Mathematics
Scope
Arithmetic (percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time–work, speed–distance–time), algebra (linear and quadratic equations, factorisation, simultaneous equations), geometry (triangles, circles, angles, similarity), trigonometry, mensuration, permutations and combinations, probability, and sequences.
Speed with accuracy
Learn the standard results so you do not re-derive them: area of a circle πr², circumference 2πr, volume of a cylinder πr²h, sum of angles in a triangle 180°, Pythagoras, and the quadratic formula. For percentages, remember that successive changes multiply: two successive discounts of 20% and 10% give 0.8 × 0.9 = 0.72, i.e. a 28% total discount - not 30%.
For time–work, convert to rates: if A finishes in 6 days and B in 3, together they do 1/6 + 1/3 = 1/2 of the work per day, finishing in 2 days. For speed, keep units consistent - convert km/h to m/s by multiplying by 5/18.
Traps
Adding percentages instead of multiplying them. Confusing simple and compound interest. Mixing area and perimeter formulas. Using the wrong base in a triangle or trapezium question. Forgetting that a 25% increase is undone by a 20% decrease, not a 25% decrease. Rounding early in a multi-step calculation.
Worked example
A shop marks a shirt at Rs 2,000 and allows two successive discounts of 20% and 10%. Final price = 2000 × 0.8 × 0.9 = Rs 1,440, a total discount of 28%.
Rule of thumb
Estimate the answer before calculating; if your exact answer is far from the estimate, recheck the setup rather than the arithmetic.