Mathematics - Arithmetic, Algebra and Geometry
Core areas
Arithmetic: percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time–speed–distance, time and work, pipes and cisterns. Algebra: linear and simultaneous equations, quadratic factorisation, algebraic identities, laws of indices, simple surds. Geometry and mensuration: angle properties, triangle and circle theorems, area and volume of standard solids. Trigonometry: ratios, standard angles, simple heights and distances. Also number series and basic counting.
Traps
- Mismatched units - km/h against metres, cm² against m². Convert before computing.
- Percentage on a moving base. A 20% rise then a 20% fall leaves 96% of the original, not 100%.
- Average speed is total distance ÷ total time, never the plain mean of two speeds.
- LCM vs HCF wording - "greatest number dividing…" is HCF; "least number divisible by…" is LCM.
- Wrong base for profit or discount - profit is taken on cost price, discount on marked price.
- Series/parallel-type shortcuts applied in the reverse direction.
Rule of thumb
Write the given data as a labelled list with units, convert everything to one system, then name the formula before substituting. Most wrong options correspond to a specific slip, so a quick magnitude check (is the answer plausible?) eliminates them.
Worked example: successive discounts of 20% and 10% mean the buyer pays 0.8 × 0.9 = 0.72 of the marked price, a single discount of 28%, not 30%.