2 = 19 440), then a fourth root taken to invert 30 000(1-r)^4 = 19 440. Multi-stage recursion items in the Q21-Q24 block form the densest separator region of Exam 1: across 2023-2025 that bucket ran at 50% separators, and in 2023 all four were separators.
• Closest measured analogue: 2023 E1 Q21 - 48%

2024 Exam 1 Q22 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: Given P0 = a, Pn+1 = R*Pn - d with a, R and d all greater than 1, count how many of four financial contexts (reducing balance loan, annuity, unit cost depreciation, perpetuity) the relation could represent.
• Evidence: A 'how many of these' item with no numbers at all, requiring four independent structural judgements about R and d. The report gives the reasoning: 'The recurrence relation given could represent a reducing balance loan, an annuity or a perpetuity.' The count-the-true-statements format is strongly separator-associated in the calibration data, and context-free recursion is the hardest recursion sub-genre.
• Closest measured analogue: 2024 E1 Q38 - count-the-true-statements format - 18%

2024 Exam 1 Q23 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium-high

• Asks: A 15-year annuity of $450 000 at 3.75% p.a. compounding monthly: in which calendar year does the balance first fall below $350 000?
• Evidence: Two chained Finance Solver runs - solve for PMT, then solve for N with FV = 350 000 - followed by converting 49.61 months to 4.13 years and then to a calendar year. The report prints both solver screens in full. Each stage compounds the error risk and the year conversion adds an off-by-one trap across options spanning 2027-2031.
• Closest measured analogue: 2023 E1 Q24 - 27%

2024 Exam 1 Q24 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: A compound-interest balance graph has one time period missing; an extra one-off deposit was made at that point. Find the deposit.
• Evidence: Reverse reasoning in two directions: derive the factor 1.08 from the early points, project forward to period 3, work backwards from period 4 by dividing by 1.08, then difference. The five options cluster between $224.03 and $231.46, so no partial reasoning survives. The report devotes a four-line worked solution to it, and Q24 closes the recursion block, the highest-density separator region of Exam 1.
• Closest measured analogue: 2024 E1 Q24 - 46%

Matrices (3 + 0)

2024 Exam 1 Q30 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

• Asks: Matrix R is the column [T, A, L, L, Y]. Count how many permutation matrices P satisfy PR = R.
• Evidence: The insight is that the repeated element L means the identity is not the only permutation fixing R - swapping rows 3 and 4 also works, giving 2. The report spells it out: 'P could equal ... where ... keeps each element in its original position, ... swaps the two elements in rows 3 and 4 of matrix R'. A November item that merely asked students to recognise a permutation matrix ran at 83%, so the counting twist is what does the separating; abstract matrix items with a novel insight are the archetype of the Exam 1 separator.
• Closest measured analogue: 2023 E1 Q32 - 18%

2024 Exam 1 Q31 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium-high

• Asks: Meerkats move between two chambers with fixed nightly proportions and constant chamber populations; given that eight arrived in A from B, find the total population.
• Evidence: Requires recognising that constant populations force the flows in each direction to be equal, then solving 8 = 0.2b and 8 = 0.4a separately. The report needs five lines to explain it. Reverse reasoning on a transition diagram, with the equal-flow insight left unstated, matches the profile of the hardest matrices multiple-choice items.
• Closest measured analogue: 2023 E1 Q30 - 39%

2024 Exam 1 Q32 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

• Asks: Given Pn+1 = T*Pn + K and the state matrix P2, find the increase in vanilla subscribers between P0 and P1.
• Evidence: The state matrix must be run backwards twice using P(n) = T^-1 (P(n+1) - K). The November 2024 paper set the identical technique - the report there reads 'S3 = TS2 + A, hence S2 = T^-1(S3 - A)', repeated three times - and only 33% of the state earned the mark. Working backwards through an Sn+1 = TSn + B recurrence is a documented, low-scoring skill.
• Closest measured analogue: 2024 E1 Q32 - working backwards through Sn+1 = TSn + B - 33%

Networks and decision mathematics (4 + 0)

2024 Exam 1 Q37 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: Decide to which of four graphs Euler's formula can be applied.
• Evidence: Planarity must be tested four times, including recognising that Graph 1 contains a complete pentagon and therefore cannot be redrawn as planar. The report redraws two of the graphs to show they are planar. A November item that asked students to redraw a single graph as planar and count its faces ran at 52%; doing it four times with a K5 subgraph to spot sits below that. Q37-Q40 is the densest separator block in Exam 1 (58% across 2023-2025).
• Closest measured analogue: 2024 E1 Q35 - redraw one graph as planar - 52%

2024 Exam 1 Q38 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: Find the maximum number of visitors per hour from entrance to exit in a directed capacitated graph.
• Evidence: The report gives the trap away: 'Minimum cut = maximum flow = 13 + 16 + 9 + 17 + 21 = 76 (12 is flowing from exit to entrance)'. One edge crosses the cut in the wrong direction and must be excluded; including it gives 88, which is offered as option D. Max-flow items with a complication run far below plain ones - a November item where the cut was simply the three edges into the sink ran at 73%, while complicated versions ran at 24% and 29%.
• Closest measured analogue: 2024 E2 Q14b - 29%

2024 Exam 1 Q39 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: A group of students all walk together along a single route from entrance to exit; find the largest possible group.
• Evidence: This is a maximum-bottleneck (widest path) question rather than a max-flow question, and it directly follows Q38, which primes max-flow thinking. Students must search routes for the one whose smallest capacity is largest. The equivalent-position November 2024 item ran at 19% and the whole Q37-40 block averaged 27% that year.
• Closest measured analogue: 2024 E1 Q39 - 19%

2024 Exam 1 Q40 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: From a table of immediate predecessors for 10 activities, identify which of five statements about the project is not true.
• Evidence: The network, including two dummy activities, must be constructed from the table before any statement can be tested, then all five checked - earliest start times, dummy placement, path tracing, latest start times and dummy count. The report's answer runs to a diagram plus five separate checks. The November 2024 twin of this item ran at 32%, and a 2025 item requiring a dummy between B and G plus a latest start time ran at 39%.
• Closest measured analogue: 2024 E1 Q40 - 32%

2024 Exam 2 (NHT) — 26 SEPARATOR, 7 BORDERLINE

Data analysis (8 + 3)

2024 Exam 2 Q1c (NHT) — Data analysis — 2 marks — BORDERLINE, confidence medium

• Asks: Show that the minimum LLT value of 0.22 m is not an outlier.
• Evidence: Two marks, both riding on displayed working because the conclusion is given. 'Show that' items are consistently separators (2023 Q7a at 32%, 2025 Q4fi at 41%) and two-mark written items ran at 88% separators. Pulling the other way, the component skills scored well in November 2024: computing the fences ran at 84% and explaining the outlier conclusion at 76%, which makes a combined success rate near 50% rather than clearly below it.
• Closest measured analogue: 2024 E2 Q2ci - compute fences - 84%

2024 Exam 2 Q1d (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

• Asks: Determine the least squares line for HHT on LLT from 15 raw data pairs, with intercept and slope rounded to four significant figures.
• Evidence: This is the most reliably reproduced separator in the corpus. VCAA has set a four-significant-figure least squares coefficient question in three consecutive November papers and every one fell well short: 2023 - 'Many students appeared to have difficulty in giving the coefficients rounded to four significant figures' (37%); 2024 - 'Significant figures remain a challenge and many students were not able to interpret values from their calculator that were written using exponent notation' (39%); 2025 - 'Significant figures remain problematic' (28%). The NHT answer (2.130 and -1.054) additionally requires the negative sign to be carried into the box.
• Closest measured analogue: 2023 E2 Q1d - four significant figures - 37%

2024 Exam 2 Q2b (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium-high

• Asks: Decide whether a two-way frequency table supports an association between the occurrence of the lowest low tide and the new moon, explaining by comparing appropriate percentages.
• Evidence: The November 2023 twin of this question was itself a separator at 50% and the report there warned that 'Students needed to ensure that they explicitly answered the question and that they indicated that the farm A percentage was higher than that of the other farm'. The NHT version is harder because the percentages are not supplied by an earlier part - students must derive the three comparison percentages themselves from the raw table, then compare them and state a conclusion, all for two marks. Two-mark written items ran at 88% separators across 2023-2025.
• Closest measured analogue: 2023 E2 Q2bii - association from a two-way table - 50%

2024 Exam 2 Q3 (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

• Asks: Given that 99.85% of time differences exceed 4.88 hours and 16% are below 5.76 hours, use the 68-95-99.7% rule to find the mean and standard deviation.
• Evidence: A reverse 68-95-99.7 problem: both quoted percentages must be converted to standard-deviation positions and the resulting pair solved simultaneously. The November 2023 question of exactly this type, also worth two marks and also asking for both the mean and the standard deviation, ran at 29%. Every standalone unlettered two-mark question in November 2023-2025 was a separator (2024 Q8 13%, 2025 Q3 47%, 2025 Q10 11%, 2025 Q16 20%), and two-mark written items ran at 88% separators overall.
• Closest measured analogue: 2023 E2 Q1e - reverse 68-95-99.7 for mean and standard deviation - 29%

2024 Exam 2 Q4a (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Draw the graph of the least squares line HHT = 2.19 - 1.08 x LLT on the scatterplot.
• Evidence: The two November analogues sit either side of the line - 2023 Q3a at 40% ('Many students showed evidence of correct coordinate points, but placed their dots at the wrong points or took insufficient care when drawing the line. A ruler should be used') and 2024 Q3b at 51% ('Some students seem to be drawing a line by eye rather than calculating appropriate points'). The mean of the two is just below 50%, which is exactly the borderline case.
• Closest measured analogue: 2023 E2 Q3a - draw the least squares line - 40%

2024 Exam 2 Q4b (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

• Asks: Given a coefficient of determination of 0.4709 and the line HHT = 2.19 - 1.08 x LLT, find r to three decimal places.
• Evidence: The November 2025 paper set this question with the identical trap and the report is explicit: '= -0.284. A large proportion of the cohort left their final response as positive 0.284, not recognising that the slope was negative in the equation of the least squares line provided in the question stem' - 21%. The NHT answer is -0.686 and the negative slope is likewise buried in the stem. The equivalent question with a positive slope ran at 69%, so the sign is doing all of the separating.
• Closest measured analogue: 2025 E2 Q4b - r from r^2 with a negative slope in the stem - 21%

2024 Exam 2 Q4d (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Interpret the slope of the least squares line in terms of HHT and LLT.
• Evidence: The November 2024 slope interpretation ran at 54% with the report noting that 'Students did not always reference the change in each of the two variables'. The NHT slope is negative, adding the further requirement to say that HHT decreases, which is a documented extra failure mode. That places it just below the 54% analogue and around the line.
• Closest measured analogue: 2024 E2 Q3e - interpret the slope - 54%

2024 Exam 2 Q4e (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

• Asks: Show that the residual for the point (0.40, 1.81) is 0.052.
• Evidence: Residual calculations worth more than one mark, and residual calculations phrased as 'show that', are both separators in every recent November paper: 2024 Q3f (2 marks) at 42% and 2025 Q4fi at 41%, where the report stressed that 'Students needed to show all working that led to the given residual value'. Because the answer is given, the entire two marks ride on displaying the predicted value and the subtraction correctly.
• Closest measured analogue: 2024 E2 Q3f - residual, 2 marks - 42%

2024 Exam 2 Q4f (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: Given that the mean of the HHT values is 1.70 m, calculate the mean of the LLT values.
• Evidence: Solvable in one line only by students who know that the least squares line passes through the point of means, then inverting 1.70 = 2.19 - 1.08 x LLTbar. Students without that fact have no route at all, so the item splits the cohort sharply rather than degrading gradually. It is also the final part of a six-part question: last parts ran at 77% separators across November 2023-2025, and parts (d) or later at 65%. No close November analogue exists, so this rests on structure.
• Closest measured analogue: none — no November question tests this task

2024 Exam 2 Q5 (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

• Asks: Determine the seasonal index for March to two decimal places, using a three-year time series plot and a table of annual averages.
• Evidence: Both November analogues were heavy separators: 2023 Q4c at 21%, where the report noted 'Both calculations were required to attract the 2 marks', and 2025 Q6b at 12%. The NHT version is harder still because the three March values must be read off a graph rather than taken from a table before the three ratios are formed and averaged. Two-mark written items ran at 88% separators.
• Closest measured analogue: 2025 E2 Q6b - seasonal index, 2 marks - 12%

2024 Exam 2 Q6 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: From a time series plot showing raw and smoothed series, state the number of points used in the median smoothing.
• Evidence: Requires reversing the smoothing process: count how many days the smoothed line is truncated at each end and infer that seven lost at each end means 15-median smoothing. This is a rarely-set inversion of a standard skill and depends on careful reading of where the thick line begins on a 60-day axis. It also closes the data analysis section; last parts of a topic block ran at 77% separators in November 2023-2025.
• Closest measured analogue: none — no November question tests this task

Recursion and financial modelling (4 + 2)

2024 Exam 2 Q7c (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium-high

• Asks: Use the 6% per annum interest rate in a calculation to show that the multiplication factor in the recurrence relation is 1.005.
• Evidence: 'Show that' items for the multiplying factor or the interest rate are separators in every recent November paper: 2023 Q7a at 32%, where the report warned that 'Students needed to show all working steps that led to the given result. A response with solve CAS syntax was not considered appropriate'; 2025 Q9a at 37%; 2025 Q9bii ('R = 1 + ... = 1.0013') at 30%. The arithmetic is trivial - the mark is lost by not displaying the division by 12.
• Closest measured analogue: 2023 E2 Q7a - show that the rate is 7.8% - 32%

2024 Exam 2 Q7d (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

• Asks: Complete the next line of the amortisation table (repayment, interest, principal reduction, balance).
• Evidence: Four entries must all be correct for one mark, which is unforgiving, and the interest must be computed from the monthly rate rather than read off. Amortisation-table items in November sit close to the line: 2025 Q7c at 40%, where the report stressed that 'Students were instructed to use the values in the table', and the recursive-calculation item 2023 Q5b at 51%. It is also a well drilled routine, which argues upward.
• Closest measured analogue: 2025 E2 Q7c - amortisation table balance - 40%

2024 Exam 2 Q7e (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: Determine the value of the slightly higher final monthly repayment that fully repays the loan, to the nearest cent.
• Evidence: The classic two-stage Finance Solver problem: find the balance after 239 payments, then compute the final payment from it. Every November instance is a separator - 2023 Q7c at 32%, 2023 Q7bii at 40%, 2025 Q7d at 41%. It is also the last part of a five-part question, a position that ran at 77% separators.
• Closest measured analogue: 2023 E2 Q7c - final payment to the nearest cent - 32%

2024 Exam 2 Q8d (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

• Asks: For what value of R would $50 000 of equipment be valued at $42 868.75 after three months of reducing balance depreciation?
• Evidence: Requires inverting R^3 = 0.857375 with a cube root rather than any linear shortcut; students who divide the total depreciation by three arrive nowhere near 0.95. Reverse rate questions of this kind are separators in November (2025 Q9bii 'R = 1 + ... = 1.0013' at 30%, 2025 Q9a at 37%). It is also the last part of a four-part question (77% separator rate for last parts).
• Closest measured analogue: 2025 E2 Q9bii - find R by inversion - 30%

2024 Exam 2 Q9a (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

• Asks: Write a recurrence relation modelling the quarterly balance of a $35 000 loan at 10% p.a. compounding quarterly with $1722 repayments.
• Evidence: The multiplying factor must be derived from the annual rate (10%/4 = 2.5%, so R = 1.025). The November analogues straddle the line: 2023 Q6c at 41%, where 'Calculation of the correct multiplying factor proved challenging for some students', and 2024 Q5c at 59%. The NHT conversion is cleaner than either, which argues upward.
• Closest measured analogue: 2023 E2 Q6c - write the recurrence relation - 41%

2024 Exam 2 Q9b (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence high

• Asks: Determine the total interest paid over the first two years of a loan where the quarterly repayment rises from $1722 to $2000 after year one.
• Evidence: Very likely the hardest question on the paper. The report's solution runs to nine lines and requires two separate balance computations, two loan reductions, two interest subtotals and a sum. Both two-mark Finance Solver questions in the recent November corpus collapsed: 2024 Q8 at 13% ('Many students found the 288 but left the total cost blank. Some students misunderstood the meaning of the total cost of the loan') and 2025 Q10 at 11%. Two-mark written items ran at 88% separators.
• Closest measured analogue: 2024 E2 Q8 - total cost of a loan, 2 marks - 13%

Matrices (7 + 2)

2024 Exam 2 Q10c (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium-high

• Asks: Identify the single barn in which a new incoming link from barn I should be installed so that I reaches every other barn in one or two steps.
• Evidence: A search-and-verify task: barn I currently has an all-zero row, so students must test each candidate barn's outgoing row against the requirement that it covers J, K and L. Communication-matrix reasoning questions that go beyond reading an entry are consistent separators - 2023 Q10bii at 25%, where the report noted that 'Students who dealt with each element separately tended to write more accurate responses', and 2023 Q13c at 12%, where 'Very few students had both pairs correct'. It is also the final part of the question.
• Closest measured analogue: 2023 E2 Q10bii - communication matrix interpretation - 25%

2024 Exam 2 Q11a (NHT) — Matrices — 1 mark — BORDERLINE, confidence medium

• Asks: Complete the matrix equation that converts total carton weights into average egg weights.
• Evidence: Requires identifying the scalar 1/12 and producing the resulting row matrix. The 2023 November scalar-multiple item was a separator at 25% - 'Many students demonstrated difficulty in determining the correct scalar multiple' - but the scalar there had to be deduced, whereas here 12 eggs per carton is stated outright. A 2025 matrix-equation completion ran at 53%.
• Closest measured analogue: 2023 E2 Q9a - determine the correct scalar multiple - 25%

2024 Exam 2 Q11b (NHT) — Matrices — 1 mark — BORDERLINE, confidence medium

• Asks: Write a matrix calculation using matrix Q and a column matrix to show that 4824 eggs were sold.
• Evidence: Students must construct a conformable 4 x 1 column of twelves themselves - the classic failure described in the 2023 report for a 34% item: 'This question was not answered well. A row or column matrix was frequently seen.' Pulling the other way, the November 2024 item asking for a matrix product to be written ran at 78%, and the target 4824 is given, which lets students check themselves.
• Closest measured analogue: 2023 E2 Q8c - construct a matrix of the required order - 34%

2024 Exam 2 Q12a (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

• Asks: Complete a partially drawn transition diagram by adding the missing edges and proportions from the transition matrix.
• Evidence: Both November analogues are separators with explicit warnings about exactly this task. 2024 Q11ai at 24%: 'This question was not well answered. All edges required arrows otherwise it is no longer a directed graph.' 2023 Q11a at 34%: '0.5 was often given in place of 0.05. 1 was often left out or placed in the first row.' The NHT diagram is missing most of its edges including all three self-loops, and every one must be correct for the single mark.
• Closest measured analogue: 2024 E2 Q11ai - complete a transition diagram - 24%

2024 Exam 2 Q12b (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium-high

• Asks: After how many weeks will more than 44% of customers first be expected to purchase free-range eggs?
• Evidence: Requires iterating the state matrix and then applying a strict 'first exceeds' threshold, where an off-by-one is the standard error. The November analogues are both separators: 2024 Q11b ('5 years') at 39% and 2024 Q12d ('2027. The fourth year was also an acceptable answer') at 26%.
• Closest measured analogue: 2024 E2 Q11b - first time a threshold is crossed - 39%

2024 Exam 2 Q12c (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

• Asks: With 2000 customers per week, find the expected number of additional free-range purchasers at the end of the 10-week campaign compared with the start.
• Evidence: Three compounding demands: run the state matrix to S10, scale by 2000, and take a difference against the starting figure rather than reporting the end figure. The November items with exactly this difference-not-total structure collapsed: 2024 Q12c at 12% ('Some students did not subtract the departed workers and answered 190') and 2025 Q12b at 13% ('Many students answered 115 by including the children who had left the centre'). Rounding only at the final step is also required - the 2025 report flagged premature rounding on a 9% item.
• Closest measured analogue: 2024 E2 Q12c - difference rather than total - 12%

2024 Exam 2 Q12d (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

• Asks: Complete column F of a transition matrix so that shoppers eventually buy only free-range eggs.
• Evidence: Tests recognition of an absorbing state - the column must become (0, 1, 0). The November 2024 paper tested the same idea and the report is direct: 'Students who recognised that the 1 in the transition matrix would result in an absorbing state performed well on this question' - 24%. This is also the final part of a four-part question (77% separator rate for last parts).
• Closest measured analogue: 2024 E2 Q12b - absorbing state recognition - 24%

2024 Exam 2 Q13b (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

• Asks: Of the 8962 chickens expected in North field after two days, how many are expected to have started in North field?
• Evidence: A conditional two-step path-tracing question: students must either recognise that the answer is the (N,N) entry of T-squared scaled by 10 000, or trace all four two-step routes by hand, as the report does (3000 x 0.3 + 1400 x 0.12 + 2400 x 0.3 + 3200 x 0.2 = 2428). Conditional 'how many of these came from' items are the lowest-scoring matrices content in November: 2024 Q12c at 12%, 2025 Q12b at 13%, 2025 Q13bi at 9%.
• Closest measured analogue: 2025 E2 Q13bi - conditional proportion within a Markov chain - 9%

2024 Exam 2 Q13c (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

• Asks: Of the chickens expected in East field after three days, what percentage were also expected to be in East field after both one day and two days?
• Evidence: A triple-conditional path calculation - stay in East on day 2, stay again on day 3, then express as a percentage of all chickens in East after three days - for a single mark with rounding to a whole number. The nearest November items all sit near 10%: 2025 Q14c at 11% ('Only a small proportion of students showed an understanding of the effect of the identity matrix'), 2025 Q13bi at 9%, 2024 Q12c at 12%. It is also the final part of the final matrices question.
• Closest measured analogue: 2025 E2 Q14c - hardest matrices item of the paper - 11%

Networks and decision mathematics (7 + 0)

2024 Exam 2 Q14c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: If each of five friends visits one planned attraction and the number of different attractions visited is minimised, list the attractions visited.
• Evidence: This is a minimum set cover on a bipartite graph - students must find the smallest set of attractions covering all five friends and then list exactly that set, with no partial credit. The November items that ask for the set satisfying a global optimisation condition are heavy separators: 2024 Q14c at 22% ('This question was not answered well, with many other alternative pairs given by students') and 2023 Q13c at 12%. It is also the final part of the question.
• Closest measured analogue: 2024 E2 Q14c - identify the set meeting an optimisation condition - 22%

2024 Exam 2 Q15b (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: With reference to the degrees of the vertices, explain why the inspector cannot walk every path exactly once starting at the entrance.
• Evidence: The mark depends on citing the degree condition explicitly, not on naming the route type. The November 2025 twin is a separator at 40% with the same required content: 'Two vertices (C and E) are of odd degree. The intended Eulerian Circuit requires all vertices to be of even degree.' Explanation questions where VCAA prescribes the exact concept that must appear are consistently below the line.
• Closest measured analogue: 2025 E2 Q17a - explain using vertex degrees - 40%

2024 Exam 2 Q15c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: With the B-T path closed, find the length of the shortest closed route from the entrance that visits every attraction.
• Evidence: An open-ended optimisation with repeats allowed and no algorithm that guarantees the answer - students must search routes and compare totals, arriving at exactly 371 m for one mark. The November analogues are 2025 Q17b at 27%, where the report simply lists a twelve-term sum, and 2024 Q15c at 10%. It is also the final part of the question.
• Closest measured analogue: 2025 E2 Q17b - shortest route length by search - 27%

2024 Exam 2 Q15aii (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: Write down one route that starts and finishes at the entrance and visits each attraction exactly once.
• Evidence: Constructing a Hamiltonian cycle in a seven-vertex graph where, on the report's evidence, essentially only one cycle exists (the two answers given are the same route reversed). The November analogue is a separator at 44% and the report describes precisely the failure mode: 'Many students had a mostly correct response but missed or misplaced a landmark in the middle of the sequence or did not end the route with G.'
• Closest measured analogue: 2023 E2 Q13b - write a Hamiltonian cycle - 44%

2024 Exam 2 Q16c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: What is the latest starting time, in days, for activity I?
• Evidence: Requires a full backward pass through a 12-activity network after the critical path has been found. Both November analogues are separators: 2025 Q18b at 46% ('Latest start time = 20 - 4 - 4 - 3 = 9') and 2023 Q14c at 35%, where 'Some students erroneously counted the dummy activity'.
• Closest measured analogue: 2025 E2 Q18b - latest start time - 46%

2024 Exam 2 Q16d (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: Which activity has the longest float time?
• Evidence: Floats must be computed for every non-critical activity and then compared, for a single all-or-nothing mark. Both November analogues are separators and one has the identical answer: 2024 Q15b ('E') at 34% and 2025 Q18c ('F') at 47%, where the report added that 'if they provide additional information in their response, it must be correct'.
• Closest measured analogue: 2024 E2 Q15b - activity with the longest float - 34%

2024 Exam 2 Q16e (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: Complete a table of individual activity reductions that achieves the maximum reduction in completion time for the minimum cost.
• Evidence: Crashing is the single most reliable separator in the corpus. The final networks question of each recent November paper asked it and the results were 2023 Q14e at 9%, 2024 Q15e at 7% and 2025 Q18d at 21% - the report for the last reading 'Current time = 25 days, New time = 22 days, Reduce: A - 2, H - 1, K - 1'. The NHT version demands six correct table entries for one mark after the critical path has been recomputed as it shortens.
• Closest measured analogue: 2024 E2 Q15e - crashing for minimum cost - 7%

---

2025 NHT — 51 listed (39 SEPARATOR, 12 BORDERLINE)

Evidence base: neither paper is readable — both PDFs lack a text layer. Exam 1 rests on the report's worked solutions for 39 of 40 questions; Exam 2 rests on the full assessment guide, which states the mark scheme, plus the report. Exam 1 offers four options (A–D).

2025 Exam 1 (NHT) — 15 SEPARATOR, 5 BORDERLINE

Data analysis (5 + 3)

2025 Exam 1 Q6 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: Use the 68-95-99.7% rule with two given percentage statements to recover the mean and standard deviation of a normal distribution.
• Evidence: The report describes the work required: 'Using the 68-95-99.7% rule, and the information given, set up two equations ... Solving these equations leads to ...'. Setting up and solving a pair of simultaneous equations is the hardest normal-distribution skill on the course, and the November papers that set it as a written question scored well below the line both times it appeared.
• Closest measured analogue: 2023 E2 Q1e - reverse 68-95-99.7 for mean and standard deviation - 29%

2025 Exam 1 Q10 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: Determine the equation of a least squares line after applying a base-10 logarithmic transformation to the explanatory variable.
• Evidence: The report sets out three distinct CAS operations for a single mark: 'Step 1. Using a CAS, enter the data into a spreadsheet. Step 2. Transform the time variables using a logarithmic (base 10) transformation. Step 3. Determine the equation of the least squares line using the transformed time variables as the X list and proportion as the Y List.' Data entry, transformation and regression must all be executed correctly with no partial credit, and transformation items are the hardest data-analysis multiple-choice content in the calibration set.
• Closest measured analogue: 2024 E1 Q12 - transformation MCQ - 48%

2025 Exam 1 Q11 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Decide which one of four statements comparing boxplots of adult male height across census years is correct.
• Evidence: Four independent reads of several boxplots, each at a different location on the display: the report has to check ranges in 1996 versus 1946, the largest value in 1896 against the median in 1996, and the minimum in 1896 (153 cm). The check-every-statement format is separator-associated. Pulling the other way, boxplot reading is among the best-held skills in the course and the paper offers only four options.
• Closest measured analogue: 2024 E1 Q38 - check-each-statement format - 18%

2025 Exam 1 Q12 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: Reconstruct a least squares line from scattered given information, then determine the residual of the point (3, 4).
• Evidence: The report shows the line has to be rebuilt before the question can be answered at all: 'Step 1. Collate the information given. A point on the least squares line will be (2, 4.5). Step 2. Determine the equation of the least squares line ... The point (3,4) is below the least squares line and has a residual of ...'. Residual calculations are separators in every recent November paper even when the line is handed to students; here it must first be derived.
• Closest measured analogue: 2024 E2 Q3f - residual, 2 marks - 42%

2025 Exam 1 Q13 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Identify which of four plots correctly shows a smoothed version of a given time series.
• Evidence: The report's method is to compute three smoothed points and eliminate: 'Find the first three smoothed points. Approximately (2, 3625), (3, 3632), (4, 3625). Eliminate options A, B and C. Further points could then be used to confirm that option D is correct.' Three smoothing calculations plus graph matching is substantial for one mark, but the elimination route is efficient and the smoothed values are widely separated.
• Closest measured analogue: 2024 E1 Q15 - six-mean smoothing with centring - 70%

2025 Exam 1 Q14 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Interpret what a seasonal index of 0.75 means as a percentage relative to the seasonal average.
• Evidence: Requires the benchmark that the average seasonal index is 1 and then the correct direction and base for the percentage: '0.75 is 0.25, or 25%, less than the seasonal average.' Reporting the correction as a percentage is a documented confusion - the November written items on seasonal index calculation ran at 21% and 12%. Against that, this is a single interpretation step with no calculation beyond a subtraction.
• Closest measured analogue: 2023 E2 Q4c - seasonal index calculation - 21%

2025 Exam 1 Q15 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: One of four seasonal indices is missing; find the deseasonalised number of umbrellas sold in autumn.
• Evidence: Two chained steps, both printed in the report: 'Step 1. Determine the seasonal index for autumn. 4 - (0.75 + 1.28 + 1.10) = 0.87. Step 2. Calculate the deseasonalised value of the number of umbrellas sold in autumn. Deseasonalised value = 10 884.' The November item that tested only the first of these steps still ran at 58%, so adding the deseasonalisation should carry it below the line.
• Closest measured analogue: 2024 E1 Q16 - seasonal indices sum to n - 58%

2025 Exam 1 Q16 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: Decide which of four stated features (seasonality, trend, irregular fluctuations, structural change) are present in a time series plot.
• Evidence: Four independent readings of the same plot, with the report checking each in turn and resting statement I on identifying peaks at months 13, 25 and 37. Identifying time series features is one of the most reliably low-scoring written skills in November - 2024 Q4b at 24%, where students 'erroneously referred to an irregular fluctuation', and 2025 Q6a at 32%, after which the report warned that students 'need to be very clear on the key knowledge and key skills contained in the study design'. The check-every-statement format compounds it.
• Closest measured analogue: 2024 E2 Q4b - identify time series features - 24%

Recursion and financial modelling (4 + 1)

2025 Exam 1 Q19 (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

• Asks: Derive the annual interest rate from the information given, then determine the regular quarterly payment on a $500 000 annuity.
• Evidence: Two stages, per the report: 'Step 1. Determine the value of the annual interest rate. Step 2. Use Finance Solver to determine the regular quarterly payments', with the solver run at P/Y = C/Y = 4. Two-stage Finance Solver items in this position sit right on the line in November - 2025 Q19 at 49% and 2024 Q20 at 48% - which is the definition of borderline.
• Closest measured analogue: 2025 E1 Q19 - two-stage recursion MCQ - 49%

2025 Exam 1 Q21 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

• Asks: Find how many years an investment takes to more than double in value.
• Evidence: The report shows the trap sits in the last step: 'n = 7.83.... Therefore, it takes 8 years for the investment to be more than double its initial value.' Solving gives a non-integer that must be rounded up rather than to nearest, and 'more than double' makes the direction strict. Q21-Q24 is the densest separator block of Exam 1 - 50% across 2023-2025, and all four were separators in 2023.
• Closest measured analogue: 2023 E1 Q21 - 48%

2025 Exam 1 Q22 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: Determine the value of the final repayment on a loan, given a rate that must first be converted to a per-period rate.
• Evidence: A three-stage problem compressed into one multiple-choice mark. The report runs: convert the rate, solve for N (288.00007), solve for the balance after 288 repayments, then 'The last repayment could be 2076.19 + 0.15 = 2076.34.' Final-payment questions are separators every time November sets them as written questions worth a full mark each, and the two-mark Finance Solver questions collapsed to 13% and 11%.
• Closest measured analogue: 2023 E2 Q7c - final payment to the nearest cent - 32%

2025 Exam 1 Q23 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium-high

• Asks: Recover the nominal interest rate from an effective rate, then calculate the interest paid in the first year.
• Evidence: The report gives two stages: 'Step 1. Determine the nominal interest rate. The nominal rate is 6.2196. Step 2. Calculate the amount of interest in the first year.' Inverting the effective-rate formula is unusual - November normally asks for the effective rate, not the nominal one - and the effective-rate concept itself is documented as poorly held: 'Many students had some understanding of the effective interest rate and could even define it, but could not explain in simple terms why the nominal rate was lower.'
• Closest measured analogue: 2024 E2 Q6b - effective versus nominal interest rate - 26%

2025 Exam 1 Q24 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: Compare the total repaid under a full repayment schedule against paying out the balance early, and find the saving.
• Evidence: Four Finance Solver stages in the report: solve for N (40 repayments), find the balance after 20 repayments ($94 693.18), total the two repayment schedules, then difference them. This is Exam 2 work carrying a single multiple-choice mark. The equivalent-position November items ran at 27% and 46%, and the two-mark November question that asked for the total cost of a loan ran at 13%.
• Closest measured analogue: 2024 E1 Q24 - 46%

Matrices (3 + 1)

2025 Exam 1 Q27 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium-high

• Asks: Build a Leslie matrix from the given information and determine the long-term behaviour of the population.
• Evidence: The report shows the question cannot be answered by inspection: 'Determine the Leslie matrix ... Set up a sample calculation L x Sn, where the initial population is, for example, 400. By cycle number 25 the population will be 359, and by cycle 50 it will be 334. Total population is expected to decrease in the long term.' Construction plus a 50-cycle simulation plus a long-run judgement. A November item that asked only for the Leslie matrix to be recognised ran at 78%, so the long-run simulation is what does the separating; long-run and steady-state interpretation is a documented sub-50% family.
• Closest measured analogue: 2024 E1 Q30 - recognise a Leslie matrix - 78%

2025 Exam 1 Q29 (NHT) — Matrices — 1 mark — BORDERLINE, confidence medium

• Asks: Determine the order matrix X must have for the product X x (C - B) transpose to exist.
• Evidence: Abstract order reasoning through a subtraction and a transpose, as the report sets out: '(C - B) gives a 2 x 4 matrix. (C - B)T gives a 4 x 2 matrix. X must be a 1 x 4 matrix.' Abstract matrix-order questions are a recognised sub-50% family across the November archive. Against that, a November item asking which of four products was defined ran at 70%, and elimination works well with four options.
• Closest measured analogue: 2025 E1 Q31 - which matrix products are defined - 70%

2025 Exam 1 Q30 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium-high

• Asks: Count the permutation matrices that produce a given reordering of a column of test labels.
• Evidence: The report's answer requires several candidate orderings to be constructed and tested against one another before concluding 'There are two possible permutation matrices.' A November item that merely asked students to recognise a permutation matrix among four candidates ran at 83%; counting how many exist requires generating and checking them, which is the same novel-insight profile as the hardest matrices multiple-choice items.
• Closest measured analogue: 2023 E1 Q32 - 18%

2025 Exam 1 Q32 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

• Asks: Build a transition matrix from a description, find the constant k that keeps the first-level enrolment at 1000, then find when a condition is met.
• Evidence: Three separate demands set out by the report: 'Step 1. Determine the transition matrix. Step 2. Determine the value of k. To ensure that the number of students studying at the first level remains at 1000, k = 800. Repeat the recursive equations ... 8 years after the start of 2025.' Solving for the added constant in Sn+1 = T*Sn + B and then iterating eight times is the exact family that sits at the bottom of the November distribution.
• Closest measured analogue: 2024 E1 Q32 - working backwards through Sn+1 = TSn + B - 33%

Networks and decision mathematics (3 + 0)

2025 Exam 1 Q38 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

• Asks: Three people travel from the station to the town hall by their own shortest routes; compare the distances.
• Evidence: The report has to solve three separate shortest-path problems to answer one multiple-choice question: 'Alex will travel a shortest distance of 620 m (Station, A, D, H, J, Town Hall). Bishnu will travel a shortest distance of 620 m ... Cassie will travel a shortest distance of 630 m'. Two of the three tie, so an imprecise search gives the wrong comparison. A single shortest-path question in November ran at 71%; three of them, compared, sits well below that. Q37-Q40 is the densest separator block of Exam 1 (58% across 2023-2025).
• Closest measured analogue: 2023 E2 Q13a - shortest path through a network - 71%

2025 Exam 1 Q39 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: Decide which single capacity increase produces the greatest improvement in the maximum flow through a network.
• Evidence: The report computes the maximum flow five times - once for the original network and once for each option: 'The original maximum flow through the network is 26 litres per second ... Option A will lead to 30 ... Option B will lead to 35 ... Option C ... remaining at 26. Option D ... remaining at 26.' Two options change nothing, which is exactly the trap. Complicated max-flow items are heavy separators in November.
• Closest measured analogue: 2024 E2 Q14b - maximum flow - 29%

2025 Exam 1 Q40 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: A project network must be built from a table; when activity F is lengthened by four days, find the increase in the minimum completion time.
• Evidence: The report draws the whole network, identifies the original critical path A-C-E-J at 37 days, then shows the critical path migrating to B-F-J at 38 days for an increase of just one day - the trap being that lengthening F by four days does not lengthen the project by four. Building a network from a table and then re-deriving the critical path after a change is a separator in every recent November paper.
• Closest measured analogue: 2025 E1 Q40 - critical path after a change - 39%

2025 Exam 2 (NHT) — 24 SEPARATOR, 7 BORDERLINE

Data analysis (8 + 3)

2025 Exam 2 Q1ci (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Show that 15 is an outlier for this data set.
• Evidence: The assessment guide compresses two requirements into one mark and says so: 'UF = 6 + 1.5 x (6 - 2) = 12, 15 > 12' with the note 'Must see both parts'. Students must both compute the fence and state the comparison. The two component skills scored well in November 2024 - computing fences at 84% and explaining the outlier conclusion at 76% - which puts the joint requirement close to the line rather than clearly below it.
• Closest measured analogue: 2024 E2 Q2ci - compute the fences - 84%

2025 Exam 2 Q3a (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

• Asks: Complete a two-way table of percentages for daughter height against number of brothers.
• Evidence: The assessment guide awards the first mark for 'Any 2 correct numbers', which means the second mark requires all six percentages correct, each to one decimal place, with the second column formed over an awkward denominator (39.6, 16.5, 43.9). Two-mark written parts ran at 88% separators across November 2023-2025, and percentaging a two-way table over the correct margin is a documented difficulty.
• Closest measured analogue: 2023 E2 Q2ai - complete a frequency table - 95%

2025 Exam 2 Q3b (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

• Asks: Decide whether the data supports an association between daughter height and number of brothers, justifying by comparing percentages.
• Evidence: The assessment guide prescribes a two-part scheme: the A1 needs 'Yes or statement of affirmation and mention difference/comparison' and the H1 needs 'Correct percentages of taller daughters for both situations with proportion or correct percentages of shorter daughters (25% and 43.9%)'. Both the verdict and two correctly quoted percentages are required. The November twin of this question was itself a separator at 50%, with the report warning that students had to 'explicitly answer the question' as well as compare.
• Closest measured analogue: 2023 E2 Q2bii - association from a two-way table - 50%

2025 Exam 2 Q3c (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

• Asks: Determine the least squares line predicting daughter height from mother height, writing the coefficients in the boxes provided.
• Evidence: The assessment guide splits the marks as 'Evidence of correct numbers in any order' then 'All correct', so full marks demand both coefficients placed correctly against the right variables. VCAA has set this exact question in three consecutive November papers and it fell short every time: 2023 at 37% ('difficulty in giving the coefficients rounded to four significant figures'), 2024 at 39% ('Significant figures remain a challenge'), 2025 at 28% ('Significant figures remain problematic'). Misplacing coefficients and variables was explicitly noted in 2023.
• Closest measured analogue: 2023 E2 Q1d - least squares coefficients in boxes - 37%

2025 Exam 2 Q4b (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Draw the least squares line on the scatterplot.
• Evidence: The guide states tight tolerances - 'suggested margins of error for axis intercepts (left side: 1.695 - 1.705, right side: 1.81 - 1.82)' - a window only 0.01 wide at each end, and lists four key points. The two November analogues sit either side of the line: 2023 Q3a at 40%, where 'Many students showed evidence of correct coordinate points, but placed their dots at the wrong points', and 2024 Q3b at 51%.
• Closest measured analogue: 2023 E2 Q3a - draw the least squares line - 40%

2025 Exam 2 Q4c (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: Given r = 0.3744, find the percentage of the variation in son's height that is not explained by father's height.
• Evidence: Three steps compressed into one mark, all shown in the guide: square r to get 14.017%, round to a whole number, then take the complement (100 - 14 = 86%). Taking the complement is the step students omit. Coefficient-of-determination questions phrased in words are separators in November - 2025 Q5b at 44% - and even the direct, non-complemented version ran at only 52%.
• Closest measured analogue: 2025 E2 Q5b - coefficient of determination in words - 44%

2025 Exam 2 Q4d (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Describe the association in terms of strength and direction.
• Evidence: With r = 0.3744 the required description is 'weak, positive', and the guide adds 'In this order'. A correlation in the 0.3-0.4 band is exactly where students disagree about weak versus moderate, and the November report documented the confusion: 'Some students wrote moderate for the strength, which indicates consideration of the coefficient of determination rather than the correlation coefficient' - 58%. A cleaner version ran at 78%.
• Closest measured analogue: 2023 E2 Q3c - strength and direction of an association - 58%

2025 Exam 2 Q4f (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

• Asks: Calculate the residual for a point, giving the answer to two decimal places.
• Evidence: Two marks with the guide awarding the first for 'Correct calculation and/or predicted value' and applying 'Rounding to 2 dp'. Residual questions worth two marks are separators in every recent November paper: 2024 Q3f at 42% and 2025 Q4fi at 41%, where the report stressed that 'Students needed to show all working that led to the given residual value'. The answer here is also negative (-0.09), adding a sign to lose.
• Closest measured analogue: 2024 E2 Q3f - residual, 2 marks - 42%

2025 Exam 2 Q4g (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: Decide whether father's or mother's height is the better predictor of son's height, and justify the choice.
• Evidence: The assessment guide requires the justification to carry the actual figures - 'CD(Father/son) > CD(Mother/son), 14% > 9.5%' or 'Accept r(F/S) > r(M/S) 0.3744 > 0.3082' - so a bare choice earns nothing and both statistics must be computed and quoted. Comparison-with-justification items are separators in November: 2025 Q1cii at 47%, where the report noted that using statistics other than those indicated 'was not appropriate'.
• Closest measured analogue: 2025 E2 Q1cii - comparison requiring the right statistic quoted - 47%

2025 Exam 2 Q5a (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium-high

• Asks: Plot the given key values on the grid and join them.
• Evidence: The guide splits the marks as 'Any two values correctly plotted' then 'All points correctly plotted, and joined', and the key values it lists (1.658, 1.657, 1.659) differ only in the third decimal place, so the plotting tolerance is extremely tight and the joining is a separate requirement. The November item on precise plotting was a separator at 41%, where the report warned that 'Students need to be precise when marking a point on a grid, taking particular care with the scale used'. Two-mark written parts ran at 88% separators.
• Closest measured analogue: 2025 E2 Q4fii - precise plotting on a grid - 41%

2025 Exam 2 Q5b (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: Use a century of height data to predict the height in 2040, to three decimal places.
• Evidence: Four chained steps for one mark, as printed in the guide: total increase over 100 years (0.157 m), convert to an increase per decade (0.0157 m), count eight decades from 1960, then add. A unit conversion into decades sits in the middle where an error is invisible, and it is the final part of the final data analysis question - last parts ran at 77% separators across November 2023-2025.
• Closest measured analogue: 2025 E2 Q6b - multi-step seasonal calculation, 2 marks - 12%

Recursion and financial modelling (5 + 1)

2025 Exam 2 Q7a (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: Show that the interest rate per period is 0.25%.
• Evidence: The assessment guide labels this explicitly: '***Show that question'. Because the answer is supplied, the entire mark rides on displaying the conversion. Every November instance of this device is a separator: 2023 Q7a at 32%, where 'Students needed to show all working steps that led to the given result. A response with solve CAS syntax was not considered appropriate'; 2025 Q9a at 37%; 2025 Q9bii at 30%.
• Closest measured analogue: 2023 E2 Q7a - show that the rate is 7.8% - 32%

2025 Exam 2 Q7c (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

• Asks: Write the recurrence relation V0 = 300 000, Vn+1 = 1.0025 x Vn - 1570.58.
• Evidence: The guide requires that 'Both parts must be correct' for the single mark, so the initial value and the full rule must both be right. The November analogue was a separator at 41% because 'Calculation of the correct multiplying factor proved challenging for some students', but here the 0.25% rate has just been established in part a and handed to students, which argues the difficulty upward; a version with the factor supplied ran at 59%.
• Closest measured analogue: 2023 E2 Q6c - write the recurrence relation - 41%

2025 Exam 2 Q7d (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

• Asks: Determine the number of repayments required, giving 260.
• Evidence: A Finance Solver solve-for-N with the result to be reported as a whole number of repayments. The November analogues are separators: 2025 Q7d at 41%, where the report had to spell out that '60 payments in total, therefore 59 payments of $15 730.88 before the final payment', and 2024 Q8 at 13%, where 'Many students found the 288 but left the total cost blank'. It is also the final part of the question, a position that ran at 77% separators.
• Closest measured analogue: 2025 E2 Q7d - number of repayments - 41%

2025 Exam 2 Q8a (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: Determine the final repayment on a loan, to the nearest cent.
• Evidence: The guide prints the whole Finance Solver screen and then the adjustment - 'Final payment = $1285.12 + $0.30 = $1285.42' - so students must run the solver, read a residual balance of -0.2984, and add it back with correct rounding. Final-payment questions are separators in every recent November paper: 2023 Q7c at 32%, 2023 Q7bii at 40%, 2025 Q7d at 41%.
• Closest measured analogue: 2023 E2 Q7c - final payment to the nearest cent - 32%

2025 Exam 2 Q8b (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence high

• Asks: Write the recurrence relation B0 = 42 623.31, Bn+1 = 1.0045 x Bn - 2470.48 for the restructured loan.
• Evidence: Three separate quantities must be derived before the relation can be written - the mid-loan balance of $42 623.31 is itself a Finance Solver result, the new rate gives 1.0045, and the new repayment is 2470.48 - and the guide awards the second mark only for a 'Fully correct recurrence relation'. The November analogue was a separator at 41% even though its opening balance was given outright, with the report noting that 'Calculation of the correct multiplying factor proved challenging for some students'. Two-mark written parts ran at 88% separators.
• Closest measured analogue: 2023 E2 Q6c - write the recurrence relation - 41%

2025 Exam 2 Q9 (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence high

• Asks: From the information given, determine both the interest rate and the original investment.
• Evidence: The guide prints two complete Finance Solver screens, the output of the first feeding the input of the second, and awards one mark for each of the two answers with different rounding rules ('Round to 1 dp applies', 'Rounding to nearest dollar applies'). Both two-mark standalone Finance Solver questions in the recent November corpus collapsed - 2024 Q8 at 13% and 2025 Q10 at 11% - and every standalone unlettered two-mark question in November 2023-2025 was a separator.
• Closest measured analogue: 2025 E2 Q10 - standalone two-mark Finance Solver - 11%

Matrices (3 + 1)

2025 Exam 2 Q12b (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium-high

• Asks: List the two-step communication routes that start and finish at D.
• Evidence: Three routes must be listed and all three are needed for the single mark (D-M-D, D-P-D, D-C-D), with no partial credit. Exhaustive-listing items are heavy separators in November: 2023 Q13c at 12%, where 'Very few students had both pairs correct', and 2024 Q14c at 22%, where 'many other alternative pairs' were offered.
• Closest measured analogue: 2023 E2 Q13c - list every qualifying pair - 12%

2025 Exam 2 Q13b (NHT) — Matrices — 1 mark — BORDERLINE, confidence medium

• Asks: State what the given feature of the transition matrix means for the long-run distribution of resorts.
• Evidence: The expected answer - 'There won't be any resorts classified as Budget' - requires reasoning about the long-run consequence of a structural zero rather than reading an entry. The November analogue on recognising what a 1 in a transition matrix implies was a separator at 24%: 'Students who recognised that the 1 in the transition matrix would result in an absorbing state performed well.' Against that, a plain interpretation of a zero entry ran at 67%, and the guide accepts 'Or similar wording'.
• Closest measured analogue: 2024 E2 Q12b - absorbing state recognition - 24%

2025 Exam 2 Q13c (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium-high

• Asks: Determine the missing transition proportion d in the matrix.
• Evidence: The guide shows an equation must be built from a matrix product and then solved: 'f = 0.1; 0.1 x 40 + 0.6 x 120 + d x 90 + 0.1 x 70 = 119; 90d = 36; d = 0.4'. Two unknowns are recovered in sequence, with a four-term linear equation in between. Solving for an unknown inside a matrix or network context is a documented low scorer - the November 2025 two-mark item of this kind ran at 20% and the report noted that 'The value for y was often given as 3'.
• Closest measured analogue: 2025 E2 Q16 - solve for an unknown, 2 marks - 20%

2025 Exam 2 Q13d (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium-high

• Asks: Express the change between two expected numbers of resorts as a percentage.
• Evidence: The guide's working is 'diff = 115 - 40 = 75, % = 187.5%', so the percentage must be taken over the smaller starting figure rather than the larger one - choosing the wrong base is the standard error and gives 65%. The November items requiring a difference or a change rather than a level collapsed: 2024 Q12c at 12% ('Some students did not subtract the departed workers') and 2025 Q12b at 13% ('Many students answered 115 by including the children who had left'). It is also the final part of the final matrices question.
• Closest measured analogue: 2024 E2 Q12c - difference rather than level - 12%

Networks and decision mathematics (8 + 2)

2025 Exam 2 Q14c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: Identify the two pairs of landmarks that satisfy the stated condition.
• Evidence: Two pairs must both be correct for one mark (G and H, B and L). The November 2023 question is the same task in the same format and the report is blunt: 'vertex L and vertex N, vertex J and vertex M. This question was not answered well. Very few students had both pairs correct' - 12%. The 2024 version ran at 22% with 'many other alternative pairs given by students'.
• Closest measured analogue: 2023 E2 Q13c - identify both qualifying pairs - 12%

2025 Exam 2 Q14ai (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: Write a route through the landmarks that visits each exactly once.
• Evidence: An eight-vertex Hamiltonian path must be constructed and the assessment guide requires it 'In this order', so a single transposition loses the mark. The November analogue was a separator at 44% with exactly this failure mode: 'Many students had a mostly correct response but missed or misplaced a landmark in the middle of the sequence or did not end the route with G.'
• Closest measured analogue: 2023 E2 Q13b - write a Hamiltonian route - 44%

2025 Exam 2 Q15a (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: Determine the capacity of the given cut.
• Evidence: The assessment guide gives the trap away in its own working: '12 + 10 + 12 (4 and 8 are directed backwards) = 34'. Two edges crossing the cut run the wrong way and must be excluded; including them gives 46. Cuts containing back-flowing edges are among the lowest-scoring network items in the archive, and complicated max-flow and cut questions in November ran at 24% and 29% while a plain cut ran at 73%.
• Closest measured analogue: 2024 E2 Q14b - flow through a network - 29%

2025 Exam 2 Q15b (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium

• Asks: Determine the minimum cut in the network.
• Evidence: Having just computed one specific cut in part a, students must now search for the minimum over all cuts and arrive at a different value (8 + 12 + 9 = 29). The preceding part primes the wrong answer. The November item requiring a genuine search was a separator at 29%, with the report noting that 'Some students used a minimum cut, others an exhaustion of paths'; the version where the cut was simply the three edges into the sink ran at 73%.
• Closest measured analogue: 2024 E2 Q14b - minimum cut requiring a search - 29%

2025 Exam 2 Q16a (NHT) — Networks and decision mathematics — 1 mark — BORDERLINE, confidence medium

• Asks: Complete the immediate predecessor table for activities Q, R and S.
• Evidence: Six entries must be read off the network and the assessment guide requires that students 'Must have ALL correct' for the single mark, so one omission costs everything. The November analogue asking which activities have given predecessors ran at 73%, which is comfortably above the line, but that question wanted two answers rather than six.
• Closest measured analogue: 2023 E2 Q14a - read predecessors from a network - 73%

2025 Exam 2 Q16b (NHT) — Networks and decision mathematics — 1 mark — BORDERLINE, confidence medium

• Asks: Determine the earliest starting time for the activity, giving 15 weeks.
• Evidence: The guide lists three different paths that all yield 15 ('N - Q - T - W or P - Q - T - W or P - R - U - W'), so a forward pass has to reconcile several converging routes rather than follow one. Forward-pass questions in November straddle the line - 2023 Q14b at 59% and 2025 Q18b, its backward-pass counterpart, at 46%.
• Closest measured analogue: 2023 E2 Q14b - forward pass through a network - 59%

2025 Exam 2 Q16c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: Determine the latest starting time (or float) for activity X.
• Evidence: The guide shows that the network has three separate critical paths - 'P - R - U - W - Y, N - Q - T - W - Y, P - Q - T - W - Y each taking 29 weeks' - all of which must be found before activity X can be placed. Backward-pass questions are separators in November even with a single critical path: 2025 Q18b at 46% and 2023 Q14c at 35%, where 'Some students erroneously counted the dummy activity'.
• Closest measured analogue: 2025 E2 Q18b - latest start time - 46%

2025 Exam 2 Q16d (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: List the activities that are not on any critical path.
• Evidence: Because three critical paths run through the network, students must reconcile all three before the four non-critical activities (M, S, V, X) can be named, and all four are needed for one mark. The November analogues are separators: 2024 Q15b at 34% for the single activity with the longest float, and 2025 Q18a at 44%, where the report had to list two critical paths and identify what was common to both.
• Closest measured analogue: 2025 E2 Q18a - reconcile multiple critical paths - 44%

2025 Exam 2 Q16ei (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: Determine the new minimum completion time after the reductions.
• Evidence: The guide notes that 'New critical path is M - S', so the critical path migrates to activities that were previously not critical at all - the standard error is to subtract the reduction from the original 29 weeks and answer something other than 25. The November item requiring a recomputed time after a change was a separator at 33%, where 'A few students wrote the new completion time of 22 days rather than the reduction in time'.
• Closest measured analogue: 2023 E2 Q14d - completion time after a change - 33%

2025 Exam 2 Q16eii (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: Determine the minimum cost of achieving the maximum reduction in completion time.
• Evidence: Crashing is the single most reliable separator in the corpus, and this is its most demanding form: the guide's answer reduces eight activities (M, N, P, Q, R, S, W, Y), explicitly leaves four alone ('Do not reduce T, U, V, X') and ends with 'ALL paths now take 25 weeks', so every path must be balanced simultaneously. The final networks question of each recent November paper asked the same thing and returned 9% (2023), 7% (2024) and 21% (2025).
• Closest measured analogue: 2024 E2 Q15e - crashing for minimum cost - 7%

---

2026 NHT — 55 listed (39 SEPARATOR, 16 BORDERLINE)

Evidence base: both papers readable in full, plus a detailed Exam 2 assessment guide with M1/A1/H1 mark allocations. The Exam 1 guide is an answer key only — no working, no commentary. Exam 1 offers four options (A–D).

2026 Exam 1 (NHT) — 17 SEPARATOR, 8 BORDERLINE

Data analysis (6 + 3)

2026 Exam 1 Q5 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: From a two-way table of 70 adults (likes only cats / only dogs / both / neither, by gender), decide which of four percentage statements is correct.
• Evidence: Each of the four statements uses a different denominator - of the females, of those who like only cats, of those who like neither, of the males - so students must pick the right base four times. The keyed statement also requires realising that 'like dogs' includes the 15 who like both, not just the 8 who like only dogs. Choosing the wrong margin when percentaging a two-way table is a documented failure, and the check-every-statement format is separator-associated in the calibration data.
• Closest measured analogue: 2024 E1 Q38 - check-each-statement format - 18%

2026 Exam 1 Q6 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: Two tests both have mean 70; 2.5% score above 86 on the first and 34% score between 54 and 70 on the second. Find the sum of the two standard deviations.
• Evidence: Two independent reverse 68-95-99.7 deductions - 86 sits two standard deviations above the mean, 54 sits one below - followed by a sum, so a single slip in either destroys the answer. One such deduction, set as a two-mark written question in November 2023, ran at 29%, and the 2025 version at 47%. Doing it twice and combining sits below both.
• Closest measured analogue: 2023 E2 Q1e - reverse 68-95-99.7 - 29%

2026 Exam 1 Q9 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Estimate Pearson's correlation coefficient between minimum temperature and day from a five-point graph.
• Evidence: Five whole-number values must be read from the graph and entered before the CAS returns r, and the four options (-0.019, -0.139, 0.019, 0.039) are clustered near zero with two signs in play, so a single misread point flips the answer. Against that, the data are whole numbers so the reading should be exact, and once entered the CAS does the rest.
• Closest measured analogue: 2023 E2 Q3b - correlation coefficient from data - 69%

2026 Exam 1 Q10 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Choose the transformation most suitable for linearising a plot of annual health cost against age.
• Evidence: Requires reading the curvature of the plotted relationship and then selecting the matching transformation from the circle of transformations, with one distractor transforming the response variable instead of the explanatory one. Transformation questions are the hardest data-analysis multiple-choice content in the calibration set, but this one asks only for a choice, with no calculation to get wrong.
• Closest measured analogue: 2024 E1 Q12 - transformation MCQ - 48%

2026 Exam 1 Q11 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: Given 1/(completion time) = 0.2 - 0.01 x training time, decide what the least squares line suggests about training time and completion time.
• Evidence: Two direction reversals must be composed: the negative slope means more training lowers the reciprocal, and a lower reciprocal means a longer completion time. Two of the four options also swap association for causation, so a student who reasons correctly about direction can still lose the mark on the second axis. Reciprocal transformations and association-versus-causation are separately documented difficulties; this question requires both at once.
• Closest measured analogue: 2024 E1 Q12 - transformation MCQ - 48%

2026 Exam 1 Q12 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

• Asks: For a person with 11.5 hours of training whose residual is -0.005, find the completion time in hours.
• Evidence: Three steps with two inversions: evaluate the reciprocal model at 11.5, apply the residual in the transformed scale rather than the original scale, then take the reciprocal of the result to recover a time. Applying a residual in a transformed scale is a step November has never scored above the line on - residual questions alone ran at 42% and 41% in 2024 and 2025 with no transformation involved.
• Closest measured analogue: 2024 E2 Q3f - residual, 2 marks - 42%

2026 Exam 1 Q14 (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Using three-mean smoothing on ten days of closing share prices, identify the day with the largest smoothed value.
• Evidence: Eight separate smoothed values must be computed and compared for a single mark, with the graph read to the nearest cent each time. The November item asking for one six-mean smoothed value with centring ran at 70%, so the arithmetic is well within reach; it is the volume of it, and the closeness of the candidate days, that pushes this towards the line.
• Closest measured analogue: 2024 E1 Q15 - six-mean smoothing with centring - 70%

2026 Exam 1 Q15 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence high

• Asks: Fit a least squares line to twelve deseasonalised quarterly sales figures and use it with the seasonal indices to predict actual sales in quarter 4 of year 5.
• Evidence: Four chained operations for one mark: enter twelve values, run the regression, index quarter 4 of year 5 correctly as time period 20, then reseasonalise by multiplying by 1.49. Indexing the prediction period and remembering to multiply rather than divide by the index are two separate traps. The November written questions combining seasonal indices with a calculation ran at 21% and 12%.
• Closest measured analogue: 2023 E2 Q4c - seasonal index calculation, 2 marks - 21%

2026 Exam 1 Q16 (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: With the quarter 1 seasonal index missing and quarter 4 actual sales exactly double quarter 1, find the ratio of the deseasonalised quarter 4 sales to the deseasonalised quarter 1 sales.
• Evidence: Entirely abstract - no sales figures are given, so students must recover the missing index from the sum-to-four rule and then carry an unknown through a ratio of two deseasonalised values. The November item that tested only the sum-to-n step ran at 58%; this adds an algebraic ratio on top. It is also the closing data analysis question, a position that returned 43% in 2023 and 50% in 2025.
• Closest measured analogue: 2024 E1 Q16 - seasonal indices sum to n - 58%

Recursion and financial modelling (4 + 2)

2026 Exam 1 Q17 (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

• Asks: For T0 = a, Tn+1 = 2Tn + 1 with T2 = 15, find a.
• Evidence: A context-free recursion item that must be run backwards two steps, either by unwinding 4a + 3 = 15 algebraically or by testing the options forwards. Abstract recursion is the sub-genre that separates most reliably - every question in this block was a separator in November 2023 and the abstract 2024 Q17 ran at 36% - but testing four options forwards is a quick and reliable route here.
• Closest measured analogue: 2024 E1 Q17 - abstract recursion - 36%

2026 Exam 1 Q19 (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

• Asks: How many years until $2500 invested at 4% p.a. compounding annually has first earned at least $1000 in interest?
• Evidence: Two traps sit at the end: the target is the interest earned, not the balance, and the non-integer solution must be rounded up rather than to nearest, with the rounded-down value offered as option A. November items turning on exactly this 'first exceeds' rounding were separators at 48% and 39%, which places this close to the line rather than clearly past it.
• Closest measured analogue: 2023 E1 Q21 - 48%

2026 Exam 1 Q20 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

• Asks: A $10 000 asset depreciated by reducing balance halves in value after exactly five years; find the annual depreciation rate.
• Evidence: Requires inverting (1 - r)^5 = 0.5 with a fifth root; any linear shortcut (such as dividing 50% by five or by four) lands on one of the distractors. The four options are spaced barely 0.3 percentage points apart across 12.5%, 12.7% and 13.0%, so an approximate method cannot succeed. Reverse-rate questions are separators in November - 2025 Q9bii at 30% and 2025 Q9a at 37% - and Q17-Q24 is the densest separator block of Exam 1.
• Closest measured analogue: 2025 E2 Q9bii - find the rate by inversion - 30%

2026 Exam 1 Q22 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: For a $400 000 annuity paying $4021.35 monthly at 3.85% p.a., decide which of four values is not a monthly balance within the first five months.
• Evidence: Five successive balances must be generated recursively and each rounded to the nearest dollar before the odd one out can be identified - four correct calculations still fail if the fifth is wrong. Recursive-calculation questions in November lose marks precisely here: 'Many students were not paid the mark for this question because they did not show recursive calculations, they rounded values too early'. The 'which is not' format compounds it, running at 18% and 32% in November 2024.
• Closest measured analogue: 2024 E1 Q38 - which statement is not true - 18%

2026 Exam 1 Q23 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium-high

• Asks: Mel invests $10 000 at 8% simple interest and Teresa $9900 at 10% simple interest; express the amount by which Teresa's balance exceeds Mel's after n years.
• Evidence: Two of the four options are written in compound form, so the first hurdle is recognising that simple interest gives a linear rule; the second is that the $100 difference in principal survives into the constant term, giving 190n - 100 rather than 190n. A context-free algebraic recursion item of exactly this kind ran at 36% in November 2024, and in November 2023 every question in this block was a separator.
• Closest measured analogue: 2024 E1 Q17 - abstract recursion rule - 36%

2026 Exam 1 Q24 (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: A quarterly reducing balance loan is restructured after five years to monthly repayments at a new rate; find the number of monthly repayments then required.
• Evidence: Two complete stages with a change of compounding period between them: run the quarterly recurrence 20 times (or solve for the balance after five years), then run Finance Solver monthly at 4.2% with the new repayment to solve for N. Options B and D differ by a single repayment, so the rounding convention at the end also has to be right. The November two-mark question requiring two linked Finance Solver outputs ran at 13%.
• Closest measured analogue: 2024 E2 Q8 - two linked Finance Solver outputs, 2 marks - 13%

Matrices (3 + 2)

2026 Exam 1 Q28 (NHT) — Matrices — 1 mark — BORDERLINE, confidence medium

• Asks: Identify the matrix product that returns the total volume and the total number of soft drinks sold.
• Evidence: The correct product requires a column of ones to be appended alongside the volumes so that a single multiplication returns both totals - the device the November report described students failing at when 'A row or column matrix was frequently seen' (34%). Against that, three of the four options can be eliminated on order alone without understanding the column of ones, and a November item asking students to write a matrix product ran at 78%.
• Closest measured analogue: 2023 E2 Q8c - construct a matrix of the required order - 34%

2026 Exam 1 Q29 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium

• Asks: Identify the 6 x 6 permutation matrix that reorders the column [L, I, S, T, E, N] into [S, I, L, E, N, T].
• Evidence: A 36-entry permutation matrix must be constructed or verified against four options that differ in only a few rows, and one distractor is not even a valid permutation matrix (it carries two ones in a row). A November item that asked only for a permutation matrix to be recognised among candidates ran at 83%, but the matrices there were small; tracking six simultaneous relocations under time pressure is the harder task that in 2023 ran at 18%.
• Closest measured analogue: 2023 E1 Q32 - 18%

2026 Exam 1 Q30 (NHT) — Matrices — 1 mark — SEPARATOR, confidence medium-high

• Asks: With one transition percentage b unknown, find the expected number of shoppers at store S after two weeks.
• Evidence: Three separate demands: recover b from the requirement that each column of the transition diagram totals 100%, build the transition matrix from the diagram, then iterate twice from 50 shoppers at each store and round. Reading a transition diagram into a matrix is a documented failure point in November - '0.5 was often given in place of 0.05. 1 was often left out' - and two-step Markov calculations sit near the bottom of the distribution.
• Closest measured analogue: 2024 E1 Q32 - multi-step transition matrix work - 33%

2026 Exam 1 Q31 (NHT) — Matrices — 1 mark — BORDERLINE, confidence medium

• Asks: For a two-state transition matrix, decide which statement about the long-run nesting distribution is true.
• Evidence: The steady state must be found and then attached to the correct location, with the distractors pairing the right percentage with the wrong one of treetops and rocky area. Long-run and steady-state interpretation is a documented sub-50% family in the November archive. Against that, repeated iteration on a CAS reaches the steady state reliably and there are only two states to keep straight.
• Closest measured analogue: 2025 E2 Q13a - interpret a transition matrix feature - 67%

2026 Exam 1 Q32 (NHT) — Matrices — 1 mark — SEPARATOR, confidence high

• Asks: Team H's results are missing from an 8 x 8 dominance matrix; using the given one-step totals, break the tie between H and M on combined one-step and two-step dominance.
• Evidence: Probably the most demanding multiple-choice question across the three NHT papers. The blank row and column for H must first be reconstructed by reconciling each team's stated one-step total against its recorded wins, then two-step dominance computed for two teams and added to the one-step totals, then four statements checked. Two-step dominance alone sits in the low 40s in the November archive, and the hardest matrices multiple-choice items run at 18% to 33%.
• Closest measured analogue: 2023 E1 Q32 - 18%

Networks and decision mathematics (4 + 1)

2026 Exam 1 Q35 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: Starting at vertex J, count how many different Eulerian circuits are possible.
• Evidence: Counting Eulerian circuits is not a skill the November papers have ever required - they ask whether one exists, or to name the route type. Students must verify that all degrees are even and then systematically enumerate distinct circuits from a fixed start, with no algorithm available and no partial credit. The option set includes 0, so students who stop at the existence check can still be wrong. This is one of the places where the NHT paper attempts something November does not.
• Closest measured analogue: none — no November question tests this task

2026 Exam 1 Q36 (NHT) — Networks and decision mathematics — 1 mark — BORDERLINE, confidence medium

• Asks: A tree has 11 vertices; one edge is added. How many faces does the resulting planar graph have?
• Evidence: Two abstract facts must be combined with nothing drawn: a tree on 11 vertices has 10 edges, and Euler's formula then gives 11 + f = 11 + 2. Students who do not know the tree edge count have no route at all, which splits the cohort sharply. The November item applying Euler's formula after redrawing a graph as planar ran at 52%, right on the line.
• Closest measured analogue: 2024 E1 Q35 - Euler's formula and faces - 52%

2026 Exam 1 Q38 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: For a 12-vertex weighted graph, how many edges of weight 5 are not included in the minimum spanning tree?
• Evidence: Two stages: build the complete minimum spanning tree over twelve vertices, then go back and count how many of the graph's many weight-5 edges were left out - a count that is wrong if even one spanning tree edge is misplaced. Building a spanning tree alone runs comfortably above the line in November (81% in 2025), so the counting layer and the graph's size are what carry this below it. Q37-Q40 is the densest separator block of Exam 1 (58% across 2023-2025).
• Closest measured analogue: 2025 E2 Q15d - draw a spanning tree - 81%

2026 Exam 1 Q39 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: From an adjacency matrix containing a loop and multiple edges, decide which of four statements about the graph is not true.
• Evidence: The graph must first be drawn from the matrix, correctly handling the loop at Q and the double edges, and then four separate properties tested - Hamiltonian cycle, Eulerian circuit, a spanning tree with four edges, and the loop. The Eulerian circuit test requires every degree to be even, with the loop contributing two. November's items in this exact family ran at 18% and 32%, and the report for the first advised students to 'Check this diagram against each statement'.
• Closest measured analogue: 2024 E1 Q38 - which statement is not true about a graph - 18%

2026 Exam 1 Q40 (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: Match an unlabelled directed network containing a dummy activity to one of four twelve-row predecessor tables.
• Evidence: The network's precedence structure, including the dummy, must be read off and then compared against four tables that agree on most rows and differ on only a few, so the discriminating rows have to be found before any answer is possible. This family is a separator in both recent November papers - 32% in 2024 and 39% in 2025, where the report noted that the network 'requires a dummy activity between the end of B and start of G'.
• Closest measured analogue: 2025 E1 Q40 - network from a predecessor table - 39%

2026 Exam 2 (NHT) — 22 SEPARATOR, 8 BORDERLINE

Data analysis (7 + 4)

2026 Exam 2 Q1d (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Explain why the chosen summary statistics are the more appropriate ones for this data.
• Evidence: The assessment guide requires the answer to 'reference skew or outlier' explicitly, so a vague appeal to robustness earns nothing. Justification questions where VCAA prescribes the concept that must appear are consistently near or below the line - the November comparison question requiring the indicated statistic was a separator at 47%. Against that, this is a heavily drilled standard response.
• Closest measured analogue: 2025 E2 Q1cii - justification using the prescribed statistic - 47%

2026 Exam 2 Q1e (NHT) — Data analysis — 2 marks — BORDERLINE, confidence medium

• Asks: Show that 240 is not an outlier for this data set.
• Evidence: Two marks, with the guide awarding M1 for the upper fence and H1 for a 'Correct statement based on their calculated UF value'. The consequential marking is unusually forgiving, which argues upward, but the interquartile range here is very wide (100 - 4.3) and two-mark written parts ran at 88% separators. The component skills scored 84% and 76% in November 2024, putting the combined requirement close to the line.
• Closest measured analogue: 2024 E2 Q2ci - compute the fences - 84%

2026 Exam 2 Q2a (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

• Asks: Determine the least squares line predicting life expectancy from brain weight and write the coefficients in the boxes provided.
• Evidence: The assessment guide awards the first mark for 'Evidence of correct numbers, any order (From 8.07151..., 0.0876032...)' and the second only when the 'Equation totally correct', so full marks need both coefficients rounded correctly and attached to the right variables - and the two coefficients round to different numbers of decimal places. VCAA set this question in three consecutive November papers and it fell short every time: 37% in 2023 ('difficulty in giving the coefficients rounded to four significant figures'), 39% in 2024 and 28% in 2025 ('Significant figures remain problematic').
• Closest measured analogue: 2023 E2 Q1d - least squares coefficients in boxes - 37%

2026 Exam 2 Q2d (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: Decide from the residual plot whether the linear model is appropriate, giving a reason.
• Evidence: The assessment guide requires both parts for the single mark: 'Must have YES (stated or implied), with reason', the reason being a random scatter with no pattern. The November twin was a separator at 40% and the report set out exactly what went wrong: 'Yes, the residual plot shows no clear pattern... The number of points above and below the line was irrelevant. Some students asserted that the prediction was reliable, despite the question indicating otherwise.'
• Closest measured analogue: 2024 E2 Q3gii - residual plot interpretation - 40%

2026 Exam 2 Q2e (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium-high

• Asks: State whether the model over- or under-predicted at a given point, with a reason.
• Evidence: The guide demands 'underprediction statement with reason' and the reason is the sign convention itself - that actual minus predicted being positive means the actual exceeds the predicted. Getting the sign of a residual or a slope the right way round is one of the lowest-scoring families in the archive, and the related November question connecting a scatterplot point to its residual was a separator at 47%.
• Closest measured analogue: 2024 E2 Q3gi - connect a point to its residual - 47%

2026 Exam 2 Q3b (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Draw the least squares line on the scatterplot.
• Evidence: The guide lists three key points to one decimal place and states acceptance limits at each end ('Lower: at least 62.5, less than 75; Upper: greater than 425, less than 450'), so the line must be plotted from calculated points rather than by eye. The two November analogues sit either side of the line: 2023 Q3a at 40%, where students 'placed their dots at the wrong points or took insufficient care', and 2024 Q3b at 51%.
• Closest measured analogue: 2023 E2 Q3a - draw the least squares line - 40%

2026 Exam 2 Q3c (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: Interpret the coefficient of determination of 0.680 in context.
• Evidence: The response must name both variables and attribute variation in one to variation in the other - 68.0% of the variation in the brain weight can be explained by the variation in the body weight. November marks this strictly: the 2024 version ran at 52% with the report noting that 'Some students did not reference the variation in both variables', and the 2025 version was a separator at 44%.
• Closest measured analogue: 2025 E2 Q5b - coefficient of determination in words - 44%

2026 Exam 2 Q3d (NHT) — Data analysis — 2 marks — SEPARATOR, confidence medium

• Asks: Interpret the slope of the least squares line, giving the value and the direction.
• Evidence: The assessment guide awards only one mark for 'One correct OR both given in incorrect order', so full marks require the value 13.9 and the word 'increase' both correct and correctly ordered. The November slope interpretation ran at 54% as a one-mark question, with the report noting that 'Students did not always reference the change in each of the two variables'; two-mark written parts ran at 88% separators across 2023-2025.
• Closest measured analogue: 2024 E2 Q3e - interpret the slope - 54%

2026 Exam 2 Q3e (NHT) — Data analysis — 2 marks — SEPARATOR, confidence high

• Asks: Calculate the residual for a body weight of 210, rounding to a whole number.
• Evidence: Two marks with the guide reserving the first for the predicted value and applying whole-number rounding to the final answer of 48.5, which rounds to 49 - a boundary case. Residual questions worth two marks are separators in every recent November paper: 2024 Q3f at 42% and 2025 Q4fi at 41%, where 'Students needed to show all working that led to the given residual value'.
• Closest measured analogue: 2024 E2 Q3f - residual, 2 marks - 42%

2026 Exam 2 Q4c (NHT) — Data analysis — 1 mark — SEPARATOR, confidence medium

• Asks: How many smoothed points result from applying the smoothing to 36 years of monthly data?
• Evidence: Two abstractions with nothing to calculate from: convert 36 years to 432 months, then recognise that a 13-point smoothing loses six points at each end, giving 432 - 12 = 420. Reasoning about how many points a smoothing window costs is rarely set and has no routine to fall back on. It is also the final part of the final data analysis question - last parts ran at 77% separators across November 2023-2025.
• Closest measured analogue: none — no November question tests this task

2026 Exam 2 Q4bi (NHT) — Data analysis — 1 mark — BORDERLINE, confidence medium

• Asks: Calculate the smoothed value by summing months 3 to 15 and dividing by 13.
• Evidence: Thirteen values must be read off and summed correctly before the division, with the result rounded to one decimal place - a long enough chain that a single misread loses the mark, and there is no partial credit. Against that, the November item asking for a six-mean smoothed value with centring, which is conceptually harder, ran at 70%, so the arithmetic volume alone may not carry this below the line.
• Closest measured analogue: 2024 E1 Q15 - six-mean smoothing with centring - 70%

Recursion and financial modelling (7 + 2)

2026 Exam 2 Q5b (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

• Asks: Show the recursive calculation of the balance after the first repayment.
• Evidence: The guide requires the substitution to be displayed, not just the answer: 'V1 = 1.0048V0 - 4215.93 = 1.0048 x 600 000 - 4215.93'. November penalises this heavily - 'Many students were not paid the mark for this question because they did not show recursive calculations, they rounded values too early' (51%). The guide also records that the 'Question stem included a typographical error which was addressed through marking', which makes the achieved outcome for this item unusually hard to infer.
• Closest measured analogue: 2023 E2 Q5b - show the recursive calculation - 51%

2026 Exam 2 Q5c (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium-high

• Asks: Determine the annual interest rate from the multiplying factor 1.0048.
• Evidence: The guide's working is 'Rate = (1.0048 - 1) x 1200% = 5.76%', so students must strip the 1, convert a monthly rate to an annual one, and express it as a percentage - three conversions in one line. Every November instance of recovering a rate from a recurrence factor is a separator: 2023 Q7a at 32%, where 'Students needed to show all working steps that led to the given result', and 2025 Q9a at 37%.
• Closest measured analogue: 2023 E2 Q7a - recover the interest rate - 32%

2026 Exam 2 Q5d (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: Determine the value of the final repayment on the loan.
• Evidence: The guide prints two full Finance Solver screens and then a further adjustment - 'Last pay = 4194.49 x 1.0048 = 4214.623...' - so the balance before the last payment must be found and then carried forward one more period. Final-payment questions are separators in every recent November paper: 2023 Q7c at 32%, 2023 Q7bii at 40% and 2025 Q7d at 41%. It is also the final part of the question, a position that ran at 77% separators.
• Closest measured analogue: 2023 E2 Q7c - final payment - 32%

2026 Exam 2 Q6b (NHT) — Recursion and financial modelling — 1 mark — BORDERLINE, confidence medium

• Asks: Write the recurrence relation for the annual value of the vehicle under unit cost depreciation.
• Evidence: The annual depreciation must first be built from the usage assumption (25 000 km per year at $0.35 per km gives 8750) before the relation can be written, and both the initial value and the rule are needed. The November analogue requiring the multiplying factor to be derived was a separator at 41%, but the version where the per-period figure was straightforward ran at 73%.
• Closest measured analogue: 2023 E2 Q6c - write the recurrence relation - 41%

2026 Exam 2 Q6c (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium-high

• Asks: Write a rule for the value of the vehicle in terms of the number of kilometres travelled.
• Evidence: The November 2025 question testing exactly this distinction was a separator at 50% and the report named the error precisely: 'Many students did not demonstrate understanding of the distinction between a rule and recurrence relation and gave a similar answer again as in part a.i.' The NHT version is harder still because the independent variable switches from years in the preceding part to kilometres here, so the coefficient changes from 8750 to 0.35.
• Closest measured analogue: 2025 E2 Q8aii - rule versus recurrence relation - 50%

2026 Exam 2 Q7 (NHT) — Recursion and financial modelling — 2 marks — SEPARATOR, confidence high

• Asks: Determine the interest rate from the amortisation table and complete the next row.
• Evidence: The guide requires 'ALL four values correct' for the second mark after the rate has itself been derived from the table (12 610/260 000 = 4.85%), and the row that results is an interest-only payment in which the principal reduction is zero and the balance does not move - a counter-intuitive outcome students are likely to reject. Amortisation-table questions in November sit at 40%, where the report stressed that 'Students were instructed to use the values in the table'; two-mark written parts ran at 88% separators.
• Closest measured analogue: 2025 E2 Q7c - amortisation table - 40%

2026 Exam 2 Q8b (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium-high

• Asks: Write the recurrence relation for the new investment.
• Evidence: Two quantities must be derived before a single symbol can be written: the opening value $259 279.54 is itself a Finance Solver result (solve for PV), and the factor 1.008 comes from converting 3.2% p.a. to a quarterly rate. The November analogue was a separator at 41% even with its opening balance supplied, because 'Calculation of the correct multiplying factor proved challenging for some students'. It is also the final part of the question.
• Closest measured analogue: 2023 E2 Q6c - write the recurrence relation - 41%

2026 Exam 2 Q8ai (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence medium

• Asks: Determine the duration of the annuity in years.
• Evidence: Two stages in the guide: convert the multiplying factor to a 3.0% annual rate, then solve for N, which returns 144 months and must then be converted to 12 years. Solve-for-N questions are separators in November - 2025 Q7d at 41%, where the report had to spell out the payment count, and 2024 Q8 at 13% - and the months-to-years conversion adds a further step.
• Closest measured analogue: 2025 E2 Q7d - number of repayments - 41%

2026 Exam 2 Q8aii (NHT) — Recursion and financial modelling — 1 mark — SEPARATOR, confidence high

• Asks: Determine the total interest earned over the first twelve payments of the annuity.
• Evidence: The guide's route is to find the balance after the twelfth payment and then form interest = balance - principal + total payments, an identity students routinely misapply. The November question asking for the total cost of a loan ran at 13% and the report is explicit that 'Some students misunderstood the meaning of the total cost of the loan'; the total-interest variant in the same family ran no better.
• Closest measured analogue: 2024 E2 Q8 - total cost of a loan, 2 marks - 13%

Matrices (2 + 1)

2026 Exam 2 Q10a (NHT) — Matrices — 1 mark — BORDERLINE, confidence medium

• Asks: Explain why the product MQ is not defined.
• Evidence: The guide requires the explanation to carry the specifics - 'Must reference M and Q OR 1 and 3 for columns/rows' - so naming the rule without the numbers earns nothing. Explanations about matrix order are a documented weakness: the November item where 'A row or column matrix was frequently seen' ran at 34%. Against that, a multiple-choice question on which products are defined ran at 70%, and the conformability rule is heavily drilled.
• Closest measured analogue: 2023 E2 Q8c - matrix order - 34%

2026 Exam 2 Q11c (NHT) — Matrices — 2 marks — SEPARATOR, confidence high

• Asks: Project the population ten years forward with the Leslie matrix and decide whether the species should be classified as endangered.
• Evidence: Four stages for two marks, all in the guide: iterate the Leslie matrix ten cycles, total the three age groups in both 2022 (159) and 2032 (46), compute the percentage reduction (about 71%), then apply the classification threshold. The guide makes the second mark depend on 'Correct percentage calculation and interpretation', so arithmetic alone is not enough. The November two-mark matrices questions requiring a projection and an interpretation ran at 17% and 12%.
• Closest measured analogue: 2025 E2 Q13bii - projection plus interpretation, 2 marks - 17%

2026 Exam 2 Q12a (NHT) — Matrices — 2 marks — SEPARATOR, confidence high

• Asks: Determine the required value, giving 1400.
• Evidence: The guide splits the marks as 'Correct state matrix (A2024 or A2023)' then 'Correct answer', so the state matrix for the right year must be generated before the figure can be extracted - and the guide's own hedge over which year is intended shows the indexing is the hard part. Off-by-one errors in the number of iterations are the standard failure: the November items of this kind ran at 12% and 13%, the reports noting students who included people who had already left. Two-mark written parts ran at 88% separators.
• Closest measured analogue: 2024 E2 Q12c - state matrix after n steps - 12%

Networks and decision mathematics (6 + 1)

2026 Exam 2 Q13c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: Identify the set of locations satisfying the stated condition (cafe, police station, shopping centre).
• Evidence: Three vertices must all be named for the single mark, with the guide accepting them 'In any order' but requiring the complete set. Exhaustive-identification items are heavy separators in November: 2023 Q13c at 12%, where 'Very few students had both pairs correct', and 2024 Q14c at 22%, where students offered 'many other alternative pairs'. It is also the final part of the question.
• Closest measured analogue: 2023 E2 Q13c - identify the complete qualifying set - 12%

2026 Exam 2 Q13bi (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: Write a route that visits each of the nine locations exactly once.
• Evidence: A nine-vertex Hamiltonian path must be constructed and written in a valid order, with no partial credit. The November analogue was a separator at 44% with exactly this failure mode: 'Many students had a mostly correct response but missed or misplaced a landmark in the middle of the sequence or did not end the route with G.' Nine vertices is longer than the November route that produced that result.
• Closest measured analogue: 2023 E2 Q13b - write a Hamiltonian route - 44%

2026 Exam 2 Q14c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence high

• Asks: Determine the capacity of the cut.
• Evidence: The assessment guide gives the trap away in its own working: 'Cut through 19 - 12 - 22 - 18 - 24 - 18, with 22, 18 and 24 not counted (wrong way). 19 + 12 + 18 = 49.' Half the edges crossing the cut run the wrong way and must be excluded; counting them all gives 113. Cuts containing back-flowing edges are among the lowest-scoring network items in the archive - the complicated November versions ran at 24% and 29% while a plain cut ran at 73%.
• Closest measured analogue: 2024 E2 Q14b - flow through a network - 29%

2026 Exam 2 Q15a (NHT) — Networks and decision mathematics — 1 mark — BORDERLINE, confidence medium

• Asks: Identify the critical path through the project network.
• Evidence: A forward and backward pass over the whole network is needed before the path A-C-E-J-M-N can be named, and every activity in it must be listed. The November analogues straddle the line: 2024 Q15a at 65% for a four-activity critical path and 2025 Q18a at 44%, where two critical paths had to be reconciled. This network's path is six activities long, which is longer than either.
• Closest measured analogue: 2024 E2 Q15a - identify the critical path - 65%

2026 Exam 2 Q15b (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: Determine the latest starting time for the activity.
• Evidence: A full backward pass is needed, working 25 - 4 - 4 - 5 back from the project completion time. The November question is the same calculation in the same shape - 'Latest start time = 20 - 4 - 4 - 3 = 9' - and was a separator at 46%; the 2023 version ran at 35% with 'Some students erroneously counted the dummy activity'.
• Closest measured analogue: 2025 E2 Q18b - latest start time - 46%

2026 Exam 2 Q15c (NHT) — Networks and decision mathematics — 1 mark — SEPARATOR, confidence medium-high

• Asks: List the activities that are not on the critical path.
• Evidence: Five activities must all be named for one mark, which the guide backs with a complete earliest-start, latest-start and float table for eight activities - that is the work required before an answer exists. The November analogues are separators: 2024 Q15b at 34% for the single activity with the greatest float, and 2025 Q18c at 47%, where the report warned that any extra information offered 'must be correct'.
• Closest measured analogue: 2024 E2 Q15b - float and the critical path - 34%

2026 Exam 2 Q15d (NHT) — Networks and decision mathematics — 2 marks — SEPARATOR, confidence high

• Asks: Determine the shortest completion time achievable and the minimum cost of achieving it.
• Evidence: Crashing is the single most reliable separator in the corpus, and the guide shows why this instance is hard: two different paths must be reduced simultaneously ('reduce A and M each by 2 minutes', 'reduce H by 1 minute') and every remaining path checked against the new 21-minute limit before the cost of five reductions can be stated. The final networks question of each recent November paper asked the same thing and returned 9% in 2023, 7% in 2024 and 21% in 2025. Two-mark written parts ran at 88% separators.
• Closest measured analogue: 2024 E2 Q15e - crashing for minimum cost - 7%

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Limitations

1. Nothing here is measured. VCAA publishes no per-question statistics for NHT sittings. Every verdict is an inference from a November analogue, a mark scheme, or a structural pattern. No percentage in this document describes an NHT question.

2. The 2025 NHT exam papers cannot be read. Both 2025 NHT PDFs were scanned without a text layer, so 2025-05_2025-NHT-generalmaths1.txt and 2025-05_2025-NHT-generalmaths2.txt are empty files. Every 2025 judgement therefore rests on the reports and the assessment guides, never on the question as the student saw it. Concretely:

• 2025 Exam 1 — the report prints a worked solution for 39 of 40 questions, which describes the work each demanded but not the stem, the diagram or the distractors. Distractor design is a real part of difficulty and I could not see it. Q28 carries no comment at all and was not assessed.
• 2025 Exam 2 — several parts are blank or uninformative in both the report and the guide and could not be assessed: the whole of Q6 (3 marks), Q10b.i and Q10c, Q11a, and Q4e. Q11b ("m = 22.3, n = 220") and Q12a were legible but not interpretable without the stem, so they were left out rather than guessed at.

3. The 2026 Exam 1 evidence is thin in a different way. The paper is fully readable, but the assessment guide gives answer letters only — no working, no commentary. Those 25 verdicts rest on my own reading of each question plus the calibration, with no VCAA signal at all. I worked each question independently; for 2026 Exam 1 Q20 my own solution (a fifth root of 0.5, giving about 12.9%) points to a different option than the keyed answer, which I could not resolve. The entry describes the task and the option spacing, and does not depend on which option is correct.

4. Text extraction is lossy. Matrices, transition diagrams, network diagrams and stacked multiple-choice options came through the PDF-to-text conversion garbled or reordered in every paper. Where a question's meaning depended on a diagram I could not reconstruct, I either relied on the report's or guide's description of it or left the question out.

5. The calibration cohort is not the NHT cohort. November percentages come from the full state entry of roughly 25 000 students. NHT sits a few hundred, typically accelerated students at schools on a northern-hemisphere timetable. These verdicts are about how demanding the question is, benchmarked against a November-like cohort. They are not predictions of what the actual NHT candidature scored, and the real NHT figures — if they existed — would very likely be higher across the board.

6. The listed share is higher than November's measured rate, and some of that is method. These papers list 119 separators across 274 assessable questions (120 multiple-choice plus 154 written parts) — 43%. The November papers of 2023–2025 measured 28 of 120 multiple-choice questions and 88 of 164 written parts as separators: 116 of 284, or 41% overall. The headline rates are close, but the distribution is not: my Exam 1 rate (47 of 120) runs well above November's measured 23%, while my Exam 2 rate (72 of 154) sits near November's 54%. Part of the gap is real — the NHT Exam 2 papers are genuinely back-loaded, with Matrices and Networks sections composed almost entirely of multi-step conditional and optimisation items that November scores at 7–35%. But part of it is the method: an inference from question demands can spot a hard question and cannot discover that a question turned out unexpectedly easy. Six of the counter-examples in CAL-5 were questions I would have called separators on structure alone. Treat the 21 SEPARATOR entries marked medium, and the BORDERLINE list as a whole, as the places where that bias is most likely to have bitten.

7. Confidence labels. Three are used: high (56 entries) means at least one November analogue tests essentially the same task and fell well short, or a mark scheme states a requirement most students will not have met; medium-high (42) means a close analogue plus supporting structure; medium (60) means the evidence points below the line but a counter-analogue exists or the analogue is not exact. Every BORDERLINE entry is medium by definition. Nothing is labelled low — questions I could not evidence at least to medium were left out of the list entirely.

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Machine-readable version: corpus/nht-general.json — one object per listed question.