SACE Stage 2 General Mathematics deep dive: Topics 3, 4 and 5 for the 2026 exam

SACEGeneral MathematicsStudy guide18 min readUpdated 23 Sep 2026

Revision deep dive for the three examined topics of SACE Stage 2 General Mathematics: bivariate statistics, linear and exponential regression and the normal distribution; saving, annuities, inflation, loans and sinking funds; and critical path analysis and assignment problems, with worked examples and links to the matching dot points.

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Why only three topics
Topic 3: Statistical models
Topic 4: Financial models
Topic 5: Discrete models
Common mistakes
Check your knowledge

Why only three topics

The SACE Stage 2 General Mathematics exam tests Topics 3, 4 and 5 only. This deep dive covers exactly those topics and links the matching dot points on this site. Topics 1 and 2 are assessed at school; they are not revised here. For exam format and strategy, see the exam strategy guide.

Topic 3: Statistical models

Bivariate statistics

Dot points: bivariate data and correlation, least-squares regression.

Identify the independent (explanatory) and dependent (response) variables from the context.
Describe the association: direction, form and strength, using $r$ and the scatter plot, plus outliers.
$r^2$ is the proportion of the variation in the dependent variable explained by the linear relationship.
A residual plot with a pattern means the data are curved; the outline then asks you to test whether an exponential model fits better.
A strong correlation is not proof of causation; coincidence or a third variable are the other explanations the outline names.

Linear or exponential?

The number of visitors to a new website (thousands) is recorded weekly for 8 weeks. A linear model gives $r = 0.95$ , but its residual plot is U-shaped. An exponential model gives $y = 120 \times 1.08^x$ , where $x$ is the week number, with a residual plot showing no pattern.

Choose the exponential model: the U-shaped residuals show the linear model is systematically wrong, even though $r$ is high.

Interpret: $a = 120$ is the predicted number of visitors (thousands) at week 0, and $b = 1.08$ means visitors grow by about 8 percent per week.

Predict for week 20: $120 \times 1.08^{20} \approx 559$ thousand. This is an extrapolation far beyond week 8, so it is unreliable: growth like this cannot continue indefinitely.

The normal distribution

Dot point: the normal distribution and z-scores.

Normal distributions are bell-shaped and symmetric about the mean $\mu$ , with spread measured by the standard deviation $\sigma$ .
The 68-95-99.7 rule gives approximate proportions within 1, 2 and 3 standard deviations of the mean.
Technology gives non-standard proportions, and inverse normal gives the value that cuts off a given area.

Inverse normal in context

Cans are filled with volumes that are normally distributed with mean 375 mL and standard deviation 4 mL. The company labels the lightest 2 percent as underweight. Find the cut-off.

Inverse normal with area 0.02 to the left: $x \approx 375 - 2.054 \times 4 \approx 366.8$ mL. Cans below about 366.8 mL are in the lightest 2 percent.

Topic 4: Financial models

Models for saving

Dot points: compound interest and annuities, depreciation.

Future value annuity: regular deposits plus compound interest. The outline states that in the exam the number of compounding periods per year equals the number of payments per year.
Effective rate: compare investments by converting to an effective annual rate, $\left(1 + \frac{r}{n}\right)^n - 1$ .
Inflation erodes purchasing power: $20 000 in 10 years, with inflation of 2.5 percent per year, is worth about $\dfrac{20\,000}{1.025^{10}} \approx \$15\,624$ in today's dollars.
Tax on interest reduces the return, because interest counts as taxable income.
Income from savings: a lump sum can fund regular withdrawals (a present value annuity) until it runs out.

The site's depreciation page is useful background for asset values and reducing-balance thinking.

Models for borrowing

Dot point: reducing-balance loans.

A car loan, then paying more

Jordan borrows $30 000 at 8.4 percent per annum, compounded monthly, over 5 years.

Repayment: $N = 60$ , $I\% = 8.4$ , $PV = 30\,000$ , $FV = 0$ gives monthly repayments of about $614.05. Total interest: $60 \times 614.05 - 30\,000 \approx \$6843$ .

What if Jordan pays $700 a month? Solving for $N$ gives about 51.1, so the loan is repaid in 52 months (51 full payments and a smaller final one), saving roughly $1050 in interest.

Paying more, paying more often, shortening the term or making a lump-sum payment all reduce the total interest, because interest is charged on a smaller balance for less time.

Interest-only loans and sinking funds. On a $400 000 interest-only loan at 6 percent per annum with monthly payments, each payment is $400\,000 \times \dfrac{0.06}{12} = \$2000$ and the principal never falls. A sinking fund (a savings annuity) can be built alongside it to repay the $400 000 at the end of the term.

Topic 5: Discrete models

The outline notes that the arithmetic in this topic can be done without technology, so practise by hand.

Critical path analysis

Dot point: critical path analysis.

A network with a dummy link

Task	Time (days)	Immediate predecessors
A	3	none
B	5	none
C	4	B
D	2	A, B
E	6	C, D

D needs both A and B, but C needs only B, so a dummy link from the end of B to the end of A is needed to show D's dependence on B without making C depend on A.

Forward scan (earliest starting times): A 0, B 0, C 5, D $\max(3, 5) = 5$ , E $\max(5 + 4, 5 + 2) = 9$ . Minimum completion time: $9 + 6 = 15$ days.

Backward scan (latest completion times): E 15, so C and D must be complete by 9; B by $\min(9 - 4, 9 - 2) = 5$ ; A by $9 - 2 = 7$ .

Slack time $=$ latest completion $-$ (task time $+$ earliest start): A: $7 - (3 + 0) = 4$ days; D: $9 - (2 + 5) = 2$ days. B, C and E have zero slack, so the critical path is B, C, E.

Assignment problems

Dot point: assignment problems.

The Hungarian algorithm, as set out in the subject outline:

Reduce rows, then columns, by subtracting each one's minimum value.
Cover all zeros with the minimum number of straight lines. If the number of lines equals the order of the array, go to step 4.
Let $m$ be the smallest uncovered element. Subtract $m$ from all uncovered elements and add it to elements covered by two lines. Return to step 2.
Find an assignment using only zeros, then apply it to the original array to find the total cost.

Maximising: subtract every entry from the largest entry to create an opportunity-loss array, then minimise. Non-square arrays: add a dummy row or column of zeros to square the array up; whoever is assigned to the dummy is left out.

Common mistakes

Where marks go missing in Topics 3 to 5

Choosing a linear model because $r$ is high while ignoring a curved residual plot.
Reading $b$ in an exponential model as the amount added each step rather than the multiplying factor.
Mixing up nominal and effective rates when comparing investments.
Leaving out a dummy link, which changes the precedence and the critical path.
Adding up the reduced array instead of the original costs at the end of the Hungarian algorithm.

Check your knowledge

An exponential model is $y = 500 \times 0.85^x$ . Interpret 0.85. (Answer: $y$ decreases by 15 percent per unit increase in $x$ .)
About what percentage of a normal distribution lies more than 2 standard deviations above the mean? (Answer: 2.5 percent.)
A task has earliest starting time 6, duration 3 and latest completion time 12. Find its slack. (Answer: 3.)

Then try the topics quiz.

Sources & how we know this

Stage 2 General Mathematics Subject Outline — SACE Board of South Australia
General Mathematics subject page, including past examinations — SACE Board of South Australia
Stage 2 General Mathematics: external assessment — SACE Board

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