June 2026
The 2025 VCE General Mathematics exams showed that CAS technology is powerful, but not automatic.
Students were permitted to use approved CAS technology in both examinations. This mattered across Data analysis, Recursion and financial modelling, Matrices, and Networks and decision mathematics. CAS could calculate standard deviations, regression equations, correlation coefficients, finance values, matrix products and repeated transitions.
But the reports made one thing clear: using technology did not remove the need for mathematical judgement.
Students still needed to enter data carefully.
They still needed to choose the correct statistic.
They still needed to interpret calculator notation.
They still needed to apply the correct sign.
They still needed to know when not to use CAS.
They still needed to show working in Examination 2.
They still needed to explain what the output meant in context.
A calculator can produce a number.
It cannot decide whether the number answers the question.
Data entry errors were still costly
Examination 2 Question 1c.i asked students to calculate the standard deviation of apartment sale prices.
The report gave the correct value as:
$346 466
It also noted that students needed to enter the data carefully into their calculator to avoid error.
This is one of the simplest but most important CAS lessons.
A calculator only works with the data it is given. If a student enters a house price into the apartment list, misses a value, duplicates a value, or selects the wrong list, the output will be wrong.
The mathematics may be easy, but the execution still matters.
Students should develop a checking routine:
Count the values entered.
Check the first and last values.
Make sure the correct group has been selected.
Confirm whether the question asks for sample or population standard deviation.
Round only as instructed.
The CAS is only as reliable as the setup.
Students had to use the statistic requested
Question 1c.ii asked students to compare the relative spread in sale prices using the information in Table 2.
Table 2 contained standard deviations.
The report noted that using other statistics such as range or interquartile range was not appropriate.
This is important because CAS makes it easy to calculate many statistics quickly. But a correct statistic is not automatically the right statistic.
The question told students to use Table 2. Therefore, the answer had to compare standard deviations.
A strong response was:
House sale prices have a lower spread than apartment sale prices because the standard deviation for houses is lower.
A response using range or IQR may have shown statistical knowledge, but it did not follow the task.
CAS can calculate range, IQR and standard deviation.
The student must decide which one the question requires.
Calculator notation needed to be understood
The Examination 2 report noted in Question 5a that significant figures remained problematic, and that many students did not interpret values written in exponent notation, such as:
1.05E6
This means:
1.05 × 10⁶ = 1 050 000
This is a practical issue, but it can cost marks quickly.
General Mathematics often deals with large numbers: house prices, loan balances, populations, project costs, matrix totals and financial values. CAS outputs may display these in scientific notation.
Students need to be fluent with this notation.
1.05E6 is not 1.05.
It is not 105 000.
It is 1 050 000.
Technology output still has to be read mathematically.
Regression output required sign awareness
Examination 2 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:
0.284
But the least squares line was:
sale price = 1 765 353 − 35 054 × distance from city centre
The slope was negative, so:
r = −0.284
The report noted that a large proportion of students left their final response as positive 0.284.
This is a classic CAS-related error.
The calculator or formula may give the magnitude of the correlation, but the student must determine the sign from the direction of association. Since the regression line had a negative slope, the correlation coefficient had to be negative.
CAS output needs interpretation.
A number without direction is incomplete.
Regression equations needed meaningful values
Question 5a required students to determine a least squares regression line. The report gave:
Sale price = 1 050 000 − 8050 × days
It also noted that significant figures remained problematic.
This shows that students need to convert CAS output into a mathematically meaningful equation.
A calculator might display a value in scientific notation or with many decimal places. Students need to write a usable model that keeps enough accuracy without becoming unreadable.
The equation also needs to make contextual sense.
A negative slope of −8050 means that, according to the model, the predicted sale price decreases by $8050 for each additional day on the market. If a student misreads 1.05E6, the whole equation becomes unusable.
Regression is not just a CAS command.
It is a model.
CAS did not remove the need for working
Examination 2 Question 4f.i asked students to show that a residual was 27 984.
The report stated that students needed to show all working that led to the given residual value.
The calculation was:
predicted value = 1 765 353 − 35 054 × 15.5 = 1 222 016
residual = actual − predicted
residual = 1 250 000 − 1 222 016 = 27 984
A student could use CAS for the arithmetic, but the working still needed to be visible.
This is one of the most important differences between performing a calculation and communicating a calculation.
In Examination 2, assessors need to see the method. CAS can assist with computation, but the student must still show the mathematical process.
Finance solver outputs needed interpretation
The 2025 finance questions showed that finance solver use was not enough by itself.
In one loan question, the finance 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. The correct interpretation was therefore 59 payments before the final payment.
This is a wording trap.
CAS gives an output. The question determines how that output should be used.
Students should always ask:
What does this output represent?
Is it total payments, payment amount, present value, future value or balance?
Does the question ask for the final payment, the payment before the final one, or the total number of payments?
Does the sign indicate money paid or money received?
The calculator does not read the question for the student.
Sign convention mattered in finance
The finance solver questions also showed that signs mattered.
In Examination 2 Question 10, the report showed entries such as:
PV = −650 000
PMT = 22 126.27
FV = 0
The signs reflect cash-flow direction.
Money borrowed, money repaid, money owed and money received should not all have the same sign. If students ignore sign convention, the finance solver may produce an error or a result that is mathematically inconsistent with the situation.
The report noted that some students found the payment correctly from the calculator but answered with an incorrect positive value.
This is why students need to understand what each value means.
A payment is not just a number.
It represents money flowing in a particular direction.
Table values sometimes mattered more than solver values
Question 7c in Examination 2 required students 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 is a major technology lesson.
Sometimes CAS gives a value that is mathematically accurate under full precision, but the task requires students to continue from rounded values already shown in a table.
If the table gives rounded intermediate values, the next row may need to be calculated from those values.
For Question 7c, the required table values were:
interest: 2885.55
principal reduction: 12 845.33
balance: 811 598.26
Using the solver instead of the table could shift the cents and cost the mark.
The instruction controls the method.
Matrix products required interpretation after calculation
CAS can multiply matrices quickly, but the 2025 reports showed that interpretation was still difficult.
In Examination 2 Question 11b, students had 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 the rows had been summed rather than the columns.
This was not a calculation issue.
It was an orientation issue.
Students needed to understand what rows and columns represented and what the resulting matrix meant. CAS can produce the matrix product, but it cannot label the answer in context.
Before multiplying matrices, students should identify:
What does each row represent?
What does each column represent?
What operation is being performed?
What will the output represent?
Without that, the correct calculation can still lead to a wrong interpretation.
Transition matrices required correct time steps
CAS is especially useful for transition matrices because it can calculate powers of matrices efficiently.
But students still need to know which power to use.
In Examination 2, a transition matrix was used to model children moving between activities from week to week. Students needed to determine the expected percentage participating in cooking in Week 10 when all children began in cooking in Week 1.
The key is that moving from Week 1 to Week 10 involves nine transitions, not ten.
CAS can calculate K⁹ or K¹⁰, but only the correct power matches the situation.
Time-step reasoning belongs to the student.
Technology does not decide the exponent.
Permutation matrices required cycle interpretation
Examination 2 Question 14 involved a permutation matrix used to rearrange activity order in a holiday program.
The report noted that only a small proportion of students understood why activities on Day 41 would be in the same order as Day 1. The explanation was that the order rotated on a four-day cycle, or that 10 cycles were completed in the 40-day program.
CAS could help calculate powers of the permutation matrix, but the explanation required conceptual understanding.
If applying the permutation four times returns the order to the identity arrangement, then the timetable cycles every four days.
Day 41 follows 40 transitions from Day 1.
Since 40 is a multiple of 4, the order returns to the original.
This is not just matrix calculation.
It is interpretation of a repeating structure.
Network questions were not always CAS-friendly
Some Networks and Decision Mathematics questions could be supported by technology, but many required visual reasoning.
A CAS will not automatically identify a bridge in a graph unless the student models the graph correctly. It will not know which edges are directed across a cut unless the student identifies the source side and sink side. It will not follow the Hungarian algorithm step requested unless the student performs the correct stage.
In Examination 1, the Hungarian algorithm question asked for the table after row reduction and then column reduction. The report noted that wrong options came from stopping after row reduction, doing column reduction only, or doing the reductions in the wrong order.
This is not a calculator issue.
It is a process issue.
Students need to know the algorithm.
Technology can help with arithmetic, but not with reading the instruction.
CAS could not replace graph reading
Several 2025 questions required reading diagrams or graphs directly.
For example:
- locating the median from a histogram
- comparing boxplots
- identifying interpolation or extrapolation from a scatterplot’s explanatory variable range
- plotting a residual accurately
- identifying bridges in a graph
- counting Hamiltonian cycles
- reading a flow network cut
- interpreting a residual plot
CAS is limited in these tasks unless the student first extracts the correct information.
The student needs to read the display.
Technology cannot compensate for misreading a graph.
CAS should be used strategically in Examination 1
Examination 1 was multiple-choice.
This means CAS use had to be efficient.
Some questions could be answered faster by reasoning than by technology. For example, rejecting causation options in a correlation question does not require CAS. Identifying a segmented bar chart for categorical data does not require CAS. Checking matrix dimensions may be faster than entering matrices.
Other questions benefit from technology: regression, standard deviation, financial calculations, matrix powers and transition outputs.
The skill is knowing when CAS saves time and when it wastes time.
Examination 1 is timed.
Students should not use CAS automatically for every question.
CAS should be documented in Examination 2
In Examination 2, students should show enough working even when CAS is used.
This might include:
- listing finance solver entries
- writing the regression equation from CAS output
- showing the residual formula and substitution
- writing the matrix recurrence relation
- showing the recurrence multiplier
- stating the relevant matrix power used
- explaining what the output represents
Students do not need to reproduce every button press, but they should make the method clear.
CAS work that stays invisible cannot earn method marks if the final response is wrong or incomplete.
Technology did not remove the need for rounding discipline
The 2025 reports repeatedly showed that rounding remained an issue.
CAS may give many decimal places. The question may ask for the nearest whole number, one decimal place, two decimal places, four decimal places, or no rounding.
Students need to follow the instruction.
For example:
- standard deviation to the nearest whole number
- correlation coefficient to three decimal places
- multiplier to four decimal places
- number of children to the nearest whole number
- percentage not rounded unless instructed
CAS output is not the final answer until it has been rounded or left exact according to the question.
Bound references should support CAS use
Students were permitted one bound reference.
This reference should not merely contain formulas. It should support the way students use technology.
A strong bound reference might include:
- CAS steps for standard deviation and regression
- finance solver field meanings
- sign convention reminders
- recurrence relation templates
- transition matrix time-step reminders
- matrix dimension rules
- residual formula
- interpolation and extrapolation explanation
- common calculator notation examples such as E6
- rounding reminders
The bound reference should help students avoid common execution errors.
It should be practical.
Why CAS-related errors happen
CAS-related errors often happen because students trust output without interpreting it.
They enter data incorrectly.
They choose the wrong statistic.
They misread scientific notation.
They forget the negative sign of r.
They use a finance solver when table values are required.
They copy total payments when the question asks for payments before the final one.
They use the wrong transition-matrix power.
They calculate a matrix product but misinterpret rows and columns.
They round calculator output too early or incorrectly.
These mistakes are preventable.
Students need to treat CAS as a tool, not an answer generator.
What future General Mathematics students should learn from 2025
The 2025 VCE General Mathematics exams show that CAS preparation needs to focus on judgement and interpretation.
Students should practise:
- checking data entry before calculating statistics
- selecting the statistic requested by the question
- reading scientific notation correctly
- writing regression equations from calculator output
- choosing the sign of r from the slope
- showing working for CAS-supported calculations
- interpreting finance solver outputs
- using correct finance sign conventions
- using table values when instructed
- interpreting matrix products in context
- choosing the correct transition-matrix power
- explaining permutation cycles
- knowing when CAS is not the best tool
- following rounding instructions exactly
- documenting CAS-supported work clearly in Examination 2
These skills make technology useful rather than risky.
CAS helps most when the student understands the mathematics behind the output.
How ATAR STAR teaches CAS use in General Mathematics
At ATAR STAR, CAS is taught as part of mathematical reasoning.
Students learn how to use technology efficiently, but also how to check inputs, interpret outputs, manage signs, follow rounding instructions and explain answers in context. They practise deciding when CAS is useful and when direct reasoning is faster or safer.
The 2025 Examination Reports confirm why this matters. High-scoring students did not simply press the right buttons.
They knew what the output meant.