Prison Officer Maths Test: Numeracy Examples With Answers

Plenty of capable candidates feel anxious about the maths part of the prison officer online test. Usually it is because they haven't done sums on paper since school. The reassuring news is that the maths is practical, everyday arithmetic, not algebra. The less reassuring news is that it is timed, so being slow or rusty costs marks. This guide explains what to expect and walks through ten worked examples.

Where the maths fits in

The HMPPS Scenario-Based Test (SBT) takes around 25 to 40 minutes and includes behavioural and numerical scenarios. When HMPPS introduced the online test in 2019, its jobs blog described the numerical part as 20 questions in up to 15 minutes, testing "simple mathematical calculations you often have to complete when at work in a prison".

That works out at about 45 seconds a question, if the format is still the same. Formats can change, so check your invitation for the number of questions, the time limit and whether you can use a calculator.

What topics come up

The calculations follow the job. Expect:

• Roll counts: how many prisoners should be on a wing, landing or activity, given who is elsewhere.
• Money: canteen spending, prison wages and account balances in pounds and pence.
• Time: the 24-hour clock, shift lengths, breaks, and how long movements or sessions take.
• Percentages and fractions: what share of a group is doing something, or how much something has changed.
• Ratios and averages: staff-to-prisoner ratios, average numbers per day.

Ten worked examples

These questions are written for this site. Try each one before reading the working.

1. Wing roll

A wing has a roll of 112. There are 34 prisoners in workshops, 27 at education, 5 at healthcare and 2 on visits. How many should be on the wing?

Working: 34 + 27 + 5 + 2 = 68. Then 112 − 68 = 44.

2. Finding a discrepancy

Landing 3 should have 38 prisoners. You count 36 in cells and 1 in the shower. How many are unaccounted for?

Working: 36 + 1 = 37. Then 38 − 37 = 1. In practice, that one person would need to be found before the count is correct.

3. Canteen spend

A prisoner has £22.50 to spend. He orders four items at 85p each, one item at £6.20 and two items at £1.75 each. How much will he have left?

Working: 4 × £0.85 = £3.40. 2 × £1.75 = £3.50. Total = £3.40 + £6.20 + £3.50 = £13.10. Left: £22.50 − £13.10 = £9.40.

4. Prison wages

A prisoner is paid £1.60 per session and works 9 sessions a week. How much does he earn in 4 weeks?

Working: £1.60 × 9 = £14.40 per week. £14.40 × 4 = £57.60.

5. Shift length

An officer works from 07:30 to 17:15 with a 45-minute unpaid break. How long are they paid for?

Working: 07:30 to 17:30 would be 10 hours, so 07:30 to 17:15 is 9 hours 45 minutes. Subtract 45 minutes: 9 hours.

6. Movement timing

Three groups need moving to the gym one after another. Each move takes 25 minutes and the first starts at 08:20. When does the last one finish?

Working: 3 × 25 = 75 minutes, which is 1 hour 15 minutes. 08:20 + 1:15 = 09:35.

7. Percentage of a group

15% of the 240 prisoners in a house block are on a waiting list for a course. How many is that?

Working: 10% of 240 = 24. 5% = 12. So 15% = 24 + 12 = 36.

8. Percentage change

Recorded incidents on a wing fell from 40 one month to 30 the next. What is the percentage decrease?

Working: the fall is 10. 10 ÷ 40 = 0.25 = 25%. Always divide by the original figure.

9. Ratio

A unit needs one officer for every 12 prisoners. How many officers are needed for 84 prisoners?

Working: 84 ÷ 12 = 7.

10. Average

A visits hall had 14, 18, 11 and 17 visits over four days. What was the average per day?

Working: 14 + 18 + 11 + 17 = 60. Then 60 ÷ 4 = 15.

Mental-maths tips that save seconds

Adding lists

Group numbers that make tens. In 34 + 27 + 5 + 2, add 34 + 5 + 2 = 41 first, then 41 + 27 = 68.

Money

Work in pence if decimals trip you up. £22.50 becomes 2,250p and £13.10 becomes 1,310p, so the change is 940p, which is £9.40. Be careful with 5p and 50p: £4.05 and £4.50 are very different.

Multiplying prices

For £1.75 × 2, think £2 × 2 = £4, minus 25p × 2 = 50p, giving £3.50. Rounding and then adjusting is quicker than long multiplication.

Time

Count up to the next whole hour, then add the rest. From 13:40 to 16:05 is 20 minutes to 14:00, then 2 hours to 16:00, then 5 minutes. That makes 2 hours 25 minutes. Remember there are 60 minutes in an hour, not 100.

Percentages

Find 10% by dividing by 10, 5% by halving that, and 1% by dividing by 100. Build the rest from those. 35% = 10% × 3 + 5%.

Percentage change

Use change ÷ original × 100. A rise from 50 to 60 is 20%. A fall from 60 to 50 is about 16.7%, not 20%, because the original figure is different.

Estimate first

Before calculating, guess roughly. If your answer is far from the estimate, check it again.

Calculator or not?

Your invitation should tell you whether you can use a calculator. Practise both ways anyway. A calculator does not help much if you set the problem up wrongly. Most mistakes in these tests come from misreading the question, such as including the people on visits when you were asked who is at work, not from the arithmetic itself.

How to practise

• Do 10–15 minutes a day of mixed questions for a fortnight, rather than one long session.
• Time yourself: aim for under 45 seconds per question.
• Keep a list of the mistakes you make. Most people repeat the same two or three types.
• Read the question twice: check who is included and which units are used (minutes or hours, pounds or pence).
• Take the free HMPPS practice test to see the screens before the real thing.

You can try ten free numeracy questions on our practice page. The Online Tests pack has 120 prison-context numeracy questions across five timed mocks.

Key points

• The numeracy questions use everyday prison maths: counts, money, time and percentages.
• HMPPS described 20 questions in up to 15 minutes in 2019. Check your invitation for your format and calculator rules.
• Speed comes from practice and simple mental shortcuts, not advanced maths.
• Read carefully: most errors are misreadings, not miscalculations.

prisonofficertest.co.uk is an independent practice site. It is not affiliated with HMPPS, the Ministry of Justice, the Scottish Prison Service, the Northern Ireland Prison Service or any prison operator. Always check your own invitation and the recruiter's current guidance.