Mathematics: Arithmetic, Mensuration and Elementary Algebra
Core topics
Build speed on the number system (HCF/LCM, divisibility rules for 2, 3, 4, 5, 8, 9 and 11), simplification and approximation, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, pipes and cisterns, speed–time–distance, trains, boats and streams, mensuration of standard 2D and 3D figures, linear equations and standard algebraic identities, and the trigonometric values for 0°, 30°, 45°, 60° and 90°.
Traps that cost marks
Unit mismatch is the quiet killer: convert km/h to m/s by multiplying by 5/18 before substituting. Distinguish "percent more" from "percent less" - a 20% rise followed by a 20% fall does not restore the original value. Average speed over two equal distances uses the harmonic form 2xy/(x+y), not (x+y)/2. In compound interest, a half-yearly rate halves r and doubles the number of periods. In time and work, efficiency is inversely proportional to days taken, so add rates, never days.
Rule of thumb
For two successive percentage changes of a% then b%, the net change is a + b + ab/100.
Worked example
A trader marks goods 40% above cost and allows a 25% discount. Net change = 40 − 25 − (40×25)/100 = 5%, so the profit is 5%, not the 15% many candidates tick.