SACE Mathematical Methods: calculus, logarithms and probability for the Stage 2 exam

The six topics

Unlike General Mathematics, the Methods exam covers every topic. The outline adds that some problems may require you to link knowledge, skills and understanding from more than one topic, so a question might use differentiation to find a maximum probability, or integration to find a probability from a density function.

Assessment and the exam

School assessment is 70%: Skills and Applications Tasks 50% (five or six tasks) and a Mathematical Investigation 20% (one report of up to 12 A4 pages, or the equivalent in multimodal form). The external exam is 30% and lasts 130 minutes. The outline says the exam is a range of problems, some on routine skills and others on analysis and interpretation, and you must use correct notation and give arguments. A formula sheet comes with the exam booklet, you may take two unfolded A4 sheets (four sides) of handwritten notes, and approved electronic technology is allowed.

Worked examples

An exponential equation (Topic 4)

Solve 3 × 2ˣ = 50. Divide by 3 and take logarithms of both sides:

Give the exact form first, then the decimal. Writing x = log₂(50/3) shows the method even before the calculator.

A confidence interval for a proportion (Topic 6)

In a random sample of 100 students, 40 prefer an early start, so the sample proportion is 0.40. A 95% confidence interval uses z = 1.96:

The interval is (0.304, 0.496). State it as an interval, and say it estimates the proportion for the whole population. Do not say there is a 95% chance that the true value lies in this particular interval, a mistake examiners watch for.

A derivative with a stationary point (Topic 1)

For f(x) = x e⁻ˣ, the product rule gives f′(x) = e⁻ˣ(1 − x), which is zero at x = 1. The second derivative is f″(x) = e⁻ˣ(x − 2), which equals −e⁻¹ at x = 1, and since this is negative, the point is a maximum.

Check a normal distribution calculation in the Probability course, then press Mark:

Grades, SATAC and your ATAR

The final grade is A+ to E−. SATAC converts the school and exam results into a raw score out of 15 (10.5 from the 70%, 4.5 from the 30%), applies subject scaling, and uses the scaled score in the university aggregate. Mathematical Methods is a 20-credit subject, so it can sit in the first 60 credits of that aggregate.

Dates

Use the daily papers as a trial

In South Australia the trial exam belongs to your school. Uni-Sine's free daily papers can act as short timed trials, each 8 questions worth 25 to 35 marks and marked as you go: Year 12 Maths Advanced and Methods for calculus and Year 11 Maths Advanced and Methods for functions. They are not 130-minute SACE exams.

• They fit: differentiation rules, stationary points, area under a curve, integration and exponentials and logarithms.
• They do not fit: parametric differentiation, partial fractions, integration by parts and differential equations are beyond Methods. For discrete and continuous random variables and confidence intervals, use the Year 12 Statistics paper.

Exam answers

Answers and a worked mark scheme come with each daily paper once it has been marked. They are Uni-Sine's own, not official SACE Board answers.

Mistakes in SACE Methods

• Treating a 95% confidence interval as a probability statement about one interval.
• Skipping the second derivative or sign test when asked to classify a stationary point.
• Writing log with no base, or confusing ln and log₁₀.
• Using the notes sheet for long worked solutions instead of a clean list of rules.

Read next

Australia · SACESACE Maths Methods formula sheet: the one-page SACE sheetThe SACE Board Mathematical Methods formula sheet for Stage 2: every formula, what is missing, the two A4 sheets of notes rule, and worked examples.