Mathematics
Core toolkit
Arithmetic carries the most marks: fractions and decimals, percentages, ratio and proportion, averages, profit and loss, simple interest, time–speed–distance, and work-rate problems. Algebra covers simplifying expressions, solving linear equations in one variable, and the laws of exponents. Geometry asks for basic angle facts (angles on a straight line, in a triangle, between parallel lines), properties of triangles and circles, Pythagoras' theorem, and area and perimeter of squares, rectangles, triangles and circles. Also revise mean, median, mode and range, and reading values from simple tables.
Traps
- Unit mismatch: convert before calculating. To change km/h to m/s, multiply by 5/18.
- Successive percentages do not add: a 20% rise then a 10% fall gives +8%, not +10%.
- "Per cent of" vs "per cent more than": check which quantity is the base.
- Averaging averages: you cannot average two group means unless the groups are the same size.
- Ratio order: in A:B = 3:5, A is the smaller share, not the larger.
Rule of thumb
In percentage questions, set the original amount equal to 100 and work with plain numbers. Substitute back only at the end, and always write the unit next to the answer so you notice a mismatch.
Worked example: A price rises 20% and then falls 10%. Start at 100 → 120 → 108. Net change = +8%. The tempting wrong answer, +10%, comes from adding the two percentages.
Show every step in the margin: neat working earns partial credit and makes your own checking reliable under time pressure.