How the PSET numeracy section works
Numeracy is one of three sections in the PSET, the 49-question, one-hour paper that comes straight after your application. The mock paper’s numeracy questions are set in policing: a driver’s speed over the limit, officers per head of population, parcel weights, a weekly cost over a year, a sentence reduced by a percentage, and distance at a given speed.
There are no answer options to choose from. You write the figure in a box, and some answers need two parts, such as years and months.
Police Scotland’s guidance on the timed test says you will be provided with a calculator.
How to answer a numeracy question
Use the same four steps each time:
- Pick out the numbers and the unit the answer needs: miles, minutes, kilos, pounds or years and months.
- Change units before you calculate. Turn years into months or minutes into hours where that makes the sum easier.
- Work it out, then convert back into the unit the question asks for.
- Sense-check the size. A speed of 400 mph or a sentence longer than it started means a slip.
Worked examples
A town of 24,000 people has one officer for every 400 residents. How many officers is that? 24,000 ÷ 400 = 60 officers.
A patrol car drives 18 miles at 36 mph. How many minutes does it take? 18 ÷ 36 = 0.5 hours, which is 30 minutes.
A 3-year sentence is cut by 25%. How long is it now? 3 years is 36 months, and 25% of 36 is 9, so 27 months remain: 2 years and 3 months.
Find the mean of 14, 9, 11, 16, 8 and 14. They add up to 72, and 72 ÷ 6 = 12.
Tips for the real PSET numeracy section
- Always write the unit, and use both boxes for answers like 1 year and 3 months.
- Learn the speed triangle: distance = speed × time. Two of the mock paper’s six numeracy questions involve speed.
- Practise percentages of time, such as 25% off 5 years, not just of money.
- Do the mock paper under time pressure and check every answer against Police Scotland’s answer sheet.
- Keep your mental arithmetic sharp even though a calculator is provided. It is faster for simple steps and catches calculator slips.
Practise PSET numeracy on CogniPrep
Our numeracy section has 20 questions in 24 minutes across seven topics: arithmetic, money, percentages, ratio, speed, distance and time, time and duration, and averages. You type each answer, with the unit printed beside the box where the real paper prints one, and two boxes for answers in years and months or hours and minutes. It has no calculator, so you practise the harder way round. The 20 questions are our estimate of the numeracy share of the 49, and your result is shown against our own reference line, not an official pass mark.