Mathematics and Numerical Reasoning
Mathematics and Numerical Reasoning checks whether you can handle the arithmetic and everyday maths required in police work: fractions, percentages, ratio, averages, measurement, simple algebra, and data in tables. Questions are usually short, but one slip in units or order of operations costs the mark.
Core rules
- Follow order of operations: brackets, indices, division/multiplication left to right, addition/subtraction left to right.
- Convert units before calculating: 1 km = 1,000 m; 1 hour = 60 minutes; 1 kg = 1,000 g.
- For percentage change: change divided by original, multiplied by 100.
- Average equals the sum of values divided by the number of values.
- Ratio: total parts equal the sum of ratio terms; one part equals total divided by total parts.
- Estimate first to catch impossible answers.
Worked example
A patrol vehicle travels 18 km at an average speed of 12 km/h. How long does the journey take? Reasoning: time equals distance divided by speed, so 18 divided by 12 equals 1.5 hours. Convert 0.5 hour to 30 minutes. Answer: 1 hour 30 minutes. Check: at 12 km/h, 1 hour covers 12 km, leaving 6 km, which is half an hour.
Traps
- Adding percentages that apply to different bases.
- Forgetting to convert minutes to hours or grams to kilograms before dividing.
- Treating 'increase by 20%' and 'decrease by 20%' as reversible.
- Reading a table's row and column labels too quickly.
- Rounding too early; keep full values until the final step.