Mathematics: Arithmetic, Algebra and Geometry
Mathematics here rewards speed on percentage, ratio, average, profit-loss, simple and compound interest, time-speed-distance, and work-rate, plus basic algebra (linear equations, simultaneous equations, exponents) and geometry (angles, triangles, circles, area and perimeter). Master the standard formulas, then practise recognising which formula a word problem is asking for.
Core relationships to memorise
- Profit % = (Profit / Cost Price) × 100 - always on cost price unless stated.
- Compound interest: A = P(1 + r/100)^n.
- Work: combined rate = sum of individual rates; time = 1 / (sum of rates).
- Speed = distance / time; average speed for equal distances = 2xy/(x+y), not the simple mean.
- Sum of angles in a triangle = 180°; exterior angle = sum of the two opposite interior angles.
Traps to expect
- Percentage on the wrong base (profit on selling price instead of cost price).
- Average speed computed as the arithmetic mean of two speeds.
- Unit mismatches (minutes vs hours, metres vs kilometres).
- Successive percentage changes - they do not add; use the multiplier method.
Rule of thumb
Convert every percentage change into a multiplier (a 20% rise is ×1.2, a 20% fall is ×0.8). Successive changes then simply multiply.
Worked example: A price rises 20% then falls 20%. Net multiplier = 1.2 × 0.8 = 0.96, so the net change is a 4% decrease, not zero.