June 2026
The 2025 VCE General Mathematics exams showed that the bound reference should not be treated as a safety blanket.
It should be a working tool.
Students were permitted one bound reference in both examinations, alongside approved CAS technology. But the reports show that many of the errors students made were not caused by a missing formula. They were caused by misreading the question, choosing the wrong statistic, rounding incorrectly, using CAS output without interpretation, confusing similar model forms or failing to explain results in context.
That means the best bound reference is not simply a collection of notes.
It is a guide for making decisions under pressure.
What statistic should I use?
What does this CAS output mean?
How do I know whether to round?
What is the difference between a recurrence relation and a rule?
How do I decide the sign of r?
How do I interpret a transition matrix?
Which edges count in a cut?
What wording should I use for interpolation or extrapolation?
These are the questions a strong bound reference should help students answer quickly.
The bound reference should reduce decision time
In General Mathematics, many exam questions are not difficult because the procedure is unknown. They are difficult because students need to decide which procedure applies.
For example, in Examination 2 Question 1c.ii, students were asked to comment on relative spread using the information in Table 2. Table 2 contained standard deviations. The report stated that using other statistics such as range or IQR was not appropriate.
A useful bound reference should therefore include a simple decision reminder:
If the question specifies a statistic or table, use that statistic or table. Do not substitute another measure.
This kind of note is more valuable than a long explanation of every measure of spread.
Under exam conditions, students need to make the right decision quickly.
Rounding rules deserved a prominent page
The 2025 Examination 2 report specifically reminded students that numerical answers should only be rounded when instructed. In Question 3, students needed to give 83.85%, not 84%.
This is exactly the kind of mistake a bound reference can help prevent.
A strong bound reference should have a visible reminder near the front:
Do not round unless instructed.
Do not round intermediate values unless necessary.
If the question asks for three decimal places, give three decimal places.
If the question asks for the nearest whole number, give a whole number.
If no rounding is requested, preserve the value.
This page should be easy to find.
Rounding errors are avoidable, but only if students remember the instruction during the exam.
Data analysis notes should focus on traps
A Data Analysis section in the bound reference should not just list definitions. It should include common VCAA-style traps.
For example:
Histogram: use frequencies to find median.
Weighted total: multiply value by frequency before adding.
Boxplot: compare medians, quartiles, IQR and outliers separately.
Outlier fence: lower fence = Q1 − 1.5 × IQR; upper fence = Q3 + 1.5 × IQR.
Categorical data: use segmented bar charts, not histograms or boxplots.
Association: correlation does not prove causation.
Residual: actual − predicted.
Interpolation/extrapolation: judge using the explanatory variable.
Each of these appeared directly or indirectly in the 2025 exams.
The point is not to write an encyclopaedia.
The point is to make the most common decisions automatic.
Association language should be pre-written
In 2025, students needed to avoid causation claims when interpreting correlation. Examination 1 Question 10 required students to conclude that more goals scored against was associated with a smaller number of wins, not that one caused the other.
A bound reference should include safe association language:
There is a [strength] [direction] association between [variable 1] and [variable 2].
As [explanatory variable] increases, [response variable] tends to [increase/decrease].
This indicates association, not causation.
This helps students avoid wording errors.
It also helps them write concise Examination 2 explanations.
Regression reminders should include r, r² and residuals
The 2025 reports showed several regression-related mark losses.
Students forgot that r needed a negative sign when the least squares line had a negative slope. Students also needed to show residual working and judge extrapolation using the explanatory variable.
A useful bound reference should include:
r² = coefficient of determination
r = ±√r²
Use the sign of the slope to choose + or −
Residual = actual − predicted
Positive residual = actual is above predicted
Negative residual = actual is below predicted
Interpolation/extrapolation depends on the x-value, not the predicted y-value
These reminders are short, but extremely useful.
They address exactly the kinds of mistakes the report identified.
CAS instructions should be practical
The bound reference should include CAS instructions, but they should be exam-focused.
Students do not need pages of screenshots they cannot navigate quickly. They need concise reminders for common tasks:
standard deviation
least squares regression
correlation coefficient
finance solver
matrix multiplication
matrix powers
transition matrix calculations
scientific notation interpretation
The 2025 report noted that students sometimes misread outputs such as 1.05E6. The bound reference should include examples:
1.05E6 = 1.05 × 10⁶ = 1 050 000
3.2E4 = 32 000
7.8E−3 = 0.0078
This kind of page can prevent simple technology-reading errors.
Finance solver notes should include signs
Finance questions in 2025 showed that sign convention remained a problem.
The bound reference should include a finance solver page with labelled fields:
N: number of payment periods
I%: annual interest rate
PV: present value
PMT: payment per period
FV: future value
P/Y: payments per year
C/Y: compounding periods per year
It should also include a sign convention reminder:
Money in and money out must have opposite signs.
Loans and repayments should not be entered with the same sign.
Interpret the output before writing the answer.
This would have helped with questions where students found the payment correctly but mishandled the sign or wording.
Finance pages should distinguish model types
A strong bound reference should place similar finance models side by side.
For example:
Simple interest:
A = P + Prn
Compound interest:
A = P(1 + r)ⁿ
Flat rate depreciation:
Vₙ = V₀ − dn
Vₙ₊₁ = Vₙ − d
Reducing balance depreciation:
Vₙ = V₀(1 − r)ⁿ
Vₙ₊₁ = (1 − r)Vₙ
Reducing balance loan:
Dₙ₊₁ = RDₙ − payment
This layout helps students identify the correct model quickly.
It also prevents common errors, such as using compound interest for simple interest or confusing flat rate depreciation with reducing balance depreciation.
Recurrence relation versus rule needed its own box
The 2025 report noted that many students did not understand the difference between a recurrence relation and a rule.
This deserves a dedicated bound-reference box.
For example:
Recurrence relation: uses the previous term.
V₀ = 40 000
Vₙ₊₁ = Vₙ − 8000
Rule: gives the term directly from n.
Vₙ = 40 000 − 8000n
A note should add:
If the question asks for both, do not write the same form twice.
This is simple, but it targets a real exam weakness.
Matrices should be labelled, not just defined
The matrices section of the bound reference should include definitions, but also interpretation prompts.
Definitions:
Binary matrix: entries are only 0 and 1.
Identity matrix: 1s on leading diagonal and 0s elsewhere.
Diagonal matrix: all non-diagonal entries are 0.
Permutation matrix: exactly one 1 in each row and column.
Inverse exists: determinant is not 0.
Interpretation prompts:
What does each row represent?
What does each column represent?
Does the product sum rows or columns?
What does the output matrix represent?
Are the dimensions compatible?
In 2025, students often calculated matrix outputs but misinterpreted rows and columns. A good bound reference should train orientation.
Matrix dimension rules should be highly visible
Matrix dimension rules are quick and often decisive.
A bound reference should include:
Addition/subtraction: dimensions must be the same.
Multiplication: inner dimensions must match.
Product size: outside dimensions.
For example:
(2 × 3)(3 × 4) = 2 × 4
This can save time in Examination 1, where students may only need to decide which operation is defined.
Students should not waste time trying to calculate undefined products.
Transition matrices need time-step reminders
Transition matrices caused interpretation issues in 2025.
A bound reference should remind students:
From Week 1 to Week 2 = 1 transition
From Week 1 to Week 10 = 9 transitions
Leading diagonal = staying in the same state
Zero on leading diagonal = no one stays in the same state
Expected number = probability or proportion × total number
These reminders are short, but they target the exact logic students often miss.
A transition matrix question is rarely just about raising a matrix to a power.
It is about choosing the correct power and interpreting the result.
Permutation matrix notes should include cycles
Examination 2 Question 14 required students to understand that a permutation returned to the original order after a four-day cycle.
The bound reference should include:
Permutation matrix: rearranges order.
If P⁴ = I, the arrangement repeats every 4 applications.
Identity matrix effect = no change to order.
Check whether the number of transitions is a multiple of the cycle length.
This helps students explain repeated arrangements, not just calculate them.
The explanation matters in Examination 2.
Networks pages should be diagram-based
Networks and Decision Mathematics is visual. The bound reference should reflect that.
Rather than long paragraphs, students should include small labelled examples for:
Hamiltonian cycle
Eulerian trail and circuit
bridge
minimum spanning tree
cut capacity
maximum flow
shortest path
Hungarian algorithm
precedence network
dummy activity
critical path
float
crashing
Each example should show the concept visually and include one line of explanation.
For example:
Bridge: removing the edge disconnects the graph.
Cut capacity: add directed edges crossing from source side to sink side.
Float: latest start − earliest start.
Critical activity: zero float.
Dummy activity: shows dependency but has zero duration.
These quick references are more useful than dense notes.
Flow-network notes should emphasise direction
In 2025, cut capacity required students to count only directed edges crossing from source side to sink side.
The bound reference should make this explicit:
For a cut, do not add every edge crossed.
Only add capacities of directed edges going from source side to sink side.
Maximum flow = capacity of minimum cut.
This is one of the most common flow-network traps.
A diagram example in the bound reference would be especially valuable.
Critical path notes should include a workflow
Critical path questions can become messy, so the bound reference should include a workflow:
- Complete forward pass for earliest start times.
- Identify project completion time.
- Complete backward pass for latest start times.
- Float = latest start − earliest start.
- Critical activities have zero float.
- Critical path is the path with zero-float activities and longest total duration.
- For crashing, reduce critical path duration at lowest additional cost.
- If there are multiple critical paths, all relevant paths must be reduced.
This sequence gives students a method to follow under pressure.
It also helps avoid guessing based on diagram appearance.
The Hungarian algorithm should be step-by-step
The 2025 Examination 1 report showed that students confused stages of the Hungarian algorithm.
The bound reference should include the exact sequence:
- Subtract the minimum value in each row from every entry in that row.
- Subtract the minimum value in each column from every entry in that column.
- Cover all zeros with the minimum number of lines.
- If the number of lines equals the number of rows or columns, make an allocation.
- If not, subtract the smallest uncovered value from all uncovered entries.
- Add it to entries at intersections of covering lines.
- Repeat until allocation is possible.
A warning should be included:
If the question asks for an intermediate table, stop at that step.
This directly addresses a 2025 issue.
Explanation templates should be included
The bound reference should include short explanation templates.
For example:
Spread:
The [group] has a lower spread because its standard deviation is lower.
Extrapolation:
This is extrapolation because [x-value] is outside the range of the explanatory variable.
Reducing balance interest:
The interest is lower because it is calculated on a smaller outstanding balance.
Association:
There is a [strength] [direction] association between [variables].
Transition diagonal:
The leading diagonal represents staying in the same state from one time period to the next.
These templates should be adapted to the question, but they give students efficient phrasing.
This is especially useful in Examination 2, where explanations are often worth one mark.
The bound reference should include common errors
A high-quality bound reference should not only include correct methods. It should include warnings.
For example:
Do not claim causation from correlation.
Do not round unless instructed.
Do not use IQR if the question asks for standard deviation.
Do not judge extrapolation from the response variable.
Do not forget the negative sign of r.
Do not use finance solver if the question says use the table.
Do not confuse recurrence relation and rule.
Do not reverse matrix row and column meaning.
Do not count all cut edges; check direction.
Do not continue the Hungarian algorithm beyond the stage requested.
These warnings are practical because they reflect real mark-loss patterns.
The best bound references are easy to navigate
A bound reference is only useful if students can find what they need quickly.
It should have:
clear tabs
large headings
topic sections
worked examples
short formulas
common traps
CAS steps
interpretation templates
minimal clutter
A beautifully detailed reference is not useful if it takes too long to search.
The exam is timed.
The bound reference should support fast action.
Students should practise using the bound reference
Many students build a bound reference and then barely use it before the exam.
That is a mistake.
Students should practise with it during SAC revision, topic tests and trial exams. They should learn where key pages are, which reminders are useful, and which pages are never used.
The bound reference should evolve.
If a student repeatedly makes a rounding error, add a rounding reminder.
If they forget finance signs, improve the finance page.
If they mix up transition powers, add a time-step example.
If they misread network cuts, add a flow diagram.
The best reference is personalised through practice.
A bound reference cannot replace fluency
The bound reference is useful, but it cannot do everything.
Students still need to know the course.
They will not have time to learn a method from scratch during the exam. The reference should remind and guide, not teach for the first time.
A strong student uses the bound reference to check a detail, confirm a formula or avoid a trap.
A weak student may spend too long searching through notes and lose time.
This is why preparation matters.
The bound reference supports fluency.
It does not replace it.
What future General Mathematics students should learn from 2025
The 2025 VCE General Mathematics exams show that the bound reference should be designed for exam execution.
Students should include:
- rounding reminders
- Data Analysis traps
- association and regression language
- residual formulas
- CAS notation examples
- finance solver fields and sign conventions
- model comparisons for interest and depreciation
- recurrence relation versus rule examples
- matrix dimension rules
- matrix interpretation prompts
- transition matrix time-step reminders
- permutation cycle notes
- network definitions and diagrams
- flow-network direction reminders
- critical path workflows
- Hungarian algorithm steps
- short explanation templates
- common error warnings
The bound reference should make students faster, calmer and more accurate.
It should help them make the right decision at the right time.
How ATAR STAR helps students build bound references
At ATAR STAR, the bound reference is treated as an exam tool, not a note archive.
Students learn how to build references that support quick decisions, CAS use, common error prevention and concise explanations. They practise using their bound reference under timed conditions so that it becomes part of their exam workflow rather than something they hope will save them on the day.
The 2025 Examination Reports confirm why this matters. High-scoring students did not just bring a reference.
They knew how to use it.