Mathematics (MAT)
What the section is really testing
The Mathematics test covers core school mathematics to Grade 12 level, but it rewards understanding over rehearsal. Expect multi-step problems, unfamiliar framings of familiar ideas, and no formula sheet. Accuracy in routine manipulation buys you the time to think about the harder items.
Concepts you must command
- Algebra: factorising, simplifying rational expressions, solving linear and quadratic equations and inequalities, simultaneous equations, the nature of roots through the discriminant.
- Exponents, surds and logs: exponent laws, rationalising denominators, log laws and solving exponential equations.
- Functions: domain and range, intercepts, turning points, transformations, and reading a graph's gradient and area in context.
- Analytical geometry: distance, midpoint, gradient, parallel and perpendicular lines (m₁m₂ = −1), equations of circles.
- Trigonometry: ratios, special angles, identities, the sine, cosine and area rules, solving triangles.
- Euclidean geometry: circle theorems and proportional reasoning in similar triangles.
- Calculus: differentiation from first principles in spirit, rules, tangents, stationary points, rates of change and optimisation.
- Financial maths and probability: compound growth and decay, simple versus compound interest, tree diagrams, independent and complementary events, counting.
Traps that appear repeatedly
Extraneous roots created by squaring; dividing by an expression that may be zero; losing the negative root; sign errors when expanding brackets with a minus in front; rounding intermediate values; forgetting domain restrictions; misreading "which is NOT"; and using the wrong rule when a triangle is not right-angled.
Worked example
Solve x + 1 = √(2x + 7). Square both sides: x² + 2x + 1 = 2x + 7, so x² = 6 and x = ±√6. Now test both: for x = √6 the left side is positive and the equation holds; for x = −√6 the left side is negative while a square root is never negative, so it fails. Answer: x = √6 only. Always substitute back after squaring.