Mathematics
Core concepts
The exam rewards fluency in algebra, proportional reasoning, geometry and elementary statistics. You should be able to solve linear and quadratic equations, manipulate powers and roots, simplify fractions and rational expressions, work with percentages and ratios, compute areas and volumes of standard figures, apply Pythagoras and similarity, and read averages, medians and simple probability.
Common traps
- Sign errors when expanding brackets: always re-multiply every term.
- Unit mismatch: speeds in km/h and times in minutes must be converted before dividing.
- Percentage of what? A 20% rise followed by a 20% fall is not a return to the original value.
- Order of operations: powers and roots before multiplication, then addition.
- Quadratic with two roots: questions often want both or the positive one only - read carefully.
Worked example
Solve 2x² − 5x − 3 = 0. Discriminant: Δ = 25 + 24 = 49, so √Δ = 7. Then x = (5 ± 7)/4, giving x = 3 or x = −1/2. Check by substitution.
Rule of thumb
When a problem mentions rates, mixtures or work done together, set up a table of quantities with consistent units before writing the equation; most lost marks are bookkeeping, not algebra.