June 2026
The 2025 VCE General Mathematics exams showed that many marks were lost in avoidable ways.
This is not to suggest that the exams were simple. They covered a wide range of content: Data analysis, Recursion and financial modelling, Matrices, Networks and decision mathematics. Students had to work across multiple-choice and written-response formats, use CAS technology effectively, interpret data displays, handle financial models, work with matrix structures and reason through networks.
But the reports reveal a clear pattern.
Many errors came from execution.
Students used the wrong statistic.
They rounded when they were not asked to.
They forgot the sign of the correlation coefficient.
They judged extrapolation using the wrong variable.
They misread calculator notation.
They treated finance-solver output as the final answer without interpreting it.
They confused matrix rows and columns.
They followed an algorithm in the wrong order.
They failed to show working in Examination 2.
These mistakes are especially important because they are fixable.
In General Mathematics, high performance depends on controlling the details.
Students rounded when they should not have
One of the clearest messages from the Examination 2 report was that students needed to follow rounding instructions exactly.
At the beginning of Examination 2, students were told that numerical answers should only be rounded when instructed. Despite this, the report noted that some students rounded an answer in Question 3 when the exact percentage was required.
The correct percentage was:
83.85%
not:
84%
This kind of mistake is frustrating because the mathematical reasoning may be correct, but the final answer does not follow the instruction.
Rounding should never be automatic.
Students should ask:
Does the question ask for rounding?
If yes, to how many decimal places or significant figures?
If no, should I preserve the exact value?
Will this value be used in a later part?
Premature rounding is one of the easiest errors to avoid.
Students used the wrong statistic
In Examination 2 Question 1c.ii, students were asked 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 specifically noted that using other statistics such as range or interquartile range was not appropriate.
This is a major lesson.
A statistic can be valid in general but wrong for a particular question.
If the question directs students to a table of standard deviations, the answer must use standard deviation. If the question asks for IQR, students should not discuss range. If the question asks for median, students should not write mean.
General Mathematics does not only assess whether students know statistics.
It assesses whether they use the statistic requested.
Students forgot that r needed a sign
Examination 2 Question 4b asked students to calculate the correlation coefficient r from the coefficient of determination:
r² = 0.0806
Taking the square root gives:
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 final response as positive 0.284.
This is a classic error because r² gives only the size of the relationship, not its direction. To find r, students must look at the direction of the association.
If the slope is negative, r is negative.
If the slope is positive, r is positive.
The square root alone is not enough.
Students confused association with causation
In Examination 1 Question 10, the correlation coefficient between games won and goals against was:
r = −0.466
The correct conclusion was that more goals scored against was associated with a smaller number of wins.
The report rejected options that claimed causation.
This distinction is central to Data analysis.
A correlation coefficient describes association. It does not prove that one variable causes another.
Students should be very cautious with options or written responses that use language such as:
causes
leads to
results in
because of
Unless the question clearly supports causal inference, the safer and more mathematically correct language is:
is associated with
tends to be related to
has a negative association with
This is not just wording.
It is statistical reasoning.
Students judged extrapolation using the wrong variable
Examination 2 Question 4d asked whether predicting the sale price of a home two kilometres from the city centre was interpolation or extrapolation.
The report explained that students needed to base this on the explanatory variable.
The explanatory variable was:
distance from city centre
Therefore, students had to decide whether 2 km lay within the distance range of the original data. Since it was outside the explanatory variable data range, the prediction was extrapolation.
The report noted that it was not appropriate to refer to the sale price being outside the data range.
This is a subtle but important point.
Regression uses an explanatory variable to predict a response variable. Therefore, interpolation and extrapolation depend on whether the explanatory value is within the original data range.
Students should remember:
Interpolation and extrapolation are judged from the x-value.
Not the predicted y-value.
Students did not show working for “show that” questions
Examination 2 Question 4f.i asked students to show that a residual was 27 984.
The required working was:
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 one of the most important Examination 2 habits.
If the question says show that, students must show the calculation. Repeating the value from the question does not demonstrate the method.
Even if the value is already given, the mark is for showing why it is correct.
Students misread calculator notation
The Examination 2 report noted that many students had difficulty interpreting calculator outputs written in exponent notation, such as:
1.05E6
This means:
1.05 × 10⁶ = 1 050 000
This issue appeared in the context of writing a regression equation, where students needed to correctly interpret large values from technology.
Misreading exponent notation can destroy an otherwise correct answer.
For example, 1.05E6 is not 1.05 and not 105 000. It is 1 050 000.
Students should practise reading CAS output until this notation feels automatic.
A calculator output is only useful if the student understands what it says.
Students entered data carelessly
In Examination 2 Question 1c.i, students had to calculate the standard deviation of apartment sale prices.
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 simple warning with broad relevance.
Many General Mathematics calculations are technology-supported. But technology cannot correct incorrectly entered data.
Students should check:
Have I entered all values?
Have I entered them in the correct list?
Have I separated groups correctly?
Have I selected the right statistic?
Have I rounded as instructed?
Careful data entry is not a low-level skill.
It is essential exam technique.
Students used CAS when the table had to be used
In Examination 2 Question 7c, students had to complete entries in an amortisation table.
The report noted that students were instructed to use the values in the table. Using a finance solver produced a different balance to the nearest cent and was not appropriate.
This matters because CAS can sometimes produce a value that is mathematically valid but not consistent with the question’s required process.
If a table contains rounded intermediate values, the next entries may need to be calculated from those table values rather than from full-precision finance-solver output.
The correct values for the table were:
interest: 2885.55
principal reduction: 12 845.33
balance: 811 598.26
The instruction controlled the method.
Students should not assume that the most advanced tool is always the correct tool.
Students confused recurrence relations and rules
In Examination 2 Question 8, students had to write both a recurrence relation and a rule.
The assessment guide gave:
V₀ = 40 000, Vₙ₊₁ = Vₙ − 8000
and:
Vₙ = 40 000 − 8000n
The report noted that many students did not understand the distinction and gave a similar answer again.
This is a common modelling error.
A recurrence relation defines a term using the previous term.
A rule gives the term directly in terms of n.
They may describe the same sequence, but they are not the same form.
When a question asks for both, students must provide both forms.
Students misinterpreted finance-solver output
In Examination 2, finance solver output was used to determine the number of payments in a reducing balance loan.
The solver gave approximately:
N = 59.9999 ≈ 60
This meant there were 60 payments in total.
But the question asked for the payment number before the final payment, so the answer was 59 payments before the final one.
This shows that calculator output is not necessarily the final answer.
Students need to read the question after obtaining the output.
Does the output give total payments?
Does the question ask for the final payment?
Does it ask for the payment before the final payment?
Does it ask for the remaining balance after a certain number of payments?
The solver gives a value.
The student must interpret it.
Students mishandled finance signs
Finance solver questions also created sign errors.
In one Examination 2 question, the report showed finance solver entries such as:
PV = −650 000
PMT = 22 126.27
FV = 0
The signs represent cash-flow direction. Money borrowed, money repaid and money remaining cannot all be treated as positive values without regard to context.
The report noted that some students found the payment correctly from the calculator but answered with an incorrect positive value.
Students need to decide what the number represents.
Is it money owed?
Money paid?
A repayment?
A remaining balance?
A debt?
A future value?
Finance signs are not decorative.
They encode the direction of money flow.
Students misinterpreted matrix rows and columns
In Examination 2 Question 11b, students were asked to interpret a matrix product.
The correct interpretation was:
Total enrolments each day of the week
The report noted that many students gave an answer suggesting that rows had been summed rather than columns.
This kind of error is common in matrix questions.
Students may know how to calculate a matrix product but fail to interpret what it means.
Before calculating, students should label:
What does each row represent?
What does each column represent?
What does the resulting matrix represent?
Matrices are organised information.
If the organisation is misunderstood, the interpretation will be wrong even if the calculation is correct.
Students missed the meaning of the leading diagonal
In Examination 2 Question 13a, students had to interpret the leading diagonal of a transition matrix for children moving between activities.
The correct interpretation was that no child does the same activity from one week to the next.
This is because the leading diagonal represents staying in the same state from one time period to the next. If those diagonal values are zero, no one remains in the same activity.
This kind of question is conceptual.
The student must know what the position in the matrix means, not just the value.
A zero can be highly meaningful in context.
Students missed matrix cycles
In Examination 2 Question 14c, students had to explain why the activities on Day 41 would be in the same order as Day 1.
The report stated that only a small proportion of students understood the effect of the identity matrix.
The explanation was that the order rotated on a four-day cycle, or that 10 cycles were completed in the 40-day program.
This is an important matrices lesson.
Permutation matrices can create cycles. If applying the permutation four times returns the order to the original arrangement, then every four days the cycle resets.
Day 41 comes after 40 transitions from Day 1.
Since 40 is a multiple of 4, the order is the same as Day 1.
Students needed to explain the cycle, not just state that the order repeated.
Students followed algorithms in the wrong order
In Examination 1 Question 39, students had to identify the table produced by the Hungarian algorithm after subtracting row minimums and then column minimums.
The report explained that incorrect options came from:
row reduction only
column reduction only
column reduction first, then row reduction
The correct answer came from following the steps in the stated order.
This is a common Networks and Decision Mathematics issue.
Algorithms must be followed exactly.
Students should not rely on a general memory of the method if the question asks for a specific intermediate stage.
Read the step.
Perform that step.
Stop where the question asks.
Students counted the wrong edges in cut questions
In Examination 1 Question 36, students had to calculate the capacity of a cut in a flow network.
The report explained that although the cut crossed six edges, only four edges had the direction of flow from source to sink. These capacities were:
7, 3, 5 and 12
The cut capacity was:
27
Students who counted every crossed edge would be wrong.
In flow networks, direction matters.
Students should mark the source side and sink side of the cut and count only the directed edges that move from source side to sink side.
This is an avoidable error with careful diagram reading.
Students plotted graph points imprecisely
In Examination 2 Question 4f.ii, students had to plot a missing residual on a residual plot.
The report noted that students needed to take particular care with the scale used.
The point was:
15.5 km, 27 984
Because the residual scale had large intervals, the point should have been only slightly above zero. A student who plotted it too high or at the wrong x-position showed that they had not read the grid carefully.
Graphing marks are often execution marks.
Students should slow down when marking points.
Read both axes.
Check the scale.
Place the point accurately.
Use the value’s sign.
Students answered with vague explanations
Some Examination 2 questions required short written explanations.
For example:
Question 4d required explaining extrapolation.
Question 4e required describing strength and direction.
Question 7b required explaining why the interest amount decreased.
Network questions required reference to vertex degrees or critical path logic.
The strongest answers were concise but specific.
Weak:
It is outside the data.
Strong:
This is extrapolation because 2 km is outside the range of the explanatory variable, distance from the city centre.
Weak:
The interest is lower because it went down.
Strong:
The interest is lower because it is calculated on a smaller outstanding balance after the first repayment.
General Mathematics explanations do not need to be long.
They need to use the right mathematical idea in context.
Why these mistakes matter
These errors matter because General Mathematics exams often contain accessible marks that depend on execution.
A student can know the topic and still lose marks by:
rounding incorrectly
using the wrong statistic
copying a calculator output without interpretation
forgetting a negative sign
misreading a table instruction
plotting a point carelessly
writing a vague explanation
confusing two model forms
reversing matrix orientation
counting the wrong network edges
This is why exam preparation needs to include accuracy habits, not only content revision.
High scores come from reducing avoidable loss.
What future General Mathematics students should learn from 2025
The 2025 VCE General Mathematics reports show that students should prepare for common mark-loss patterns directly.
Students should practise:
- reading rounding instructions before writing final answers
- using the statistic requested by the question
- determining the sign of r from the slope
- describing association without claiming causation
- judging extrapolation using the explanatory variable
- showing working for “show that” questions
- reading CAS scientific notation
- checking data entry
- using table values when instructed
- distinguishing recurrence relations from rules
- interpreting finance-solver outputs
- applying finance sign conventions
- labelling matrix rows and columns
- interpreting transition-matrix diagonals
- recognising permutation cycles
- following algorithm steps in the stated order
- counting flow-network cut edges with direction
- plotting graph points accurately
- writing concise contextual explanations
These are practical skills.
They can be trained.
How ATAR STAR reduces avoidable mark loss in General Mathematics
At ATAR STAR, General Mathematics preparation focuses on both content and execution.
Students learn the required methods, but they also practise the habits that protect marks: checking instructions, showing working, using CAS carefully, interpreting outputs, managing rounding, labelling matrices, reading network diagrams and writing concise explanations in context.
The 2025 Examination Reports confirm why this matters. Many students knew parts of the mathematics.
High-scoring students controlled the details.