##### Document Text Contents

Page 1

Math

FOR CIVIL

SERVICE TESTS

Page 116

Sample Question:

A business spent $1,000 on a shipment of products. The products were sold for only $750—a

loss for the company. What is the percent loss?

a. 50%

b. 25%

c. 20%

d. 15%

Use the proportion:

�

n

i

e

n

t

it

l

i

o

a

s

l

s

� = �10

?

0�

The net loss is 1,000 − 750 = 250 dollars and the initial amount was 1,000. The proportion becomes:

�1

2

,0

5

0

0

0� = �10

?

0�. Cross-multiplying yields 250 × 100 = 1,000 × ?, or 25,000 = 1,000 × ?, and ? = 25. Thus,

the answer is b.

� SIMPLE AND COMPOUND INTEREST

The formula for simple interest is:

I = PRT

The amount of money deposited is called the principal, P. The interest rate per year is represented

by R, and T represents the time in years.

When calculating compound interest, it is easiest to sequentially calculate the interest earned using

I = PRT. You should be familiar with the following ways of compounding interest:

� Compounded annually: interest is paid each year

� Compounded semi-annually: interest is paid two times per year

� Compounded quarterly: interest is paid four times a year

� Compounded monthly: interest is paid every month

� Compounded daily: interest is paid every day

Sample Question:

If Howard puts $30,000 in the bank at a 4% rate of interest per year, how much interest will he

make in 6 months?

a. $400

b. $600

c. $720

d. $7,200

MATH FOR CIVIL SERVICE TESTS � CHAPTER 7 Percents108

Page 117

The correct answer is choice b. Use the formula I = PRT. Where P equals $30,000, R = 4% = .04,

and T = �12� a year. Note that you must convert the 6 months into years. The formula becomes: I = PRT

= 30,000 × .04 × �12� = $600.

PRACTICE QUESTIONS

1. 15% is equivalent to which fraction below?

a. �2

3

0�

b. �1,

1

0

5

00�

c. �15�

d. �1

1

5�

2. 20% is equivalent to which decimal value below?

a. .020

b. 2.0

c. 0.2

d. .002

3. When converted to a decimal, 45% is equivalent to

a. .045

b. .45

c. 4.5

d. 45

4. 73% can be expressed as which of the following fractions?

a. �1

.7

0

3

0�

b. �1

7

0

3

0�

c. �1,

7

0

3

00�

d. �..

7

1

3

0�

5. 1.5% is equivalent to which decimal value below?

a. .15

b. 1.5

c. .0015

d. .015

Percents CHAPTER 7 MATH FOR CIVIL SERVICE TESTS 109�

Page 232

Geometric series: a series which progresses by multiplying each term by a constant number to get

the next term.

Improper fraction: a fraction whose numerator is greater than the number in the denominator, such

as �87�.

Least Common Denominator: the smallest number that is a multiple of the original denomina-

tors present.

Mean: the average of a set of values. To calculate the mean, follow these steps: Step 1— Add all the

numbers in the list. Step 2— Count the number of numbers in the list. Step 3— Divide the sum

(the result of step 1) by the number (the result of step 2).

Median: the middle number in a group of numbers arranged in sequential order. In a set of numbers,

half will be greater than the median and half will be less than the median. To calculate the median,

follow these steps: Step 1—Put the numbers in sequential order. Step 2—The middle number is

the median. (If there are two middle numbers, you find the mean (or average) of the two middle

numbers.)

Mixed Number: a number that is expressed as a whole number with a fraction to the right, such

as 1�12�.

Mode: the number in a set of numbers that occurs most frequently. To find the mode, you just look

for numbers that occur more than once and find the one that appears most often.

Numerator: the top number in a fraction.

Order of Operations: the order in which operations must be performed. An easy way to remember

the Order of Operations is to use the mnemonic PEMDAS, where each letter stands for an oper-

ation: Parentheses: Always calculate the values inside the parentheses first; Exponents: Second,

calculate exponents (or powers); Multiplication/Division: Third, perform any multiplications or

divisions in order from left to right; Addition/Subtraction: Last, perform any additions or sub-

tractions in order from left to right.

Percent change: when calculating the percent increase or decrease, equate the ratio of the amount

of change to the initial value with the ratio of a new value, x, to 100. The general proportion to

use is: �ci

h

n

a

it

n

ia

g

l

e

� = �10

x

0�.

Percent error: is found by converting the ratio between the calculated value and the actual value to

a value out of 100: = �10

x

0�.

Percent: a ratio that expresses a value as per 100 parts. For example 30% is equivalent to 30 per 100,

or �1

3

0

0

0�. You can express a percent as a fraction by placing the number before the percent symbol

over the number 100. You can express a percent as a decimal by moving the current decimal point

2 places to the left.

Perimeter: the distance around a two-dimensional geometric figure.

Prime numbers: numbers that have only 2 factors, the number 1 and itself.

Product: the answer obtained by multiplying.

Proper fraction: a fraction where the number in the numerator is less than the number in the denom-

inator, such as �12�.

difference in values

���actual values

MATH FOR CIVIL SERVICE TESTS � APPENDIX Glossary of Math Terms224

Page 233

Proportion: a pair of 2 equivalent ratios in the form �ab� = �d

c

�.

Quotient: the answer obtained by dividing.

Radius: any line that begins at the center of a circle and ends on a point on the circle.

Ratio: a comparison of 2 or more numbers.

Reciprocal: the multiplicative inverse of a number, for example, the reciprocal of �45� is �

5

4�.

Simple Interest: interest is calculated with the formula I = PRT. The amount of money deposited

is called the principal, P. The annual interest rate is represented by R, and T represents the time

in years.

Sum: the answer obtained by adding.

Symbol series: a visual series based on the relationship between images.

The Associative Law: this property applies to grouping of addition or multiplication equations and

expressions. It can be represented as a + (b + c) = (a + b) + c or a × (b × c) = (a × b) × c. For example,

10 + (12 + 14) = (10 + 12) + 14.

The Commutative Law: this property applies for addition and multiplication and can be represented

as a + b = b + a or a × b = b × a. For example, 2 + 3 = 3 + 2 and 4 × 2 = 2 × 4 exhibit the Commu-

tative Law.

The Distributive Law: this property applies to multiplication over addition and can be represented

as a(b + c) = ab + ac. For example, 3 (5 + 7) = 3 × 5 + 3 × 7.

Volume: a measure of the amount of space inside a three-dimensional shape. Volume is expressed in

cubic units.

Glossary of Math Terms APPENDIX MATH FOR CIVIL SERVICE TESTS 225�

Math

FOR CIVIL

SERVICE TESTS

Page 116

Sample Question:

A business spent $1,000 on a shipment of products. The products were sold for only $750—a

loss for the company. What is the percent loss?

a. 50%

b. 25%

c. 20%

d. 15%

Use the proportion:

�

n

i

e

n

t

it

l

i

o

a

s

l

s

� = �10

?

0�

The net loss is 1,000 − 750 = 250 dollars and the initial amount was 1,000. The proportion becomes:

�1

2

,0

5

0

0

0� = �10

?

0�. Cross-multiplying yields 250 × 100 = 1,000 × ?, or 25,000 = 1,000 × ?, and ? = 25. Thus,

the answer is b.

� SIMPLE AND COMPOUND INTEREST

The formula for simple interest is:

I = PRT

The amount of money deposited is called the principal, P. The interest rate per year is represented

by R, and T represents the time in years.

When calculating compound interest, it is easiest to sequentially calculate the interest earned using

I = PRT. You should be familiar with the following ways of compounding interest:

� Compounded annually: interest is paid each year

� Compounded semi-annually: interest is paid two times per year

� Compounded quarterly: interest is paid four times a year

� Compounded monthly: interest is paid every month

� Compounded daily: interest is paid every day

Sample Question:

If Howard puts $30,000 in the bank at a 4% rate of interest per year, how much interest will he

make in 6 months?

a. $400

b. $600

c. $720

d. $7,200

MATH FOR CIVIL SERVICE TESTS � CHAPTER 7 Percents108

Page 117

The correct answer is choice b. Use the formula I = PRT. Where P equals $30,000, R = 4% = .04,

and T = �12� a year. Note that you must convert the 6 months into years. The formula becomes: I = PRT

= 30,000 × .04 × �12� = $600.

PRACTICE QUESTIONS

1. 15% is equivalent to which fraction below?

a. �2

3

0�

b. �1,

1

0

5

00�

c. �15�

d. �1

1

5�

2. 20% is equivalent to which decimal value below?

a. .020

b. 2.0

c. 0.2

d. .002

3. When converted to a decimal, 45% is equivalent to

a. .045

b. .45

c. 4.5

d. 45

4. 73% can be expressed as which of the following fractions?

a. �1

.7

0

3

0�

b. �1

7

0

3

0�

c. �1,

7

0

3

00�

d. �..

7

1

3

0�

5. 1.5% is equivalent to which decimal value below?

a. .15

b. 1.5

c. .0015

d. .015

Percents CHAPTER 7 MATH FOR CIVIL SERVICE TESTS 109�

Page 232

Geometric series: a series which progresses by multiplying each term by a constant number to get

the next term.

Improper fraction: a fraction whose numerator is greater than the number in the denominator, such

as �87�.

Least Common Denominator: the smallest number that is a multiple of the original denomina-

tors present.

Mean: the average of a set of values. To calculate the mean, follow these steps: Step 1— Add all the

numbers in the list. Step 2— Count the number of numbers in the list. Step 3— Divide the sum

(the result of step 1) by the number (the result of step 2).

Median: the middle number in a group of numbers arranged in sequential order. In a set of numbers,

half will be greater than the median and half will be less than the median. To calculate the median,

follow these steps: Step 1—Put the numbers in sequential order. Step 2—The middle number is

the median. (If there are two middle numbers, you find the mean (or average) of the two middle

numbers.)

Mixed Number: a number that is expressed as a whole number with a fraction to the right, such

as 1�12�.

Mode: the number in a set of numbers that occurs most frequently. To find the mode, you just look

for numbers that occur more than once and find the one that appears most often.

Numerator: the top number in a fraction.

Order of Operations: the order in which operations must be performed. An easy way to remember

the Order of Operations is to use the mnemonic PEMDAS, where each letter stands for an oper-

ation: Parentheses: Always calculate the values inside the parentheses first; Exponents: Second,

calculate exponents (or powers); Multiplication/Division: Third, perform any multiplications or

divisions in order from left to right; Addition/Subtraction: Last, perform any additions or sub-

tractions in order from left to right.

Percent change: when calculating the percent increase or decrease, equate the ratio of the amount

of change to the initial value with the ratio of a new value, x, to 100. The general proportion to

use is: �ci

h

n

a

it

n

ia

g

l

e

� = �10

x

0�.

Percent error: is found by converting the ratio between the calculated value and the actual value to

a value out of 100: = �10

x

0�.

Percent: a ratio that expresses a value as per 100 parts. For example 30% is equivalent to 30 per 100,

or �1

3

0

0

0�. You can express a percent as a fraction by placing the number before the percent symbol

over the number 100. You can express a percent as a decimal by moving the current decimal point

2 places to the left.

Perimeter: the distance around a two-dimensional geometric figure.

Prime numbers: numbers that have only 2 factors, the number 1 and itself.

Product: the answer obtained by multiplying.

Proper fraction: a fraction where the number in the numerator is less than the number in the denom-

inator, such as �12�.

difference in values

���actual values

MATH FOR CIVIL SERVICE TESTS � APPENDIX Glossary of Math Terms224

Page 233

Proportion: a pair of 2 equivalent ratios in the form �ab� = �d

c

�.

Quotient: the answer obtained by dividing.

Radius: any line that begins at the center of a circle and ends on a point on the circle.

Ratio: a comparison of 2 or more numbers.

Reciprocal: the multiplicative inverse of a number, for example, the reciprocal of �45� is �

5

4�.

Simple Interest: interest is calculated with the formula I = PRT. The amount of money deposited

is called the principal, P. The annual interest rate is represented by R, and T represents the time

in years.

Sum: the answer obtained by adding.

Symbol series: a visual series based on the relationship between images.

The Associative Law: this property applies to grouping of addition or multiplication equations and

expressions. It can be represented as a + (b + c) = (a + b) + c or a × (b × c) = (a × b) × c. For example,

10 + (12 + 14) = (10 + 12) + 14.

The Commutative Law: this property applies for addition and multiplication and can be represented

as a + b = b + a or a × b = b × a. For example, 2 + 3 = 3 + 2 and 4 × 2 = 2 × 4 exhibit the Commu-

tative Law.

The Distributive Law: this property applies to multiplication over addition and can be represented

as a(b + c) = ab + ac. For example, 3 (5 + 7) = 3 × 5 + 3 × 7.

Volume: a measure of the amount of space inside a three-dimensional shape. Volume is expressed in

cubic units.

Glossary of Math Terms APPENDIX MATH FOR CIVIL SERVICE TESTS 225�