Math Review for Police Officer Exam Study Guide (page 2)
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.
Solving Math Problems
Just as with the verbal and reading skills sections of the entry exam, some of the math questions you will be presented with will be based on police situations and others will have nothing to do with policing. Some math problems will be presented within stories or situations where you have to pick out the math; others may be presented without any context attached. This is similar to the vocabulary questions, where, you may recall, some provided you with sentences and asked you to provide a synonym or antonym for an underlined word, while others provided you with just the word and no sentence to help you develop context. To some test takers, the math without a story will be easier because there is nothing to do except math, while to others this will be intimidating for the identical reason. To get you accustomed to answering math questions that do not come with a story attached, calculate the answers to the following questions.
Math-Only Sample Questions
- (13 × 9) + 14 =
- (67 – 9) + 80 =
- (80 + 20) ÷ 10 =
- none of the above
- 25 × (2 + 10) =
- none of the above
- none of the above
- c. Perform the operations in the parentheses first: 13 × 9 = 117; then add 14 to get the answer of 131.
- a. Perform the operations in the parentheses first: 67 – 9 = 58; then add 80 to get the answer of 138. Notice that the incorrect choices contain errors you might readily make. Choice b transposes two numbers from the correct answer; choice c transposes the numbers of an incorrect answer; choice d is the correct answer for the calculation within the parentheses but does not include the + 80.
- d. Perform the operations in the parentheses first: 80 + 20 = 100. Then divide by 10 to get the answer of 10.
- c. In this problem, the parentheses surrounds the second group of numbers, so you must do that calculation first: 2 + 10 = 12, then multiply by 25 to get the answer of 300.
- b. Adding fractions can be confusing. If the fractions have the same bottom numbers, just add the top numbers and write the total over the bottom. If the fractions have different bottom numbers, you must find the least common denominator, which means finding the same bottom number for each. It is always the smallest number that all the bottom numbers can be evenly divided into. In this problem, and , for a sum of . If you have no recollection of this from high school or college, you should purchase a math review book along with your other test study aids.
- b. In subtracting fractions, if the fractions have the same bottom numbers, just subtract the top numbers and write the difference over the bottom number. If they do not have the same bottom numbers, you will have to follow the rules for determining the least common denominator, which was not necessary in this question.
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