June 2026
The 2025 VCE General Mathematics Examination 1 showed that multiple-choice does not mean easy.
It means efficient.
Students had 40 questions across Data analysis, Recursion and financial modelling, Matrices, and Networks and decision mathematics. Each question was worth one mark. There were no method marks. A correct answer scored one, and an incorrect answer scored zero.
That changed the kind of control students needed.
In Examination 2, students could sometimes receive partial credit for correct working. In Examination 1, the final selected option was everything. This meant students needed to read carefully, eliminate distractors, use CAS wisely and avoid being drawn into answers that looked familiar but did not match the question.
The 2025 report repeatedly showed that distractors were not random. They often reflected predictable mistakes.
Adding frequencies instead of calculating weighted totals.
Confusing association with causation.
Forgetting the sign of a relationship.
Using compound interest when simple interest was required.
Misreading matrix orientation.
Counting the wrong edges in a network.
Following an algorithm in the wrong order.
Examination 1 rewarded students who could identify the trap before choosing the option.
Multiple-choice still required working
A major misconception about Examination 1 is that students do not need to work.
They do.
The difference is that the working is not assessed directly. It still helps students choose the correct option.
For example, Question 2 asked for the total number of avocados sold in bags. A student who simply scanned the options might choose the total number of customers or a nearby value. The correct calculation was:
1 × 4 + 2 × 11 + 3 × 3 + 4 × 9 + 5 × 5 + 6 × 7 = 138
This required written calculation.
The multiple-choice options did not remove the need for method. They made method more important because one small misread could lead to a plausible distractor.
Students should use the question book actively.
Mark frequencies.
Write formulas.
Circle key words.
Cross out impossible options.
Estimate before calculating when useful.
The answer sheet should be the final step, not the thinking space.
The first questions tested care, not complexity
The opening data questions were accessible, but they required careful reading.
Question 1 asked for the median bag size. The report explained that there were 39 customers, so the median was the 20th value. The 20th value was in the fourth column, so the answer was 4.
Question 2 then asked for total avocados sold, which required multiplying bag size by frequency.
These questions show how VCAA can test precision early.
The content was not advanced, but the trap was conceptual. The first answer required counting customers. The second required counting avocados.
Students who rush because the graph looks simple can lose marks immediately.
In Examination 1, easy-looking questions still deserve full attention.
Distractors often came from common mistakes
The Examination 1 report is valuable because it shows how incorrect options often correspond to common errors.
In Question 5, students needed to use the 68–95–99.7 rule to find the mean and standard deviation of heights. The correct answer was 164.7 and 7.1.
The incorrect options were not meaningless. They reflected likely mistakes with the position of values on the normal distribution or with solving the equations.
This is true across the paper.
A distractor may come from:
- using the wrong formula
- reversing variables
- using a positive sign instead of a negative sign
- rounding too early
- confusing total frequency with weighted total
- interpreting a graph visually instead of statistically
- applying a rule to the wrong value
- performing only the first step of an algorithm
Students should treat every option as a possible diagnosis of an error.
If an option matches a familiar shortcut too quickly, it may be a trap.
Data displays needed option-by-option checking
Question 3 asked students to interpret parallel boxplots for life expectancy.
The correct answer was that life expectancy in all Sample T countries exceeded the median life expectancy in Sample H.
The report showed that the other options failed when checked carefully against the boxplots. The interquartile range claim was wrong. The median difference claim was wrong. The quartile comparison was wrong.
This is how students should approach display-based multiple-choice questions.
Do not choose the statement that “sounds about right”.
Check each statement against the display.
Eliminate statements that are contradicted by the graph.
Use approximate values carefully.
In a boxplot question, the words median, quartile, interquartile range, minimum, maximum and exceeds all carry specific meanings.
A quick glance is not enough.
Logarithmic scales required calculation
Question 4 involved Singapore’s population density and a histogram with a logarithmic base 10 scale.
Students were given Singapore’s population and area. They needed to calculate:
population density = 6 028 460 ÷ 720 = 8372.8611
Then:
log₁₀(8372.8611) = 3.92287
This value lay between 3.5 and 4.0, placing it in the correct labelled column.
This question rewarded students who recognised the scale transformation.
The histogram was not displaying population density directly. It was displaying log₁₀(population density).
That meant students needed to calculate density first, then take the logarithm.
A common multiple-choice trap is to stop after the first calculation.
Students need to check what the axis actually shows.
Normal distribution questions needed mapped positions
Question 5 used the 68–95–99.7 rule.
The key was recognising that:
2.5% greater than 178.9 cm means 178.9 cm is two standard deviations above the mean.
16% less than 157.6 cm means 157.6 cm is one standard deviation below the mean.
This gives:
mean + 2s = 178.9
mean − s = 157.6
The answer was:
mean = 164.7
standard deviation = 7.1
In a multiple-choice setting, students might try to work backwards from the options. That can be useful, but only if they know what the percentages mean.
The 68–95–99.7 rule should be visual.
Students should sketch or mentally mark the curve: one standard deviation, two standard deviations, tail percentages.
That prevents guessing.
Categorical data questions tested variable awareness
Question 8 asked for the most appropriate display for preferred car colour by gender.
The correct answer was a segmented bar chart.
This was because the data was categorical.
The distractors included histogram, back-to-back stem plot and parallel boxplots. These are all displays students recognise, but they are not appropriate for this type of data.
This is a recurring multiple-choice pattern.
Options may all be legitimate mathematical terms. The correct one is the one that fits the variable type and context.
Before choosing a graph, students should ask:
Is the data numerical or categorical?
Is there one variable or two?
Is the question comparing groups?
Are percentages or counts being compared?
A familiar display is not always the right display.
Association questions required rejecting causation
Question 10 gave a correlation coefficient of r = −0.466 for games won and goals against.
The correct conclusion was that more goals scored against is associated with a smaller number of wins.
The report explained that the options claiming causation had to be rejected.
This is exactly the kind of trap that appears in multiple-choice questions. Two options may sound logically plausible, but they use the wrong statistical language.
A correlation coefficient supports association.
It does not establish causation.
Students should automatically cross out options that claim causes unless the question explicitly provides a design that supports causal inference.
In General Mathematics, wording is mathematical.
Least squares line questions allowed estimation
Question 9 asked for the equation of a least squares line from a scatterplot.
The report suggested using two points from the graph, such as (27, 12) and (44, 9), to estimate the slope.
The slope was approximately:
(9 − 12) ÷ (44 − 27) = −0.176
This supported the option:
games won = 16.8 − 0.178 × goals against
This is an important multiple-choice technique.
Students do not always need an exact regression calculation. If the graph is given and the options are separated enough, an estimate can eliminate wrong answers quickly.
A positive slope option could be eliminated immediately because the graph showed a negative association.
Then students could compare approximate slope and intercept.
Efficiency matters in Examination 1.
Time series questions needed centre alignment
The report’s comments on Question 13 showed that students needed to find a median from five values with Week 8 in the middle:
50, 38, 32, 35, 41
In rank order:
32, 35, 38, 41, 50
The median was 38.
This kind of question tests moving median or smoothing logic. Students need to identify the correct window of values and centre it on the correct time period.
The trap is often using the wrong five values or averaging when the median is required.
Students should mark the time period and count carefully.
In time series questions, the position of the smoothed value matters as much as the calculation.
Finance questions tested model recognition
Examination 1 included Recursion and financial modelling questions.
Question 17 asked for the expression for simple interest on $4000 over three years at 4% per annum.
The correct expression was:
4000 + 3(0.04 × 4000)
The incorrect compound interest expression 4000 × 1.04³ would have been tempting.
This is a classic multiple-choice finance trap.
Students should identify the model before looking at options.
Simple interest: interest is calculated on the original principal.
Compound interest: interest is calculated on the increasing balance.
If students look at options too soon, the more familiar expression may pull them away from the wording of the question.
Recursion questions tested sequence behaviour
Question 18 involved:
u₀ = a, uₙ₊₁ = Ruₙ + d
where a > 0, R = 0.5 and d = 0.
The sequence was geometric and decreasing.
This required students to interpret the recurrence relation. Since each term is half the previous term, and the starting value is positive, the terms decrease geometrically.
Multiple-choice recurrence questions often ask for the behaviour of a sequence rather than a specific term.
Students should check:
Is the change additive or multiplicative?
Is the multiplier greater than 1 or between 0 and 1?
Is the starting value positive or negative?
Is there a constant added each time?
The sequence type comes from the structure.
Matrix questions needed definition checking
The matrices section in Examination 1 included questions on matrix types, multiplication, inverse existence, communication matrices, Leslie matrices, entry rules, dominance matrices and defined operations.
Many of these questions could be answered quickly if students knew definitions precisely.
For example, a permutation matrix must have exactly one 1 in each row and exactly one 1 in each column. A diagonal matrix has zeros outside the main diagonal. An inverse exists only if the determinant is non-zero.
The trap is assuming from appearance.
Students should check the definition fully.
Does every row satisfy the condition?
Does every column satisfy the condition?
Are the matrix dimensions compatible?
Is the determinant zero?
What does the row represent?
What does the column represent?
Matrix multiple-choice questions often reward checking over speed.
Matrix dimensions were an efficient elimination tool
Question 31 asked which matrix computation was defined.
This kind of question should be approached using dimensions before calculation.
Addition requires identical dimensions.
Multiplication requires inner dimensions to match.
Students can eliminate invalid options quickly by writing the matrix dimensions beside each expression.
There is no need to calculate a product if the product is undefined.
This is one of the best time-saving techniques in Examination 1.
Check dimensions first.
Only calculate if necessary.
Networks required precise definitions
The networks section tested Hamiltonian cycles, bridges, minimum spanning trees, cuts, maximum flow, shortest path, Hungarian algorithm and float.
Each term has a specific meaning.
A Hamiltonian cycle visits every vertex once and returns to the start.
A bridge disconnects the graph when removed.
A minimum spanning tree connects all vertices with no cycles and minimum total weight.
A cut capacity counts directed edges crossing from source side to sink side.
A shortest path minimises total weight, not number of edges.
Float is latest start minus earliest start.
Multiple-choice network options often exploit confusion between these definitions.
Students should pause and identify the term being tested before inspecting the diagram.
Cut questions required direction awareness
Question 36 asked for the capacity of a cut.
The report stated that although the cut crossed six edges, only four were in the direction of flow from source to sink. These had capacities 7, 3, 5 and 12, giving:
27
This is a perfect example of a multiple-choice trap.
Students who add every crossed edge will get a different option. Students who ignore direction will also be pulled into a distractor.
In flow networks, direction matters.
Students should mark the source side and sink side, then count only the directed edges going from source to sink across the cut.
The Hungarian algorithm needed the specified stage
Question 39 asked for the table after row reduction and then column reduction in the Hungarian algorithm.
The report explained that:
Option A showed row reduction only.
Option C showed column reduction only.
Option D showed column reduction first, then row reduction.
Option B was correct.
This shows that algorithm questions can assess intermediate stages.
Students need to follow exactly what the question asks.
Not the final answer.
Not the first step only.
Not the steps in a different order.
The specified stage.
In multiple-choice, distractors are often different stages of the same algorithm.
That means students must be disciplined.
Answer elimination was a legitimate strategy
Examination 1 rewards efficient reasoning.
Students should use elimination whenever possible.
For example:
If a regression slope is clearly negative, eliminate any positive-slope equation.
If a display is for categorical data, eliminate numerical displays.
If an answer claims causation from correlation, eliminate it.
If a matrix operation has invalid dimensions, eliminate it.
If a sequence is clearly decreasing, eliminate increasing options.
If a graph edge is not directed across the cut correctly, eliminate that capacity.
Elimination does not mean guessing.
It means using mathematical constraints to reduce the options.
This is a powerful Examination 1 skill.
CAS should be used strategically
Students were permitted to use approved CAS technology in Examination 1.
But CAS use should be strategic.
Some questions are faster by inspection. Some require calculation. Some can be checked with technology if time allows. Others are conceptual and cannot be solved by pressing buttons.
For example:
CAS can help with standard deviation, regression, financial calculations and matrix products.
CAS is less useful for identifying whether a response claims causation, whether a graph is appropriate for categorical data, or whether an answer matches a context.
Technology should support reasoning.
It should not replace reading.
Time management mattered
Examination 1 contained 40 questions in 90 minutes.
That gives a little over two minutes per question on average, but not all questions require equal time.
Some data and definition questions can be answered quickly. Finance, matrices and networks may require more working. Students should not spend five minutes fighting one mark early in the paper if other accessible marks remain.
A sensible strategy is:
Answer straightforward questions confidently.
Mark difficult questions for return.
Use elimination to narrow options.
Avoid leaving blanks.
Check answer sheet alignment.
Return to flagged questions with remaining time.
Because there is no penalty for incorrect answers, every question should receive an answer.
But guessing should come after elimination wherever possible.
The answer sheet created its own risk
Examination 1 required students to record answers on a multiple-choice answer sheet.
This creates practical risks.
A student can solve a question correctly but shade the wrong option. A student can skip a question and misalign later answers. A student can change an answer unclearly. A student can accidentally mark more than one answer and receive no mark for that question.
These are avoidable mistakes.
Students should develop an answer-sheet routine.
Some students prefer answering in batches of five and checking alignment. Others prefer transferring each answer immediately. Either is fine if it is consistent.
The answer sheet is part of the exam process.
It deserves attention.
Why Examination 1 errors happen
Examination 1 errors often happen because students move too fast.
They see a familiar graph and estimate instead of calculating.
They choose a formula before identifying the financial model.
They forget that correlation is not causation.
They apply the Hungarian algorithm in the wrong order.
They add all cut edges instead of directed edges.
They use CAS output without checking whether the question is conceptual.
They misread one word and choose a distractor designed for that mistake.
The paper rewards speed only when it is paired with control.
Fast and careless is not efficient.
What future General Mathematics students should learn from 2025
The 2025 VCE General Mathematics Examination 1 shows that multiple-choice preparation needs to be deliberate.
Students should practise:
- writing working even when it will not be marked
- using elimination before guessing
- checking each option against graphs and displays
- distinguishing frequency from total quantity
- using the correct model for finance questions
- recognising causation traps in association questions
- checking matrix definitions and dimensions
- interpreting row and column meaning
- applying network definitions precisely
- counting cut capacity with direction
- following algorithm steps in the specified order
- using CAS strategically rather than automatically
- managing time across 40 questions
- checking answer-sheet alignment
These skills help students convert knowledge into marks under multiple-choice conditions.
Examination 1 is not a race to finish.
It is a test of accurate selection.
How ATAR STAR prepares students for Examination 1
At ATAR STAR, Examination 1 is taught as strategic multiple-choice mathematics.
Students learn to identify the question type, anticipate common distractors, use CAS efficiently, eliminate impossible options and check context before selecting an answer. They practise under timed conditions so that speed comes from fluency, not rushing.
The 2025 Examination Report confirms why this matters. High-scoring students did not simply know the content.
They selected answers with discipline.