Math Review for Police Officer Exam Study Guide

Many police exams will test your ability to solve basic math problems and other number-based questions and to read maps. As a police officer, you will be expected to calculate the value of items and to estimate distances traveled or distances from a particular point to another. Map reading tests whether you will be able to navigate streets and roadways of your jurisdiction and whether you can follow simple directions. Memory-based and observation questions test your ability to look at pictures or scenes and recall important details of what you have observed. As in the other review chapters, there are tips for improving your abilities in these crucial areas.

Questions in the math section of a police applicant exam are generally straightforward. Most will entail arithmetic operations (addition, subtraction, multiplication, division); some will require you to combine these operations to determine your answer. Each question will provide you with all the information you need to answer it. You may be given scratch paper or you may be told that you may write on the test booklet to perform your calculations. If the test itself or the proctor do not make clear where you can do your calculations, do not be afraid to ask for instructions. If you will be permitted to use a calculator, you should have received this information along with other test-day instructions. If nothing was mentioned, you might consider bringing a small calculator on the test date, but do not remove it from your bag without first learning whether it is permissible to do so.

Glossary of Terms

Denominator     The bottom number in a fraction. Example: 2 is the denominator in

Difference     Subtract. The difference of two numbers means subtract one number from the other.

Divisible by     A number is divisible by a second number if that second number divides evenly into the original number. Example: 10 is divisible by 5 (10 ÷ 5 = 2, with no remainder). However, 10 is not divisible by 3. (See Multiple of.)

Even Integer     Integers that are divisible by 2, like…–4, –2, 0, 2, 4.…(See Integer.)

Integer     Numbers along the number line, like…–3, –2, –1, 0, 1, 2, 3.… Integers include the whole numbers and their opposites. (See whole number.)

Multiple of     A number is a multiple of a second number if that second number can be multiplied by an integer to get the original number. Example: 10 is a multiple of 5 (10 = 5 × 2); however, 10 is not a multiple of 3. (See divisible by.)

Negative Number     A number that is less than zero, like…–1, –18.6, – .…

Numerator     The top part of a fraction. Example: 1 is the numerator of .

Odd Integer     Integers that aren't divisible by 2, like…–5, –3, –1, 1, 3.…

Positive Number     A number that is greater than zero, like… 2, 42, , 4.63.

Prime Number     Integers that are divisible only by 1 and themselves, like…2, 3, 5, 7, 11.… All prime numbers are odd, except for number 2. The number 1 is not considered prime.

Product     Multiply. The product of two numbers means the numbers are multiplied together.

Quotient     The answer you get when you divide. Example: 10 divided by 5 is 2; the quotient is 2.

Real Number     All the numbers you can think of, like… 17, –5, , –23.6, 3.4329, 0.… Real numbers include the integers, fractions, and decimals. (See integer.)

Remainder    The number left over after division. Example: 11 divided by 2 is 5, with a remainder of 1.

Sum     Add. The sum of 2 numbers means the numbers are added together.

Whole Number     Numbers you can count on your fingers, like… 1, 2, 3.… All whole numbers are positive.

With or without a calculator, the first step in answering the math questions, as with all questions, is to read the question carefully to determine what you are being asked to calculate and what facts you are being given to assist you. If you do not understand what you are being asked to do, you will be unable to do it. The vast majority of the calculations will have to do with distances traveled, items reported missing or stolen, travel expense vouchers, or other situations that a police officer on patrol could be expected to encounter.