Mathematics
What is tested
Arithmetic (percentages, profit and loss, ratio, average, speed–distance–time, work, simple and compound interest), the number system (LCM/HCF, simplification, BODMAS), elementary algebra (linear equations, factorisation), geometry and mensuration (angles, triangles, circles, area and volume), and basic trigonometric values. No calculator is allowed, so choosing a fast method matters as much as knowing the rule.
Core rules
- BODMAS: brackets, orders, then division/multiplication left to right, then addition/subtraction left to right.
- Percentage change is calculated on the original base unless the question says otherwise.
- Profit% and loss% are taken on cost price; discount% is taken on marked price.
- Speed = distance ÷ time; convert km/h to m/s by multiplying by 5/18.
- For two people, pipes or resistors working together, use the reciprocal sum, not the plain average.
Worked example
A shopkeeper marks an article 40% above cost and then allows a 25% discount. Find his profit percent.
Reasoning: let cost = 100. Marked price = 140. The discount is 25% of the marked price = 35, so selling price = 140 − 35 = 105. Profit = 105 − 100 = 5, giving a 5% profit. The multiplier check is quicker and safer: 1.40 × 0.75 = 1.05. Whenever a question chains a markup and a discount, multiply the multipliers instead of computing two separate amounts.
Traps
- Applying the discount to cost price instead of marked price.
- Adding percentage changes: a 20% rise then a 20% fall is a 4% net fall, not zero.
- Mixing units - minutes with hours, centimetres with metres.
- Averaging averages without weighting by group size.
- Forgetting that compound interest uses the previous year's amount as the new base.
- Leaving a numerical answer without its unit where the question expects one.