Mathematics
Core areas
Number system, HCF and LCM, fractions and decimals, percentage, ratio and proportion, average, profit and loss, discount, simple and compound interest, time-work, time-distance and mixtures. Algebra covers simplification, exponents, linear equations in one or two variables, factorisation and basic polynomials. Geometry covers angle properties of lines and polygons, triangles (congruence, Pythagoras), circles (chord, tangent, arc), and area, perimeter and volume of standard figures. Expect a light touch of trigonometric ratios, sets, elementary probability and number series.
Traps
Percentage change is always measured against the original value: a 20% rise followed by a 20% fall does not return to the start. Averages never average averages unless the counts are equal. Convert km/h to m/s by multiplying by 5/18. In time-work problems, invert the rate: if A finishes in 6 days and B in 12, together they do 1/6 + 1/12 = 1/4 per day, so 4 days.
Worked example
A man drives 60 km at 60 km/h and returns at 30 km/h. Total distance is 120 km; total time is 1 + 2 = 3 hours; average speed is 120/3 = 40 km/h, not the 45 you get by averaging 60 and 30. Rule of thumb: for average speed, always total distance divided by total time.