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

SACE Specialist Mathematics is on Tuesday 10 November at 9 am.

I've gone through the 2025 examiner advice. A lot of the useful revision here is about finishing the mathematics properly: exact answers, valid proofs and using the result the question just gave you.

Here are four things worth fixing before you walk in.

1. Question 2: Integration by parts

Where students went wrong: The report identifies missing differentials, bracket errors, mistakes applying the limits and answers that did not preserve the required exact form.

What they should have done: Write the integration-by-parts structure clearly, then treat evaluating the antiderivative as a separate step. Put the entire expression in brackets before substituting the upper and lower bounds.

For your own practice, differentiate your antiderivative before applying the limits. That catches a sign error while you can still fix it. Keep fractions, logarithms and radicals exact when the question asks for an exact answer.

2. Question 4(b): Mathematical induction

Where students went wrong: Students needed a justified base case, an explicit assumption and a valid step from the kth derivative to the next derivative. A concluding sentence could not rescue a missing proof.

What they should have done: State the proposition, establish the first case, assume it for k, then differentiate that assumed expression and rearrange it into the required form for k + 1.

When checking your practice solution, cover the final line. Does the working actually establish the next case, or have you simply written down what you were trying to prove?

3. Question 6: Complex-number sets

Where students went wrong: This was the examination's most challenging question. The advice highlights the excluded origin on an argument ray and students giving Cartesian equations when the requested form used complex variables.

What they should have done: Check both the geometry and the requested notation. The argument of zero is undefined, so a ray described by an argument condition needs an open endpoint at the origin.

An extra practice check: for |z − a| = r, identify the centre from the complex number a and the radius from r before drawing anything. Then check whether your final answer uses the variables specified in the question.

4. Question 8: Lines and planes

Where students went wrong: Some responses confused a normal line with a plane or did not complete the line–plane intersection calculation.

What they should have done: Write the line parametrically, substitute its coordinates into the plane equation and solve for the parameter. Substitute that value back into all three coordinates.

Your answer is a point, not just a parameter value. As a quick check, that point should satisfy both the original line and the plane.

The broader habit: when a question says “hence”, look back before starting again. When it says “show that”, demonstrate the result without assuming it is already true.

Source: 2025 SACE Specialist Mathematics examiner advice. The practice checks above are my revision suggestions.

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