Mathematics
What you must know
Candidates need arithmetic without a calculator, fractions and decimals, ratio and proportion, percentages, powers and roots, simple and compound interest, and basic algebra (transposing formulae, solving linear equations). Geometry essentials include area and volume of common shapes (rectangle, triangle, circle, cylinder, sphere, cone), the Pythagorean theorem, and unit conversion (inches to mm, litres to gallons, kg to lb).
Traps to watch
- Unit mixing: converting mm to cm before multiplying areas; forgetting that area scales with the square of a linear conversion factor and volume with the cube.
- Percentage change: a 20% rise followed by a 20% fall does not return to the original value (it ends at 96%).
- Order of operations: evaluate brackets, then powers, then multiply/divide, then add/subtract.
- Rounding too early in multi-step problems; carry extra digits and round only at the end.
- Transposition sign errors when moving terms across the equals sign.
Worked example
A rectangular fuel tank measures 60 cm x 40 cm x 25 cm. Its volume is 60 x 40 x 25 = 60,000 cm³ = 60 litres (since 1000 cm³ = 1 litre). If it is 75% full, fuel present = 0.75 x 60 = 45 litres. Rule of thumb: for a box, volume in litres = length x width x height in cm divided by 1000.
Rule of thumb
Convert every quantity to one consistent unit system before computing, and sanity-check that an answer's magnitude is plausible (a tank is not 6 litres if it is the size of a desk).