Mathematics
What is actually examined
Module mathematics is applied arithmetic and algebra for engineering, not pure theory. You must be fluent with: fractions, powers and roots, scientific notation and SI prefixes; ratio, proportion and percentage; transposition of formulas; linear and simultaneous equations; simple quadratics; and logarithms used for decibel-type problems. Geometry covers areas and volumes of rectangles, triangles, circles, cylinders and spheres. Trigonometry covers Pythagoras, the sine, cosine and tangent ratios, the sine and cosine rules, and the graphs of trigonometric functions.
Traps in questions
- Units before numbers. Convert every term to base units first. Mixing mm and m in a stress or area calculation is the single most common arithmetic failure.
- Order of operations - work brackets, indices, then multiply/divide, then add/subtract.
- Angle mode. Calculators must be in degrees unless radians are stated.
- Percentage change uses the original value as denominator, not the new one.
- Rounding early. Carry full precision and round only the final answer.
Worked example
An aircraft climbs 500 ft while covering 4000 ft over the ground. The climb angle is the inverse tangent of the ratio: tan θ = 500/4000 = 0.125, so θ = tan⁻¹(0.125) ≈ 7.1°. The flight path length (hypotenuse) is √(500² + 4000²) = √(16 250 000) ≈ 4031 ft. Note that for small angles the path length is close to the ground distance.
Rule of thumb
1 inch = 25.4 mm, 1 kg = 2.205 lb, 1 hp ≈ 0.746 kW, 1 bar = 100 kPa. Memorise these conversions; they save time and prevent unit slips.