Mathematics
Mathematics in the SLAF Officer Cadet selection test measures speed and accuracy on school-level arithmetic, algebra, geometry and basic trigonometry under strict time pressure, usually without a calculator. Items are short, so choosing the fastest correct method matters more than long computation.
Core rules and concepts
- Percentages, ratio and proportion, averages, profit and loss, simple and compound interest.
- Time–speed–distance and time–work; pipes and cisterns.
- Linear equations, simultaneous equations, indices, factorisation of quadratics, inequalities.
- Angles and parallel lines, triangle properties, Pythagoras, similarity, circle theorems (chord, tangent, angle in a semicircle).
- Areas and volumes of rectangles, triangles, circles, cylinders, cones and spheres.
- Sine, cosine and tangent ratios; standard values at 0°, 30°, 45°, 60° and 90°; sine and cosine rules.
Worked example
A 150 m train crosses a 300 m bridge at 54 km/h. How long does it take? Convert the speed: 54 × 5/18 = 15 m/s. The distance that must pass the far end of the bridge is the train plus the bridge: 150 + 300 = 450 m. Time = 450 ÷ 15 = 30 seconds. Crossing a signal pole instead would take 150 ÷ 15 = 10 seconds, because only the train’s own length passes that point.
Traps that cost marks
- Forgetting to add the train’s length when a platform or bridge is involved.
- Unit slippage: km/h to m/s is ×5/18, not ×18/5.
- A 20% increase followed by a 20% decrease leaves 96% of the original - a 4% loss, not zero change.
- Using simple interest where the question says “compounded annually”.
- Answering for the whole set when the question asks for the average of the remainder.
Check units, and check whether the question wants the total, the remainder or a per-unit value, before you mark an answer.