Mathematics: Arithmetic, Algebra and Mensuration
Core syllabus
Number systems, HCF and LCM, fractions and decimals, ratio and proportion, percentages, profit and loss, simple and compound interest, average, speed–time–distance, time and work, basic algebra (linear equations, identities, factorisation), geometry (angles, triangles, circles, area and perimeter), and elementary trigonometry (sine, cosine, tangent of standard angles).
Traps to watch
- Percentage change: a 20% rise followed by a 20% fall does not return to the original value; it ends at 96%.
- Average speed: for equal distances at speeds a and b, average speed is 2ab/(a+b), not (a+b)/2.
- Compound interest: interest is added to the principal each period; never apply simple interest for multi-year problems.
- Unit mismatch: minutes against hours, centimetres against metres. Convert before computing.
- Ratio order: "A to B is 3:5" means A/B = 3/5; reversing it is the commonest careless error.
- Time and work: combine rates (1/x + 1/y), not times.
Rule of thumb
Write the formula first, substitute with units attached, and estimate the answer before calculating. If your result is wildly different from the estimate, recheck the setup rather than the arithmetic.
Worked example
A boat covers 60 km downstream in 3 hours and returns in 5 hours. Find the speed of the stream. Downstream speed = 60/3 = 20 km/h. Upstream speed = 60/5 = 12 km/h. Stream speed = (20 − 12)/2 = 4 km/h. The trap is to subtract the times instead of the speeds.