Mathematics and Basic Numeracy
Mathematics and Basic Numeracy in Paper II rewards formula accuracy and shortcut control: percentage, ratio and proportion, average, profit and loss, simple and compound interest, time-speed-distance, mensuration, and data interpretation.
Core rules
Percentage change = (change ÷ original) × 100. Successive changes multiply: a 20% rise then a 20% fall gives 1.20 × 0.80 = 0.96, a 4% net fall, not zero. Profit percent is always on cost price; discount percent is always on marked price. SI = P × R × T ÷ 100; CI = P[(1 + R/100)^T − 1]. For equal distances, average speed is 2xy/(x + y), not (x + y)/2.
Worked example
A trader marks an item 40% above cost and allows a 25% discount. Find the profit percent. Let CP = 100. MP = 140. SP = 140 × 0.75 = 105. Profit = 5 on CP 100, so 5%. Check with fractions: the discount leaves 3/4 of the marked price, and the marked price is 7/5 of cost, so SP/CP = (7/5)(3/4) = 21/20 = 1.05.
Mensuration and DI cautions
Use π = 22/7 only when the options are built for it; otherwise keep 3.14. In DI, read the axis unit and base year before computing growth, and distinguish "percent" from "percentage points".
Traps
Adding successive percentages; computing profit on selling price; using the arithmetic mean for average speed; ignoring unit conversion (cm to m, minutes to hours); misreading compound interest compounded half-yearly, where the rate is halved and the time doubled.