Mathematics
Core areas
The mathematics paper samples across the secondary curriculum: algebra and functions, quadratics and inequalities, sequences and series, trigonometry, exponential and logarithmic equations, analytic geometry and vectors, combinatorics and probability, and introductory calculus. You should be able to sketch a function from its equation, identify domain and range, solve equations exactly, and interpret a derivative as a rate of change and an integral as accumulated area.
Traps
Most lost marks come from procedure, not from unfamiliar content. Always state the domain before cancelling: dividing by a variable expression can remove a valid solution or introduce an invalid one. When squaring both sides, check for extraneous roots. In trigonometry, watch degrees versus radians and the full solution set - sin x = 0.5 has more than the calculator's first answer. In logarithms, reject arguments that are non-positive. In probability, distinguish independent from mutually exclusive events, and with and without replacement. In calculus, include the constant of integration and check whether a definite integral needs a sign change when the curve crosses the axis.
Worked example
Solve 2^(x+1) + 2^(x−1) = 20. Factor the smaller power: 2^(x−1)(2^2 + 1) = 20, so 5·2^(x−1) = 20, giving 2^(x−1) = 4 = 2^2. Therefore x − 1 = 2 and x = 3. Verify: 2^4 + 2^2 = 16 + 4 = 20.
Rule of thumb: convert to a common base or factor out the smallest power, then substitute and solve. Finally, substitute back into the original equation, not into an intermediate line.