Mathematics
Mathematics in the PN Cadet initial test is speed-based school mathematics: arithmetic, percentages, ratio and proportion, averages, algebra, geometry, mensuration, and basic trigonometry. You are tested on clean method as much as the final number.
Core rules
- Apply BODMAS: brackets, orders, division/multiplication left to right, addition/subtraction left to right.
- Percentage change = (change ÷ original) × 100; a 20% rise followed by a 20% fall does not return to the original value.
- Average speed = total distance ÷ total time, not the mean of two speeds.
- For right triangles, use Pythagoras and the ratios sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
- Convert units before calculating: 1 km/h = 5/18 m/s.
Worked example
A 120 m train passes a pole in 6 s. Its speed is 120 ÷ 6 = 20 m/s. To pass a 180 m platform, it must cover 120 + 180 = 300 m. Time = 300 ÷ 20 = 15 s. In km/h, 20 m/s = 20 × 18/5 = 72 km/h. The reasoning matters: the platform problem adds the train’s own length because the whole train must clear the platform.
Traps
Watch unit mismatches (minutes vs hours, cm vs m). Do not confuse perimeter with area, or diameter with radius. In ratio questions, keep the same order on both sides. In algebra, distribute negative signs carefully. If options are far apart, approximate to save time; if they are close, calculate exactly.