Mathematical Ability: Arithmetic, Algebra, Geometry and Statistics
Mathematical Ability is Section B: 75 one-mark questions. Arithmetic dominates - percentages, profit and loss, ratio, averages, time-work, time-speed-distance, simple and compound interest, mixtures - with smaller blocks of algebra, geometry, mensuration, trigonometry and statistics.
Multipliers, not successive arithmetic
Model percentage changes as multiplying factors. A 20% increase is ×1.20; a 25% decrease is ×0.75. Successive changes multiply in order, so the net factor is the product. Profit and loss are calculated on cost price; discount is calculated on marked price.
Formula anchors
For a circle, area = πr², circumference = 2πr. For a right triangle, a² + b² = c². For a cylinder, volume = πr²h; for a cone, volume = (1/3)πr²h. Mean = sum/count; for grouped data use class midpoints.
Worked example
A trader marks an item 40% above cost and then gives a 25% discount. Let cost = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 5 on 100, so 5% profit. Note that 40% − 25% = 15% would be wrong because the two percentages use different bases.
Traps
Using selling price as the profit base; subtracting percentages instead of multiplying; mixing units (km/h with metres); rounding before the final step; forgetting that compound interest adds interest to principal each period.