Police Math Test Police Test Study Guide

Tutorial: Police Math Questions Review.

Mar 7th, 2024
tutorial police math questions

Tutorial Introduction

Police math questions are not necessarily difficult, though many applicants do have significant problems with this part of the police officer exam. Part of the reason for this is because the subject is often taught badly. Often, people are taught to memorize ways of solving problems rather than understanding the problems themselves i.e. the logic behind each step.

In other words, many people often memorize a method rather than knowing how to critically think through the problem. If you find yourself learning math through this kind of memorization approach, you may need to reconsider. Ultimately, it has limited success. By memorizing a method, it means you only know how to answer one version of a math problem. What if the police exam throws up a version you are unfamiliar with? How are you equipped to solve this problem?

Ultimately, success at any math problem involves understanding the step-by-step approach to answering the question – really knowing why each step is used and how you can work through similar problems. These are the kind of critical thinking skills that police departments search for in their assessment of candidates. The candidates that try to “wing it” through rapid memorization approaches will almost always fail, or never score as high. Those candidates who take the initiative, as well as the time to understand, math problems – in the end – almost always succeed.

With this in mind, take a few moments to read through the following five police math questions. Take out a notepad and work through all five in your own time. Don’t consult Google or other texts. Instead, it should just be you and the questions – just as it would be on exam day.

Later, you can compare your methods with the answer explanations we have provided below. This manual assessment will help you identify any knowledge gaps you may have. Don’t worry if you don’t score them all correct. Ultimately, this exercise is about identifying any weak spots so, if anything, it can only be a good thing to identify them and remedy it – permanently.

Sample Police Math Questions

Question 1

Officer Jones conducted a speed enforcement operation on a highway and observed vehicles traveling at 75 mph, 80 mph, 70 mph, 85 mph, and 65 mph. What is the average speed of these vehicles?

a. 70 mph

b. 75 mph

c. 80 mph

d. 85 mph

Question 2

Philadelphia police department has for its 2024 budget allocated $480,000 for new patrol cars. If each patrol car costs $25,000, what percentage of the budget remains after the maximum number of patrol cars have been purchased?

a. 1%

b. 5%

c. 8%

d. 10%

    Question 3

    Officer Smith is investigating a crime scene that is 7.5 miles away from New York police department. If Officer Smith drives to the crime scene at an average speed of 40 miles per hour for the first half of the distance and an average speed of 45 miles per hour for the second half of the distance, how many minutes will it take Officer Smith to reach the crime scene?

    a. 5 minutes

    b. 6.5 minutes

    c. 8 minutes

    d. 10.6 minutes

    Question 4

    During a surveillance operation in downtown Las Vegas, Officer Brown observed a murder suspect walking from point A to point B – a distance covering 600 feet. If the suspect walked at a pace of 3 feet per second, how many minutes did it take the suspect to arrive at point B and return to point A?

    a. 3

    b. 6.7

    c. 200

    d. 400

    Question 5

    Officer Thompson is assigned to monitor a protest event that is expected to last for 5 hours from the beginning of his shift. Officer Thompson ends up working for 8 hours, with a 45-minute lunch break after the protest. If Officer Thompson earns $55 per hour with a 10% bonus for hours of overtime, how much will he have earned during the protest event?

    a. $275.00

    b. $325.00

    c. $395.00

    d. $425.00

    Police Question Answer Explanations

    Answer to Question 1: 75 mph

    To find the average of anything, you need to sum up all figures and divide by the number of figures. In this case, we need to total all five speeds, then divide that number by the number of figures, which is 5.

    75 mph + 80 mph + 70 mph + 85 mph +65 mph = 375

    375 / 5 = 75

    The average speed that Officer Jones observed was 75 miles per hour.

    Answer to Question 2: 1%

    Philadelphia police department has allocated $480,000 for new patrol cars. Each car costs $25,000, so that means they can purchase a maximum of 19 patrol cars within that budget.

    $480,000 / $25,000 = 19.2

    19 patrol cars x $25,000 = $475,000

    Given that $475,000 has been spent, that only leaves $5,000 left of the budget. The question asks us to find the percentage of the budget remaining, therefore:

    $5,000 / $480,000 x 100 = 1.04% or, when rounded down, 1%.

    After all the patrol cars have been purchased, only 1% of the budget remains.

    Answer to Question 3: 10.6 minutes

    First, we must divide the 7.5 miles into two parts – and work on each separately.

    Officer Smith drives at 40 mph for the first 3.75 miles.

    Time = Distance / Speed


    Time = 3.75 / 40 = 0.094 hours

    0.094 hours x 60 = 5.6 minutes

    Now we must do the same process with the second half of the drive.

    Time = 3.75 / 45 = 0.083 hours

    0.083 x 60 = 5 minutes

    Therefore, it took Officer Smith 10.6 minutes to arrive at the crime scene.

    Answer to Question 4: 6.7 minutes

    600 feet is the distance between Point A and Point B.

    If the suspect walked at a pace of 3 ft per second, then 600 / 3 = 200 seconds it took for him to cover that distance.

    It would also take him 200 seconds to return to point A. That gives us a total of 400 seconds.

    However, the question asks us to answer the question in minutes, therefore we must divide by 60 minutes.

    400 seconds / 60 minutes = 6.66 minutes – or rounding up, 6.7 minutes.

    Answer to Question 5: $275.00

    Wording matters here.

    You are asked to find out how much Thompson earned during the 5-hour protest event. You are also told superfluous, irrelevant detail – such as his overtime rate. Often in police exam questions, extra detail that has nothing to do with the question will be included. Your job is to find out what detail is relevant and then work through the problem.

    The protest event lasted for the first 5-hours of his shift, and he earned $55 per hour during that period.

    Therefore, Thompson earned $275.00 for monitoring the protest.

    Tutorial Review

    We hope you found this tutorial on police math questions helpful.

    What matters at this stage is any notes you have taken, particularly for questions where you didn’t secure the correct answer.

    Other take-home points worth considering include:

    • How you may have inadvertently misread the question.
    • How you may have rushed into choosing an incorrect answer.
    • How you didn’t work through the problem in a step-by-step manner.
    • How you may have misinterpreted the question.
    • How you may have missed a key element in your answer attempt.

    Learning from any mistakes here means that the next time you encounter similar questions, you will not repeat the same mistakes. That alone makes this exercise very beneficial.

    If you scored all sample questions correctly, try to ascertain whether you could have answered the questions better. There may be room for improvement that you didn’t previously consider.

    If you found this helpful, you may consider becoming a full member of our complete online course, where you can practice many more police exam questions to help you study and pass the police officer exam.


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