Data analysis

VCE Further Mathematics (2006–2022) → VCE General Mathematics (2023–2026)

Source corpus: corpus/text\*.txt — every VCAA Further Maths / General Maths exam paper, examination report, assessment (marking) guide and specification document available, 2006–2026, including NHT (Northern Hemisphere Timetable) papers.

Every claim below is traceable to a named corpus file. Quotations are reproduced as they appear in the plain-text conversions (the conversions mangle some symbols: × often appears as � or is dropped, − may appear as –/-, and superscripts are flattened — e.g. r 2, km2, eggs/m2). Where a symbol was lost in conversion it is restored in square brackets.

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0. How Data Analysis is examined — structural context

0.1 Three distinct eras

Consequence for question design: Data analysis is the single largest content block in both exams — 40% of Exam 1 marks and 40% of Exam 2 marks under the current (2023–2027) study design.

0.2 Exam 2 Data-analysis question counts and mark profile (current era)

Individual parts are almost always 1 or 2 marks. Three-mark parts exist but are rare (e.g. 2016 Exam 2 Q3bi, 2017 NHT Exam 2 Q3b — both "find the least squares equation + round", 3 marks).

2025-04_General_Maths_Examination_2.txt (Chief Assessor Mark O'Connell's 2024 assessment PL presentation) states the marking model explicitly:

"Questions in 2024 were all worth one or two marks, and full marks were awarded for a clear correct answer that addressed all the requirements of a question regardless of working out shown. In two mark questions, sometimes a method mark was available. This was given where indicated on the Marking Guide for a major and relevant mathematical step that follows requirements and leads towards the solution. A third type of mark is the consequential or H mark. … A consequential mark will only be given if allowed for on a marking guide, and then only if the working out is shown."

Marking-guide symbols seen in 2025-11_2025-GeneralMaths2-assessment-guide.txt etc.: A1 = answer mark, M1 = method mark, H1 = consequential/hold mark.

0.3 Corpus caveats

• 2025-05_2025-NHT-generalmaths1.txt and 2025-05_2025-NHT-generalmaths2.txt are empty stubs (32 bytes) — the 2025 NHT papers themselves are not in the corpus, but the 2025 NHT report (2025-10_2025-NHT-general-maths2-report.txt) and assessment guide (2025-06_2025NHT-GeneralMath2-assessment-guide.txt) are.
• Documents_exams_mathematics_2024_2024GeneralMaths1-w.txt / ...2024GeneralMaths2-w.txt are also text-less (vector-only) PDFs; the 2024 content is recoverable from 2025-03_2024generalmaths1-report.txt, 2025-03_2024generalmaths2-report.txt and 2025-04_2024generalmathematics2-assessment-guide.txt.
• Documents_exams_mathematics_2011furmath1-w.txt / ...2011furmath2-w.txt have a broken text layer (question text renders as 7KHVWHPSORWLQ)LJXUH…). The 2011 content is recoverable from Documents_exams_mathematics_furthermaths2_assessrep_11.txt and Documents_exams_mathematics_further1_assessrep_11.txt.
• Documents_exams_mathematics_genmath1-sample-w.txt / genmath2-sample-w.txt are the March 2023 VCAA sample General Maths papers. The sample Exam 2 Data-analysis section is a near-verbatim reuse of 2019 NHT Further Maths Exam 2 (same mammal sleep-time dataset, same question wording). Anything "new" in the sample is therefore actually 2019 NHT wording.

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1. COMPLETE QUESTION-TYPE CATALOGUE

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1.1 Types of data / variable classification

What it looks like. Either (a) a named-variable list or data table followed by "how many … are categorical / numerical / nominal / ordinal variables?", or (b) a pure MC item naming two variables with their category labels and asking for their joint classification. VCAA deliberately picks variables where the category labels look numeric (postcode, number of moths in bands, day number, bag size).

Marks. 1 mark. Where. Both exams; near-universal — appears in essentially every Exam 2 DA section from 2013 onwards as the opening 1-marker, and 1–2 times per Exam 1.

Real examples

• 2018 Exam 2 Q1a & Q1b (Documents_exams_mathematics_2018_2018furmath2-w.txt, lines 137–142):

  "The four variables in this data set are: • city – name of city • congestion level – traffic congestion level (high, medium, low) • size – size of city (large, small) • increase in travel time – increase in travel time due to traffic congestion (minutes per day).
  a. How many variables in this data set are categorical variables? … b. How many variables in this data set are ordinal variables?" Report answers (...2018_FM2_examrep18.txt): 1a = "3 (city, congestion level, size)"; 1b = "2 (congestion level, size)". Comment: "The definition of a categorical variable was not always understood."

• 2016 Exam 1 Q2 (Documents_exams_mathematics_2016_2016furmath1-w.txt, line 94):

  "The variables blood pressure (low, normal, high) and age (under 50 years, 50 years or over) are A. both nominal variables. B. both ordinal variables. C. a nominal variable and an ordinal variable respectively. …" Report (...2016_FM1_examrep16.txt): "Both variables are ordinal. However, many students incorrectly identified the variable age (under 50 years, 50 years or over) as nominal. The variable age … is ordinal because the process of allocating each of the people to one of these two categories 'under 50 years' or '50 years or over' orders the group of people by age."

• 2019 Exam 2 Q1a (...2019furmath2-w.txt line 108): "Which of the two variables in this data set is an ordinal variable?" — variables are day number (1–15) and minimum temperature. Report answer: "The answer is day number." (83% correct; "A small number of students answered 'neither'.")

• 2025 Exam 2 Q1b (2025-11_2025-GeneralMaths2.txt line 115): "State whether the variable type is numerical, nominal or ordinal." (type = apartment/house). Answer: Nominal (77%).

• 2026 NHT Exam 2 Q1a (2026-06_2026-NHT-GeneralMaths2.txt): "Is the variable mammal an ordinal variable or a nominal variable?" Guide answer: Nominal.

• 2021 Exam 2 Q1a: "Write down the number of numerical variables in Table 1." Answer 3. Report: "A common error was counting the number of values (45) instead of variables."

• 2022 Exam 2 Q3ai: "the number of numerical variables in Table 1" — answer 5. Report: "6 was a common error by students who had chosen 'day number' as a numerical variable." (Note this directly contradicts nothing — day number is ordinal/categorical here.)

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1.2 Frequency tables, percentage frequency, bar charts, segmented bar charts

What it looks like. (i) Complete a frequency and/or percentage column of a table from raw data; (ii) construct a percentage segmented bar chart on a supplied template with a key; (iii) read a value or difference off a segmented bar chart; (iv) MC: "which display is most appropriate for these data?"

Marks. 1 mark per table completion, 1 mark for the chart construction (rarely 2). Where. Both.

Real examples

• 2023 Exam 2 Q2a (...2023genmath2-w.txt): raw list of 20 oyster sizes → "i. Use the data above to complete the following frequency table." (Number / Percentage (%) columns) 1 mark; "ii. Use the percentages in Table 2 to construct a percentage segmented bar chart below. A key has been provided." 1 mark.
• 2018 NHT Exam 2 Q4b (...2018_nht_2018FM2-nht-w.txt line 186): "Use the percentages in Table 1 to construct a percentaged segmented bar chart. A template is provided below to assist you in completing this task. Use the key to indicate the segment of your bar chart that corresponds to each beak size." Report: "The three sections could be in any order."
• 2008 Exam 2 Q1a (...2008furmath2-w.txt): 25 raw responses → "complete the following frequency table" (walked / sat or stood / ran / Total 25), then "determine the percentage of Year 8 girls who ran".
• 2025 Exam 2 Q1d (2025-11_2025-GeneralMaths2.txt): complete a two-column percentage table (House % / Apartment %) from raw data; marking guide: "Must have ALL five numbers correct" (2025-11_2025-GeneralMaths2-assessment-guide.txt).
• 2025 Exam 1 Q8 (2025-11_2025-GeneralMaths1_0.txt): "Which one of the following is the most appropriate way to graphically display the data shown in the table above? A. a histogram B. a back-to-back stem plot C. parallel boxplots D. a segmented bar chart". Report comment: "Each bar represents a gender with the segments being number/percentage of respondents for each colour."
• 2026 NHT Exam 1 Q1: percentage segmented bar chart of 300 days' weather in 4 categories → "The number of days when the weather was rainy is …"

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1.3 Histograms, stem plots, dot plots — reading, constructing, describing shape

What it looks like. 1. Reading: count in an interval, number/percentage above or below a value, modal interval/mode, median, range, IQR. 2. Constructing a histogram on a supplied grid with a stated interval width. 3. Completing a stem plot from extra data values. 4. Describing the shape: "Describe the shape of the distribution" (Exam 2) / "The shape of this distribution is best described as …" (Exam 1).

Marks. Reading = 1 mark each; histogram construction = 2 marks; stem-plot completion = 1 mark; shape = 1 mark.

Real examples

• 2016 Exam 2 Q1d (...2016furmath2-w.txt line 97): "Use the grid below to construct a histogram that displays the distribution of daily rainfall for the month of September. Use interval widths of two with the first interval starting at 0." (2 marks). Report: "Many students inappropriately drew columns with interval widths of only one."
• 2022 Exam 2 Q1c: "On the grid below, use the data from the stem plot on page 2 to construct a histogram that displays the distribution of wind speed for November 2021. Use class intervals of widths of five, starting at 15 km/h." (2 marks). Report: "Some students missed one column. The outlier was often not placed correctly."
• 2019 Exam 2 Q1b: "Complete the stem plot above by adding the data values for days 11 to 15." (1 mark). Report: "Some students entered only the values for day 11 and day 15 rather than the five days from day 11 to day 15."
• 2020 Exam 2 Q1a (...2020furmath2-w.txt line 91): "a. Describe the shape of the distribution." (1 mark). Report answer: "Positively skewed. Most students recognised the distribution was positively skewed. It was acceptable to add that there were no outliers."
• 2018 Exam 2 Q1f: "Describe the shape of the distribution of the increase in travel time for the 23 cities." Answer: "Positively skewed". Report: "some students went on to comment on the centre and spread, which was not required and made it difficult to determine if the student understood which had been asked for. The mark could not be awarded in this case."
• 2018 NHT Exam 2 Q3a: "Describe the shape of the distribution displayed in Histogram 1. Note the number of possible outliers, if any." Answer: "Positively skewed with 3 (or at least 3) possible outliers".
• 2023 Exam 1 Q2: "The shape of this distribution is best described as A. positively skewed with one or more possible outliers. B. positively skewed with no outliers. C. approximately symmetric with one or more possible outliers. D. approximately symmetric with no outliers. E. negatively skewed with one or more possible outliers."
• 2026 NHT Exam 2 Q1c: "Describe the shape of this distribution." Guide: "Positively skewed (with one outlier)".

Related sub-type — mean vs median choice: - 2026 NHT Exam 2 Q1d (2026-06_2026-NHT-GeneralMaths2.txt): "The mean body weight is 67 kg, rounded to the nearest whole number. Explain why the median is a better measure of the centre of the body weight data than the mean." Guide answer: "Due to data being skewed and/or the presence of an outlier. Must reference skew or outlier" (2026-06_2026-NHT-GeneralMaths2-assessment-guide.txt). - 2010 Exam 2 Q1d: answer "The distribution is approximately symmetric." Report: "Many students simply defined median and mean without reference to the given data. Some described the data in vague terms such as 'evenly distributed', while many referred to the absence of outliers. Neither of these terms is sufficient or specific enough … Several explanations suggested that the data was 'symmetrically skewed'; a skewed distribution is not symmetrical."

Sub-type — log₁₀-scaled histograms (post-2016, very common and consistently the hardest DA MC item): - 2019 Exam 1 Q3: "The histogram below shows the population size for these 48 countries plotted on a log₁₀ scale. Based on this histogram, the number of countries with a population size that is less than 100 000 people is …" - 2023 Exam 1 Q6: log₁₀(price) histogram → "How many of the six car prices listed above are in the modal class interval?" - 2025 Exam 1 Q4: log₁₀(population density) histogram → "In which labelled column does the value of log₁₀(population density) for Singapore lie?" Report working: "Population density = 6 028 460 ÷ 720 = 8372.8611; log₁₀(8372.8611) = 3.92287 which sits between 3.5 and 4.0". - 2026 NHT Exam 1 Q4: log₁₀(annual income) histogram → "The third quartile of the annual income data, in dollars, could be …" - 2016 Exam 1 Q7 report: "This question required students to recognise that, on a log₁₀ scale, 1 is plotted as 0, because, by definition, 1 = 10⁰ means that log₁₀(1) = 0."

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1.4 Summary statistics: mean, median, mode, range, IQR, standard deviation, quartiles, five-number summary

What it looks like. "For these 12 men, determine i. their median age … ii. the mean of their body density"; "Complete the five-number summary"; "Determine the mean and standard deviation … Round your answers to one decimal place"; "Write down the modal wingspan"; percentage-above/below calculations.

Marks. 1 mark each part (a five-number-summary completion is often 2 marks).

Real examples

• 2020 Exam 2 Q4a: "For these 12 men, determine i. their median age, in years (1 mark) ii. the mean of their body density, in kilograms per litre (1 mark)." Answers 24 and 1.065. Report: "Some students gave a rounded value when it was not required."
• 2021 Exam 2 Q1b: "Complete Table 2 below by calculating the mean height jumped for the high jump, in metres, by the 15 athletes." Answer 1.81.
• 2017 Exam 2 Q2c: "Use the information in the back-to-back stem plot to complete the table below" (minimum, Q1, median, Q3, maximum for two groups) — 2 marks.
• 2026 NHT Exam 2 Q1b: "Complete the five-number summary in the table below for the variable body weight, in kilograms, by writing in the values for the minimum and the median." (2 marks, "1 mark for each correct").
• 2025 Exam 2 Q1ci: "Complete the table below by finding the standard deviation, to the nearest whole number, for the sale price of apartments in the sample." Answer $346 466. Report: "Students needed to enter the data carefully into their calculator to avoid error."
• 2023 NHT Exam 2 Q1b: "Determine the mean and standard deviation of the foot length of the 10 students. Round your answers to one decimal place."
• 2020 Exam 2 Q1b: "Determine the median BMI for this group of men." Answer 24.55. Report: "A considerable number of students chose 24.5 or 24.6 instead of averaging these two values."
• Exam 1 variants: 2019 Exam 1 Q4/Q5 (range and IQR from a stem plot); 2026 NHT Exam 1 Q3 ("The person with a shoe size of 13 is removed from the data set. For the variable shoe size, this would cause A. the mean to increase and the standard deviation to increase…").

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1.5 Boxplots — construction, fences, outliers

What it looks like. 1. Construct a boxplot from a five-number summary or from a dot/stem plot, "showing any outliers if appropriate". 2. Determine the value of the upper/lower fence. 3. Show that / explain why a given value is (or is not) an outlier — the single most repeated "justify" question in the topic. 4. Read percentages off a boxplot (25%/50%/75% questions). 5. Explain a missing whisker.

Marks. Construction 1–2; fence 1; outlier justification 2.

Real examples

• 2020 Exam 2 Q2c: "Use the five-number summary to construct a boxplot, showing any outliers if appropriate, on the grid below." (2 marks). Report: "Many drew a boxplot from the five-number summary without consideration of outliers. Those who found the two outliers often extended the whiskers to the lower and upper fence values rather than to the second-lowest and second-highest values. Lower and upper fences are not part of the data set and therefore should not be plotted on a box plot."
• 2017 Exam 2 Q2d: "Show that the moth captured in the forest that had a wingspan of 52 mm is an outlier." (2 marks). Report: "Upper fence = 32 + 1.5 × 12 = 50 / 52 > 50, therefore outlier. … A concluding statement that clearly showed that the student understood why 52 was an outlier given that the upper fence was 50 was required."
• 2022 Exam 2 Q1b: "The wind speeds for November are to be used to construct a boxplot. Show that the wind speeds of 59 km/h and 70 km/h would appear as outliers in this boxplot." (2 marks). Answer: "Wind speeds of 59 and 70 are outliers as they are greater than the upper fence of 54.5."
• 2018 Exam 2 Q1g: "The data value 52 is below the upper fence and is not an outlier. Determine the value of the upper fence." Answer 52.5. Report: "some students added the relationship between the data value and the upper fence, which was not part of this question."
• 2024 Exam 2 Q2c.i / Q2c.ii (2025-03_2024generalmaths2-report.txt): show-that both fences, then "explain why there are no outliers". Guide (2025-04_2024generalmathematics2-assessment-guide.txt): "SHOW THAT question — MUST see BOTH fence calculations*"; model: "The minimum value is 1.67 and the maximum value is 2.06. Both these values lie between the lower fence and upper fence so there are NO outliers.**"
• 2025 Exam 2 Q2b: "Calculate the upper fence for the sale price data in the boxplot." Answer: 900 000 + 1.5 × (900 000 − 600 000) = $1 350 000.
• 2026 NHT Exam 2 Q1e: "The body weight of the okapi is removed… Explain whether or not the typical body weight value of the new mammal is an outlier. Include a relevant calculation in your answer." Guide: "Upper fence = 100 + 1.5 × (100 − 4.3) = 243.55; As 240 < 243.55, it is not an outlier — Correct calculation for UF / Correct statement based on their calculated UF value (M1H1)".
• 2021 Exam 2 Q1e: "Explain why the boxplot has no whisker at its upper end." Answer: "Maximum value = Q3". Report: "Many responses mentioned that the maximum was 1.87 without indicating this was also Q3."
• 2024 Exam 2 Q2b: "determine the smallest possible number of values below the lower quartile" — answer 1; only 3% correct. Report: "Students did not recognise that only 1 value is needed to extend the whisker beyond the IQR."
• Exam 1 fence items: 2025 Exam 1 Q6 ("How many outliers would be displayed at the lower end of a boxplot…"); 2024 Exam 1 Q6 ("IQR = 48 − 5 = 43, Upper fence = 48 + 1.5 × 43 = 112.5; The smallest discrete value above 112.5 is 113"); 2014 Exam 1 Q6 (match boxplot to dot plot using the upper fence).

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1.6 The 68–95–99.7% rule and standardised z-scores

What it looks like. 1. Forward: given µ and σ, find a percentage or an expected number of observations above/below/between values. 2. z-score: "Calculate [name]'s standardised score (z)". 3. Reverse (very common since 2017): given two percentile statements, "use the 68–95–99.7% rule to determine the mean and standard deviation". 4. Expected vs actual comparison.

Marks. 1 mark each; the reverse mean-and-SD question is 2 marks.

Real examples

• 2017 Exam 2 Q1b: "In a large population of moths, the number of eggs per cluster is approximately normally distributed with a mean of 165 eggs and a standard deviation of 25 eggs. Using the 68–95–99.7% rule, determine i. the percentage of clusters expected to contain more than 140 eggs ii. the number of clusters expected to have less than 215 eggs in a sample of 1000 clusters." Report: "Many students overlooked the requirement to convert from percentage to quantity and gave an answer of 97.5%."
• 2023 Exam 2 Q1e (reverse): "Measurements made on recently harvested oysters showed that: • 97.5% of the electronic images contain less than 4.6 megapixels • 84% of the electronic images contain more than 4.3 megapixels. Use the 68–95–99.7% rule to determine, in megapixels, the mean and standard deviation of this normal distribution." (2 marks)
• 2024 NHT Exam 2 Q3: "• 99.85% of the time differences are more than 4.88 hours • 16% of the time differences are less than 5.76 hours. Use the 68-95-99.7% rule to determine the mean and standard deviation for this normal distribution." Answer: Mean = 6.2, SD = 0.44.
• 2025 Exam 2 Q3: "The sale prices … are normally distributed with a mean of $1 400 000. A home … that sold for $952 000 has a standardised score of z = −1.60. Using the 68–95–99.7% rule, calculate the percentage of homes sold in this suburb with a sale price between $560 000 and $1 680 000." Answer 83.85% — see §2.16 for the rounding enforcement on this item.
• 2021 Exam 2 Q1c/Q1d: "Calculate Jamilia's standardised score (z). Round your answer to one decimal place." / "Chara's jump … would give her a standardised score of z = −1.0. Use the 68–95–99.7% rule to calculate the percentage of athletes who would be expected to jump higher than Chara." Answer 84%; "The most common incorrect answer was 16%."
• 2020 Exam 2 Q2bi/bii: "i. How many of these 250 men are expected to have a neck size that is more than three standard deviations above or below the mean? … ii. How many of these 250 men actually have a neck size that is more than three standard deviations above or below the mean?"
• Exam 1: 2019 Exam 1 Q6/Q7; 2023 Exam 1 Q4 & Q5; 2025 Exam 1 Q5 (reverse mean/SD); 2026 NHT Exam 1 Q6 & Q7.

2025-04_General_Maths_Examination_2.txt: "Note that units should not be included with z-scores."

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1.7 Two-way frequency tables, percentaged tables, and association between two categorical variables

What it looks like. 1. Complete a two-way frequency table from raw data or a data table. 2. Calculate a conditional percentage ("of the small cities, what percentage…"). 3. The association question — "Does the information in the table support the contention that X is associated with Y? Justify your answer by quoting appropriate percentages." 4. MC: identify which pairing of variables is suitable for a two-way table.

Marks. Table completion 1–2; percentage 1; association justification 2 marks (1 for the conclusion + change statement, 1 for the correctly quoted percentages).

Real examples

• 2018 Exam 2 Q1d/Q1e: "Use the data in Table 1 to complete the following two-way frequency table, Table 2." (2 marks) / "What percentage of the small cities have a high level of traffic congestion?" Answer 25%. Report: "some students gave 17% by taking the percentage of all 23 cities."
• 2019 NHT Exam 2 Q5a/Q5b (...2019_NHT_2019FM2-nht-w.txt): "Use this data to complete the two-way frequency table below." … "ii. Of those mammals that had a medium likelihood of attack, what percentage also had a low exposure to attack during sleep?" … "iii. Does the information in the table above support the contention that likelihood of attack is associated with exposure to attack during sleep? Justify your answer by quoting appropriate percentages. It is sufficient to consider only one category of likelihood of attack when justifying your answer." (2 marks)
• 2023 Exam 2 Q2b.ii: "The farmer believes that farm A has a greater capacity to grow larger oysters than farm B. Does the information in Table 3 support the farmer's belief? Explain your conclusion by comparing the values of two appropriate percentages. Round these percentages to the nearest whole number." (2 marks)
• 2024 NHT Exam 2 Q2b: "Does the data in Table 4 support the contention that the occurrence of the LLT is associated with the appearance of the new moon? Explain your conclusion by comparing the values of appropriate percentages." (2 marks). Report model: "Yes, as the percentages differ from 'before' to 'on' to 'after'. The LLT occurred after the New Moon on 75% of the days compared to 8.3% on the New moon and 16.7% before the New moon."
• 2025 NHT Exam 2 Q3a/Q3b: complete a percentaged table, then justify. Guide (2025-06_2025NHT-GeneralMath2-assessment-guide.txt): "YES. The percentage of taller daughters with no brothers (62.5%) was greater than the percentage of taller daughters with one or more brothers (39.6%) — Yes or statement of affirmation and mention difference/comparison (A1); Correct percentages of taller daughters for both situations (H1)".
• 2011 Exam 2 Q2b (from ...furthermaths2_assessrep_11.txt): "Does the information in Table 1 support the opinion that, for the years 1986, 1996 and 2006, the age of women at first marriage was associated with year of marriage? Justify your answer by quoting appropriate percentages. It is sufficient to consider one age group only when justifying your answer." Report model: "The data … does support the opinion that age at first marriage is associated with the year of marriage. For example, of all first marriages, the percentage of women aged 25–29 years increased from 23.4% (1986) to 31.7% (1996) to 34.5% (2006)."
• 2014 Exam 2 Q1c — the negative version: "From the graph above, it appears that there is no association between the percentage of people in the 15–64 age group and the country in which they live. Explain why, quoting appropriate percentages to support your explanation." Report model: "All three countries have approximately the same percentage: 67%, 64% and 64%."
• Exam 1: 2019 Exam 1 Q8 — "Percy conducted a survey … He constructed a two-way frequency table involving two variables. One of the variables was attitude towards shorter working days (for, against). The other variable could have been A. age (in years). B. sex (male, female). …" Report: "Students needed to recognise that for a two-way frequency table to be used, both variables had to be categorical variables."

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1.8 Percentaged segmented bar chart as an association tool

Marks. 2 marks in Exam 2 for the justification; 1 mark in Exam 1.

• 2008 Exam 2 Q2: "Does the percentage segmented bar chart support the opinion that, for these girls, the lunch time activity (walked, sat or stood, ran) undertaken is associated with year level? Justify your answer by quoting appropriate percentages." (2 marks) — the earliest full instance of the template; see §2.6 for the model answer.
• 2021 NHT Exam 2 Q1d.ii: "Does the percentaged segmented bar chart support the contention that, for these participants, the event chosen (12 km walk, 6 km walk, 12 km run, 6 km run) is associated with gender? Justify your answer by quoting appropriate percentages."
• 2018 NHT Exam 2 Q4c: "Does the information provided above support the contention that beak size is associated with sex? Justify your answer by quoting appropriate percentages. It is sufficient to consider one beak size only when justifying your answer."
• Exam 1 MC version (2017 Q6, 2021 Q2 — near-identical stems):

  2021 Exam 1 Q2: "The data displayed in the percentaged segmented bar chart supports the contention that there is an association between preferred travel destination and age because A. more visitors favour international travel. B. 35% of visitors under 55 years favour international travel. … D. 65% of visitors under 55 years favour domestic travel while 45% of visitors 55 years and over favour domestic travel."
  2017 Exam 1 Q6: same stem; correct option E: "20% of sugar traps contained more than 500 moths while 10% of light traps contained more than 500 moths." The correct option is always the one that compares the same category across two different groups.

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1.9 Parallel boxplots / back-to-back stem plots — comparing distributions

What it looks like. A numerical variable displayed against a categorical variable. Reading questions (IQR, median difference, counts) plus the flagship 2-mark "is there an association / support the contention" question requiring a named statistic with values quoted.

Marks. Reading 1 mark; the association question 2 marks (1 = statement that the statistic changes/differs; 1 = correct values quoted for all groups).

Real examples

• 2019 Exam 2 Q3: "Explain why the information given above supports the contention that minimum daily temperature is associated with the month. Refer to the values of an appropriate statistic in your response." (2 marks; only 36% got full marks)
• 2020 Exam 2 Q3d: "Do the boxplots support the contention that BMI is associated with neck size? Refer to the values of an appropriate statistic in your response." (2 marks)
• 2022 Exam 2 Q2b: "Do the boxplots support the contention that there is an association between relative humidity and time of day? Refer to the values of an appropriate statistic in your answer." (2 marks)
• 2017 Exam 2 Q2e: "The back-to-back stem plot suggests that wingspan is associated with place of capture. Explain why, quoting the values of an appropriate statistic." (2 marks)
• 2017 NHT Exam 2 Q1d: "The parallel boxplots suggest that the amount of energy generated is associated with the month of the year. Explain why, quoting the values of an appropriate statistic." (2 marks)
• 2016 Exam 2 Q2biii: "Using the information from the boxplots, explain why the maximum daily temperature is associated with the month of the year. Quote the values of appropriate statistics in your response."
• 2023 NHT Exam 2 Q2c: "Does the information in the back-to-back stem plot support the contention that, at the same age, boys tend to have wider feet than girls? Refer to the values of an appropriate statistic in your response."
• 2015 Exam 2 Q2b: "Explain why life expectancy for these countries is associated with the year. Refer to specific statistical values in your answer."
• 2008 Exam 2 Q3b: "The three parallel box plots suggest that arm span and year level are associated. Explain why."
• 2006 Exam 2 Q1f: "The three parallel boxplots suggest that height and age (18 months, 27 months, 36 months) are positively related. Explain why, giving reference to an appropriate statistic."
• Comparing spread variant — 2022 Exam 2 Q2ai: "Determine whether the relative humidity in November is more variable at 9 am or 3 pm. Give the approximate values of both the interquartile ranges in your answer."
• Comparing spread variant — 2025 Exam 2 Q1c.ii: "Using the information in Table 2, comment on the relative spread in the distribution of the sale prices of houses compared with apartments in this sample."

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1.10 Scatterplots — describing direction, form, strength

What it looks like. "Describe the association between A and B in terms of strength, direction and form" (3-element version, pre-2021 and 2023) or "in terms of strength and direction" (2-element version, 2020–2025). Newer papers supply a labelled answer table so students cannot add extra elements.

Marks. 1 mark (2 marks when a table with two rows is supplied, e.g. 2025 Q4e).

Real examples

• 2016 Exam 2 Q3a: "Use the scatterplot to describe the association between apparent temperature and actual temperature in terms of strength, direction and form." Answer: "Strong, linear, positive".
• 2023 Exam 2 Q3c: "Describe the association between average monthly ice cream consumption and average monthly temperature in terms of strength, direction and form." — with pre-printed lines strength / direction / form.
• 2022 Exam 2 Q4b: "Describe the association between relative humidity and temperature in terms of strength and direction." Answer: "Strong, negative".
• 2025 Exam 2 Q4e: "Describe the linear association between sale price and distance from city centre in terms of its strength and direction. Answer in the table below." (2 marks) — table rows strength / direction; answers weak / negative.
• 2024 NHT Exam 2 Q4c: "Describe the association between HHT and LLT in terms of form and direction." (table rows form / direction) — answers linear / negative.
• 2020 Exam 2 Q6b: "Describe this association in terms of strength and direction." Answer: "Strong negative".
• 2014 Exam 2 Q4a: "…in terms of strength, direction and form." Answer: "Weak, negative, linear" (only 30% correct).
• 2007 Exam 2 Q3e: "…in terms of strength, direction and form." Answer: "Strong, positive and linear".

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1.11 Pearson's r and the coefficient of determination r²

What it looks like. 1. Calculate r from raw data ("Round your answer to three decimal places"). 2. Convert between r and r² (both directions) — the sign trap. 3. Calculate r or the slope from summary statistics via b = r·s_y/s_x. 4. Calculate r² as a percentage. 5. Interpret r² in words. 6. "What percentage of the variation … is not explained…?" 7. Compare two associations by r or r².

Marks. 1 mark each; 2 marks when derived from summary statistics.

Real examples

• 2025 Exam 2 Q4b: "Calculate the value of the correlation coefficient r. Round your answer to three decimal places." Answer −0.284. Only 21% correct — see §3.
• 2021 Exam 2 Q2b: "The equation of the least squares line is time800 = 0.03931 + 5.2756 × time200. Use this information to calculate the coefficient of determination as a percentage. Round your answer to the nearest percentage." (2 marks) Answer 38%.
• 2022 Exam 2 Q3c: "Calculate the coefficient of determination for the association between the daily maximum temperature and the daily minimum temperature. Write down its value as a percentage, rounded to one decimal place." Answer 61.1%. Report: "0.6 was a common incorrect response."
• 2017 NHT Exam 2 Q2a.ii and 2023 NHT Exam 2 Q4f: "What percentage of the variation in foot width is NOT explained by the variation in foot length?" Answer 58.9%.
• 2019 Exam 2 Q5e.i: "Use the equation of the least squares line and the information in Table 4 to show that the correlation coefficient for this data, rounded to three decimal places, is r = 0.966."
• 2025 NHT Exam 2 Q4g: "Father's height as Coefficient of determination is higher: 14% > 9.5% or Correlation coefficient is higher: 0.3744 > 0.3082" — a "which is the better predictor" comparison.
• Exam 1: 2019 Exam 1 Q10 ("The coefficient of determination was calculated to be 0.893743. The value of the correlation coefficient, rounded to three decimal places, is …" — answer −0.945); 2021 Exam 1 Q14 ("percentage of variation not explained"); 2024 NHT Exam 1 Q12 (rank three coefficients of determination).

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1.12 Least squares regression: finding, drawing, interpreting, predicting

This is the densest sub-topic. Six distinct question types:

(a) Determine the equation from raw data, writing intercept and slope in boxes, with a rounding instruction. 2 marks (occasionally 3).

2019 Exam 2 Q4b: "Determine the values of the intercept and the slope of this least squares line. Round both values to three significant figures and write them in the appropriate boxes provided. humidity 3 pm = ▢ + ▢ × humidity 9 am"
2022 Exam 2 Q3b: "With unrounded values for the intercept and slope, the equation of the least squares line is maximum temperature = 9.235946… + 1.002493… × minimum temperature. Round the intercept and slope to four significant figures. Write your answers in the boxes provided."
2023 Exam 2 Q1d: "…determine the equation of this least squares line. Use the template below to write your answer. Round the values of the intercept and slope to four significant figures."
2025 Exam 2 Q5a: "Use the data in the table above to find the equation of the least squares line. Write your answers in the boxes below, rounding both values to four significant figures."
2026 NHT Exam 2 Q2a: "Round the numbers representing the intercept and slope to three significant figures."

(b) Name the explanatory / response variable. 1 mark. Appears nearly every year.

2019 Exam 2 Q4a: "Name the explanatory variable." | 2018 Exam 2 Q2b: "Name the response variable in this equation." | 2022 Exam 2 Q4a | 2023 Exam 2 Q3c.i | 2025 Exam 2 Q4a | 2026 NHT Exam 2 Q3a | 2020 Exam 2 Q4bi.

(c) Draw the least squares line on a scatterplot / time series plot. 1 mark. Requires calculating two points and a ruler.

2020 Exam 2 Q5a; 2022 NHT Exam 2 Q3a; 2023 Exam 2 Q3a; 2023 NHT Exam 2 Q4a; 2024 NHT Exam 2 Q4a; 2026 NHT Exam 2 Q3b; 2017 Exam 2 Q3bi; 2014 Exam 2 Q2b; 2009 Exam 2 Q3a.
Marking guides specify tolerance in terms of edge intercepts: 2024 guide — "Edge intercepts. left side: >1.930, <1.940; right side: >2.08, ≤2.090. Line must cover the range of Wgold values from 1.92 to 2.06 and extrapolate to correct edge intercepts."

(d) Use the equation to predict. 1 mark, usually with rounding.

2019 Exam 2 Q5b: "Use the equation of the least squares line to predict the atmospheric pressure at 3 pm when the atmospheric pressure at 9 am is 1025 hPa. Round your answer to the nearest whole number."
2023 Exam 2 Q3e: "Use the equation of the least squares line to predict the average monthly ice cream consumption … when the monthly average temperature is −6 °C."
2025 Exam 2 Q4c: "Use the equation of the least squares line to predict the sale price for a three-bedroom home, located in the city centre of Melbourne…" (i.e. distance = 0 → the intercept.)

(e) Interpolation vs extrapolation. 1 mark. See §2.12.

(f) Interpret the slope / interpret the intercept. 1 mark. See §2.1 and §2.2.

Related: fitting a line by eye / from two named points (2020 Exam 2 Q6c: "The line on the scatterplot passes through the points (20, 168) and (85, 157). Using these two points, determine the equation of this line." Report: "Many students, however, used all the data values from the original table and, using technology, then found a least squares line that was not the required response.").

Exam 1 versions: estimate the equation from a drawn line (2017 Q8, 2018 Q8, 2023 Q7, 2024 Q8, 2025 Q9, 2025 NHT Q8); compute the slope from two given (x, ŷ) pairs (2023 Q9); back-solve for x from a prediction (2024 Q10); derive the slope from summary statistics + r (2018 Q13, 2019 Q11).

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1.13 Residuals and residual plots

What it looks like. 1. Calculate a residual ("Determine the residual value when…"), often 2 marks: predicted value then actual − predicted. 2. Show that a stated residual is correct. 3. Plot a residual point on a residual plot. 4. The assumption question: "A residual plot can be used to test an assumption … What is this assumption?" (answer: linearity). 5. The justification question: "Does the residual plot support this assumption? Explain your answer." 6. Over-prediction / under-prediction from a residual's sign.

Marks. Residual calculation 1–2; assumption 1; justification 1.

Real examples

• 2019 Exam 2 Q5f.i/ii: "i. The residual plot above can be used to test one of the assumptions about the nature of the association between the atmospheric pressure at 3 pm and the atmospheric pressure at 9 am. What is this assumption?" (answer: "linearity" — "A one-word answer was all that was required.") "ii. The residual plot above does not support this assumption. Explain why." (answer: "the residuals have a clear pattern")
• 2016 Exam 2 Q3d.i/ii: same pair; answers "That the association is linear" and "Yes, since there is no clear pattern in the residual plot."
• 2020 Exam 2 Q5g: "Does this residual plot support the assumption of linearity that was made when fitting this line to this data? Briefly explain your answer." Answer: "Yes – residuals have no clear pattern (or are randomly scattered)."
• 2023 NHT Exam 2 Q4g: "In part a., a least squares line was fitted to the scatterplot. Does this residual plot justify this? Briefly explain your answer."
• 2026 NHT Exam 2 Q2d/Q2e: "d. Does this residual plot support the assumption of linearity that was made when fitting this line to this data? Briefly explain your answer. e. Based on this residual plot, for the mammal with a brain weight of 180 g, was the life expectancy value overpredicted or underpredicted by the equation of the least squares line? Briefly explain your answer." Guide for (e): "UNDERPREDICTED. (Actual – Predicted) has a positive value indicating that the Actual value is greater than the Predicted value. Must have underprediction statement with reason"
• 2025 Exam 2 Q4f.i/ii: "i. Show that the value of the missing residual is 27 984. ii. Plot the residual from part i by placing an X on the residual plot above." Guide tolerance: "Residual is horizontally midway between 15 and 16, just above the zero horizontal axis and below one-third up from this axis towards the nearest gridline."
• 2024 Exam 2 Q3g.i: plot the residual point; the guide gives the exact point "(2.02, 0.0328); Cross MUST be on the 2.02 m line horizontally; Cross must be ABOVE 0.030 and BELOW 0.035".
• 2018 Exam 2 Q2d: "Determine the residual value when the equation of the least squares line is used to predict the evening congestion level when the morning congestion level is 47%. Round your answer to one decimal place." (2 marks) Answer −1.8.
• 2007 Exam 2 Q3c (earliest): "Explain why this residual plot supports the assumption of linearity for this relationship." Answer: "There is no clear pattern to the random scatter of points."

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1.14 Data transformation (log x, 1/x, x², and y-transformations)

What it looks like. 1. A scatterplot/time-series is declared non-linear; a named transformation is applied and the least squares line found, with a rounding instruction. 2. Choose the appropriate transformation (Exam 1, and 2020 Exam 2 Q6d). 3. Use the transformed equation to predict, then un-transform (10^, square root, reciprocal). 4. Comment on reliability of the prediction.

Marks. 2 marks for fitting; 1 mark for predicting.

Real examples

• 2017 Exam 2 Q4: "The association between area of forest eaten and year is non-linear. A log₁₀ transformation can be applied to the variable area to linearise the data. … b. Perform the log₁₀ transformation to the variable area and determine the equation of the least squares line … Round your answers to three significant figures." Then Q4c.i: "The least squares line predicts that the log₁₀(area)… will be approximately 2.85. Using this value of 2.85, calculate the expected area …"
• 2021 Exam 2 Q5a: "Apply a reciprocal transformation to the variable difference to linearise the data. Fit a least squares line to the transformed data and write its equation below. Round the values of the intercept and the slope to four significant figures." (2 marks)
• 2020 Exam 2 Q6d (choose-your-own): "Apply an appropriate transformation to the variable mean age to linearise the data. Fit a least squares line to the transformed data and write its equation below. Round the values of the intercept and the slope to four significant figures." Answer: mean height = 167.9 – 0.001621 × (mean age)².
• 2012 Exam 2 Q4a/b: "A squared transformation can be applied to the variable ws3.00pm to linearise the data… b. Use this equation to predict the wind speed at 3.00 pm on a day when the wind speed at 9.00 am is 24 km/h." Report: students "gave an incorrect rounded answer of 162. They needed to find the square root."
• 2014 Exam 2 Q3a/b: log transformation of area: population = 7.7 + 7.7 × log₁₀(area); then predict for 90 km². Report: "many then failed to use the log function in this final calculation and calculated 7.7 + 7.7 × 90 = 700.7"
• 2008 Exam 2 Q5a: "A reciprocal transformation applied to the variable television hours can be used to linearise the scatterplot." Report: "The majority of students did not seem to understand the term 'reciprocal'. … An equation written as 'homework hours = 5.12 + 102.90 (reciprocal) TV hours' was not accepted."
• Exam 1: 2019 Q12 (squared transform of x); 2023 Q11 (reciprocal of age); 2025 Q11 (log₁₀ of life as response) and Q12 (squared transform of doctors); 2026 NHT Q10 ("Which transformation would linearise…", options (age)², log₁₀(age), 1/age, (health cost)²); 2026 NHT Q11–12 (reciprocal of completion time as the response variable, including a residual on the transformed scale).

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1.15 Time series

What it looks like. 1. Plot / complete a time series plot from a table. 2. Describe the qualitative features — trend, seasonality, irregular fluctuations, structural change, outliers. 3. Smoothing: moving mean (3-, 5-, 7-, 9-, 13-point), moving median (3-, 5-, 13-point, "median smoothing is a graphical technique"), moving mean with centring (2-mean, 4-mean, 6-mean). 4. How many smoothed points result? 5. Seasonal indices: calculate from data, complete a set so they sum to n, deseasonalise, re-seasonalise, interpret an index. 6. Fit and use a least squares trend line on time series data, including "average rate of increase". 7. Forecast, and state the assumption behind the forecast.

Marks. 1–2 each; seasonal-index calculation is usually 2 marks.

Real examples — description

• 2022 Exam 2 Q5a: "The time series plot contains irregular fluctuations. Give two other descriptions of the pattern in this time series plot." Answer: "Decreasing trend with seasonality." Report: "Structural change was often mentioned. Students needed to mention both terms to receive full marks."
• 2024 Exam 2 Q4b: asked for "qualitative features". Answer: "Increasing trend and irregular fluctuations." Guide: "Accept 'upward trend' or 'random fluctuations'."
• 2025 Exam 2 Q6a: "Excluding any possible outliers, identify two qualitative features of the time series plot." (2 marks) Answer: "Seasonality and irregular fluctuations."
• 2026 NHT Exam 2 Q4a: "The time series plot contains irregular fluctuations. Identify one other qualitative feature of this time series plot."
• 2023 Exam 2 Q4a: "Identify a feature of this plot that is consistent with this time series having a seasonal component."
• 2017 NHT Exam 2 Q3a: "Describe the trend in the time series plot." Answer: "Increasing trend".
• 2009 Exam 2 Q2c: "Describe the general pattern in rainfall that is revealed by the smoothed time series plot."
• 2011 Exam 2 Q3a: "Use this plot to describe, in general terms, the way in which the average age of women at first marriage in this country has changed during the period 1915 to 1970." Model: "The average age … remained relatively constant from 1915 to around 1935, and then decreased during the period 1935 to 1970."

Real examples — smoothing

• 2016 Exam 2 Q4a: "Five-median smoothing has been used … The first four smoothed points are shown as crosses (×). Complete the five-median smoothing by marking smoothed values with crosses (×) on the time series plot above." (2 marks)
• 2016 Exam 2 Q4b: "Two-mean smoothing with centring has been used… Using the data given in the table, show that the two-mean smoothed rainfall centred on October is 157.25 mm." (2 marks)
• 2022 Exam 2 Q5b/c: "Write down the value of the five-median smoothed rainfall for month 20." / "Calculate the nine-mean smoothed rainfall for month 7." / "how many smoothed points over the full 36-month period?" (answer 28).
• 2026 NHT Exam 2 Q4b/c: "Astronomers … use 13-point smoothing … ii. Find the 13-point median smoothed value for month 9" and "How many points would there be in the smoothed plot if 13-point smoothing was applied to the entire data set from January 1975 to December 2010?" (answer 420).
• Exam 1: 2019 Q13 ("Both three-median smoothing and five-median smoothing … result in the same smoothed value on day number"); 2019 Q16 ("If seven-mean smoothing is used … the number of smoothed data points would be"); 2024 Q15 (six-mean with centring); 2025 Q13 (five-median) and Q15 (four-mean with centring: "Calculation 1: (78 + 187 + 106 + 166) ÷ 4 = 134.25; Calculation 2: (187 + 106 + 166 + 124) ÷ 4 = 145.75; Centring = (134.25 + 145.75) ÷ 2 = 140").

Real examples — seasonal indices

• 2019 Exam 2 Q6a/b: "Use the values in Table 5 to find the seasonal indices for summer, autumn and spring. Write your answers in Table 6, rounded to two decimal places." / "Use the appropriate seasonal index from Table 6 to deseasonalise the total rainfall for winter in 2017. Round your answer to the nearest whole number."
• 2023 Exam 2 Q4b/c: "The long-term seasonal index for April is 1.05. Determine the deseasonalised value for average monthly ice cream consumption in April 2010 (month 4)." / "Show that, when rounded to two decimal places, the seasonal index for July 2011 estimated from this data is 1.10." (2 marks)
• 2025 Exam 2 Q6b: "A seasonal index can be calculated for each month based on the four-year period. Calculate this seasonal index for September, the ninth month in the calendar year. Round your answer to three decimal places." (2 marks; 74% scored 0)
• 2009 Exam 2 Q4a/b/c: complete the fourth index so the four sum to 4; deseasonalise; then "What does a seasonal index of 1.05 tell us about the rainfall in autumn?" Model: "The autumn rainfall is 5% above the average for the four seasons of the year." Report: "A common incorrect answer suggested that the autumn rainfall was 5% above the monthly average."
• Exam 1 "correct for seasonality" percentage items (recurring almost annually): 2014 Q12, 2017 Q16, 2020 Q15, 2021 Q16, 2025 Q16.

  2025 Exam 1 Q16: "The seasonal index for the number of meat pie sales in winter is 1.75. To correct for seasonality, the actual number of meat pie sales for winter should be reduced, to the nearest whole percentage, by A. 25% B. 43% C. 57% D. 75%". Report: "Multiplying by 0.57 is equivalent to a 43% reduction (100 − 57)%".
  2017 Exam 1 Q16 report: "A sales figure would be divided by the seasonal index of 1.6, which is the equivalent of multiplying by 0.625 … The deseasonalised value will be 62.5% of the original value, which means the original value has been reduced by 100% − 62.5% = 37.5%."

Real examples — trend line and forecasting

• 2018 Exam 2 Q3b.ii: "Use the equation of the least squares line to determine the average rate of increase in percentage congestion level for the period 2008 to 2016 in Sydney." Answer: "1.15% per year". Report: "many students did not realise that the slope of the least squares line was a measure of the average rate of increase."
• 2018 Exam 2 Q3b.iii: "Use the least squares line to predict when the percentage congestion level in Sydney will be 43%." (answer 2020)
• 2021 Exam 2 Q3e.i/ii: "Show that the predicted winning time … in 2032 is 49.252 seconds." / "What assumption is being made when this equation is used to predict the winning time … in 2032?" Answer: "Same decreasing trend continues in the future." (only 18% correct)
• 2021 NHT Exam 2 Q4b.iii: same question; answer "A similar decreasing trend continues beyond 2018."
• 2021 Exam 2 Q3c: "Write down the average decrease in winning time, in seconds per year…". Report: "The instruction to 'write down' the average decrease suggested no calculation was required."
• 2026 NHT Exam 1 Q… / 2026 NHT Exam 1 seasonal forecasting: "A least squares line is fitted to the deseasonalised quarterly sales data and is used, along with the quarterly seasonal indices, to predict the actual sales…" (the deseasonalise → predict → re-seasonalise chain).

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1.16 Historical-only question types (pre-2016 study design)

These no longer appear but dominate 2006–2015 papers; flag them so a taxonomy built from the full corpus does not treat them as live.

• Three-median line — fit it, mark the three medians with crosses, calculate its slope, interpret its slope, and explain why it is robust.

  2013 Exam 2 Q4: "A three median line will be used to model the increasing trend … i. On the time series plot above, mark the location of each of the three medians with a cross (X). ii. Draw the three median line … b. Calculate the slope of the three median line. c. Interpret the slope of the three median line in terms of the relationship between the variables average pay rate and year."
  2006 Exam 2 Q3c: "The three median line is not as influenced by extreme values such as (20, 93)."
  Exam 1: 2007 Q12, 2009 Q13, 2013 Q9/Q12.

• Computing the least squares equation by hand from b = r·s_y/s_x and a = ȳ − b·x̄ — 2013 Exam 2 Q3b was a "show that" of exactly this. Still tested in Exam 1 (2018 Q13, 2019 Q11) but no longer in Exam 2.
• The term "dependent / independent variable" — used up to 2014 (2014 Exam 2 Q2a "Write down the dependent variable"); replaced from ~2015 by response / explanatory variable.
• "Relationship" instead of "association" — 2012 Exam 2 Q2c "Describe the relationship between the maximum temperature and the minimum temperature in terms of strength and direction". From 2014 onwards VCAA consistently writes association.

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2. THE VCAA WORDING BANK

This is the heart of the topic. VCAA recycles a small number of stems almost verbatim. For each, the question template, the years it recurs, the model answer form, and the mandatory elements as prescribed by the reports/marking guides.

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2.1 INTERPRETING THE SLOPE of a least squares line

Question template (near-identical wording, 2008 → 2026)

"Interpret the slope of [this / the] least squares line in terms of [variable 1] and [variable 2]." — 1 mark

Instances (exact, with file):

The examiner's model answers (verbatim from reports)

2008 Q4c — "On average, arm span increases by 1.09 cm for each 1 cm increase in height" (Documents_exams_mathematics_further_maths2_assessrep_08.txt)
2012 Q2d — "On average, it is predicted that the maximum temperature increases by 0.67 °C for each 1 °C increase in the minimum temperature." (...2012_fm2_assessrep12.txt)
2014 Q2c — "On average, population increases by 2680 people for each additional square kilometre of area." (...2014_FM2_examrep14.txt)
2015 Q3a — "On average, male life expectancy increased by 0.88 years for each one-year increase in female life expectancy." (...2015_FM2_examrep15.txt)
2017 Q3b.ii — "On average, egg density increases by 31.3 eggs/m² for each additional female moth caught." (...2017_fm2_examrep17.txt)
2017 NHT Q2b.ii — "On average, relative humidity decreases by 4.38% for each 1 °C increase in temperature."
2019 Q5a — "On average, pressure at 3 pm increases by 0.8894 hPa for each one unit (hPa) increase in pressure at 9 am." (...2019_FM2_examrep19.txt)
2019 NHT Q4c — "On average, life span decreases by 1.9 years for each additional hour of sleep time."
2020 Q5d — "On average, body density decreases by 0.001512 kg/l for each 1 cm increase in waist measurement." (...2020furmaths2-exam-report.txt)
2022 Q4c — "On average, relative humidity decreases by 3.417% for each 1 degree increase in temperature."
2022 NHT Q2d.i — "On average, the number of finishers increases by 0.3648 for each increase of 1 in the number of starters."
2023 NHT Q4d — "On average, foot width increases by 0.2479 cm for each 1 cm increase in foot length."
2024 Exam 2 Q3e — "On average, for each 1 metre increase in Wgold, Wbest increases by 0.86 metres." (2025-03_2024generalmaths2-report.txt)
2024 NHT Q4d — "On average, when the LLT increases by 1 m, the HHT decreases by 1.08 m."

The prescribed answer form — mandatory elements

The 2020 report gives the definitive accept/reject list (Documents_exams_mathematics_2020_2020furmaths2-exam-report.txt, Q5d):

"Three examples of acceptable answers are:
• Body density decreases by 0.001512 for each 1 cm increase in waist measurement.
• Body density decreases by 0.001512 for each additional cm in waist measurement.
• Body density decreases by 0.001512 for each cm increase in waist measurement.

Three examples of responses that were not acceptable answers are:
• Body density decreases by –0.001512 for each 1 cm increase in waist measurement. ← double negative
• Body density decreases by 0.001512 for each 1 cm in waist measurement. ← no change in x
• Body density decreases by 0.001512 for each increase in waist measurement. ← no quantified change in x
The latter suggests that the same body density decrease applies to any increase in waist measurement, be it 1, 2, 5 or 10."

The 2017 report is equally explicit (...2017_fm2_examrep17.txt, Q3b.ii):

"Interpretation of the slope needed reference to a ratio of changes – a change in response variable compared to a change in explanatory variable. Both variables needed to show change. Some acceptable answers were:
• egg density increases by 31.3 as the number of female moths increases by 1
• egg density increases by 31.3 for an increase of 1 in the number of female moths caught
• egg density increases by 31.3 for each additional female moth caught.
The following examples missed the key element that both variables have a quantifiable change:
• egg density increases by 31.3 for each female moth
• egg density increases by 31.3 for each increase in the number of female moths caught."

Other prescriptive statements: - 2022 report: "The interpretation of the slope must refer to a change in the response variable for each unit change in the explanatory variable." - 2024 marking guide (2025-04_2024generalmathematics2-assessment-guide.txt): "3e | (On average), for each 1 m increase in Wgold, Wbest increases by 0.860 m | A1 | Must be clear reference to the change in both variables" — note "(On average)" is bracketed, i.e. treated as optional in the 2024 guide. - 2024 Chief Assessor PL (2025-04_General_Maths_Examination_2.txt): "It was essential that students reference the change in the response variable for each one unit change in the explanatory variable." - 2019 report: "Many gave a response that was almost correct but failed to reference the one-unit increase in pressure 9 am. Interpreting the slope … required identifying the correct constant and then describing it. Describing both constants was to ignore the first step; specific knowledge was required, not various statements provided in the hope of including something relevant." - 2013 report (three-median line, Q4c) on units: "The interpretation of the slope had to relate to the average pay rate and the year. This means that appropriate units must have been given, in this case in dollars per hour per year. An answer that simply indicated 'an increase of 0.8 each year' did not explain what the number 0.8 referred to and was not accepted."

Mandatory-element checklist for a full-mark slope interpretation 1. Direction word matching the sign of b: increases / decreases (never write the minus sign and "decreases"). 2. The numerical value of the slope, correctly rounded as given. 3. The units of the response variable (or the response variable named so the units are implied). 4. "for each 1 [unit] increase in" — the explanatory variable's change must be quantified as one unit ("each additional", "each 1 cm", "for an increase of 1"). 5. BOTH variable names, in the correct roles. 6. "On average" — present in every VCAA model answer 2008–2024; bracketed as optional only in the 2024 marking guide. Always include it.

Fill-in-the-box variant (2023 onwards — the new format)

2023 Exam 2 Q1c.ii: "Complete the following sentence by filling in the box provided. This equation predicts that, on average, each 10 g increase in the weight of an oyster is associated with a ▢ cm³ increase in its volume." (1 mark)
2026 NHT Exam 2 Q3d: "Complete the following sentence by filling in the boxes below. The equation of the least squares line predicts that, on average, each 10 kg increase in body weight is associated with a ▢ gram ▢ in brain weight." (2 marks) — guide answer "13.9 / increase; One correct OR both given in incorrect order (A1); Completely correct (A1)"
2006 Exam 2 Q2a (earliest ancestor): "Complete the following sentence. On average, the height of a boy increases by ▢ cm for each one-month increase in age."

Note the deliberate shift: these use "is associated with" rather than a causal verb, and scale the x-change to 10 units, so the student must multiply the slope.

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2.2 INTERPRETING THE INTERCEPT

Question template

"Interpret the intercept of the least squares line in terms of the variables [response] and [explanatory]."

Model answers

2016 Q3b.ii (Documents_exams_mathematics_2016_FM2_examrep16.txt): "On average, when the actual temperature is 0 °C, the apparent temperature is −1.7 °C.
Another accepted answer was: When the actual temperature is 0 °C, the predicted apparent temperature is −1.7 °C.
A common incorrect answer confused intercept and slope. Another common incorrect answer mixed up the response variable (apparent temperature) and the explanatory variable (actual temperature)."
2012 Q2b: "On average, it is predicted that, when the minimum temperature is 0 °C, the maximum temperature will be 13 °C."

Mandatory elements 1. State the explanatory variable = 0 (with its units). 2. State the predicted / average value of the response variable (with units). 3. Both variables named, correct roles. 4. Use "on average" or "predicted" — the intercept is a model value, not an observation.

Related 1-mark disguise — 2025 Exam 2 Q4c asks for the intercept without naming it: "Use the equation of the least squares line to predict the sale price for a three-bedroom home, located in the city centre of Melbourne" → distance = 0 → $1 765 353.

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2.3 INTERPRETING THE COEFFICIENT OF DETERMINATION r²

Question template

"Interpret the coefficient of determination in terms of [variable 1] and [variable 2]." — 1 mark
or the calculation-only version: "What percentage of the variation in [response] can be explained by the variation in [explanatory]?"

Model answers (verbatim)

2006 — "56.9% of the variation in height is explained by the variation in age."
2009 — "80.81% of the variation in the rainfall can be explained by the variation in the percentage of clear days."
2015 — "95% of the variation in male life expectancy can be explained by the variation in female life expectancy."
2016 — "97% of the variation in apparent temperature can be explained by the variation in actual temperature."
2019 NHT — "41.6% of the variation in life span can be explained by the variation in sleep time."
2024 — "85.7% of the variation in Mgold can be explained by the variation in year."
2025 — "75% of the variation in sale price can be explained by the variation in days."
2026 NHT — "68.0% of the variation in the brain weight can be explained by the variation in the body weight." (guide adds: Accept "…is explained by..")

Prescriptive examiner advice

2009 report (Documents_exams_mathematics_further2_assessrep_09.txt): "The coefficient of determination refers to the relationship in which the variation in the dependent variable can be explained by the variation in the independent variable. It does not imply any causation between the two variables. Unacceptable causation terms for this relationship include 'is determined by', 'is due to', 'is caused by' and 'is because of'. Other common errors included students reversing the variables … Others incorrectly referred to the absolute values of one or both of the variables rather than to the variation in them."
2016 report: "Some students mixed up the response variable and the explanatory variable in this statement and wrote, '97% of the variation in actual temperature can be explained by the variation in apparent temperature'. Other common unacceptable answers used terms that suggested variation in actual temperature caused the variation in apparent temperature. An example was, '97% of the variation in actual temperature was due to the variation in apparent temperature'."
2006 report: "Common incorrect interpretations referred to causation. A common incorrect answer was '56.9% of the variation in height is due to the variation in age.'"
2019 NHT report: "Answers that referred to the variance in each variable were not acceptable."
2024 report: "Some students did not reference the variation in both variables. Some rounded to 86% in a question where rounding did not apply."
2024 Chief Assessor PL: "This student was not awarded the mark as they did not reference the variation in each variable, and the word 'attributed' suggests a causal relationship."

Mandatory-element checklist 1. The percentage (r² × 100), correctly rounded — 2024 guide: "Accept only 85.7%*". 2. The words "of the variation in" before the response variable. 3. "can be explained by the variation in" before the explanatory variable. 4. Both variables named, correct order (response first). 5. No causal verbs: due to, caused by, determined by, because of, attributed to, results in. 6. Say variation, not variance, and not the raw variable ("97% of apparent temperature" is wrong).

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2.4 SIGN AND VALUE OF r

Not an interpretation question, but a wording-sensitive calculation that recurs every single year.

• 2020 Exam 2 Q5f: "Write down the value of the correlation coefficient r. Round your answer to three decimal places." Answer −0.824. Report: "Many students did not recognise that the negative square root value was required. Students should understand that the sign of the correlation coefficient matches the sign of the slope."
• 2021 Exam 2 Q3b: answer −0.938. "Many students found 0.938 but left off the negative sign."
• 2025 Exam 2 Q4b: answer −0.284 (only 21% correct). "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."
• 2017 NHT Exam 2 Q2a.i: "Since the gradient of the least squares line is negative, the correlation coefficient, r, must also be negative."
• 2009 Exam 2 Q3c.ii: "Many students failed to include the negative sign as indicated by a generally negative slope of the data in the graph."
• Exam 1 mirror: 2018 Q9 and 2019 Q10 — both "Many students incorrectly took the positive square root value and chose option E."

Association-not-causation MC stems (the recurring distractor design):

2025 Exam 1 Q10: "The correlation coefficient between games won and goals against is r = −0.466. Based on the correlation coefficient, it can be concluded that A. fewer goals scored against is associated with a smaller number of wins. B. fewer goals scored against causes a smaller number of wins. C. more goals scored against causes a smaller number of wins. D. more goals scored against is associated with a smaller number of wins." Report: "Reject Options B and C as causation cannot be concluded."
2008 Exam 1 Q10 — the earliest instance of the identical design: "A large study of Year 12 students shows that there is a negative association between the time spent doing homework each week and the time spent watching television. The correlation coefficient is r = −0.6. From this information it can be concluded that … D. if a student spends less time watching television, they will do more homework. [causal distractor] … E. an increased time spent watching television is associated with a decreased time doing homework. [correct]"
2023 Exam 1 Q10: "A study of Year 10 students shows that there is a negative association between the scores of topic tests and the time spent on social media. The coefficient of determination is 0.72. From this information it can be concluded that A. a decreased time spent on social media is associated with an increased topic test score. B. less time spent on social media causes an increase in topic test performance. … D. too much time spent on social media causes a reduction in topic test performance."
2026 NHT Exam 1 Q11 uses the same four-option association/causation grid on a reciprocal-transformed equation.

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2.5 "DESCRIBE THE ASSOCIATION BETWEEN …"

Question template

"[Use the scatterplot to] describe the association between [variable 1] and [variable 2] in terms of strength, direction and form." (3-element form: 2007, 2014, 2015, 2016, 2023)
"Describe the [linear] association between [v1] and [v2] in terms of strength and direction." (2-element form: 2012, 2019 NHT, 2020, 2022, 2025)
"Describe the association between [v1] and [v2] in terms of form and direction." (2024 NHT)
"Write down the direction of the association between [v1] and [v2]." (2026 NHT Q2c — single element)

Model answers

Prescriptive examiner advice — DO NOT ADD EXTRA ELEMENTS

2022 report (...2022furmaths2-report.txt general comments): "Where descriptive answers are required to a question, students are strongly advised to keep answers brief. An answer in point form is acceptable and additional information should not be provided. For example, in Core Question 4b., students were only asked to describe the association in terms of strength and direction. It was not appropriate to further comment on form or possible outliers."
2020 report general comments: "in Core Question 6b. students were asked to describe the strength and direction … Many students recognised that the association was strong and negative but then gave unnecessary additional information that the association was of linear (or non-linear) form." and at Q6b: "Some students gave additional information that negated an otherwise correct answer."
2015 report Q4a: "Many students did not state the form as linear." (when form was asked for)
2014 report Q4a: "Another common, incorrect answer offered a discussion about the coefficient of determination … Others referred to skewness, which is not applicable to a bivariate data plot."
2014 report Q2c: "Some students inappropriately referred to the data being skewed. The term 'skewed' only applies to univariate data plots, whereas this question referred to a bivariate data plot."
2016 report Q3a: "A relatively common incorrect response was 'Strong, linear and positively skewed'."
2007 report Q3e: "A common error was to analyse the residual plot for strength, direction and form, incorrectly concluding that there was no relationship between the variables."
2024 report Q3d and 2024 PL: "Some students wrote the strength as moderate." (recurring — the same complaint appears in 2022 Q4b: "Many students chose moderate for the strength.")

Mandatory elements: exactly the elements asked for, in the order given by the question/table, no more. Vocabulary is fixed: strength ∈ {weak, moderate, strong}; direction ∈ {positive, negative}; form ∈ {linear, non-linear}.

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2.6 "COMMENT ON / IS THERE AN ASSOCIATION?" — TWO CATEGORICAL VARIABLES

Question templates (three interchangeable wordings)

(A) "Does the [percentage segmented bar chart / information in Table X] support the [opinion / contention] that [variable 1] is associated with [variable 2]? Justify your answer by quoting appropriate percentages." — often with the concession "It is sufficient to consider one [category] only when justifying your answer."
(B) "Does the information in Table X support [person]'s belief? Explain your conclusion by comparing the values of two appropriate percentages." (2023)
(C) "Explain why … there is no association … quoting appropriate percentages to support your explanation." (2014 — the negative case)

Recurrences: 2008 Q2, 2011 Q2b, 2014 Q1c, 2018 NHT Q4c, 2019 NHT Q5b.iii, 2021 NHT Q1d.ii, 2023 Q2b.ii, 2024 NHT Q2b, 2025 NHT Q3b. Exam-1 MC mirrors: 2017 Q6, 2021 Q2.

The prescribed full-mark structure (two marks)

The 2019 NHT and 2021 NHT reports state the two-mark split most explicitly:

2021 NHT report: "A statement that clearly indicates the contention is supported with a change or difference in one category of event was required for the first mark. For the second mark a statement similar to the following (choosing one category) using appropriate percentages was required:
'The percentage of females who participated in the 12 km walk (34%) was higher than the percentage of males who participated in that event (16%).'"
2019 NHT report Q5b.iii: "A statement that clearly indicated the contention is supported with a change or difference in one category of likelihood of attack considered and a statement similar to one of the following using column percentages was required. Approximate percentages were acceptable.
• The percentage of animals with low likelihood of attack decreases with increased exposure to attack during sleep – low exposure 91%, medium exposure 89%, high exposure 11%
• The percentage of animals with medium likelihood of attack changes with increased exposure … – low exposure 6%, medium exposure 0%, high exposure 11%
• The percentage of animals with high likelihood of attack increases with increased exposure … – low exposure 3%, medium exposure 11%, high exposure 79%"

Other model answers:

2008 Q2 (..._further_maths2_assessrep_08.txt): "The percentaged segmented bar chart does support the opinion that lunch time activity (walked, sat or stood, ran) is associated with year level. For example, the percent that ran changed from around 78% to 40% to 10% from Years 6–8 and 8–10.
There are several ways of observing support from the bar chart. In general terms, an association is indicated by the percentage of girls undertaking a particular activity changing with the year level. Note that this change does not have to be a consistent increase or decrease, but it can be. …
Some students referred to the changes in the percentages for an activity but then did not comment on whether the segmented bar chart supported the opinion that the association exists. Others forgot to quote relevant percentages as required to support their argument."
2011 Q2b: "The data for each of the four age groups in the table does support the opinion that age at first marriage is associated with the year of marriage. For example, of all first marriages, the percentage of women aged 25–29 years increased from 23.4% (1986) to 31.7% (1996) to 34.5% (2006)." Report: "Many students tried to work down the table despite the direction to work across a row."
2018 NHT Q4c: "Students needed to give a statement that clearly indicated the contention is supported with a change or difference in one beak size considered and then give a statement similar to one of the following. Approximate percentages were acceptable.
• 50% of males had large beaks, which was higher than females, with 7%. …"
2024 NHT Q2b: "Yes, as the percentages differ from 'before' to 'on' to 'after'. The LLT occurred after the New Moon on 75% of the days compared to 8.3% on the New moon and 16.7% before the New moon."
2025 NHT Q3b guide: "YES. The percentage of taller daughters with no brothers (62.5%) was greater than the percentage of taller daughters with one or more brothers (39.6%) — A1: Yes or statement of affirmation and mention difference/comparison; H1: Correct percentages of taller daughters for both situations with proportion* … Ignore minor rounding errors"
2014 Q1c (no-association case): "All three countries have approximately the same percentage: 67%, 64% and 64%. … some students contradicted the given statement* and claimed that 'there was an association because…'"

Mandatory-element checklist 1. An explicit Yes / No / "does support" verdict (or unmistakable affirmation). 2. A comparison word: greater than, higher than, lower than, differs, changes, increases with, decreases with. 3. At least two percentages, quoted with their category labels, for the same response category across different groups (i.e. compare across the bars/columns, never down a single column). 4. The percentages must be conditional (column or group percentages), not percentages of the grand total. 5. Naming the variables/categories, so it is clear which percentage belongs to which group.

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2.7 "IS X ASSOCIATED WITH Y?" — NUMERICAL vs CATEGORICAL (boxplots / stem plots)

Question template

"Do the boxplots support the contention that [numerical variable] is associated with [categorical variable]? Refer to the values of an appropriate statistic in your response." (2020, 2022)
"Explain why the information given above supports the contention that [numerical] is associated with [categorical]. Refer to the values of an appropriate statistic in your response." (2019)
"The [parallel boxplots / back-to-back stem plot] suggest that [numerical] is associated with [categorical]. Explain why, quoting the values of an appropriate statistic." (2016, 2017, 2017 NHT)
"Explain why [variable] for these countries is associated with the year. Refer to specific statistical values in your answer." (2015)

Model answers (verbatim)

2019 Exam 2 Q3 (...2019_FM2_examrep19.txt): "A statement that a decrease or change in median (or IQR) signals an association was required for the first mark to be awarded. Median (or IQR) values for all three months needed to be quoted correctly for the second mark to be awarded.
Successful responses focused on one statistic only (usually the median) and quoted the values from the table rather than estimating from the boxplots.
Incorrect answers included using the word 'averages' or 'means' rather than medians and quoting only two medians rather than all three.
Some students went on to comment on the minimums and maximums; this additional information compromised an otherwise correct answer. Comments about the shape of the boxplots were also not appropriate.
Questions of this type require reasoning rather than comments about which season each month falls in."
2020 Exam 2 Q3d: "Yes, as seen by the increase in median BMI values as neck size increases. For below average neck sizes, the median BMI is 21.6, which increases to 24.6 for average neck sizes and increases again to 28.1 for above average neck sizes.
A statement that an increase or change in median (or IQR) signals an association was required for the first mark. Median (or IQR) values for the neck sizes needed to be quoted correctly for the second mark. …Some students went on to also quote other statistics, such as the maximums or ranges, and this additional information devalued an otherwise correct answer."
2022 Exam 2 Q2b: "Yes, as the medians differ from 9 am to 3 pm. The median at 9 am of 75 is greater than the median at 3 pm of 63.
Many students gave the correct values for each median but did not specifically mention a change or difference."
2017 Exam 2 Q2e: "Forest 21 / Grassland 30 / Medians differ from forest to grassland.
Full marks were awarded to students who described a change in the median values and quoted these medians for both places of capture.
The mean is not part of a stemplot five-number summary and was not appropriate to use because of the outlier of 52 in the forest data.
Students who initially gave the required median comparisons and then went further by quoting comparisons of other irrelevant statistics were not awarded full marks."
2016 Exam 2 Q2b.iii: "The medians for the two months differ. In May, the median maximum temperature is about 14.5 °C, while in July, the median maximum temperature is about 9 °C.
The answer needed to refer to the difference between the two median temperatures. Simply quoting the two median values was not sufficient. …
Alternatively, comparing the two interquartile range (IQR) values could have been used as the difference in the IQRs also indicates the presence of an association. …
Some students referred to average or mean temperatures; however, this cannot be accurately determined from a boxplot unless the distributions are clearly symmetric."
2017 NHT Q1d: "The median amount of solar energy collected differs from month to month as indicated for April (11 MJ), May (7 MJ) and June (5.8 MJ)."
2023 NHT Q2c: "Yes, as the median foot width of the boys, 9.15 cm, is greater than the median foot width of the girls, 8.8 cm. OR No, as the Interquartile range for boys and girls are both equal to 0.8." ← note VCAA accepted either verdict provided the statistic supported it.
2015 Exam 2 Q2b: "Median life expectancy changes with year. For example, in 1953 the median was 52, in 1973 the median was 63 and in 1993 the median was 69. Observing the change in IQR values … was also acceptable. Some students referred to mean values, which are not discernible from a box plot unless it is perfectly symmetrical."
2008 Exam 2 Q3b: "• The median arm span increases with year level • The IQR of arm span decreases with year level or the range of arm span decreases with year level. … To compare the boxplots, one appropriate summary statistic for arm span (dependent variable) had to be compared across the year levels (independent variable)."
2006 Exam 2 Q1f: "The median height increases with age. … Reference to a boxplot statistic was required, therefore, consideration of the mean height was not appropriate."

Mandatory-element checklist 1. A verdict word: Yes / supports / "the medians differ". 2. One statistic only — the median (or the IQR). Never mean, never average. 3. An explicit change/difference/increase/decrease statement. 4. Values quoted for EVERY group in the display (all three months, all three neck sizes, both times of day). 5. Values taken from the supplied table where one exists, not estimated off the plot. 6. Nothing else — no minimum/maximum, no range, no shape commentary, no contextual speculation.

Spread-comparison sibling (2022 Q2ai, 2025 Q1c.ii) — same rules but with a spread statistic:

2022 Q2a.i model: "More variable at 9 am. IQR at 9 am of 35 is higher than IQR of 29 at 3 pm." Report: "Some students did not demonstrate which was more variable despite calculating each IQR value correctly. Some stated the values of each IQR but gave no conclusion."
2025 Q1c.ii model: "House sale prices have a lower spread than apartment sale prices as shown by the lower standard deviation." Guide: "Must have comparative word, spread or standard deviation and the two variables." Report: "The question clearly indicated using the information in Table 2, so using other statistics such as range and IQR was not appropriate."

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2.8 "EXPLAIN WHY A RESIDUAL PLOT …" / JUSTIFYING LINEARITY

Question templates

(A) "A residual plot can be used to test an assumption about the nature of the association between two numerical variables. What is this assumption?" — 1 mark (2016, 2019, 2022 NHT)
(B) "Does the residual plot above support this assumption? Explain your answer." — 1 mark (2016)
(C) "Does this residual plot support the assumption of linearity that was made when fitting this line to this data? Briefly explain your answer." — 1 mark (2017 NHT, 2020, 2026 NHT)
(D) "The residual plot above does not support this assumption. Explain why." — 1 mark (2019)
(E) "In part a., a least squares line was fitted to the scatterplot. Does this residual plot justify this? Briefly explain your answer." (2023 NHT)
(F) "Explain why this residual plot supports the assumption of linearity for this relationship." (2007)

Model answers

Prescriptive advice

2016 report Q3d.ii: "Reference to a lack of pattern or the randomness of the plot was required. An unacceptable answer was that the '… points are all scattered evenly above and below …' with no mention of randomness."
2024 report Q3g.ii: "It was acceptable to say the residuals were randomly scattered. The number of points above and below the line was irrelevant."
2024 marking guide: "3gii | Yes, the residual plot shows no clear pattern | A1 | MUST say YES, (or implied affirmation). Accept randomly scattered"
2026 NHT guide: "2d | YES Plot shows a random scatter/distribution of points; Plot has no pattern | A1 | Must have YES (stated or implied), with reason"
2019 report Q5f.i: "A one-word answer was all that was required. Some gave long answers that contradicted what was expected of them in Question 5f.ii."
2019 report Q5f.ii: "A common mistake was to ignore the given statement that the residuals did not support the assumption and to state that linearity was confirmed. Many students had difficulty with responses to Questions 5f.i. and 5f.ii., often contradicting themselves or writing definitions directly from a bound reference without any link to the question. Some confused residuals and the correlation coefficient."

Mandatory elements: (1) an explicit Yes/No; (2) the words "no clear pattern" or "randomly scattered"; (3) nothing about counts of points above/below the axis; (4) for the assumption question, the single word linearity (or "the association is linear").

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2.9 "DESCRIBE THE SHAPE OF THE DISTRIBUTION" AND OUTLIER STATEMENTS

Question template

"Describe the shape of the distribution [of ... ]." — 1 mark. Sometimes "Note the number of possible outliers, if any." (2018 NHT)
Exam 1 form: "The shape of this distribution is best described as A. positively skewed with one or more possible outliers. …"

Model answers and accepted forms

2018 report general comments: "in Question 1f. of the Core section when asked to describe the shape of the distribution, some students gave additional information concerning the centre and spread. Attention needed to be given to the type of statistical description required."
2021 Exam 1 Q1 report (the canonical shape-reasoning paragraph): "The centre of this distribution is in the group 56–57. Disregarding the possible outlier, we can see that the graph is more spread to the left of the centre than it is to the right. That is, the lower tail is longer than the upper tail. Therefore, we say that the shape of the distribution is negatively skewed (skewed to the left), with a possible outlier."

Vocabulary permitted: positively skewed / negatively skewed / approximately symmetric, each optionally "with (n) outlier(s)" or "with no outliers". Banned: symmetrically skewed, evenly distributed, bell shaped, normally distributed (for a sample display), and skewed applied to a scatterplot.

Outlier show-that / explain-why wording

2013 Exam 2 Q2b: "Write down an appropriate calculation and use it to explain why the country with a development index of 70 is an outlier for this group of countries."
Model: "Q1 − 1.5 × IQR = 75 − 1.5 × 3 = 70.5. Therefore, 70 is an outlier because it is less than 70.5."
Report: "Many students calculated a value of 70.5 and then wrote that 'it is therefore an outlier'. Further explanation, including a direct comparison between 70 and 70.5, was expected. Other common, incomplete or unacceptable answers included • 70 is outside the bulk of the data – this does not compare 70 with Q1 − 1.5 × IQR • it is outside 2SD from the mean – standard deviations do not define an outlier • there is no other country close to it – this does not compare 70 with Q1 − 1.5 × IQR."
2008 Exam 2 Q3c: "Many students correctly calculated the lower boundary (fence) … and then said that 'it was therefore still an outlier' without any numerical comparison shown or suggested. As this does not explain what 'it' is, nor why 'it' is still an outlier, the actual value of 140 cm should be stated as still being lower than the calculated value of the fence."
2011 Exam 2 Q1c: "Most calculated the 28.25 but then did not discuss how 26.0 related to this. Mathematical symbols were sometimes used incorrectly; for example, 28.25 < 26.0 < 32.65."
2024 Exam 2 Q2c.ii report: "Some students did not clearly explain the conditions for an outlier because they tried to combine their explanations for both fences into one, which resulted in a mathematically incorrect statement."
2024 PL: "In this second sample response, this student did not qualify for the mark as there was no reference to either the lower or upper fence."

Mandatory elements for an outlier justification: (1) the IQR; (2) the fence calculation shown in full (Q3 + 1.5 × IQR or Q1 − 1.5 × IQR); (3) an explicit numerical inequality comparing the data value with the fence (52 > 50, 240 < 243.55); (4) the conclusion word therefore it is / is not an outlier. Never combine two fences into one chained inequality.

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2.10 COMPARING DISTRIBUTIONS USING A NAMED STATISTIC

Covered in §2.7 (median/IQR association) and the spread siblings. Additional formulations:

• 2018 Exam 2 Q3e — comparing two fitted lines: "Since 2008, the equations of the least squares lines for Sydney and Melbourne have predicted that future traffic congestion levels in Sydney will always exceed those in Melbourne. Explain why, quoting the values of appropriate statistics." (2 marks) Model: "2008 Sydney value higher, 29.2 > 24.5, and Sydney line slope greater, 1.15 > 0.7667". Report: "Only a small proportion of students answered the question entirely correctly. Many students focused on the starting values … from the table rather than the least squares lines. Some gave gradient figures … but did not clearly say that Sydney's slope was greater."
• 2025 NHT Exam 2 Q4g — which predictor is better: "Father's height as Coefficient of determination is higher: 14% > 9.5% or Correlation coefficient is higher: 0.3744 > 0.3082".

Pattern: whenever VCAA says "quoting the values of appropriate statistics" (plural), two statistics are required; "an appropriate statistic" (singular) means pick ONE and quote it for every group.

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2.11 "USE THE … TO PREDICT …" AND THE INTERPOLATION / EXTRAPOLATION JUSTIFICATION

Question templates

"Use the equation of the least squares line to predict [response] when [explanatory] is [value]. Round your answer to …" — 1 mark
"Is the prediction made in part b. an example of extrapolation or interpolation?" (2019) / "When using the equation of this least squares line to make the prediction in part b., are you extrapolating or interpolating?" (2020) / "Identify whether the prediction in part b. is an interpolation or an extrapolation." (2023 NHT) / "Is the prediction made in part b. an interpolation or an extrapolation?" (2022 NHT)
"Would the predicted sale price be an example of interpolation or extrapolation? Briefly explain your answer." (2025)
"Give a reason why this prediction may have limited reliability." (2017)

Model answers

The critical 2024–2025 prescription (repeated verbatim two years running)

2024 report (2025-03_2024generalmaths2-report.txt) Q3h: "While predictions from a regression line focus on the response variable, their effectiveness as interpolation or extrapolation comes from the explanatory variable. It was not appropriate to refer to either 1964 or 1.934 as being outside the data range."
2025 report (2026-01_2025-GeneralMaths2-report.txt) Q4d: "Students needed to be careful that they recognised in their answer that while predictions from a regression line focus on the response variable, their effectiveness as interpolation or extrapolation comes from the explanatory variable. It was not appropriate to refer to the sale price as being outside the data range."
2025 marking guide: "4d | Extrapolation as 2 km lies outside explanatory variable data range | A1 | OR equivalent MUST reference explanatory variable range"
2015 report Q5b.ii: "This question required a response related to the given statistical data rather than any sociological possibilities. Many students wrote about the likely impact of future technological advances, wars, famines, viruses or advances in medicine, or simply stated 'You don't know what's going to happen in the future'. Such responses were not accepted."

Mandatory elements: (1) the single word interpolation / extrapolation; (2) where a reason is asked, "because [value] lies outside/inside the range of the EXPLANATORY variable data"; (3) never justify by reference to the response variable or to real-world speculation.

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2.12 TIME SERIES TREND / SEASONALITY DESCRIPTION

Question templates

"Describe the trend in the time series plot." (2017 NHT)
"The time series plot contains irregular fluctuations. Give two other descriptions of the pattern in this time series plot." (2022)
"Excluding any possible outliers, identify two qualitative features of the time series plot." (2025) — 2 marks
"Identify one other qualitative feature of this time series plot." (2026 NHT)
"Identify a feature of this plot that is consistent with this time series having a seasonal component." (2023)
Exam 1: "Which one of the following options best describes the qualitative features of the time series graph above?" (2025) / "The time series plot is best described as having …" (2016, 2017, 2018 NHT, 2021, 2023 NHT)

Model answers

Prescriptive advice

2025 report Q6a: "There was no evidence of any increasing or decreasing trend. It should be noted that irregular fluctuations are present in all time series plots. Overall, students need to be very clear on the key knowledge and key skills contained in the study design … and to use the formal terminology within the course. This question asked for qualitative features of a time series plot. The possible features are all clearly named within the study design."
2024 report Q4b: "There was no evidence of an outlier, of seasonality or of structural change. Some students erroneously referred to 'an irregular fluctuation'. It should be noted that irregular fluctuations are present in all time series plots."
2024 PL: "To qualify for the mark, the response needed to include ONLY correct features. This response listed a feature for which there was no evidence and so did not qualify for the mark."
2018 NHT Exam 1 report: "Irregular fluctuations are a feature of all time series plots."
2021 Exam 1 Q12 report: "The times series plot shows a decreasing trend with irregular fluctuations. To indicate the presence of seasonality we would expect to see regular fluctuations in the plot as well."
2017 Exam 1 Q13 report: "The existence of 'peaks' and 'troughs' is not enough information to determine seasonality; they must exist with regular intervals of time between them."
2011 report Q3a: "Many students noted a 'decreasing trend from 1915 to 1970', without considering the two sections of the plot. Some gave very specific answers rather than answering in general terms. Many students said the data was either 'positively skewed' or 'negatively skewed', neither of which is an applicable expression for a time-series plot."
2009 report Q2c: "In answering such questions, students must always refer to the given data rather than their own personal experiences. Some students referred to the seasons of the year but there was no indication in the data to suggest that these figures belonged to the southern hemisphere."

The permitted vocabulary (from the study design, as VCAA insists): trend (increasing/decreasing/upward/downward), seasonality, irregular (random) fluctuations, structural change, outliers. Nothing else. Never skewed. Adding a feature not evidenced loses the mark.

Forecast-assumption wording:

2021 Q3e.ii: "Same decreasing trend continues in the future." Report: "Students found it hard to convey the idea of the trend continuing. It was common to see reference to extrapolation or linearity but without linking it to the given equation."
2021 NHT Q4b.iii: "A similar decreasing trend continues beyond 2018."

Seasonal-index interpretation wording:

2009 Q4c: "The autumn rainfall is 5% above the average for the four seasons of the year." (not "above the monthly average")
2025 NHT Exam 1 Q14 report: "The average season index is 1. 0.75 is 0.25, or 25%, less than the seasonal average."

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2.13 "SHOW THAT …" QUESTIONS IN DATA ANALYSIS

Question template

"Show that …" / "Write down an appropriate calculation and use it to explain why …" / "Show, with calculations, that …" / "Use the equation … to show that …"

Data-analysis instances: 2013 Q3b (LS equation from summary statistics); 2016 Q4b (two-mean centred smoothing = 157.25 mm); 2017 Q2d (outlier); 2019 Q5e.i (r = 0.966); 2020 Q5e (residual = −0.02); 2021 Q3e.i (predicted 49.252 s); 2022 Q1b (two outliers); 2023 Q4c (seasonal index 1.10); 2023 NHT Q4b (predicted foot width 9.8 cm) and Q4e (r = 0.641); 2024 Q2c.i (both fences); 2024 NHT Q1c (0.22 not an outlier) and Q4e (residual 0.052); 2025 Q4f.i (residual 27 984); sample GM2 Q2a ("Show, with calculations, that a boxplot constructed from this five-number summary will not include outliers").

The prescribed standard (identical across reports, 2018–2025)

2018 report: "Some questions on the examination asked students to 'show that' a particular answer could be obtained. Students must work towards the given result with all relevant steps shown in their response. The answer the student is asked to show may be relevant in a subsequent part of the question."
2020 report: "Students must work towards the given result with all relevant steps shown. … In other words, if a student starts with the answer they have been asked to show, they will not be eligible for the mark. … In each case above the result that is required must be the conclusion to the process. Marks are awarded for showing the process of obtaining the required result."
2019 report (worked illustration): "This means students must show each iteration by writing down the relevant calculation … To state V₁ = 54 000 without showing how this was obtained does not address the instruction to 'show'."
2024 marking guide: "2ci | … | A1 | *SHOW THAT question — MUST see BOTH fence calculations*"; "3f | Predicted value = 0.300 + 0.860 × 2.02 = 2.0372; Residual = 2.07 – 2.0372 = 0.0328 | M1A1 | MUST see the predicted value calculation / MUST see residual calculation"
2025 report Q4f.i: "Students needed to show all working that led to the given residual value."
2024 PL: "Question 3f was a show that question. Two clear calculations were required."
2016 report Q4b: "The data needed for these calculations should have been taken from the table rather than from the graph."
2024 report general comments — the self-check list: "Students are strongly encouraged to read the question again after writing their final answer, and consider the following: Has the question been fully answered? Does the answer match the value provided in a 'show that' question? Is the answer reasonable in a practical context?**"

Mandatory elements: every intermediate line written out (predicted value line, then residual line; both fences, not one; each smoothing average, then the centring average), and the given value must be the last line, reached — not assumed.

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2.14 ROUNDING INSTRUCTIONS AND HOW THEY ARE ENFORCED

The instruction wordings used

The blanket exam instruction (current era)

2025-03_2024generalmaths2-report.txt and 2026-01_2025-GeneralMaths2-report.txt both quote it verbatim:

"the instructions section at the beginning of the examination clearly states that 'In all questions where a numerical answer is required, you should only round your answer when instructed to do so.' Students often rounded when an exact answer should have been given. For example, in Question 1e the percentage quoted needed to be 85.7% not 86%."
2025: "in this question the percentage given needed to be 83.85% not 84%."

How it is enforced

• Rounding where none was asked = absolute error, zero marks.

  2024 PL: "If a student rounds in a question where rounding does not apply, this is considered an absolute error, and no answer mark is awarded."
  2018 report: "In Question 2c. of the Core section the required answer was 63.8% and since rounding did not apply an answer of 64% could not be accepted." (echoed at Q2c: "Rounding did not apply, so an answer of 64% was not accepted.")
  2017 report Q3b.iii: "Rounding did not apply to this question, so −412.5 was the only acceptable answer."
  2020 report: "in Core Question 4a.ii. the required answer was 1.065, and since rounding did not apply, an answer such as 1.07 was not accepted."
  2014 report Q1c: "An answer rounded to one decimal place was expected. A number of students simply wrote 16% or an unrounded figure. This answer was not accepted. It could not be considered as a rounding error as there was no evidence that rounding had occurred."

• Decimal places ≠ significant figures — flagged in the general comments of 2016, 2017, 2018, 2019, 2020, 2021 and in the specific comments of 2021 Q2a ("Many students rounded to three decimal places rather than three significant figures") and 2016 Q3b.i ("The number 0.9 has only one significant figure, whereas 0.90 has two significant figures.").
• Designated rounding questions — the marking guides flag some items "Designated rounding question — Accept only this answer*" (2025 guide Q1c.i, Q7c) or "Rounding to 3 dp applies". 2024 PL: "For a rounding error to be considered, firstly, rounding must apply to the question, then the assessor must see either a correct calculation shown prior to the final rounded answer, or additional correct decimal places."
• Round only at the end. 2025 report (Matrices 13b.i, but stated generally): "Rounding should only be done at the final step." 2017 report: "students should … keep all decimal places in their calculator for intermediate steps and then only round the final answer to the required accuracy." 2021 report Q4b: "rounding too soon from calculations was common."
• Calculator exponent notation is not an answer. 2025 report Q5a: "many students did not interpret values from their calculator that were written using exponent notation (such as 1.05E6)." 2024 report Q1d: "Significant figures remain a challenge and many students were not able to interpret values from their calculator that were written using exponent notation (5.16E-3)." 2014 report Q1b: "Technology syntax is not to be used in providing answers; standard mathematical notation is to be used" (re "2.944E7").
• Chained rounding across parts. 2017 report Q4b: "Some students did not recognise that the rounded slope value from part a. was a required value in part b." 2018 report Q3d: "Some who correctly rounded in Question 3c. used −1514.7556 in Question 3d."

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2.15 OTHER RECURRING MICRO-STEMS (with fixed accepted answers)

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2.16 QUICK REFERENCE — MANDATORY WORDS BY QUESTION TYPE

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3. TRAPS AND EXAMINER COMPLAINTS

Grouped by theme; each entry gives the years the complaint was raised and the file.

3.1 Answering more than was asked ("further engagement")

This is the single most repeated complaint in the topic. - 2016 (Q2b.iii, Q3a) — adding a second statistic or an extra descriptor. - 2017 (Q2e) — "Students who initially gave the required median comparisons and then went further by quoting comparisons of other irrelevant statistics were not awarded full marks." - 2018 (Q1f, Q1g) — "some students went on to comment on the centre and spread, which was not required … The mark could not be awarded in this case." - 2019 (Q3, Q5f.i) — "this additional information compromised an otherwise correct answer." - 2020 (Q3d, Q4c, Q6b) — "this additional information devalued an otherwise correct answer"; "The mark could not be awarded due to this incorrect further engagement." - 2022 (Q4b, general comments) — "It was not appropriate to further comment on form or possible outliers." - 2024 (general comments) — "Students need to be careful that if they provide additional information in their response, it must be correct. … where a student further engaged to provide an incorrect delay time in their response, the mark was not awarded." - 2025 (Networks Q18c, but the principle is stated generally) — "Only the activity F needed to be written to obtain the mark."

3.2 Rounding

Raised in every year 2013–2026. See §2.14. Headline instances: 2014 Q1c and Q2d.ii; 2016 Q3b.i (decimal places vs sig figs); 2017 Q3b.iii and Q4a; 2018 Q2c and Q3c; 2019 Q6a ("the calculated value for autumn of 0.9975 was often rounded to the nearest whole number rather than to two decimal places"); 2020 Q1c and Q4a.ii and Q4b.ii; 2021 Q2a; 2022 Q3b ("the second number … was often rounded to four decimal places"); 2024 Q1d and Q1e; 2025 Q3, Q5a.

3.3 Sign errors

• Correlation coefficient sign: 2009 Q3c.ii, 2018 E1 Q9, 2019 E1 Q10, 2020 Q5f, 2021 Q3b, 2025 Q4b (79% got it wrong).
• Residual sign: 2007 Q2b.ii ("The negative sign was required"), 2012 Q2f, 2014 Q2d.i, 2017 Q3b.iii ("The most common incorrect calculation led to a positive residual of 412.5"), 2021 Q3d.
• Slope sign in an interpretation: 2020 Q5d ("Body density decreases by –0.001512 …" listed as unacceptable).
• Residual formula direction: 2019 Q5d — "Many found the predicted value correctly but then subtracted from 1013 rather than from the pressure 3 pm value of 1015."; 2012 Q2f — "Many students incorrectly calculated the residual as 12.2 − 11.1 = 1.1"; 2022 Q4d — "A number of students simply calculated the predicted value and did not go on to determine the residual."

3.4 Variable-type confusion

• 2013 E1 Q4 — "Most students decided that there were only two categorical variables, possibly rejecting postcode because its data values were numbers. … If students are in doubt about classifying a variable as categorical or numerical, they should ask, 'Does it make sense to calculate the mean of this variable?' If the answer is 'No', the variable is categorical."
• 2016 E1 Q2 — age (under 50 / 50 or over) is ordinal, not nominal.
• 2017 E1 Q7 — "many incorrectly chose option C, evidently because they incorrectly assumed that the variable number of moths was numerical because it involved numbers. The use of numbers in a variable definition does not automatically make the variable numerical."
• 2018 Q1a — "The definition of a categorical variable was not always understood."
• 2021 Q1a — "A common error was counting the number of values (45) instead of variables."
• 2022 Q3a.i — counting day number as numerical.

3.5 Choosing the wrong display / wrong statistic for the data type

• 2014 E1 Q8 — "only a back-to-back stem plot was suitable for displaying the association between a car's speed (numerical) and the sex of the driver (categorical with two categories). A parallel box plot would also have been appropriate."
• 2016 E1 Q8 — "Parallel boxplots are one of the statistical graphs that can be used to investigate the association between a numerical variable and a categorical variable."
• 2019 E1 Q8 — a two-way frequency table needs both variables categorical.
• 2024 NHT E1 Q7 — "Age is a numerical variable and uses public transport is a categorical variable, so parallel boxplots are the appropriate form of display."
• Mean from a boxplot: 2006 Q1f, 2015 Q2b, 2016 Q2b.iii, 2017 Q2e, 2019 Q3, 2020 Q3d — "this cannot be accurately determined from a boxplot unless the distributions are clearly symmetric."

3.6 Boxplot construction and reading

• 2015 E1 Q6 and 2017 E1 Q2 — "when a boxplot displays outliers, these values cannot be ignored when determining the minimum and maximum values in the distribution." / "Even though the points are identified as outliers, they are still valid data points within the data set and must be used as maximum and minimum values if appropriate."
• 2020 Q2c — whiskers must end at the second-lowest/second-highest actual data values; "Lower and upper fences are not part of the data set and therefore should not be plotted on a box plot."
• 2014 E1 Q6 — estimating the fence eliminates two of five options; students over-counted outliers.
• 2006 Q1d — "Many students lost marks through inaccurate, careless placement of quartiles."

3.7 Graph drawing (lines, points, smoothing crosses)

• 2007 Q3b.ii — "The line was very often badly plotted with two close points apparently chosen to locate the line. It is expected that the points be a reasonable distance apart."
• 2009 Q3a — "By choosing two points that were close to each other, many students were unable to plot this line within an acceptable accuracy. … Students are expected to draw straight lines with the aid of a ruler … Freehand drawings are inaccurate and will generally lead to errors that are penalised."
• 2014 Q2b — "Many seemed to draw the line by eye, with no reference to the least squares regression equation given in the question. … Students are encouraged to use the whole grid, plotting a point at area = 0 and area = 9."
• 2017 Q3b.i — "Many students did not realise that the scale on the horizontal axis started at 10 and not 0. It was clear that some students did not take a ruler into the examination."
• 2020 Q5a — "It is necessary to calculate appropriate points and plot them in order to get an accurate line. Students should ensure that their line extends across the whole set of axes."
• 2021 Q4a — "Students who wrote the endpoints of (1908, 75.256) and (2020, 48.04) on the graph tended to be successful."
• 2024 Q3b / 2025 Q4f.ii — "Students need to be precise when marking a point on a grid, taking particular care with the scale used."
• 2009 Q2b (median smoothing) — "median smoothing is to be treated as a graphical technique. … students are expected to locate medians directly from the graph by inspection, not by listing out the coordinates of each point and then performing the task numerically. Tackling such problems by first listing out the coordinates is unnecessary, time-consuming and usually inaccurate."
• 2016 Q4a — "Median smoothing is a graphical technique and requires some accuracy in the correct placement of crosses or dots. Reading the values from points on the graph is unlikely to produce accurate enough placement of points and should be discouraged."
• Non-attempt: "A significant number of students did not answer this question" appears at 2007 Q3b.ii, 2009 Q1a & Q3a, 2016 Q1b & Q4a & Q4b, 2018 Q3b.i, 2020 Q5a, 2021 Q4a, 2024 Q3g.i. VCAA repeatedly links this to not using the 15 minutes' reading time.

3.8 Reading the question / answering a remembered question

• 2019 general comments: "It was clear that many students did not read the questions carefully enough and often gave answers that appeared to be based on a similar kind of question from their studies and revision."
• 2020 general comments: "Often answers seemed to be copied from notes based on a similar problem but not applied to the exam question."
• 2009 report (r² interpretation): "It was apparent that some students transcribed material from their bound reference notes and gave inappropriate answers that made reference to variables such as age, cost or profit."
• 2009 report (seasonal index): "students simply copied material from their bound reference notes and gave answers that referred to autumn 'sales'."
• 2013 report Q4c: "Several students wrote 'strong, positive, linear relationship' but this was not appropriate. These students may have copied this from their bound book of notes."
• 2018 Q1c: "some students did not read the question carefully as they gave the full list of all cities with a medium level of congestion instead of giving only the large cities."
• 2024 report: "Students should read the question carefully, and accept as correct what is specified in the question. For example, in Question 3h some students claimed the prediction would be reliable, despite the question indicating otherwise." (repeated for 2024 Q3g.ii)
• 2024 Q2b: "The emphasis on 'smallest' in the question was overlooked… The question asked for the number of heights, not an actual height."
• 2021 Q3c: "The instruction to 'write down' the average decrease suggested no calculation was required."
• 2017 Q1b.ii: "Many students overlooked the requirement to convert from percentage to quantity."

3.9 Answer-presentation traps

• Sentences where a number was wanted: 2019 general comments — "Many questions … were worth one mark only … Generally there was no need to put the answer into a sentence." 2024 report — "in Question 1a.ii an answer of 50% was sufficient … There was no need to write '50% of the Mgold values are greater than 2.25 m'." 2020 report Q4c — "Students did not need to answer in a sentence; the value of 29% was sufficient."
• Point form is acceptable: 2019, 2020, 2022, 2024 general comments — "A response in point form is also acceptable."
• Show working for 2-mark questions: 2018/2019/2020/2022/2025 general comments — "An incorrect answer on its own will not be awarded any marks in a two-mark question; however, often a method mark can be awarded for appropriate working."
• Variables, not x and y: 2006 Q3b, 2008 Q4b ("The variables arm span and height were required in the equation rather than y and x"), 2010 Q3c ("Students were expected to use the variables given in the question rather than just x and y").
• Reversed intercept and slope in the answer boxes: 2024 PL — "This student was also awarded one mark out of two. It was clear that the student found the two values correctly, but in the final answer had reversed the slope and the intercept."
• Transcription: 2020 report — "Copying/transcribing numbers directly from technology output … was often not done accurately"; 2024 report — "Transcription errors were often seen."
• Legibility/scanning: 2018, 2019, 2020, 2024 general comments — "Scanned images are used for assessing"; 2024 — "write in a dark colour (for example, blue or black pen or 2B pencil)".

3.10 Technology / method traps

• 2016 Q3b.i: "Regression analysis by technology, and not the use of formulas, was required … The first column contained the response variable rather than the explanatory variable. Students who did not notice this gave their answer as (2.4, 1.0)."
• 2015 Q4b: "Some inappropriately used the data from the first column as the independent variable."
• 2011 Q4a: "For some students it did not register that the dependent variable was in the first column of the table and hence calculated the regression line incorrectly."
• 2013 Q3a (z-score): "The rule on the formula sheet was given as z = (x − x̄)/s_x and applied to … the independent variable, x. However, the question asked for the z score for the development index (the dependent variable, y) … Many students failed to use brackets: (91 − 85.6) ÷ 2.99. Without brackets, this calculation becomes 91 − 85.6/2.99 = 62.371…"
• 2014 Q3a: "A log transformation, using base 10, was required … Students need to distinguish between use of the base 10 logarithm and the natural logarithm when using technology."
• 2019 Q5e.i: "Some responses attempted to use the formula … This is not part of the current study design."
• 2017 Q4b: "Some students appeared to have renumbered the values of the variable year as 1, 2, 3, etc. This was not asked for and was inappropriate given the increments of 10 in the given values."
• 2013 report: "There are several concepts in the Core that are often confused. … some students found the 13 points that would result from three-median smoothing instead of the three-median line as required."

3.11 Answers that are absurd in context

• 2011 Q4b: "Very commonly, answers were inappropriate in the context of the question. For example, many answers were in the thousands, millions or were written as dollars. Answers such as these could not apply to a question about the average age at first marriage."
• 2008 Q5b: "an answer of 1239.9 hours of homework per week would be rather exhausting, and impossible with only 168 hours in a week. Equally, a negative number of hours would also present some difficulties."
• 2015 Q5b.i: "Some students found negative values for life expectancies. Negative values are non-consistent with the context."
• 2014 Q4b.ii: "Some incorrect answers were greater than the number of suburbs in the city."

3.12 Hardest items — the empirical difficulty ranking (current era)

From the Exam 2 mark distributions, the parts where ≥70% of students scored zero:

Consistent pattern across every Exam 1 report 2016–2022: "Students generally answered … well, particularly questions that required standard, routine calculations. Questions that required the use or analysis of graphical or tabular information were answered less well." (...2017_fm1_examrep17.txt, ...2018_fm1_examrep18.txt, ...2019_FM1_examrep19.txt, ...2020furmaths1-exam-report.txt, ...2021furthermath1-report.txt)

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4. FILE INDEX FOR THIS RESEARCH

All paths relative to corpus/text\.

Exam 2 papers (Data analysis section line ranges as extracted): Documents_exams_mathematics_2006furmath2-w.txt (81–249) · 2007furmath2.txt (81–288) · 2008furmath2-w.txt (82–270) · 2009furmath2-w.txt (82–231) · 2010furmath2-w.txt (82–240) · 2011furmath2-w.txt (82–291, broken text layer) · 2012_2012furmath2-w.txt (79–293) · 2013_2013furmath2-w.txt (82–229) · 2014_2014furmath2-w.txt (75–316) · 2015_2015furmath2-w.txt (75–323) · 2016_2016furmath2-w.txt (72–351) · 2017_2017furmath2-w.txt (72–285) · 2018_2018furmath2-w.txt (72–349) · 2019_2019furmath2-w.txt (72–434) · 2020_2020furmath2-w.txt (71–420) · 2021_2021furmath2-w.txt (71–358) · 2022_2022furmath2-w.txt (71–352) · 2023_2023genmath2-w.txt (63–342) · 2025-11_2025-GeneralMaths2.txt (50–347) · 2026-06_2026-NHT-GeneralMaths2.txt (49–371)

NHT Exam 2 papers: 2017_nht_2017FM2-nht-w.txt (78–306) · 2018_nht_2018FM2-nht-w.txt (72–…) · 2019_NHT_2019FM2-nht-w.txt · 2021_NHT_2021FM2-nht-w.txt · 2022_NHT_2022furmath2-nht-w.txt (71–334) · 2023_NHT_2023FM2-nht-w.txt (71–335) · 2024_NHT_2024GM2-nht-w.txt (48–347)

Exam 1 papers: 2006furmath1-w.txt … 2023_2023genmath1-w.txt (72–290) · 2025-11_2025-GeneralMaths1_0.txt (49–365) · 2026-05_2026-NHT-GeneralMaths1.txt (53–371)

Exam 2 reports (DA sections): furthermaths2_assessrep_06.txt (121–282) · further2_assessrep_07.txt (239–349) · further_maths2_assessrep_08.txt (203–352) · further2_assessrep_09.txt (179–352) · further2_assessrep_10.txt (145–273) · furthermaths2_assessrep_11.txt (64–193) · 2012_fm2_assessrep12.txt (89–209) · 2013_FM2_examrep13.txt (55–207) · 2014_FM2_examrep14.txt (85–261) · 2015_FM2_examrep15.txt (112–287) · 2016_FM2_examrep16.txt (81–323) · 2017_fm2_examrep17.txt (92–343) · 2018_FM2_examrep18.txt (83–315) · 2019_FM2_examrep19.txt (116–402) · 2020_2020furmaths2-exam-report.txt (36–187) · 2021_2021furthermath2-report.txt (32–127) · 2022_2022furmaths2-report.txt (30–128) · 2025-03_2024generalmaths2-report.txt (27–136) · 2026-01_2025-GeneralMaths2-report.txt (3–118)

NHT Exam 2 reports: 2017_nht_fm2nht_examrep17.txt · 2018_nht_furthermaths2nht_examrep18.txt · 2019_NHT_fm2nht_examrep19.txt · 2021_NHT_2021-NHT-Further-Maths-2-exam-report.txt · 2022_NHT_2022-furthmaths2-NHT-report.txt · 2023_NHT_2023furthermaths2NHT-report.txt · 2024_NHT_2024NHTgeneralmaths2-report.txt · 2025-10_2025-NHT-general-maths2-report.txt

Marking / assessment guides (the most prescriptive documents in the corpus): 2025-04_2024generalmathematics2-assessment-guide.txt · 2025-11_2025-GeneralMaths2-assessment-guide.txt · 2025-06_2025NHT-GeneralMath2-assessment-guide.txt · 2026-06_2026-NHT-GeneralMaths2-assessment-guide.txt · 2025-11_2025-GeneralMaths1-assessment-guide.txt

Exam 1 reports (DA commentary): furthermaths1_assessrep_06.txt · further1_assessrep_07.txt · further_maths1_assessrep_08.txt · further1_assessrep_09.txt · further1_assessrep_10.txt · further1_assessrep_11.txt · 2012_FM1_assessrep_12.txt · 2013_FM1_examrep13.txt · 2014_FM1_examrep14.txt · 2015_FM1_examrep15.txt · 2016_FM1_examrep16.txt · 2017_fm1_examrep17.txt · 2018_fm1_examrep18.txt · 2019_FM1_examrep19.txt · 2020_2020furmaths1-exam-report.txt · 2021_2021furthermath1-report.txt · 2022_2022furmaths1-report.txt · 2025-07_2023generalmaths1-report.txt · 2025-03_2024generalmaths1-report.txt · 2026-02_2025-GeneralMaths1-report.txt · 2026-02_2024-NHTgeneralmaths1-report.txt · 2025-10_2025-NHT-general-maths1-report.txt

Meta documents: 2025-04_genmath-specs-w.txt (examination specifications) · 2025-04_General_Maths_Examination_2.txt (2024 Chief Assessor assessment-PL transcript — the richest single source on marking principles) · 2025-10_MCAS_GeneralMaths1.txt (MC answer sheet, confirms A–D) · Documents_exams_mathematics_generalmaths1-formula-w.txt / generalmaths2-formula-w.txt (formula sheet) · Documents_exams_mathematics_genmath1-sample-w.txt / genmath2-sample-w.txt (March 2023 sample papers)