Mathematics
What the exam expects
The mathematics paper tests both technical fluency and rigour of proof. Core areas: algebra (polynomials, equations and inequalities, systems, complex numbers, sequences), analysis (limits, continuity, differentiability, integration, logarithmic and exponential functions, sequences and series), geometry (vectors, dot and cross products, plane and space geometry), and probability and statistics (combinatorics, conditional probability, binomial and normal distributions, descriptive statistics). Candidates must also be able to structure a proof: hypothesis, theorem invoked, conclusion.
Traps that recur
- Dividing by zero or by an expression that may vanish, thereby losing or inventing solutions.
- Confusing necessary and sufficient conditions in implications.
- Forgetting to verify domain restrictions before solving irrational or logarithmic equations.
- Confusing the derivative of a product with the product of derivatives.
- Misapplying the binomial coefficient: order matters for arrangements, not for combinations.
- Using the normal approximation to the binomial without checking that np and n(1-p) are both large enough.
Rule of thumb
Every result must be checked against the domain. Solve, then substitute back, then state the solution set explicitly. In probability, identify whether the experiment is with or without replacement before choosing a formula.
Worked example
Solve log₂(x) + log₂(x − 2) = 3. Domain: x > 2. Combine: log₂(x(x − 2)) = 3, so x² − 2x = 8, giving x² − 2x − 8 = 0, roots x = 4 and x = −2. Only x = 4 lies in the domain. Solution set: {4}.