Norman Hall's State Trooper & Highway Patrol Exam Preparation Book by Norman Hall

Author:Norman Hall
Language: eng
Format: epub
Tags: ebook, book
Publisher: F+W Media
Published: 1999-01-15T00:00:00+00:00

Chapter 7

Mathematics

As a State Police Officer, you will need to have good mathematical ability to determine everything from property values to blood alcohol levels. Mathematics is important beyond your career, as well. The implications in your personal life can be as far-reaching as calculating depreciation values on real estate for tax purposes to simply balancing your checkbook.

Mathematics treats exact relations existing between quantities in such a way that other quantities can be deduced from them. In other words, you may know a basic quantity, but to derive further use from that quantity, it is necessary to apply known relationships (that is, formulas).

For example, let’s say you wanted to know how many revolutions a tire would have to make to roll a distance of exactly 20 feet. Outside of physically rolling the tire itself and using a tape measure, it would be impossible to solve such a problem without mathematics. However, by applying math, we can exploit known relationships to derive the answer.

If we know that the diameter of the tire is 40 inches, we can easily determine the tire’s perimeter or circumference. In geometric terms, the tire is a circle and the known formula for determining the circumference of a circle is to multiply the diameter by π (which is 3.1416). The symbol π is referred to in mathematics as pi. Therefore, our tire’s circumference is 40 × 3.1416 = 125.66 inches.

Since we now know that the circumference of the tire is 125.66 inches, we can learn how many revolutions a tire with this circumference would need to go exactly 20 feet. However, we cannot simply divide 125.66 inches into 20 feet because we are dealing with two entirely different units of measure, inches and feet.

Therefore, we need to convert feet into inches. We know that there are 12 inches in 1 foot, so 20 feet × 12 inches = 240 inches. Now we can divide 125.66 inches into 240 inches to find the answer we need. In this case, the tire would have to make 1.91 revolutions to roll exactly 20 feet. You can see by this example how known relationships can help find an unknown.

This chapter is designed with the purpose of reviewing only those aspects of math that have been predominantly seen on past exams. If you find any areas of weakness after completing the exercises, it would be in your best interest to get additional reference material from your library.

The subjects reviewed in this section include fractions, decimals, ratios, proportions, and geometry. Each of these areas is discussed briefly, and some examples demonstrate its application. At the end of this section, there are practice exercises for you to complete. Answers and explanations are provided separately so you can check your performance.

MATHEMATICAL PRINCIPLES

A. FRACTIONS

Fractions are essentially parts of a whole. If you have ½ of something, this means you have 1 of 2 equal parts. If you have 7/8 of something, this means you have 7 of the 8 equal parts available.

The 1 of ½ is the numerator, which tells the number of parts used.

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