Police Math Test: Practice Questions, Answers and Prep Guide

The police math test measures whether you can solve basic numerical problems that may appear on police written exams, deputy sheriff exams, state trooper exams and other law enforcement hiring tests.

Police math is usually not advanced. Most questions test practical skills such as:

• addition;
• subtraction;
• multiplication;
• division;
• percentages;
• averages;
• time calculations;
• distance and speed;
• ratios;
• schedules;
• charts and tables;
• word problems;
• basic report-related calculations.

Recommended prep:

These are original police-style math practice questions for study purposes. They are not official questions from any police department, sheriff’s office, POST commission, civil service commission or test provider.

What Is on the Police Math Test?

Police math questions vary by agency and test provider, but they usually focus on everyday reasoning rather than advanced formulas.

Common topics include:

Topic	What It Tests
Addition and subtraction	Counts, totals and remaining amounts
Multiplication and division	Groups, rates and equal distribution
Percentages	Increases, decreases and proportions
Averages	Mean values from reports or logs
Time	Shift length, elapsed time and schedules
Distance	Travel distance and route problems
Speed	Miles per hour and response timing
Ratios	Comparing quantities
Tables and charts	Reading numerical information accurately
Word problems	Translating a scenario into a calculation

Some police exams do not include much math. Others include a dedicated numerical reasoning section.

Always check the official candidate guide for your agency.

Police Math Practice Test

Answer each question before checking the explanation.

Recommended timing:

25 questions
25 minutes

For a harder timed drill:

25 questions
18 minutes

Section 1: Basic Arithmetic

Question 1: Addition

An officer issued 14 citations during one shift and 19 citations during the next shift. How many citations were issued total?

• A. 29
• B. 31
• C. 33
• D. 35

Answer and Explanation

Correct answer: C. 33

14 + 19 = 33

Question 2: Subtraction

A department has 85 traffic cones. Officers use 37 cones during a public event. How many cones remain?

• A. 42
• B. 46
• C. 48
• D. 52

Answer and Explanation

Correct answer: C. 48

85 - 37 = 48

Question 3: Multiplication

Each patrol vehicle carries 4 safety flares. There are 16 patrol vehicles. How many flares are carried total?

• A. 48
• B. 56
• C. 64
• D. 72

Answer and Explanation

Correct answer: C. 64

16 × 4 = 64

Question 4: Division

A training unit distributes 96 practice forms equally among 8 recruits. How many forms does each recruit receive?

• A. 10
• B. 11
• C. 12
• D. 14

Answer and Explanation

Correct answer: C. 12

96 ÷ 8 = 12

Section 2: Percentages

Question 5: Percentage of a Number

What is 25% of 120?

• A. 20
• B. 25
• C. 30
• D. 35

Answer and Explanation

Correct answer: C. 30

25% is one quarter.

120 ÷ 4 = 30

Question 6: Percentage Increase

A unit handled 80 calls last month and 100 calls this month. What was the percentage increase?

• A. 20%
• B. 25%
• C. 30%
• D. 40%

Answer and Explanation

Correct answer: B. 25%

Increase:

100 - 80 = 20

Percentage increase uses the original value:

20 ÷ 80 × 100 = 25%

Question 7: Percentage Remaining

A storage room contains 200 evidence bags. Officers use 15% of them. How many evidence bags are used?

• A. 20
• B. 25
• C. 30
• D. 35

Answer and Explanation

Correct answer: C. 30

15% of 200 = 0.15 × 200 = 30

Question 8: Percentage Full

A fuel tank holds 500 gallons and is 60% full. How many gallons are in the tank?

• A. 200
• B. 250
• C. 300
• D. 350

Answer and Explanation

Correct answer: C. 300

0.60 × 500 = 300

Section 3: Averages and Ratios

Question 9: Average

An officer completes reports in 20, 25, 30 and 35 minutes. What is the average report completion time?

• A. 25 minutes
• B. 27.5 minutes
• C. 30 minutes
• D. 32.5 minutes

Answer and Explanation

Correct answer: B. 27.5 minutes

Add the times:

20 + 25 + 30 + 35 = 110

Divide by 4:

110 ÷ 4 = 27.5

Question 10: Average Calls

A dispatcher logs 42 calls on Monday, 38 calls on Tuesday and 40 calls on Wednesday. What is the average number of calls per day?

• A. 38
• B. 39
• C. 40
• D. 42

Answer and Explanation

Correct answer: C. 40

42 + 38 + 40 = 120
120 ÷ 3 = 40

Question 11: Ratio

A training class has 3 recruits for every 1 instructor. If there are 24 people total, how many are recruits?

• A. 18
• B. 20
• C. 21
• D. 22

Answer and Explanation

Correct answer: A. 18

Ratio:

3 recruits : 1 instructor

Total parts:

3 + 1 = 4

Each part:

24 ÷ 4 = 6

Recruits:

3 × 6 = 18

Question 12: Ratio Comparison

A department has 12 marked vehicles and 4 unmarked vehicles. What is the ratio of marked vehicles to unmarked vehicles?

• A. 1:3
• B. 2:1
• C. 3:1
• D. 4:3

Answer and Explanation

Correct answer: C. 3:1

12:4

Divide both sides by 4:

3:1

Section 4: Time Calculations

Question 13: Shift Length

A patrol shift starts at 6:45 a.m. and ends at 3:15 p.m. How long is the shift?

• A. 7 hours 30 minutes
• B. 8 hours
• C. 8 hours 30 minutes
• D. 9 hours

Answer and Explanation

Correct answer: C. 8 hours 30 minutes

6:45 a.m. to 2:45 p.m. = 8 hours
2:45 p.m. to 3:15 p.m. = 30 minutes
Total = 8 hours 30 minutes

Question 14: Elapsed Time

An officer arrives at a scene at 9:20 p.m. and clears the scene at 10:05 p.m. How long was the officer on scene?

• A. 35 minutes
• B. 40 minutes
• C. 45 minutes
• D. 50 minutes

Answer and Explanation

Correct answer: C. 45 minutes

9:20 to 10:00 = 40 minutes
10:00 to 10:05 = 5 minutes
Total = 45 minutes

Question 15: Schedule End Time

A training session begins at 1:35 p.m. and lasts 50 minutes. What time does it end?

• A. 2:15 p.m.
• B. 2:20 p.m.
• C. 2:25 p.m.
• D. 2:30 p.m.

Answer and Explanation

Correct answer: C. 2:25 p.m.

1:35 + 50 minutes = 2:25

Question 16: Time Between Events

A call is received at 7:18 p.m. Officers arrive at 7:31 p.m. How many minutes passed between call receipt and arrival?

• A. 11 minutes
• B. 12 minutes
• C. 13 minutes
• D. 14 minutes

Answer and Explanation

Correct answer: C. 13 minutes

7:18 to 7:31 = 13 minutes

Section 5: Distance and Speed

Question 17: Speed

An officer drives 18 miles in 30 minutes. What is the average speed in miles per hour?

• A. 24 mph
• B. 30 mph
• C. 36 mph
• D. 40 mph

Answer and Explanation

Correct answer: C. 36 mph

30 minutes is half an hour.

If 18 miles are traveled in half an hour:

18 × 2 = 36 mph

Question 18: Distance

A patrol car travels at 45 miles per hour for 20 minutes. Approximately how far does it travel?

• A. 10 miles
• B. 15 miles
• C. 20 miles
• D. 25 miles

Answer and Explanation

Correct answer: B. 15 miles

20 minutes is one third of an hour.

45 × 1/3 = 15

The patrol car travels 15 miles.

Question 19: Time

A vehicle travels 60 miles per hour. How long does it take to travel 15 miles?

• A. 10 minutes
• B. 15 minutes
• C. 20 minutes
• D. 30 minutes

Answer and Explanation

Correct answer: B. 15 minutes

At 60 mph, the vehicle travels 1 mile per minute.

15 miles = 15 minutes

Question 20: Distance Word Problem

An officer drives 12 miles to one location and 8 miles to a second location. The officer then returns 20 miles to the station. How many miles are driven total?

• A. 32
• B. 36
• C. 40
• D. 44

Answer and Explanation

Correct answer: C. 40

12 + 8 + 20 = 40

Section 6: Tables and Charts

Use the table below for Questions 21–23.

Day	Calls for Service
Monday	42
Tuesday	38
Wednesday	47
Thursday	51
Friday	44

Question 21: Highest Number

Which day had the highest number of calls?

• A. Monday
• B. Wednesday
• C. Thursday
• D. Friday

Answer and Explanation

Correct answer: C. Thursday

Thursday had 51 calls, the highest number in the table.

Question 22: Total Calls

How many calls were recorded on Monday and Tuesday combined?

• A. 78
• B. 80
• C. 82
• D. 84

Answer and Explanation

Correct answer: B. 80

42 + 38 = 80

Question 23: Difference

How many more calls were recorded on Thursday than Tuesday?

• A. 11
• B. 12
• C. 13
• D. 14

Answer and Explanation

Correct answer: C. 13

51 - 38 = 13

Section 7: Word Problems

Question 24: Evidence Count

An evidence locker has 126 items. Officers add 18 items and remove 9 items for court. How many items are now in the locker?

• A. 133
• B. 135
• C. 137
• D. 139

Answer and Explanation

Correct answer: B. 135

Start with 126.

126 + 18 = 144
144 - 9 = 135

Question 25: Multi-Step Problem

A department orders 15 boxes of forms. Each box contains 40 forms. Officers use 175 forms during the month. How many forms remain?

• A. 375
• B. 400
• C. 425
• D. 450

Answer and Explanation

Correct answer: C. 425

Total forms ordered:

15 × 40 = 600

Forms remaining:

600 - 175 = 425

Police Math Test Answer Key

Question	Skill Tested	Correct Answer
1	Addition	C
2	Subtraction	C
3	Multiplication	C
4	Division	C
5	Percentage	C
6	Percentage increase	B
7	Percentage	C
8	Percentage	C
9	Average	B
10	Average	C
11	Ratio	A
12	Ratio	C
13	Time	C
14	Elapsed time	C
15	Schedule time	C
16	Time difference	C
17	Speed	C
18	Distance	B
19	Time / speed	B
20	Distance total	C
21	Table reading	C
22	Table calculation	B
23	Difference	C
24	Word problem	B
25	Multi-step word problem	C

How to Solve Police Math Questions

Step 1: Identify What the Question Asks

Before calculating, ask:

What am I being asked to find?

Examples:

• total;
• remaining amount;
• difference;
• average;
• percentage;
• time elapsed;
• speed;
• distance;
• number of items.

Many wrong answers come from solving the wrong problem.

Step 2: Pull Out the Key Numbers

Example:

A department orders 15 boxes.
Each box contains 40 forms.
Officers use 175 forms.
How many forms remain?

Key numbers:

15
40
175

Step 3: Choose the Correct Operation

Question Wording	Likely Operation
total, combined, altogether	Add
remain, left, fewer	Subtract
each, per, groups of	Multiply or divide
average	Add, then divide
percent of	Multiply by percentage
increase or decrease	Compare change to original
miles per hour	Speed formula
elapsed time	Time difference

Step 4: Solve in Small Steps

Multi-step questions should be broken down.

Example:

15 boxes × 40 forms = 600 forms
600 - 175 used = 425 remaining

Step 5: Check the Unit

Police math answers may use:

• minutes;
• hours;
• miles;
• mph;
• items;
• calls;
• citations;
• percentages;
• people;
• vehicles.

A correct number with the wrong unit can lead to a wrong answer.

Police Math Formulas to Know

Topic	Formula
Average	total ÷ number of values
Percentage of a number	decimal percentage × total
Percentage increase	increase ÷ original × 100
Speed	distance ÷ time
Distance	speed × time
Time	distance ÷ speed
Remaining amount	starting amount + added - removed
Ratio total parts	add ratio parts
Difference	larger number - smaller number

Useful Percentage Shortcuts

Percentage	Shortcut
10%	Divide by 10
20%	Divide by 5
25%	Divide by 4
50%	Divide by 2
75%	Find three quarters
100%	Whole amount

Examples:

25% of 120 = 120 ÷ 4 = 30
50% of 86 = 43
10% of 250 = 25
75% of 800 = 600

Time Calculation Strategy

For elapsed time, break the problem into parts.

Example:

9:20 p.m. to 10:05 p.m.

Calculate:

9:20 to 10:00 = 40 minutes
10:00 to 10:05 = 5 minutes
Total = 45 minutes

For shifts crossing noon or midnight, write the times carefully and use a timeline.

Speed, Distance and Time Strategy

Use this relationship:

Speed = distance ÷ time
Distance = speed × time
Time = distance ÷ speed

Important conversion:

30 minutes = 1/2 hour
20 minutes = 1/3 hour
15 minutes = 1/4 hour

Example:

45 mph for 20 minutes
20 minutes = 1/3 hour
45 × 1/3 = 15 miles

Common Police Math Mistakes

Mistake 1: Misreading the Final Question

Example:

How many were used?

is different from:

How many remain?

Read the final sentence carefully.

Mistake 2: Using the Wrong Percentage Base

For percentage increase, divide by the original value.

Example:

80 to 100
Increase = 20
20 ÷ 80 = 25%

Do not divide by the new value.

Mistake 3: Confusing Minutes and Hours

30 minutes is not 0.30 hours.

30 minutes = 0.5 hours
20 minutes = 1/3 hour
15 minutes = 0.25 hours

Mistake 4: Rushing Basic Arithmetic

Police math is usually not conceptually difficult. Most errors come from rushing.

Check simple calculations:

85 - 37
14 + 19
15 × 40
600 - 175

Mistake 5: Forgetting to Simplify Ratios

Example:

12:4 = 3:1

Do not leave a ratio unsimplified if the answer choices are simplified.

Mistake 6: Ignoring Tables

For table questions, use the exact values shown.

Do not estimate unless the question asks for an estimate.

Police Math vs Police Reading Comprehension

Police math and reading comprehension often overlap.

Many math questions are word problems. You must first understand what the scenario asks before calculating.

Related guide:

• Police Reading Comprehension

Police Math vs Police Report Writing

Police math may appear in report-related situations:

• times;
• distances;
• number of items;
• evidence counts;
• call totals;
• shift durations.

Report writing requires clear and accurate factual communication.

Related guide:

• Police Report Writing Test

How to Prepare for the Police Math Test

Use this process:

1. Review basic arithmetic.
2. Practice percentages.
3. Practice averages and ratios.
4. Review elapsed time.
5. Practice speed, distance and time.
6. Practice chart and table questions.
7. Complete police-style word problems.
8. Review every wrong answer.
9. Practice under time limits.
10. Combine math with full police exam practice.

Recommended prep:

Best Police Math Test Prep

JobTestPrep is useful for police math preparation because it offers law enforcement-style practice across major police written exam topics, including math, reading comprehension, report writing, situational judgment and reasoning.

Use JobTestPrep for:

• police math practice;
• arithmetic and percentages;
• time and distance questions;
• word problems;
• full police written exam practice;
• timed tests;
• answer explanations.

Recommended prep:

Free vs Paid Police Math Practice

Prep Type	Best Use
Free math questions	Learn common question types
Official candidate guides	Confirm whether math is included
Arithmetic drills	Build fundamentals
Timed word problems	Build speed
Paid JobTestPrep	More law-enforcement-style practice
Full police practice tests	Build test readiness

Free practice is useful for basics. Paid prep is more useful when the exam is competitive, timed or ranked.

7-Day Police Math Study Plan

Day	Study Focus
Day 1	Diagnostic math practice and arithmetic review
Day 2	Percentages
Day 3	Averages and ratios
Day 4	Time calculations
Day 5	Speed, distance and word problems
Day 6	Tables, charts and mixed timed practice
Day 7	Review errors and take full police practice test

24-Hour Police Math Study Plan

If your exam is tomorrow:

1. Review percentage shortcuts.
2. Practice 10 basic arithmetic questions.
3. Practice 10 word problems.
4. Review elapsed time.
5. Review speed, distance and time.
6. Practice 5 table questions.
7. Take one timed mixed drill.
8. Review all wrong answers.
9. Rest.

Police Math Test-Day Checklist

Before the exam, confirm:

[ ] I know whether math is included.
[ ] I know whether calculators are allowed.
[ ] I know the time limit.
[ ] I can solve percentage questions.
[ ] I can calculate averages.
[ ] I can calculate elapsed time.
[ ] I can solve speed and distance questions.
[ ] I can read tables carefully.
[ ] I have practiced word problems.
[ ] I will check units before answering.

When your hiring step includes mixed sections, pre-employment assessment practice can support broader review before test day.

Yes. Situational judgment test practice can offer practice materials for similar assessment formats.

Police exam practice can support extra practice with explanations when you want more timed drills.

For additional preparation, pre-employment assessment practice may be useful when your invitation includes similar question types.

Before test day, situational judgment test practice can help you rehearse timed sections and build answer consistency.

Police exam practice can help candidates become familiar with common question formats before the live assessment.

When your hiring step includes mixed sections, pre-employment assessment practice can support broader review before test day.

Yes. Situational judgment test practice can offer practice materials for similar assessment formats.

Police exam practice can support extra practice with explanations when you want more timed drills.

For additional preparation, pre-employment assessment practice may be useful when your invitation includes similar question types.

Before test day, situational judgment test practice can help you rehearse timed sections and build answer consistency.

Police exam practice can help candidates become familiar with common question formats before the live assessment.

Related Police Exam Guides

Use these related pages to continue preparing:

Guide	Best For
Police Exam Practice Test	Full police practice test
Police Written Exam	Exam overview
How to Pass Police Exam	Strategy guide
Police Reading Comprehension	Reading passages
Police Report Writing Test	Report writing
Police Situational Judgment Test	Judgment scenarios
Police Memory Test	Memory and observation
Sheriff Exam	Sheriff / deputy exam prep
Common Public Safety Test Mistakes	Mistakes to avoid
Public Safety Test Study Plan	Study schedule

Sources / Information to Verify Before Publication

Before publication, verify police math test details with current official and agency sources.

Use sources such as:

• official police exam announcement;
• official police candidate guide;
• city or county civil service exam notice;
• POST-style study guides;
• agency study guides;
• Honolulu PD written exam guide;
• DART Police study guide;
• DPS careers POST resources;
• GoLawEnforcement police written exam guide;
• Peterson’s law enforcement prep;
• JobTestPrep police exam prep;
• PoliceTest.info police exam resources.

Verify:

• exact exam name;
• test provider;
• whether math is included;
• math topics included;
• whether calculators are allowed;
• time limits;
• passing score;
• retest rules;
• whether report writing is included;
• whether situational judgment is included;
• whether memory or observation is included;
• current JobTestPrep product contents;
• current affiliate URL;
• access duration and refund terms.

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