Retired modules

Scope: the four Further Mathematics modules that no longer exist in VCE General Mathematics Units 3 & 4 (Study Design 2023–2027):

Evidence base: every VCAA Further Mathematics / General Mathematics examination paper and examination report 2006–2026 held in corpus/text/ (128 files). Citations use the form YEAR Exam N Module M Question X. NHT (Northern Hemisphere Timetable) papers are flagged explicitly.

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1. Exam architecture, by era

You cannot read a legacy citation without knowing which shell it sat in.

Era A — 2006–2015 ("old" Further Mathematics: Core = Data analysis only)

Source: structure-of-book table, 2012 Exam 1 and 2012 Exam 2.

Module order: 1 Number patterns · 2 Geometry and trigonometry · 3 Graphs and relations · 4 Business-related mathematics · 5 Networks and decision mathematics · 6 Matrices.

So: each legacy module was worth 9 MCQ marks in Exam 1 and 15 marks in Exam 2.

Era B — 2016–2022 (Core = Data analysis + Recursion and financial modelling)

Source: structure-of-book table, 2019 Exam 1 and 2019 Exam 2.

Module order: 1 Matrices · 2 Networks and decision mathematics · 3 Geometry and measurement · 4 Graphs and relations.

Each surviving legacy module was worth 8 MCQ marks in Exam 1 and 12 marks in Exam 2.

2020 only — COVID "Adjusted Study Design"

Source: 2020 Exam 1 structure table; 2020 Exam 2 examination report, General comments.

Exam 1: Core 30 MCQ + one module of 10 MCQ = 40. Exam 2: Core 45 marks + one module of 15 marks = 60. So 2020 module questions are longer than 2016–2019/2021–2022 ones and should not be used to calibrate length.

Era C — 2023 onwards (current General Mathematics)

Source: VCE General Mathematics (From 2023) — Examination specifications.

"The examination will be divided into four content areas: data analysis, recursion and financial modelling, matrices, and networks and decision mathematics."
Exam 1: 40 MCQ — 16 data analysis, 8 recursion and financial modelling, 8 matrices, 8 networks.
Exam 2: 60 marks — 24 data analysis, 12 recursion and financial modelling, 12 matrices, 12 networks.

There is no module choice, and no fifth or sixth content area. Multiple-choice questions now have four options (A–D), not five (see 2025 Exam 1 Question 17); every legacy MCQ has an extra distractor.

The 2022 Exam 2 examination report states it plainly:

"This was the last year of the Further Mathematics study design and examination. In 2023, VCE Further Mathematics will be renamed VCE General Mathematics Units 3–4 and will follow the revised study design and examination specifications."

The final Further Mathematics papers ever set are the 2023 NHT papers (2023FM1-nht, 2023FM2-nht), which still contain Module 3 Geometry and measurement and Module 4 Graphs and relations.

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2. The formula sheet is the cleanest proof of retirement

Further Mathematics formula sheet, 2012 (Era A) carried, per module:

• Module 1 Number patterns: arithmetic series sum n/2[2a + (n−1)d] = n/2(a + l); geometric series sum a(1−rⁿ)/(1−r); infinite geometric series a/(1−r), |r| < 1
• Module 2 Geometry and trigonometry: area of a triangle ½bc sin A; Heron's formula; circumference; area of a circle; volume of sphere/cone/cylinder/prism/pyramid; surface area of a sphere; Pythagoras' theorem; sine rule; cosine rule
• Module 3 Graphs and relations: gradient m = (y₂−y₁)/(x₂−x₁); y = mx + c
• Module 4 Business-related mathematics: simple interest I = PrT/100; compound interest A = PRⁿ, R = 1 + r/100; hire purchase effective rate of interest 2n × flat rate / (n+1)

Further Mathematics formula sheet, 2022 (Era B) kept Geometry and measurement (triangle area, Heron, sine rule, cosine rule, circle/arc/sector, sphere, cone, prism, pyramid) and Graphs and relations (gradient, y = mx + c), but the Number patterns and Business-related blocks were already gone — replaced by a single Core entry u₀ = a, u_{n+1} = bu_n + c plus the effective-rate formula.

General Mathematics formula sheet, 2024 onward (Era C) contains only:

• Data analysis: standardised score, boxplot fences, least squares line, residual value, seasonal index
• Recursion and financial modelling: u₀ = a, u_{n+1} = Ru_n + d; effective rate of interest
• Matrices: determinant, inverse, S_{n+1} = TS_n + B, Leslie matrix recurrence
• Networks: Euler's formula v + f = e + 2

No Pythagoras. No sine/cosine rule. No mensuration. No gradient. No series sums. No simple/compound-interest closed forms.

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3. Module popularity (context for how much legacy material exists)

Percentages of students selecting each module, from the Exam 2 examination reports. Era A figures are reconstructed from column-misaligned text extractions but are cross-validated: each report repeats the previous year's column, and the 2015 report's table extracted cleanly and anchors the ordering.

Era B (choose 2 of 4). 2016–2018 are quoted as % of students; 2019–2022 reports quote % of module slots (halved scale) — read them as-published.

Geometry was the most chosen module of the old six (65–91%), so 2006–2015 papers contain a very large stock of geometry material — and all of it is now out of scope.

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4. Geometry and trigonometry (Module 2, 2006–2015) → Geometry and measurement (Module 3, 2016–2022, NHT to 2023)

4.1 Years and numbering

The 2016 rename was not cosmetic. Spherical geometry — latitude/longitude, great-circle and small-circle distance, time zones — does not exist anywhere in 2006–2015. A corpus-wide search for latitude|longitude|great circle returns zero hits before 2016 and hits in every year 2016–2023. Likewise time zone first appears in 2016 Exam 1. Conversely, Era A leaned harder on contour maps and scale drawings (contour map appears 17 times across the FM corpus, concentrated in 2010–2015).

4.2 Exam 1 question-type catalogue (9 MCQ in Era A, 8 in Era B, 10 in 2020)

Standing instruction on every module opener:

"Before answering these questions, you must shade the 'Geometry and measurement' box on the answer sheet for multiple-choice questions and write the name of the module in the box provided."

4.3 Exam 2 question-type catalogue (15 marks Era A, 12 marks Era B, 15 marks in 2020)

Era A was typically 3–5 questions built around one scenario; Era B settled into three questions — one mensuration, one spherical-geometry/time, one triangle trigonometry.

Mensuration and composite solids - 2006 Exam 2 Module 2 Question 3 — cylindrical tank with 0.25 m walls: internal radius (1 mark), maximum water volume to the nearest cubic metre (2 marks) - 2007 Exam 2 Module 2 Questions 1–4 — one block of wood carved successively into a rectangular prism, a triangular prism, a right rectangular pyramid, then a frustum; includes total surface area (2 marks) and volume (1 mark) - 2009 Exam 2 Module 2 Question 4 — hemisphere-based cylindrical filter volume (2 marks); cone partially emptied, percentage of original volume removed (2 marks) - 2013 Exam 2 Module 2 Question 2 — staircase cross-section of identical rectangles: shaded rectangle area (1 mark), volume of the solid staircase (2 marks) - 2014 Exam 2 Module 2 Question 3 — cylinder + hemisphere water container: hemispherical surface area (2 marks), maximum volume (2 marks) - 2018 Exam 2 Module 3 Question 1 — tennis-ball container, 5 marks: diameter, total outside surface area, and two "Write a calculation that shows that the volume ... is 164.6 cm³ / 740.9 cm³" parts - 2019 Exam 2 Module 3 Question 1 — cargo ship, 4 marks: shaded composite area, container volume, container surface area, and a packing part ("What is the maximum number of barrels that can fit in one shipping container?") - 2021 Exam 2 Module 3 Question 1 — squash ball in a cube, 4 marks: show the volume is 33.51 cm³, empty space in the box, total surface area, maximum number of boxes fitting a 17.0 × 12.5 × 8.5 cm space - 2022 Exam 2 Module 3 Question 1 — airship, 6 marks: floor areas, window length from a total area, Pythagoras for cable height, cylinder-plus-two-hemispheres fabric area

Circles, arcs, sectors, segments - 2013 Exam 2 Module 2 Question 3 — 400 m athletics track: "Show how this value could be obtained" for the 63.66 m diameter, grassed area, then the volume of 0.1 m deep rubber resurfacing (2 marks) - 2016 Exam 2 Module 3 Question 5 — sprinkler covering a 100° sector: given 147.5 m², find the radius; then a composite sector region (3 marks) - 2017 Exam 2 Module 3 Question 3 — circle inscribed against a square: cosine rule to show an angle is 81°, perimeter of the composite grassed area, chord length (4 marks)

Similarity and scale - 2008 Exam 2 Module 2 Question 1b — "On a plan of the concrete slab, a 3 cm line is used to represent a length of 6 m. i. What scale factor is used to draw this plan? ii. What is the area of this surface on the plan?" (1 + 1) - 2007 Exam 2 Module 2 Question 4b — "What fraction of the volume of the pyramid in Figure 4 remains in Figure 5?" (2 marks) - 2012 Exam 2 Module 2 Question 4c — similar triangles, area of one given, find the other (2 marks) - 2013 Exam 2 Module 2 Question 4 — surface areas 500 cm² and 720 cm²: "By what value can the volume of the intermediate discus be multiplied to give the volume of the senior discus?" (2 marks) - 2014 Exam 2 Module 2 Question 3c — volume ratio three-quarters, one surface area known, find the other (2 marks) - 2017 Exam 2 Module 3 Question 1b — "The volume of the large storage box is eight times the volume of the small storage box ... What is the length of the large storage box?" (1 mark) - 2020 Exam 2 Module 3 Question 2d — "The area of the enlarged logo is four times the area of the original logo. What is the height ... of the enlarged logo?" (1 mark) - 2022 Exam 2 Module 3 Question 3b — sight-line / similar-triangles problem (1 mark)

Non-right triangle trigonometry: sine rule, cosine rule, area of a triangle, Heron - 2006 Exam 2 Module 2 Question 1 — seven-part farm-allotment question: angle, length, bearing, shortest distance, area of a triangle (1 mark), "Use the cosine rule to show how this length can be found" plus angle ABC, and an area-constrained fence length (2 marks) - 2007 Exam 2 Module 2 Question 3c — "Using AY as 37 cm, demonstrate the use of Heron's formula to calculate the area ... of the triangular face YAB" (2 marks) - 2009 Exam 2 Module 2 Question 3 — regular pentagon: show angle POQ is 72°, show OP is 25.52 cm, area of the pentagon (2 marks) - 2010 Exam 2 Module 2 Question 1d–e — area enclosed by three paths, "Show that the length of path GW is 115.3 metres", then an isosceles-triangle angle and side (1 + 1 each) - 2013 Exam 2 Module 2 Question 1b — distance XY by the cosine rule, then the area of triangle XGY (1 mark each) - 2014 Exam 2 Module 2 Question 2 — "The sine rule can be used to calculate the length of the wall AX. Fill in the missing numbers below.", then the length and the area (6 marks in total) - 2015 Exam 2 Module 2 Question 4 — two guy wires, sine rule to find a vertical offset x (2 marks) - 2016 Exam 2 Module 3 Question 4 — "Use the cosine rule to find the distance travelled by this ball" across two bearing legs, then the closing bearing (3 marks) - 2018 Exam 2 Module 3 Question 3c — ambiguous case: "Determine two possible values for angle AQP ... If point Q is within the boundary of the court, what is the value of x?" - 2019 Exam 2 Module 3 Question 3 — show AC is 20 m by Pythagoras, angle ACB, cosine rule with a 120° rotation, three-dimensional chain geometry (5 marks) - 2021 Exam 2 Module 3 Question 2c — "Show that the distance between Wei-Yi and Bao is 5 m, rounded to the nearest metre" (cosine rule, 1 mark)

Bearings and navigation - 2008 Exam 2 Module 2 Question 3 — elevation of a tree, "Show that, correct to one decimal place, the distance NT is 12.6 m", bearing of T from N, and "Is it possible for the tree to hit the shed if it falls? Explain your answer showing appropriate calculations" (2 marks) - 2009 Exam 2 Module 2 Question 2 — yacht at 210°, ferry at 135°: label the ferry on the diagram, angle between, distance, back-bearing (4 marks) - 2010 Exam 2 Module 2 Question 1a–c — reverse bearing, and "How many metres north of the entry gate is the canoeing activity?" - 2012 Exam 2 Module 2 Question 2c — "Determine the bearing of i. point S from point P ii. point S from point R" (1 + 1) - 2014 Exam 2 Module 2 Question 4 — bearing of a chicken from its owner, both located relative to a gate (2 marks) - 2015 Exam 2 Module 2 Question 2 — "How far north of the cable car station is the communications tower?", then "Use the cosine rule to find the bearing of the camp site from the communications tower" - 2017 Exam 2 Module 3 Question 2b — "What is the three-figure bearing of the hostel from the Nemuro railway station?" - 2020 Exam 2 Module 3 Question 3d–e — "Show that the bearing of the hotel from the airport is 104°, correct to the nearest degree", then a return leg on a bearing of 282°

Angles of elevation and depression - 2006 Exam 2 Module 2 Question 2 — tower height from a 20° elevation, then the angle of depression of a second point (1 + 1) - 2009 Exam 2 Module 2 Question 1 — "Show that the gradient of the line FC in the diagram is 0.125", then the angle of elevation, then the slant distance - 2012 Exam 2 Module 2 Question 3b — 22° elevation to the top of a tree, find the tree height - 2015 Exam 2 Module 2 Question 1d — angle of elevation from a horizontal distance of 2500 m and a straight-line distance of 2596 m

Contour maps, slope, cross-sections (Era A only) - 2010 Exam 2 Module 2 Question 2 — "On the contour map, 1 centimetre represents 2 metres on the horizontal level." Horizontal distance DF; "Show that the staircase between points D and F on the contour map above would be considered unsafe" (elevation greater than 45°); then a slope of 0.8 giving a map length (2 marks) - 2011 Exam 2 Module 2 Question 1 — horizontal distance from a contour map; "Calculate the average slope between point B and the lighthouse" - 2012 Exam 2 Module 2 Question 2 — height difference between two contour points, and "Sketch the cross-section of the block of land along the horizontal axis, PQ, below" (1 mark) - 2015 Exam 2 Module 2 Question 1 — height difference, average slope B to C, map distance from a scale factor of 1 : 50 000, angle of elevation, and "Draw a cross-section of the mountain from A to C on the graph" (2 marks)

Spherical geometry: latitude, longitude, great and small circles, time zones (Era B only) - 2016 Exam 2 Module 3 Question 3 — "A golf tournament is played in St Andrews, Scotland, at location 56° N, 3° W. Assume that the radius of Earth is 6400 km. Find the shortest great circle distance to the equator from St Andrews." plus a day-and-time conversion (3 marks) - 2017 Exam 2 Module 3 Question 2 — flight arrival day and time; radius of the small circle at 43° N; "Find the shortest great circle distance between Melbourne (38° S, 145° E) and Nemuro (43° N, 145° E)" (5 marks) - 2018 Exam 2 Module 3 Question 2 — travel duration in hours and minutes; "Write a calculation that shows that the radius of the small circle of Earth at latitude 11° N is 6282 km, rounded to the nearest kilometre"; then the shortest small circle distance between two cities on the same parallel (3 marks) - 2019 Exam 2 Module 3 Question 2 — "Explain, with reference to the information provided, how we know that Sydney is closer to the equator than Magadan."; great-circle distance along the 151° E meridian (answer 10 500 km); travel time across a two-hour time difference (3 marks) - 2020 Exam 2 Module 3 Question 3 — small-circle radius at 24° N is 5847 km; small-circle distance Dhaka to Abu Dhabi; arrival time across a two-hour difference (5 marks including bearings) - 2021 Exam 2 Module 3 Question 3 — "Which players are from the Northern Hemisphere?"; "On the diagram above, mark with an 'X' the location of Istanbul"; show the small-circle radius at 41° N is 4830 km; distance Istanbul to New York City; a two-flight time-difference comparison (5 marks) - 2022 Exam 2 Module 3 Questions 2–3 — departure weekday and time given a 23-hour flight and a nine-hour difference; small-circle radius 5702 km at 27° S; small-circle distance along 27° S; great-circle distance south along the 141° E meridian

4.4 Recurring VCAA wording (quoted verbatim)

• "Assume that the radius of Earth is 6400 km." — 21 occurrences across 2016–2023. It is always given in the stem; it was never on the formula sheet.
• "Find the shortest great circle distance between ... Round your answer to the nearest kilometre." (7 occurrences) and its partner "shortest small circle distance" (3 occurrences).
• "Write a calculation that shows that the radius of the small circle of Earth at latitude 11° N is 6282 km, rounded to the nearest kilometre." (2018 Exam 2 Module 3 Question 2bi). The Write a calculation that shows ... stem appears 14 times in the corpus.
• "Write your answer, in metres, correct to one decimal place." / "Round your answer to the nearest degree." — the standard rounding tail on almost every trigonometry part.
• "What is the bearing of X from Y?" — 80 occurrences of bearing of. The word from names the observer, and that is the single most common source of reversed answers.
• "Show that, correct to two decimal places, the length OP is 25.52 cm." (2009 Exam 2 Module 2 Question 3b) — the Era A form of the show-that instruction.
• "On the contour map, 1 centimetre represents 2 metres on the horizontal level." (2010 Exam 2 Module 2 Question 2).
• "Before answering these questions, you must shade the 'Geometry and measurement' box on the answer sheet for multiple-choice questions and write the name of the module in the box provided."

4.5 What the assessors said

From the 2019 Exam 2 examination report, Module 3: - Question 2a (explain why Sydney is closer to the equator): 59% scored the mark. "Responses that simply said that 34° is less than 60° failed to identify the key point that the equator is a line of 0° latitude ... Responses needed to explain using the information given, not calculate using the information given." - Question 2c (travel time with a time difference): 20%. "Some responses subtracted the two-hour time difference rather than adding it. Many ignored the number of days." - Question 3ai (show AC is 20 m): "Using the equation ... then solving with technology does not show the mathematics to obtain the result."

From the 2022 Exam 2 examination report, Module 3: - Question 2a (time zones): 27%. "Time zone questions were not well responded to by many students." - Question 2bi (show the small-circle radius): 45%. "This question was a 'show that' question, which meant that students could not just write an equation involving r that needed to be solved. An acceptable alternative was 6400 × sin 63°." - Question 3b (final trigonometry part): 9%. "A challenging final question that was often not attempted or was incorrectly answered." - General comments: "in Geometry Question 1a., the required answer was 18.75 square metres; as rounding did not apply, an answer such as 18.8 could not be accepted."

From the 2020 Exam 2 examination report: "In Geometry Question 3d. students were asked to show that the bearing of the hotel from the airport was 104°. This required the calculation (involving tan) that resulted in the appropriate angle that rounded to 14° or 76° and then to also show the step that leads to the bearing: either 90° + 14° = 104° or 180° − 76° = 104°."

4.6 Verdict on current relevance

Residual overlap: essentially none. Three things should be named so students do not mistake them for survivals:

1. Euler's formula v + f = e + 2 is still on the General Mathematics formula sheet — but under Networks and decision mathematics (planar graphs), which is where it always sat. The Geometry module never used it.
2. Generic exam skills transfer — reading dimensions off a diagram, obeying a stated rounding, "show that" discipline. The assessor commentary quoted in §4.5 is worth reading for that reason alone. The mathematics does not transfer.
3. Measurement and trigonometry do appear in VCE Foundation Mathematics and in Units 1 & 2 General Mathematics. Those are different studies with different examinations and are not what Units 3 & 4 past papers are being used to prepare for.

Bottom line: do not attempt any Geometry and trigonometry or Geometry and measurement past-paper question for Units 3 & 4 revision. That is 9 Exam 1 marks plus 15 Exam 2 marks per year for 2006–2015, and 8 plus 12 per year for 2016–2022, of entirely inert material.

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5. Graphs and relations (Module 3, 2006–2015 → Module 4, 2016–2022, NHT to 2023)

5.1 Years and numbering

Unlike Geometry, the content of this module barely changed across the rename. The same four strands run from 2006 to 2023: read/interpret a graph, build and use a linear model, handle piecewise and step relations, and solve a linear programming problem. Frequency across the extracted module text: inequalit* 189, constraint 76, feasible region 54, objective function 28, line segment 14, break even 15, step graph 7, slope/gradient 20 combined.

5.2 Exam 1 question-type catalogue (9 MCQ Era A, 8 MCQ Era B, 10 in 2020)

5.3 Exam 2 question-type catalogue (15 marks Era A, 12 marks Era B, 15 marks in 2020)

The Era B structure was remarkably stable: Question 1 reads a graph, Question 2 builds and manipulates a linear or piecewise model, Question 3 is the linear programming problem (usually 4–5 marks).

Reading and interpreting graphs - 2006 Exam 2 Module 3 Question 1 — call-out fee step graph: read a fee, read a maximum distance, then "Draw this information on the graph above" to add a new step (1 mark) - 2008 Exam 2 Module 3 Question 1 — pulse-rate line-segment graph: read a value, compute an increase, then write an equation from a verbal rule and apply a percentage band (2 marks) - 2013 Exam 2 Module 3 Question 1 — distance–time graph of a bus journey: constant speed in stage 1, minutes stopped in stage 2, "Draw a line segment on the graph above to represent stage 3", average speed over three hours, and the value of k in a three-branch piecewise definition of D (5 marks) - 2015 Exam 2 Module 3 Questions 1–2 — flight cost by date; then a currency conversion graph where "The slope of this graph is the exchange rate ... How many yen will Ben receive for each dollar?" - 2018 Exam 2 Module 4 Question 1 — daily gold-price chart: lowest day, greatest consecutive increase (2 marks) - 2019 Exam 2 Module 4 Question 1 — membership numbers 2008–2018: read a value, "Show that the average rate of change of membership numbers from 2013 to 2018 was −6 members per year", then extrapolate to 2021 (3 marks) - 2020 Exam 2 Module 4 Question 1 — distance–time graph: arrival time, average speed, and the value of k in the segment equation d = k − 80n (3 marks)

Linear models: equations, revenue/cost, break-even - 2006 Exam 2 Module 3 Question 2 — fuel-remaining line: "Determine the equation of the line shown in the graph above" (2 marks), distance until empty, refuel rate - 2008 Exam 2 Module 3 Question 2 — R = 35x, C = 50 625 + 12.5x, break-even competitor count, profit (4 marks) - 2010 Exam 2 Module 3 Question 1 — revenue equation, cost at 30 units, "Draw the graph of C = 500 + 40x on the axes above", break-even (4 marks) - 2013 Exam 2 Module 3 Question 3 — "Write an expression for the profit that the organisers will make in terms of n", then a minimum n for a $500 profit (2 marks) - 2015 Exam 2 Module 3 Question 3 — a line through (100, 8075) and (200, 17 575): "Use the point (100, 8075) to show that the value of k is 1425", the horizontal intercept, and "Interpret the intercept on the horizontal axis in the context of converting dollars to yen" (3 marks) - 2016 Exam 2 Module 4 Question 2 — cost = 1200 + 1.5 × number of balls: inverse evaluation, sketch, break-even at 200 balls giving a selling price (3 marks) - 2018 Exam 2 Module 4 Question 2 — direct proportion: "Show that M = 28.35", then forward and inverse use (3 marks) - 2020 Exam 2 Module 4 Question 3 — R = 80n and C = 36n + 5000: "Sketch the monthly cost, C, of making n seat covers on the graph above", least number for a profit, a re-pricing question (4 marks) - 2022 Exam 2 Module 4 Question 1 — P = 130n − 1560: evaluate, sketch for 0 ≤ n ≤ 40, then "Complete this equation by filling in the boxes below. C = ___ × n + ___" (4 marks)

Piecewise, step and non-linear relations - 2015 Exam 2 Module 3 Question 4 — luggage cost: read an airport step graph, evaluate a two-branch online formula, "sketch a graph of the online cost ... Include the end points" (2 marks), then the weight at which the two costs are equal (5 marks overall) - 2018 Exam 2 Module 4 Question 3c — a four-branch fee relation: "The step graph below representing this relation is incomplete. Complete the step graph by sketching the missing information." - 2019 Exam 2 Module 4 Question 2 — a step graph of annual fee per member: smallest number of members, "Complete the inequality by writing the appropriate symbol and number in the box provided", sketch a linear proposal over the step graph, then list every membership number for which the two proposals agree (4 marks) - 2020 Exam 2 Module 4 Question 2c — inverse proportion F = k/s from two data points, evaluated at 80 km/h (1 mark) - 2020 Exam 2 Module 4 Question 3d — two-branch cost function, find m given a point on the second branch - 2022 Exam 2 Module 4 Question 2c–d — a two-branch bulk-discount total T, find p; then F = kx (a spring constant) used forwards and backwards

Linear programming - 2006 Exam 2 Module 3 Question 3 — dog washing and clipping: "Draw the line that represents 20x + 25y = 200 on the graph below"; write Inequality 4 from "the number of dogs clipped is at least twice the number of dogs washed"; "draw and clearly indicate the boundaries of the region represented by Inequalities 1 to 4"; write the objective P; find the optimal (x, y) and the maximum profit (8 marks) - 2008 Exam 2 Module 3 Question 3 — six inequalities: "Explain the meaning of Inequality 3 in terms of the context of this problem"; "draw and label the lines x = 120 and y = 1.5x"; "clearly shade the feasible region represented by Inequalities 1 to 6"; then two constrained-optimum parts (7 marks) - 2010 Exam 2 Module 3 Question 3 — "Explain the meaning of Inequality 1 in terms of the context of this problem"; state k; draw x = 30; shade; maximum weekly revenue; derive a new inequality 3x + y ≤ 150 from a verbal rule; write the new revenue equation; re-optimise (10 marks) - 2013 Exam 2 Module 3 Question 4 — write the coefficients a and b in ax + by ≤ 48; write inequality 4 from "at least two unpowered sites for every powered site"; "show the points that satisfy inequalities 1, 2, 3 and 4"; minimum number of sites; minimum cost; then a re-optimisation with an equal-numbers constraint (6 marks) - 2015 Exam 2 Module 3 Question 5 — "Describe Inequality 4 in terms of the lessons that Ben must attend"; "shade the region that contains the points that satisfy these inequalities"; maximum number of English lessons (3 marks) - 2016 Exam 2 Module 4 Question 3 — read Constraint 5 off a labelled boundary line; maximise P = 62x + 86y; then the inverse problem: given a maximum profit of $42 000 occurring at (400, 100), find m and n (5 marks) - 2018 Exam 2 Module 4 Question 4 — "mark with a cross (×) the five integer points that satisfy Inequalities 1 to 4"; maximum total cost; then a re-optimisation after two constraints change (3 marks) - 2019 Exam 2 Module 4 Question 3 — write Inequality 4 from a carrying-capacity rule; "mark clearly, with a circle, the remaining integer points that satisfy Inequalities 1 to 4"; cost for 60 members; minimum cost for 55 members; and a slope-threshold question: "If the increase in the cost of hiring each car is more than k dollars, then the maximum cost ... can only occur when using six cars and two minibuses. Determine the value of k" (5 marks) - 2020 Exam 2 Module 4 Question 4 — "Explain the meaning of Inequality 1 in the context of this problem"; maximum number of employees implied by a constraint; a conditional maximum given x = 20; "List the points within the feasible region that will result in a maximum profit for the day" (5 marks) - 2022 Exam 2 Module 4 Question 3 — minimum production from a constraint; conditional maximum at y = 15; maximum weekly profit; then "Below what value must this profit fall so that the maximum weekly profit will result only at the point (20, 28)" (4 marks)

5.4 Recurring VCAA wording (quoted verbatim)

• "The shaded region in the graph below represents the feasible region for a linear programming problem." — the standard Exam 1 stem (2008, 2012, 2013, 2015, 2016, 2017 Exam 1).
• "Explain the meaning of Inequality 1 in terms of the context of this problem." (Era A, 2008/2010) which becomes "Explain the meaning of Inequality 1 in the context of this problem." (Era B, 2020).
• "On the graph above, shade the region that contains the points that satisfy these inequalities." / "clearly shade the feasible region represented by Inequalities 1 to 6."
• "On the graph above, mark with a cross (×) the five integer points that satisfy Inequalities 1 to 4." — the Era B integer-lattice variant (2018, 2019).
• "Write down the inequality that represents Constraint 5." (2016 Exam 2 Module 4 Question 3b).
• "Find the maximum profit that the company can make from the sale of the hockey sticks." (2016) / "Calculate the maximum weekly profit." (2022).
• "Sketch this equation on the graph for Proposal 1, shown below." and "(Answer on the graph above.)" — the standing marker that the answer is a drawing.
• "Determine the equation of the line shown in the graph above." (2006 Exam 2 Module 3 Question 2a).
• "The step graph below representing this relation is incomplete. Complete the step graph by sketching the missing information." (2018 Exam 2 Module 4 Question 3c).

5.5 What the assessors said

2019 Exam 2 examination report, Module 4: - Question 1bi (show an average rate of change of −6): 36%. "Some responses gave a slope calculation leading to positive 6 and then described it as a decreasing trend. Some misread the scale on the vertical axis." - Question 2c (sketch a line over a step graph): 50%. "Many responses were successful by using a ruler, often writing the coordinates of the two endpoints as (0, 12.25) and (25, 6)." - Question 3b (mark the remaining integer points): 42%. "Many responses only identified two or three of the five required points." - Question 3e (the slope-threshold question): 7%. "Cost equation becomes C = (70 + k)x + 100y with a gradient of −(70 + k)/100. Will touch only (6, 2) if gradient < −1."

2022 Exam 2 examination report: "Students should bring a ruler to accurately draw straight lines, which are often required in both data analysis and graphs and relations." Module 4 Question 1c (sketch): 40%. "Generally, students who wrote down the coordinates of the endpoints placed their graphs the best." Question 3d (the sliding-line threshold): 12%.

2015 Exam 2 examination report, common errors list: "referring to the vertical axis rather than the horizontal axis (Module 3: Graphs and relations)" and "shading outside the required region instead of inside".

5.6 Verdict on current relevance

Bottom line: skip the Graphs and relations module. The only part worth borrowing is the handful of "find/interpret the gradient and intercept of a straight line, in context" parts — for example 2015 Exam 2 Module 3 Question 3b, 2018 Exam 2 Module 4 Question 2a, 2019 Exam 2 Module 4 Question 1bi — and even those are better practised on current Data analysis and Recursion questions, which use the current notation.

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6. Number patterns (and applications) — Module 1, 2006–2015

6.1 Years and numbering

Module 1: Number patterns on every Exam 1 and Exam 2 from 2006 to 2015 inclusive. It did not survive the 2016 restructure; its recursion content was promoted into the compulsory Core as "Recursion and financial modelling", which is exactly the area of study that exists today. It was consistently the least-chosen module (25–49% of students, §3).

Formula-sheet support in Era A: arithmetic series sum, geometric series sum, infinite geometric series — nothing else. There was no nth-term formula on the sheet.

6.2 Exam 1 question-type catalogue (9 MCQ)

Using 2014 Exam 1 Module 1 as the model year:

6.3 Exam 2 question-type catalogue (15 marks)

Almost every year follows the same three-beat shape: an arithmetic strand, a geometric strand, then a difference equation (linear recurrence) strand, all set in one context.

Arithmetic sequences - 2006 Exam 2 Module 1 Question 1 — 48 000 kg of fruit, 3000 kg picked daily: term, then "The number of kilograms of fruit, Fₙ, remaining ... can be written as Fₙ = 48 000 + d × n. The value of d is", then the number of days to finish (3 marks) - 2009 Exam 2 Module 1 Question 1a–c — 28, 29, 30 seats in successive rows: seats in row 10, number of rows given the last row has 70, and "Find the total number of seats in the first 20 rows" (3 marks) - 2010 Exam 2 Module 1 Question 1a — "$4.50, $6.20, $7.90 ... Show that the common difference for this sequence is $1.70"; a term; an inverse term ("One motorist paid $16.40 ... How many sections of road did this motorist travel along?"); a 15-term sum (2 marks); then "Write the values of m and k in the boxes below" for Aₙ₊₁ = mAₙ + k (7 marks total) - 2012 Exam 2 Module 1 Question 1 — 168, 162, 156: "Show that the common difference for this sequence is −6"; sixth term; a difference of two terms; sum of the first 18; and how many blocks remained (6 marks) - 2015 Exam 2 Module 1 Question 1 — "Write down a calculation that shows that the common difference for this sequence is 150"; week 5 weight; total over eight weeks; the first week the cumulative total exceeds 14 000 kg; then "Write down the rule for this difference equation in the box provided below. Cₙ₊₁ = ___, C₁ = 2000" (5 marks)

Geometric sequences - 2006 Exam 2 Module 1 Question 2 — 625, 500, 400 hours: "Show that the common ratio of this sequence is r = 0.8"; the fifth term; "Write an expression that gives the number of hours, Hₙ, the gardeners will work in the nth month"; the difference between the sixth and seventh months; the first month below 100 hours; and the total over the next nine months (7 marks) - 2009 Exam 2 Module 1 Question 1d–f — r = 1.01 revenue by row: terms, the total revenue from the first 30 rows, then a per-seat price requiring a combined arithmetic and geometric step (4 marks) - 2012 Exam 2 Module 1 Question 2 — r = 1.5 building approvals: a term; the first year exceeding 100; the sum of the first five years; the first year the cumulative total exceeds 1000; then "Write down the values of a, b and c" for tₙ₊₁ = a × tₙ + b, t₁ = c (6 marks) - 2010 Exam 2 Module 1 Question 2 — six sections summing to 100 km increasing 5% each: find the first section from the series sum (2 marks), then write the difference equation (1 mark) - 2015 Exam 2 Module 1 Question 2a–c — r = 1.6 whitefly counts: "use a cross to plot the number ... expected at the beginning of week 4"; the first week exceeding 500; and "What is the percentage increase ... from the beginning of any week to the beginning of the next week?"

Fibonacci-related sequences - 2013 Exam 2 Module 1 Question 1 — "The number of trees planted in successive rows of the orchard follows a Fibonacci-related sequence ... How many trees should be drawn in row 2? ... How many trees would be planted in the sixth row?" (2 marks) - 2014 Exam 1 Module 1 Question 7 — the algebraic version (see §6.2)

Difference equations (first-order linear recurrence) - 2006 Exam 2 Module 1 Question 3 — "The volume of water, Vₙ, in the tank on the morning of the nth day is modelled by the difference equation Vₙ₊₁ = rVₙ + d where V₁ = 45 000 litres. a. Find r and d." (2 marks); a specific term; the first day below 30 000; and "In the long term, how many litres of water will be in the tank each morning?" (1 mark) - 2009 Exam 2 Module 1 Question 2 — Rₙ₊₁ = 1.02Rₙ with R₆ = 2601 given: the percentage increase, then work backwards to R₄ (2 marks) - 2009 Exam 2 Module 1 Question 3 — Tₙ₊₁ = 0.8Tₙ + 1000, T₁ = 12 000: predict week 3; "Show that the sequence generated by this difference equation is not arithmetic"; the first week below 6000; and "What does the difference equation indicate about the long-term future of this variety concert? Justify your answer by showing appropriate working" (5 marks) - 2010 Exam 2 Module 1 Question 1b — Bₙ₊₁ = 0.9Bₙ + 3, B₁ = 5: "Explain the meaning of B₁ = 5 in terms of the context of this problem"; find B₃; "This difference equation indicates that there is a maximum charge ... What is this maximum charge?" (3 marks); then part c compares two pricing models (2 marks) - 2012 Exam 2 Module 1 Question 3 — Pₙ₊₁ = 0.96Pₙ + 500, P₁ = 50: a term; the first year exceeding 4000; and "what is the greatest possible population of the housing estate?" (3 marks) - 2015 Exam 2 Module 1 Question 2d — Wₙ₊₁ = 1.6Wₙ − k, W₃ = 128: "Find the value of k if the number of whiteflies per square metre is to remain constant"; evaluate for k = 50; then solve for k across two steps (4 marks) - 2015 Exam 2 Module 1 Question 3 — two coupled recurrences Gₙ₊₁ = 1.25Gₙ − m and Fₙ₊₁ = 0.65Fₙ + m: "Explain what m represents, referring to the difference equations above in your answer"; then find f so both populations stay constant (3 marks)

6.4 Recurring VCAA wording (quoted verbatim)

• "Show that the common difference for this sequence is −6." / "Write down a calculation that shows that the common difference for this sequence is 150." / "Show that the common ratio of this sequence is r = 0.8"
• "... is modelled by the difference equation Vₙ₊₁ = rVₙ + d where V₁ = 45 000 litres." — difference equation appears 64 times in the extracted Module 1 text. The word "recurrence" appears zero times.
• "In the long term, how many litres of water will be in the tank each morning?" / "what is the greatest possible population ...?" / "there is a maximum charge which motorists ... may pay" — three phrasings of the same steady-state idea.
• "Explain the meaning of B₁ = 5 in terms of the context of this problem."
• "Write down the rule for this difference equation in the box provided below. Cₙ₊₁ = ____ C₁ = 2000"
• "Write the values of m and k in the boxes below." / "Write down the values of a, b and c."
• "In which month will the gardeners first work less than 100 hours?" / "At the end of which year ... will the population ... exceed 4000 people?" — the standard first-exceeds/first-falls-below form.
• "How many hours, in total, will the gardeners work in the next nine months?" — the series-sum form.

6.5 What the assessors said

2015 Exam 2 examination report, Module 1: - Questions 1a–2c as a block: average 5.8 out of 8; 25% scored full marks. Question 2c (percentage increase for r = 1.6): "A common incorrect answer was 160%." - Questions 2di–3b as a block: average 1.7 out of 7; 42% scored zero. - Question 3b (the coupled-recurrence steady state): "This question was not answered well. Most students were unable to see the link between Gₙ, Gₙ₊₁ and 1200 to find the value of m that was needed to then find f." The published solution runs: constant G means Gₙ₊₁ = Gₙ = 1200, so 1200 = 1.25 × 1200 − m, m = 300; then f = 0.65f + 300 gives f = 857.

6.6 Verdict on current relevance

The recursion half of this module is the current Recursion and financial modelling area of study. The sequence-formula half is gone.

Two notation traps when reusing this module:

1. Indexing. Every Number patterns question starts at t₁ / V₁ / u₁. The current course starts at u₀ (2023 Exam 2: "V₀ = 60000, Vₙ₊₁ = 1.0015Vₙ − d"; 2025 Exam 2: "L₀ = 50000, Lₙ₊₁ = RLₙ − 75"). Off-by-one errors are guaranteed if this is not converted.
2. Vocabulary. VCAA said difference equation then and says recurrence relation now. The current formula sheet writes u₀ = a, uₙ₊₁ = Ruₙ + d; the old sheet had no recurrence formula at all.

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7. Business-related mathematics — Module 4, 2006–2015

7.1 Years and numbering

Module 4: Business-related mathematics on every Exam 1 and Exam 2 from 2006 to 2015. Like Number patterns, it was absorbed into the compulsory Core in 2016 — as the financial half of "Recursion and financial modelling". Chosen by 30–64% of students.

Formula-sheet support in Era A: simple interest I = PrT/100; compound interest A = PRⁿ, R = 1 + r/100; and the hire purchase conversion "effective rate of interest = 2n × flat rate / (n + 1)".

7.2 Exam 1 question-type catalogue (9 MCQ)

Using 2014 Exam 1 Module 4 as the model year:

7.3 Exam 2 question-type catalogue (15 marks)

Depreciation — three methods, usually compared - 2006 Exam 2 Module 4 Question 1 — flat rate 10% of the purchase price (annual amount, value after three years, the year the value reaches $12 000) and reducing balance V = 60 000 × 0.85ⁿ (percentage rate, value after three years, the year it first falls below $12 000), then "At the end of which year will the value of the machine first be less using flat rate depreciation than it will be using reducing balance depreciation?" (8 marks) - 2009 Exam 2 Module 4 Question 4 — flat rate at 12% p.a. versus reducing balance at 16% p.a. over four years, then which gives the greater depreciation (4 marks) - 2012 Exam 2 Module 4 Question 2 — unit cost at 22 cents per hour with 3800 hours of use per year; "Show that, in any one year, the flat rate method ... with a depreciation rate of 10% per annum will give the same annual depreciation as the unit cost method"; the write-off year; then reducing balance at 14% over ten years (4 marks) - 2013 Exam 2 Module 4 Question 1 — flat rate read off a graph: "Show that the bike depreciates in value by $1500 each year"; value after five years; then a unit cost equivalence at $0.25 per kilometre (4 marks) - 2015 Exam 2 Module 4 Question 2 — "Assuming the flat rate method of depreciation was used, show that the value of the sound system was depreciated by $325 each year"; years to reach $550; then a reducing balance rate recovered from two values five years apart (3 marks)

Simple and compound interest, and investments with regular deposits - 2006 Exam 2 Module 4 Question 3 — $7000 at 6.25% simple interest for eight years (2 marks); $10 000 at 6% compounding quarterly; $500 plus $200 monthly deposits at 6.5% compounding monthly (4 marks total) - 2009 Exam 2 Module 4 Question 3 — "Show that the interest rate per quarter is 1.1%"; value after three years; interest earned over six years (4 marks) - 2013 Exam 2 Module 4 Question 2 — $5000 at 4.8% p.a. monthly; then the same with $200 added monthly; then the total interest over 12 months (3 marks) - 2015 Exam 2 Module 4 Question 4 — $4000 at 3.6% p.a. monthly for six months; "The equation below can be used to determine the balance ... account balance = 2000 × (1 + 0.008) + 200. Show that the annual compounding rate of interest is 3.2%"; then the balance after five years of quarterly $200 additions (3 marks)

Loans (reducing balance) - 2006 Exam 2 Module 4 Question 4 — $20 000 at 10% p.a. monthly, 24 equal instalments, total interest (2 marks) - 2009 Exam 2 Module 4 Question 5 — $200 000 at 4.65% p.a. with $1500 monthly: principal outstanding after five years; total interest over five years; then a new repayment after the rate rises to 5.65% (3 marks) - 2012 Exam 2 Module 4 Question 3 — $40 000 at 7.8% p.a. monthly: the monthly payment; the number of months at $1000 per month; "Write down a calculation that shows that the balance of the loan account after the first 12 months will be $43 234"; then the interest-only monthly payment (4 marks) - 2013 Exam 2 Module 4 Question 4 — how much of $25 000 has been repaid after two years of a four-year quarterly loan (2 marks) - 2015 Exam 2 Module 4 Question 5 — $50 000 repaid at $485.60 per month for 12 years: recover the annual rate (2 d.p.); the principal repaid in the first year; then "Determine how much time Jane and Michael will save in repaying their loan" after a one-off $3500 payment (4 marks)

Perpetuities - 2012 Exam 2 Module 4 Question 4 — $80 000 returning $1260 per quarter: the annual rate; how much remains after 20 payments; then a finite drawdown reducing to $7000 after ten years (3 marks) - 2015 Exam 2 Module 4 Question 3 — "Determine the minimum amount they must invest in the perpetuity to fund the scholarship" (answer $12 500), then "For how many years will they be able to provide the scholarship?" (2 marks)

Hire purchase and flat-rate loans (no current analogue) - 2009 Exam 2 Module 4 Question 2 — credit card at 1.5% per month; then "Calculate the annual flat interest rate charged" from $6 interest per month on $250 - 2010 Exam 2 Module 4 Question 1 — "Determine the annual flat interest rate that is applied to this hire-purchase agreement" - 2013 Exam 2 Module 4 Question 3 — $7500 at a flat interest rate of 8% per annum over 24 instalments: the monthly instalment; "Find the effective rate of interest per annum charged on this hire-purchase agreement"; and "Explain why the effective interest rate per annum is higher than the flat interest rate per annum" (2 marks)

GST, discounts, deposits, inflation (no current analogue) - 2009 Exam 2 Module 4 Question 1 — a $120 discount off a $500 RRP, then "Find the discount as a percentage of the recommended retail price" - 2012 Exam 2 Module 4 Question 1 — a 15% deposit; instalment total and interest; then "The price, $8360, included 10% GST (Goods and Services Tax). Calculate the price of the equipment before the GST was added" - 2015 Exam 2 Module 4 Question 1 — "The $88 per hour includes a 10% goods and services tax (GST). Calculate the amount of GST included in the $88 hourly rate." then a 12.5% rate increase (3 marks) - 2006 Exam 2 Module 4 Question 2 — inflation at 2% per annum over eight years

7.4 Recurring VCAA wording (quoted verbatim)

• "Write your answer in dollars correct to the nearest cent." — 27 occurrences. The rounding instruction is never optional; see §7.5.
• "Use the flat rate depreciation method with a depreciation rate of 12% per annum to find the depreciated value of the lawn mowers after four years." (2009 Exam 2 Module 4 Question 4a)
• "Use the reducing balance depreciation method with a depreciation rate of 16% per annum to calculate the depreciated value ..." (2009 Exam 2 Module 4 Question 4b)
• "The value of the equipment will be depreciated using the unit cost method. The initial value of the equipment is $8360. It will depreciate by 22 cents per hour of use." (2012 Exam 2 Module 4 Question 2)
• "Interest on the unpaid balance is charged to the loan account monthly." / "The club will establish a reducing balance loan and pay interest monthly at the rate of 4.65% per annum."
• "Determine the monthly payment, correct to the nearest cent." / "Determine the total amount of interest that will be paid on this loan."
• "Arthur invested $80 000 in a perpetuity that returns $1260 per quarter." — perpetuity appears 20 times in the extracted Module 4 text.
• "Find the effective rate of interest per annum charged on this hire-purchase agreement." (2013 Exam 2 Module 4 Question 3b) — the sense of "effective rate" that no longer exists.
• "Calculate the price of the equipment before the GST was added." — GST appears 17 times in the extracted Module 4 text and zero times in any 2023–2026 General Mathematics paper.

Two words the module never used: annuity (0 occurrences in every 2006–2015 Exam 2) and amortisation (0 occurrences). Both are central to the current course.

7.5 What the assessors said

2015 Exam 2 examination report, Module 4: - Question 1a (GST inside $88): 42% scored full marks on the 1a–1c block. "A common incorrect answer was 10% of 88 = $8.80." - Question 2a (show the flat rate is $325 per year): "The 325 should not have been substituted into a calculation. It needed to be the result of a calculation." - Question 3b (how long will the perpetuity last): "Many students did not know that perpetuities pay out only the interest earned, while the principal remains unchanged. The most common incorrect answer was 12 500 / 460 ≈ 27 years." Correct answer: "It will last forever." - Question 4a: "$4072.54 ... Answers rounded to $4072.55 or $4072.50 were not accepted." Question 4c: "Answers of $6664.60 or $6664.65 were not accepted." - The report's list of common errors includes "using the compound formula for a flat rate question (Module 4: Business-related mathematics)".

2021 Exam 2 examination report (Core, but the same content): "the definition of a perpetuity is that its value does not change over time. This accessible question was incorrectly answered by many students."

7.6 Verdict on current relevance

This is the most reusable of the four retired modules. Roughly three-quarters of it is now compulsory content.

Two traps when reusing this module:

1. "Effective rate of interest" changed meaning. In 2006–2015 it converted a flat rate on a hire purchase into a comparable reducing-balance rate. From 2016 it means the annualised equivalent of a nominal compounding rate. A legacy answer key will teach the wrong formula.
2. The financial mathematics is no longer separable from recursion. Every legacy Business question can be solved with a finance solver alone. Current questions routinely demand the recurrence relation as well — writing it, reading R and d out of it, or showing recursive calculations step by step. Practising legacy items without also writing the recurrence leaves half the current skill untrained.

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8. Master summary table — legacy topic to current status

Status key: DEAD = not examinable in General Mathematics Units 3 & 4 (2023–2027). LIVE = still examinable, in the named current area of study. PARTIAL = the underlying skill survives but the legacy framing does not.

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9. Practical guidance for using legacy papers

1. Where the live material actually is. For Recursion and financial modelling, the richest legacy source is not Module 1 or Module 4 — it is the compulsory Core of the 2016–2022 papers, which was written against the same key knowledge as the current course and already uses recurrence notation, amortisation tables and the modern "effective rate" formula. Use 2006–2015 Modules 1 and 4 as a supplement, filtered by §6.6 and §7.6.
2. Mark weight is different. A legacy module was 15 marks (Era A) or 12 marks (Era B) of Exam 2. Current Recursion and financial modelling is 12 marks of Exam 2 and 8 of Exam 1. A whole legacy module is roughly one current content area.
3. Multiple choice has one fewer option now. Legacy MCQs offer A–E; current General Mathematics offers A–D (2023 onward). The extra distractor changes the guessing arithmetic and sometimes the intended misconception.
4. Index from zero. Convert every legacy t₁/V₁/u₁ to u₀ before checking an answer against a current-style solution.
5. Say "recurrence relation", not "difference equation". The 2024 Exam 2 report is explicit: "students need to be very clear on the key knowledge and key skills contained in the VCE Mathematics Study Design 2023–2027 for General Mathematics, and to use the formal terminology within the course."
6. Answers exist for everything. Every legacy question has a published examination report giving the mark distribution, the accepted answer and the common errors. These are the files named *_examrep*, *_assessrep* and *-report in the corpus.
7. Ignore the legacy formula sheet. It carries eight geometry formulas, two graph formulas, three series formulas and three interest formulas that are no longer provided. Working a legacy question with the legacy sheet builds a dependency the current exam will not honour.
8. The 2023 NHT Further Mathematics papers are the last ones ever written. After that the series is General Mathematics, and the module structure is gone.

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10. Sources

All paths are relative to corpus/text/.

Examination specifications and formula sheets - 2025-04_genmath-specs-w.txt — VCE General Mathematics (From 2023) examination specifications; the four content areas and their mark allocations - Documents_exams_mathematics_generalmaths1-formula-w.txt, ...generalmaths2-formula-w.txt — current formula sheet - Formula sheets embedded at the end of Documents_exams_mathematics_2012_2012furmath1-w.txt (Era A) and Documents_exams_mathematics_2022_2022furmath2-w.txt (Era B)

Era A papers (2006–2015) — Documents_exams_mathematics_2006furmath1-w, 2006furmath2-w, 2007furmath1, 2007furmath2, 2008furmath1-w, 2008furmath2-w, 2009furmath1-w, 2009furmath2-w, 2010furmath1-w, 2010furmath2-w, 2011furmath1-w, 2011furmath2-w, 2012_2012furmath1-w, 2012_2012furmath2-w, 2013_2013furmath1-w, 2013_2013furmath2-w, 2014_2014furmath1-w, 2014_2014furmath2-w, 2015_2015furmath1-w, 2015_2015furmath2-w

Era B papers (2016–2022, plus NHT to 2023) — 2016_2016furmath1-w through 2022_2022furmath2-w; NHT: 2017_nht_2017FM1/2-nht-w, 2018_nht_2018FM1/2-nht-w, 2019_NHT_2019FM1/2-nht-w, 2021_NHT_2021FM1/2-nht-w, 2022_NHT_2022furmath1/2-NHT-w, 2023_NHT_2023FM1/2-nht-w

Examination reports cited — furthermaths2_assessrep_06, further2_assessrep_07, further_maths2_assessrep_08, further2_assessrep_09, further2_assessrep_10, furthermaths2_assessrep_11, 2012_fm2_assessrep12, 2013_FM2_examrep13, 2014_FM2_examrep14, 2015_FM2_examrep15, 2016_FM2_examrep16, 2017_fm2_examrep17, 2018_FM2_examrep18, 2019_FM2_examrep19, 2020_2020furmaths2-exam-report, 2021_2021furthermath2-report, 2022_2022furmaths2-report, 2025-03_2024generalmaths2-report

Current General Mathematics papers used for the negative evidence — Documents_exams_mathematics_2023_2023genmath1-w, 2023_2023genmath2-w, 2024_2024GeneralMaths1-w, 2024_2024GeneralMaths2-w, 2024_NHT_2024GM1-nht-w, 2024_NHT_2024GM2-nht-w, 2025-11_2025-GeneralMaths1_0, 2025-11_2025-GeneralMaths2, 2026-05_2026-NHT-GeneralMaths1, 2026-06_2026-NHT-GeneralMaths2, genmath1-sample-w, genmath2-sample-w

Method note. Module sections were extracted programmatically from each paper by splitting on the Module N – <name> headings (truncating at the formula sheet), producing 245 per-module text files; question-type catalogues were then read directly from those extracts. "Zero hits" claims are literal case-insensitive searches across the thirteen current General Mathematics papers listed above. Two 2011 files and one 2017 NHT file contain a font-encoding artefact in the source PDF conversion (runs of text rendered as FRQWLQXHG-style mojibake); content for those was cross-checked against the corresponding examination reports rather than the papers.