June 2026
The 2025 VCE General Mathematics Examination 2 showed that written mathematics is not just about getting the answer.
It is about showing the reasoning that leads to the answer.
This is one of the biggest differences between Examination 1 and Examination 2. In Examination 1, students select an answer from multiple-choice options. In Examination 2, students need to write responses, show working, mark points on graphs, complete tables, explain reasoning and interpret outputs in context.
The 2025 report repeatedly showed that students lost marks not because the mathematics was impossible, but because their working was incomplete, their rounding was inappropriate, their calculator output was misread, or their explanation did not match the question.
Examination 2 rewards students who can communicate mathematically.
What value did you substitute?
What statistic did you use?
What does the calculator output mean?
Did you round only when instructed?
Did you show the step that verifies the given value?
Did you use the explanatory variable when discussing extrapolation?
Did your answer interpret the result in the context of the question?
These details mattered throughout the paper.
Working was assessable
The assessment guide made clear that where a question explicitly required working, full marks depended on correct working and a correct response. It also explained that partial marks could be awarded for correct key steps, and that consequential errors could be considered in multi-step questions.
This is very important for students.
Working is not rough space.
It is part of the response.
A student who writes only a final answer may miss method marks. A student who makes a small arithmetic error but shows the correct process may still receive partial credit. A student who uses technology but does not communicate what they entered or how they used the output may leave too much invisible.
In Examination 2, the assessor needs to see the mathematics.
Rounding instructions had to be followed exactly
The front of Examination 2 instructed students that numerical answers should only be rounded when instructed.
The report specifically reminded students of this in Question 3. Students needed to calculate the percentage of home sale prices between two values using the 68–95–99.7 rule. The correct answer was 83.85%, not 84%.
This seems minor, but it reflects a broader exam habit.
Students often round because a rounded answer feels neater. But VCAA instructions matter. If a question does not ask for rounding, students should not round unnecessarily. If a question asks for a particular number of decimal places, that instruction should be followed exactly.
Rounding is not a personal preference.
It is part of the answer.
Standard deviation required careful data entry
Question 1c.i asked students to find the standard deviation of apartment sale prices to the nearest whole number.
The correct value was:
$346 466
The report noted that students needed to enter the data carefully into their calculator to avoid error.
This is a useful reminder that technology does not remove the possibility of mistakes. The CAS calculator can calculate a standard deviation accurately, but only if the correct values are entered and the correct statistic is selected.
Students should practise checking lists before calculating.
Did every value go in?
Were the house and apartment values separated correctly?
Was the correct statistical measure selected?
Did the question ask for population or sample standard deviation?
Was the answer rounded as instructed?
Calculator use is still mathematical work.
The question told students which statistic to use
Question 1c.ii asked students to comment on the relative spread in sale prices using the information in Table 2.
Table 2 contained standard deviations.
The correct response was that house sale prices had a lower spread than apartment sale prices because the standard deviation for houses was lower.
The report noted that using other statistics such as range or interquartile range was not appropriate.
This is one of the clearest examples of task control in Examination 2.
A student may know how to compare spread using several measures. But if the question says to use Table 2, the answer must use Table 2.
The correct method is not just a mathematically valid method.
It is the method requested by the task.
“Show that” questions required the missing steps
Question 4f.i asked students to show that the residual for the home furthest from the city centre was 27 984.
The least squares equation was:
sale price = 1 765 353 − 35 054 × distance from city centre
The home was 15.5 km from the city centre and sold for $1 250 000.
Students needed to show:
predicted value = 1 765 353 − 35 054 × 15.5
predicted value = 1 222 016
Then:
residual = actual − predicted
residual = 1 250 000 − 1 222 016
residual = 27 984
The report noted that students needed to show all working that led to the given residual value.
This is exactly what a “show that” question demands.
Students cannot simply write the number given in the question. They must demonstrate why it is correct.
Residuals needed correct direction
The residual formula used in the report was:
residual = actual value − predicted value
This matters because reversing the order changes the sign.
In Question 4f.i, the actual value was higher than the predicted value, so the residual was positive.
A positive residual means the actual sale price was above the price predicted by the regression line. A negative residual would mean the actual sale price was below the predicted value.
Students should understand the meaning of the sign, not just the calculation.
This also helps when plotting residuals.
Graph plotting required scale awareness
Question 4f.ii asked students to plot the residual from part i on the residual plot.
The report noted that students needed to be precise when marking a point on a grid and pay particular attention to the scale.
The point had coordinates:
distance from city centre = 15.5
residual = 27 984
Because the residual axis used large intervals, 27 984 was only slightly above zero. Students who placed the point too high showed that they had not read the scale carefully.
This is a common Examination 2 issue.
Graph marks can be lost through careless placement even when the calculation is correct.
Students should always check:
What is each axis measuring?
What is the scale?
Where does the point sit relative to marked gridlines?
Should the point be above or below zero?
Is the x-value between two labelled values?
Precision matters on graphs.
The sign of r required interpretation, not just calculation
Question 4b asked students to calculate the correlation coefficient r from the coefficient of determination.
The coefficient of determination was:
0.0806
Taking the square root gives:
√0.0806 = 0.284
But the least squares line had a negative slope:
sale price = 1 765 353 − 35 054 × distance from city centre
Therefore:
r = −0.284
The report noted that many students left the answer as positive 0.284, failing to recognise that the slope was negative.
This is a classic Examination 2 error.
The calculator can give the magnitude, but the student must interpret the direction. Since r² is always positive, the sign of r must come from the direction of the association.
If the slope is negative, r is negative.
That decision cannot be skipped.
Interpolation and extrapolation depended on the explanatory variable
Question 4d asked whether a predicted sale price for a three-bedroom home located 2 km from the city centre was interpolation or extrapolation.
The report explained that students needed to base this on the explanatory variable, not the response variable.
The explanatory variable was distance from city centre.
So students needed to decide whether 2 km lay inside or outside the range of distances in the original data. Since it was outside the explanatory variable data range, the prediction was an example of extrapolation.
It was not appropriate to discuss whether the predicted sale price was outside the sale price range.
This is a subtle but important modelling point.
Regression predictions are made from x-values. Interpolation and extrapolation are therefore judged by the x-value.
Calculator notation needed to be understood
The report noted in Question 5a that significant figures remained problematic, and that many students did not interpret calculator values written in exponent notation, such as 1.05E6.
This is a practical but significant issue.
1.05E6 means:
1.05 × 10⁶ = 1 050 000
It does not mean 1.05. It does not mean 105 000. It is scientific notation.
Students who misread calculator output can lose marks even when their calculator has produced the correct value.
This is especially relevant in General Mathematics because the contexts often involve large values: house prices, loans, payments, populations, capacities and project costs.
Students should practise reading calculator output confidently.
Regression equations needed correct significant figures
Question 5a asked students to find a least squares line for sale price against days on the market.
The report gave the model:
Sale price = 1 050 000 − 8050 × days
It also noted that significant figures were problematic.
This tells students something important.
When writing a regression equation from CAS output, students need to convert calculator notation into sensible values and maintain enough precision. Over-rounding too early can distort later predictions.
A regression equation is not just an answer to one part. It may be used in later parts of the question.
Students should preserve enough accuracy to support subsequent calculations.
Written explanations needed the right variable
Examination 2 repeatedly required short explanations.
These were often only worth one mark, but they were still precise.
For example, Question 4d required students to explain interpolation or extrapolation using the explanatory variable. A student could not simply write “extrapolation because it is outside the data range” without identifying what was outside the data range.
A stronger answer would be:
This is extrapolation because 2 km is outside the range of the explanatory variable, distance from the city centre, in the data set.
This answer is short, but complete.
It names the concept, the reason and the relevant variable.
Contextual comments had to use the information provided
Question 1c.ii required a comment on spread using Table 2. Question 4e required describing linear association in terms of strength and direction. Question 7b required explaining why interest was lower in a reducing balance loan. These questions were not calculation-heavy, but they still demanded mathematical language.
A response should not be vague.
For spread:
House sale prices have a lower spread because their standard deviation is smaller.
For association:
The association is weak and negative.
For reducing balance interest:
The interest is lower because it is calculated on a smaller outstanding balance after the first repayment.
These are concise, but they directly answer the question.
Examination 2 explanations should be clear rather than long.
Finance questions required solver outputs to be interpreted
The finance questions in Examination 2 showed that CAS output must be interpreted carefully.
In one loan question, students used finance solver entries to determine the number of payments. The solver output gave approximately 60 total payments. But the question asked for the payment number before the final payment, so the answer was 59 payments before the final one.
This kind of wording matters.
A calculator might give the total number of payments. The question may ask for the number before the final payment, the final payment amount, the remaining balance, the interest component, or the principal reduction.
Students should not write the first output they see.
They should match the output to the question.
Recurrence relation and rule required different forms
The report noted that in Question 8, many students did not understand the difference between a recurrence relation and a rule.
For a flat depreciation model, the recurrence relation was:
V₀ = 40 000, Vₙ₊₁ = Vₙ − 8000
The rule was:
Vₙ = 40 000 − 8000n
These are not interchangeable.
The recurrence relation uses the previous term.
The rule gives the value directly.
This is another communication issue.
Students may understand the depreciation pattern, but they need to write it in the form requested. If the question asks for both, repeating the same form twice is not sufficient.
Matrix interpretations needed row-column control
In the matrices section, the report noted that many students misinterpreted a matrix product in Question 11b, suggesting that rows had been summed rather than columns.
This was not a calculator problem.
It was an interpretation problem.
Students needed to track what rows and columns represented and what the resulting matrix meant in context. In this case, the correct interpretation was total enrolments each day of the week.
Matrix working should therefore include labels whenever possible.
Rows and columns are not anonymous.
They carry the meaning of the matrix.
Network questions required explanations, not just labels
In the networks section, some questions required students to justify route or project decisions.
For example, an Eulerian route question required students to refer to vertex degrees when explaining why repeated edges were needed. A critical path question required students to identify common activities, latest start times, float and crashing cost.
These responses needed mathematical reasoning.
A student should not simply write “because it is not possible” or “because it is on the critical path” without showing the relevant condition.
In networks, explanations often depend on definitions.
Odd degree vertices.
Zero float.
Critical path duration.
Maximum flow.
Minimum cut.
Predecessor activity.
Dummy activity.
Using the correct term helps, but the reasoning must fit the graph.
Working helped protect against consequential errors
Because Examination 2 includes multi-step questions, one error can affect later answers.
The assessment guide explains that consequential errors may be considered where a question requires sequential steps. This means students can sometimes still receive credit for later reasoning if their method is clear, even when an earlier value is wrong.
This is another reason to show working.
If the assessor can see that the student used a previous answer correctly, some credit may still be available.
If the student writes only final answers, there is less evidence of method.
Working is a safety net.
The strongest responses were concise but complete
Examination 2 did not require long written explanations for most questions.
It required complete mathematical communication.
A strong response might be only one sentence or one line of working, but it directly addresses the question.
For example:
The association is weak and negative.
This is extrapolation because 2 km is outside the range of the explanatory variable.
The interest is lower because the outstanding balance has decreased.
Residual = actual − predicted = 1 250 000 − 1 222 016 = 27 984.
These answers are not verbose.
They are precise.
Why Examination 2 marks were lost
The 2025 report suggests that marks were often lost because students:
- rounded when not instructed
- entered data incorrectly into CAS
- used a statistic other than the one requested
- forgot the negative sign of r
- judged extrapolation using the response variable
- did not show working for “show that” questions
- plotted points inaccurately on graphs
- misread calculator exponent notation
- gave a recurrence relation when a rule was required
- misinterpreted matrix rows and columns
- gave vague contextual explanations
- copied calculator outputs without interpreting the wording
These are not content mysteries.
They are execution issues.
The strongest students knew the mathematics and communicated it carefully.
What future General Mathematics students should learn from 2025
The 2025 VCE General Mathematics Examination 2 shows that students need to prepare for written mathematical communication.
Students should practise:
- showing working for multi-step questions
- preserving exact values unless rounding is requested
- following rounding instructions exactly
- checking CAS data entry
- interpreting calculator notation such as 1.05E6
- using the statistic specified by the question
- choosing the sign of r from the slope
- explaining interpolation and extrapolation using the explanatory variable
- calculating residuals as actual minus predicted
- plotting residuals accurately using the grid scale
- writing recurrence relations and rules in different forms
- labelling matrix rows and columns
- giving concise contextual explanations
- interpreting finance solver outputs before writing final answers
These skills are exam skills, not just topic skills.
They turn knowledge into marks.
How ATAR STAR prepares students for Examination 2
At ATAR STAR, Examination 2 is taught as mathematical communication.
Students learn to set out working clearly, use CAS efficiently, interpret outputs, follow rounding instructions, and write concise explanations in context. They practise showing enough method to access marks while avoiding unnecessary working that wastes time.
The 2025 Examination Report confirms why this matters. High-scoring students did not simply arrive at answers.
They showed how the answers were obtained and what they meant.