WACE Mathematics Methods: the ATAR exam, Units 3 and 4

The WACE Methods exam: two sections, two kinds of thinking

The design brief splits the paper by calculator use, and the split changes how you should prepare. Section One questions are chosen so that they can reasonably be done by hand, without heavy algebra or slow arithmetic. Section Two assumes you own a calculator with a Computer Algebra System (CAS), so it is where the longer modelling problems live.

Reading time is five minutes before Section One and ten before Section Two, and there is a changeover of up to 15 minutes in between when you may not work. Section One allows no special items. In Section Two you may bring notes on two unfolded A4 sheets, and the supervisor provides a formula sheet. Any question or part worth more than two marks needs working or justification for full marks, so a correct answer alone is not enough.

What Unit 3 and Unit 4 contain

Unit 3 adds the derivatives of exponential and trigonometric functions, the second derivative and its meaning, and integration both as reversing differentiation and as area, linked by the fundamental theorem of calculus. Unit 4 turns to the logarithmic function and its derivative, then continuous random variables, where probabilities are definite integrals, and ends with statistical inference, limited to estimating proportions in two-outcome populations. Our Calculus course and Probability course cover the foundations.

Worked examples

A product rule derivative

Differentiate x e²ˣ and find where its gradient is zero.

Since e²ˣ is never zero, the gradient is zero only when 1 + 2x = 0, so at x = −½. In Section One you would write the product rule line in full, because the working earns marks even when the arithmetic is simple.

A definite integral by antiderivative

The step e^(2 ln 2) = 4 is the kind of exact-value detail that a calculator-free section rewards, since e^(2 ln 2) = (e^(ln 2))² = 2².

Probability and the normal distribution are the Unit 4 half of the exam. Try a normal distribution question in the Probability course, then press Mark:

School assessment and the ATAR

SCSA sets the school weightings for Year 12 Methods: response tasks 40%, investigation 20% and examination 40%. Response tasks are tests, assignments and multimedia work, and the investigation uses the mathematical thinking process on a problem you plan and report on. The school then gives an A to E grade and a mark out of 100. Your school mark is moderated against the ATAR exam marks at your school and averaged with your exam mark, and TISC turns the combined marks into an ATAR.

Dates

Use the daily papers as a trial

Schools set their own trial exams, and SCSA publishes none. Uni-Sine's free daily papers can work as short timed trials: Year 12 Maths Advanced and Methods for calculus and Year 11 Maths Advanced and Methods for functions. Each is 8 questions worth 25 to 35 marks, marked as you go, and neither is a full WACE paper.

• They match: differentiation rules, stationary points, area under a curve, integration and exponentials and logarithms.
• They do not match: the calculus paper also covers parametric differentiation, integration by substitution and parts, differential equations and Maclaurin-type material that sits outside Methods, and neither track covers discrete random variables or confidence intervals. For those, use the Year 12 Statistics paper.
• Calculator practice: the daily paper does not separate calculator-free from calculator-assumed marks, so do the first half of each paper by hand.

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 SCSA answers or past paper solutions.

Common WACE Methods mistakes

• Leaving the chain or product rule line out in Section One and losing the method marks.
• Using a CAS answer without showing a setup in Section Two, in a question worth more than two marks.
• Reporting a confidence interval for a proportion as a single number, when the question asks for an interval.
• Writing log with no base, or mixing natural and base-10 logarithms.

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