Mathematics: Arithmetic, Algebra and Geometry
What to master
School-level items cluster around percentage and profit-loss, ratio and proportion, average, time-work and time-speed-distance, simple and compound interest, basic algebra (simplification, linear equations, exponents), and geometry (angles, triangles, circles, area and perimeter). Number properties such as divisibility, LCM-HCF, and unit digits also recur.
Traps that catch candidates
- Percentage change on a changed base: a 20% rise followed by a 20% fall does not return to the original value.
- Profit-loss percent is calculated on cost price unless the question states otherwise.
- Time-work: rates add, times do not. Two workers finishing in 6 and 12 days combine as 1/6 + 1/12, not as an average of 6 and 12.
- Unit mismatch: minutes versus hours, centimetres versus metres.
- “At least” versus “exactly” in counting problems; enumerate carefully.
Rule of thumb
Write the given quantities with units, convert to one unit, then set up a single equation. Estimate the answer's rough size before computing so a misplaced decimal stands out.
Worked example
A shopkeeper marks an item 25% above cost and gives a 10% discount. What is the profit percent? Let cost = 100. Marked price = 125. Selling price = 125 × 0.90 = 112.5. Profit = 12.5 on cost 100, so profit is 12.5%. The trap is applying the discount to cost instead of to the marked price.