2026 WACE Mathematics Specialist exam: What to learn from last year's mistakes

WACE Mathematics Specialist is on Monday 9 November at 9:20 am, WA time.

Last year's mean was 62.33%. The examiner report says routine techniques were generally stronger than unfamiliar applications and deeper conceptual questions.

I've pulled out four useful revision targets. The explanations and mini-example below are my own study suggestions.

1. Question 2(a): Check the domain of the composition

Where students went wrong: Finding the domain of a composite function was a reported difficulty.

What they should have done: Check both stages of the composition, including the restrictions on the inner function and whether its output can enter the outer function.

An original example: if f(u) = √u and g(x) = 1/(x − 2), then f(g(x)) requires x ≠ 2 and 1/(x − 2) ≥ 0. Together these give x > 2. Listing the denominator restriction alone misses the square root's requirement.

2. Question 12(b)–(c): Distance is not change in displacement

Where students went wrong: Candidates struggled to distinguish these quantities in vector motion.

What they should have done: Decide which quantity the question requests before integrating.

My check: displacement is the change in the position vector. Distance travelled is the integral of speed, the magnitude of velocity. A particle can return to its starting point with zero net displacement after travelling a positive distance. Use that simple journey to test whether your method makes sense.

3. Question 17: Read the actual differential equation

Where students went wrong: Many treated the unfamiliar growth-rate equation as though it were the familiar logistic equation.

What they should have done: Analyse the equation supplied instead of importing a remembered graph.

My practice routine: find equilibrium values, check the sign of the rate between them and use the initial condition. Only then sketch the behaviour. A model's name is less useful than knowing why the solution increases, decreases or approaches a particular value.

4. Question 18: Make the vector proof readable

Where students went wrong: The report highlights weak notation in the three-dimensional geometry proof and difficulty working with vector expressions.

What they should have done: Define vectors clearly, distinguish vectors from scalars and present a logical chain ending in the required conclusion.

My revision check: read each equals sign as a claim that two objects are the same. Are both sides vectors, or both scalars? If a step uses perpendicularity, parallelism or a geometric property, say which property justifies it.

Try one unfamiliar problem from each area before repeating another routine exercise. After marking, write down the decision that unlocked the question, not just the final formula.

Source: 2025 SCSA Mathematics Specialist examiner report.

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