Mathematics: Method Over Memorisation
Scope
The mathematics section covers algebra, functions, sequences, geometry, probability, and statistics at the level of the extended secondary curriculum. You should be fluent with quadratic equations and inequalities, logarithms and exponentials, trigonometric identities, arithmetic and geometric sequences, analytic geometry of lines and circles, and basic combinatorics.
Traps that cost marks
Most lost points come from domain restrictions, not from hard ideas. Check that denominators are non-zero, that expressions under even roots are non-negative, and that logarithm arguments are positive. In inequalities, remember that multiplying by a negative number reverses the sign. In geometry, distinguish the radius from the diameter and confirm whether an angle is inscribed or central. Probability questions often hide the phrase at least one, which is usually easiest via the complement.
Rule of thumb
Write the domain before solving, and substitute your answer back into the original equation. A quick substitution catches extraneous roots introduced by squaring.
Worked example
Solve log₂(x−1) + log₂(x−3) = 3. The domain requires x > 3. Combining logs gives log₂((x−1)(x−3)) = 3, so (x−1)(x−3) = 8, hence x² − 4x − 5 = 0, giving x = 5 or x = −1. The domain eliminates −1, so x = 5. Notice that the algebra alone would have produced a wrong answer; the domain check is part of the solution, not an optional extra. Practise writing that check every time until it becomes automatic.