Mathematics
What the exam tests
The mathematics paper spans algebra, functions, trigonometry, geometry, and introductory probability and statistics. Expect manipulation of expressions, solving equations and inequalities, working with sequences, analyzing function behavior, and applying geometric theorems to figures described in text.
Concepts to master
- Algebra: factoring, rational expressions, quadratic equations, and systems; the discriminant and Vieta's formulas.
- Functions: domain and range, monotonicity, parity, graphs of linear, quadratic, exponential, and logarithmic functions.
- Trigonometry: the unit circle, identities, and solving equations on a stated interval.
- Geometry: triangle congruence and similarity, circle theorems, areas and volumes, coordinate geometry.
- Probability: classical probability, complementary events, and basic combinatorics.
Traps
Domain restrictions are the most common pitfall: forgetting that a logarithm's argument must be positive or that a denominator cannot vanish. In trigonometry, solutions are often lost or extra ones introduced when dividing by a trigonometric factor. Geometry items may describe a figure ambiguously, so check whether the stated lengths are consistent. Always substitute answers back.
Rule of thumb
When an equation looks hard, state the domain first, then simplify. For probability, compute the complement when «at least one» appears.
Worked example
Solve log₂(x−1) = 3. The domain requires x−1 > 0, so x > 1. Rewrite as x−1 = 2³ = 8, giving x = 9, which satisfies the domain. The tempting answer x = 7 comes from misreading the base; the tempting x = 9 without checking would fail if the base were different. Always verify the domain.