June 2026
The 2025 VCE General Mathematics exams made one thing clear: high-scoring students were not simply better at using formulas.
They were better at reading the question, selecting the correct method, using technology carefully, interpreting results, and communicating the answer in the required form.
This mattered across both examinations.
Examination 1 tested 40 multiple-choice questions across Data analysis, Recursion and financial modelling, Matrices, and Networks and decision mathematics. Examination 2 required written responses across the same areas of study, with students needing to show working, interpret results and handle multi-step reasoning.
The strongest students were accurate, controlled and attentive to detail.
They knew when to use CAS.
They knew when to calculate by hand.
They knew when a statistic had to come from a specific table.
They knew when a prediction involved interpolation or extrapolation.
They knew when to round and when not to.
They knew that a recurrence relation and a rule are not the same thing.
They knew that a graph, matrix or network has to be interpreted in context.
In General Mathematics, the marks often sit in the details.
Data analysis rewarded careful reading of displays
The first section of Examination 1 began with a histogram showing avocado bag sizes. Question 1 asked for the median bag size. The report showed that students needed to sum the frequencies, identify that there were 39 customers, and locate the 20th value. That value fell in the fourth column, giving a median bag size of 4.
This is a simple example, but it reveals a major General Mathematics skill.
Students should not estimate the median from the visual centre of the graph. They need to use the frequencies.
The next question asked for the total number of avocados sold. This required multiplying each bag size by its frequency:
1 × 4 + 2 × 11 + 3 × 3 + 4 × 9 + 5 × 5 + 6 × 7 = 138
This is not the same as adding the number of customers.
The graph showed customers. The question asked for avocados.
That distinction mattered.
Graph interpretation needed exact statistical language
The 2025 reports repeatedly showed that students needed to interpret statistical displays precisely.
In Examination 1, students compared boxplots showing life expectancy for two samples. The correct statement was that life expectancy in all Sample T countries exceeded the median life expectancy in Sample H. This came from inspecting the minimum of Sample T and comparing it with the median of Sample H.
The incorrect options were tempting because they referred to familiar measures: interquartile range, median and quartiles. But each had to be checked against the graph.
This is a common General Mathematics issue.
Students recognise the vocabulary but do not always test the statement.
A high-scoring student checks each claim against the display.
The 68–95–99.7 rule required structure
Normal distribution questions appeared in both exams.
In Examination 1, students were told that 2.5% of heights were greater than 178.9 cm and 16% were less than 157.6 cm. Using the 68–95–99.7 rule, students needed to recognise that 178.9 cm corresponded to two standard deviations above the mean, while 157.6 cm corresponded to one standard deviation below the mean.
This produced:
mean + 2s = 178.9
mean − s = 157.6
Solving gave a mean of 164.7 and a standard deviation of 7.1.
In Examination 2, students used a z-score of −1.60 and the 68–95–99.7 rule to find a percentage. The report noted that students sometimes rounded when they should not have. The required percentage was 83.85%, not 84%.
This is an important lesson.
In General Mathematics, rounding is not a casual decision.
If the instruction says not to round unless directed, students must preserve the required exactness.
Calculator use was powerful but not automatic
The Examination 2 report made several comments about technology.
In Question 1c.i, students needed to enter data carefully into their calculator to find the standard deviation of apartment sale prices. The correct value was $346 466.
This was a calculator-supported question, but the risk was still human error.
If students enter values incorrectly, select the wrong list, use the wrong statistic or misread the output, the calculator will not protect them.
Question 5a showed another technology-related issue. Significant figures remained problematic, and many students did not interpret calculator outputs written in exponent notation, such as 1.05E6.
This matters enormously.
A CAS calculator can produce the correct output, but students must know what the output means. 1.05E6 means 1 050 000, not 1.05, not 105 000, and not an approximate mystery value to ignore.
Technology helps students who understand it.
It does not replace understanding.
Students had to use the statistic requested
Question 1c.ii in Examination 2 asked students to comment on the relative spread in sale prices using the information in Table 2. Table 2 gave the standard deviations for houses and apartments.
The report noted that using other statistics such as range or IQR was not appropriate.
This is one of the clearest examples of task alignment.
The question told students what information to use. Therefore, the comparison had to be based on standard deviation.
A correct response would state that house sale prices had a lower spread than apartment sale prices because the standard deviation for houses was lower.
A student might know how to compare range or IQR, but that was not the task.
In General Mathematics, using the wrong valid statistic can still be wrong.
Association questions required direction, strength and causation control
Several 2025 questions tested association and regression.
In Examination 1, a negative correlation coefficient of r = −0.466 appeared in a question about games won and goals against. The correct conclusion was that more goals scored against is associated with a smaller number of wins.
The word associated mattered.
The report rejected options involving causation. A correlation coefficient does not prove that one variable causes the other.
This is a foundational data analysis skill.
Students need to describe association without overclaiming.
In Examination 2, students were given a least squares line for sale price against distance from Melbourne’s city centre. The coefficient of determination was 0.0806. Students needed to calculate the correlation coefficient and recognise that the slope was negative, so r = −0.284.
The report noted that many students left the answer as positive 0.284, failing to recognise the negative slope.
This is a classic trap.
The coefficient of determination gives r². To find r, students must choose the sign based on the direction of the association.
Interpolation and extrapolation depended on the explanatory variable
Question 4d in Examination 2 asked whether a predicted sale price for a home two kilometres from the city centre was interpolation or extrapolation.
The report noted that students needed to recognise that interpolation and extrapolation are determined by the explanatory variable.
This means students needed to consider whether 2 km lay inside or outside the data range for distance from the city centre. It was not appropriate to refer to the sale price being outside the data range.
This is a subtle but important point.
Regression uses the explanatory variable to make a prediction about the response variable. Therefore, the interpolation or extrapolation judgement depends on whether the explanatory value is within the original x-data range.
A student who understands the formula but not the modelling context can easily lose this mark.
Residuals required working and graph precision
Question 4f in Examination 2 asked students to show that a missing residual was 27 984 and then plot it on the residual plot.
The predicted value was:
1 765 353 − 35 054 × 15.5 = 1 222 016
The residual was:
1 250 000 − 1 222 016 = 27 984
The report noted that students needed to show all working that led to the given residual value. It also noted that students needed to be precise when marking a point on a grid, taking particular care with the scale.
This shows two sides of Exam 2.
The calculation must be shown.
The graphical response must be plotted accurately.
A student may know the residual formula but still lose a mark if the plotted point is placed carelessly.
General Mathematics often rewards careful execution rather than difficult theory.
Recursion and financial modelling required exact model form
The 2025 reports showed that recursion and financial modelling were not simply calculator exercises.
In Examination 2, Question 8 asked students to write both a recurrence relation and a rule for a depreciating value. The report noted that many students did not understand the distinction and gave a similar answer again.
This is a major learning point.
A recurrence relation defines a term from the previous term, such as:
V₀ = 40 000, Vₙ₊₁ = Vₙ − 8000
A rule gives the value directly in terms of n, such as:
Vₙ = 40 000 − 8000n
These are related, but they are not the same.
Students need to recognise the form being requested.
If the question asks for a recurrence relation, give recurrence.
If the question asks for a rule, give an explicit rule.
Finance questions exposed sign and entry errors
The Examination 2 report’s finance comments showed that solver entries and sign conventions mattered.
In Question 10, students used finance solver entries involving values such as N = 40, I% = 6.4, PV = −650 000, PMT = 22 126.27, FV = 0, and P/Y & C/Y = 4.
The report noted that some students found the payment correctly from the calculator but answered with an incorrect positive value.
This is a common finance problem.
Students may know how to use the finance solver but misunderstand the cash-flow signs or copy a value incorrectly.
In financial modelling, signs are not cosmetic. They show the direction of money flow.
Students need to understand what each finance solver value represents, not simply enter numbers and hope.
Matrices required orientation
Matrices appeared in both examinations.
In Examination 2, Question 11b asked students to interpret a matrix product. The report noted that many students gave an answer suggesting that the rows had been summed rather than the columns.
This is a typical matrix issue.
Students may understand that multiplication or summing has occurred, but they misread what the rows and columns represent.
A high-scoring student tracks orientation carefully.
What does each row represent?
What does each column represent?
What does the resulting matrix represent?
Has the operation summed rows, columns or transitions?
Matrices are not just arrays of numbers.
They are organised information.
Transition matrices required conceptual interpretation
The matrices section also included transition matrices.
Students needed to interpret leading diagonal values, calculate expected percentages after repeated transitions, and find expected numbers moving between activities.
One assessment guide response stated that values on the leading diagonal indicated that no child does the same activity from one week to the next. This is a conceptual interpretation of the matrix structure, not a calculation.
This is important.
General Mathematics matrix questions often ask students what a value means in context.
A zero on the leading diagonal is not just a zero.
It means there is no transition from an activity back to the same activity in the next time period.
Students need to connect matrix entries to the real situation.
Networks rewarded methodical inspection
Networks and decision mathematics appeared at the end of Examination 1 and in Examination 2.
Students worked with Hamiltonian cycles, bridges, minimum spanning trees, cuts, maximum flow, shortest paths, the Hungarian algorithm, Eulerian trails and critical path networks.
These questions reward methodical inspection.
For example, Examination 1 Question 33 asked for the number of Hamiltonian cycles in a graph starting from a specified vertex. The assessment guide explained that only two Hamiltonian cycles could be created when starting at E: one forward and one backward around the graph.
Question 34 asked for the number of bridges. The assessment guide identified the top three edges as bridges because removing them caused the graph to become disconnected.
These tasks are not about applying a long formula.
They require careful graph reasoning.
Maximum flow and cuts required direction
In Examination 1, students worked with a flow network involving a source and sink. One question asked for the capacity of a cut; another asked for the maximum flow.
The assessment guide showed that Cut 1 involved four edges going into the cut with capacities 7, 3, 5 and 12, giving a total of 27. The maximum flow was determined by the minimum cut, 7 + 4 + 6 = 17.
This is another area where students need to know exactly what is being counted.
Not every edge near a cut is included.
Not every capacity in the diagram is relevant.
The direction of flow matters.
A high-scoring student marks the cut carefully and only includes the correct edges.
Critical path questions required project logic
The Examination 2 networks section included a home gym construction project with activities, completion times, critical paths, latest start times, float and crashing.
This kind of question tests both calculation and project interpretation.
Students needed to identify activities common to both critical paths, determine latest start time, identify the activity with the longest float, and calculate the minimum extra cost to reduce the project by three days.
Critical path questions can become confusing because several concepts interact.
Earliest start.
Latest start.
Float.
Critical activity.
Crash cost.
Maximum reduction.
Common activities across critical paths.
The strongest students organise the network logically and avoid treating each number in isolation.
Examination 2 rewarded showing working
The assessment guides emphasised that where working is required, full marks depend on correct working and correct response. Partial marks can be awarded for correct key steps, and consequential errors may be considered in multi-step responses.
This is one of the major differences between Examination 1 and Examination 2.
In Examination 1, students select an option.
In Examination 2, they must show enough reasoning for assessors to see how the answer was obtained.
This is why setting out matters.
A student who writes only a final answer may lose access to method marks. A student who makes a small arithmetic error but shows correct method may still earn partial credit.
Working is not just rough thinking.
It is assessable communication.
Rounding instructions mattered
The Examination 2 report specifically reminded students that numerical answers should only be rounded when instructed.
This is one of the easiest marks to protect.
If the question asks for three decimal places, round to three decimal places.
If it asks for the nearest whole number, round to the nearest whole number.
If it does not ask for rounding, do not round prematurely.
Premature rounding can change later answers. Over-rounding can lose exactness. Under-rounding can fail the instruction.
Students should underline rounding instructions in the question.
The strongest students used the context
General Mathematics is highly contextual.
Homes, sale prices, distance from the city centre, sports results, avocados, loans, activities, networks and projects are not just stories around the maths. They determine what the numbers mean.
For example:
A lower standard deviation means lower spread.
A negative slope means sale price decreases as distance increases.
A residual is actual minus predicted.
A finance repayment depends on cash-flow direction.
A matrix entry may represent enrolments, transitions or connections.
A network edge may represent a road, pipe, walkway or activity dependency.
The context tells students how to interpret the calculation.
High-scoring students do not detach the numbers from the scenario.
What future General Mathematics students should learn from 2025
The 2025 VCE General Mathematics reports show that students need to prepare for precision, not just procedures.
Students should be able to:
- read histograms, boxplots and scatterplots carefully
- distinguish frequency from total quantity
- use the 68–95–99.7 rule with correct standard deviation positions
- avoid rounding unless instructed
- use CAS accurately and interpret calculator notation
- compare spread using the statistic requested
- distinguish association from causation
- determine the sign of r from the slope
- identify interpolation and extrapolation using the explanatory variable
- calculate and plot residuals precisely
- distinguish recurrence relations from explicit rules
- use finance solver signs correctly
- interpret matrix rows, columns and entries in context
- analyse networks methodically
- show working clearly in Examination 2
These skills are not glamorous, but they are decisive.
General Mathematics rewards students who are careful, accurate and context-aware.
How ATAR STAR approaches VCE General Mathematics
At ATAR STAR, General Mathematics is taught as structured problem-solving.
Students learn to identify the question type, select the correct method, use technology efficiently, interpret outputs, and communicate answers in the form VCAA expects. They practise both multiple-choice strategy for Examination 1 and written working for Examination 2, with particular attention to rounding, CAS entry, context interpretation and common examiner traps.
The 2025 Examination Reports confirm why this matters. High-scoring students did not simply know procedures.
They executed them carefully.
That is what VCE General Mathematics rewards.