Mathematics
Core ideas
Algebra rewards structure: factor before expanding, check domain restrictions, and verify roots in the original equation. For functions, know domain, range, composition, and inverse; a function has an inverse only if it is one-to-one. In trigonometry, distinguish degrees from radians, memorise the sine and cosine rules, and use identities such as sin²θ + cos²θ = 1 to simplify rather than compute blindly. Geometry questions often combine area, volume, similarity, and circle theorems; draw a labelled sketch and convert all lengths to one unit first. In basic statistics, separate mean, median, mode, and range, and remember that the mean is sensitive to outliers while the median is not.
Traps
Typical traps include extraneous solutions from squaring, forgetting that division by zero is undefined, mixing radius and diameter, using the sine rule in the ambiguous SSA case without checking two possible angles, and reading a graph's y-intercept as a root. In statistics, do not confuse frequency with relative frequency, and do not average percentages without weighting.
Worked example
Solve 2x² − 5x − 3 = 0. Factor: (2x + 1)(x − 3) = 0, so x = −1/2 or x = 3. Check by substitution. Rule of thumb: factor first, then use the quadratic formula only when factoring fails.