Question 1

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the equation.
-  = -9

Accepted Answer

A)  { 81} 
B)  { 18} 
C)  ? 
D)  {-81} 
A)  { 81} 
B)  { 18} 
C)  ? 
D)  {-81}

Question 2

Find the length of the unknown side of a right triangle with legs a and b and hypotenuse c. Round to the nearest thousandth, if necessary.
-a = 6, c = 10

Accepted Answer

A)  b = 8 
B)  b = 10 
C)  b = 9 
D)  b = 7 
A)  b = 8 
B)  b = 10 
C)  b = 9 
D)  b = 7

Question 3

Solve the problem. Give the answer to the nearest thousandth if necessary.
-A long-distance runner runs 2 miles south and then 10 miles east. How far is the runner from the starting point?

Accepted Answer

A)  10.198 mi 
B)  11.198 mi 
C)  4.899 mi 
D)  12 mi 
A)  10.198 mi 
B)  11.198 mi 
C)  4.899 mi 
D)  12 mi

Question 4

Rationalize the denominator. Assume that all variables represent positive real numbers.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

Find all square roots of the number
-100

Accepted Answer

A)  1, -1 
B)  11, -11 
C)  9, -9 
D)  10, -10 
A)  1, -1 
B)  11, -11 
C)  9, -9 
D)  10, -10

Question 6

Perform the indicated operations and express the result in simplest form.
-

Accepted Answer

A)  4 
B)  4   
C)  2   
D)  2   
A)  4 
B)  4   
C)  2   
D)  2

Question 7

Solve the problem.
-Fill in the blank.13   + 7   cannot be simplified because the _________ are not the same.

Accepted Answer

A)  roots or indexes 
B)  variables 
C)  radicands 
D)  coefficients 
A)  roots or indexes 
B)  variables 
C)  radicands 
D)  coefficients

Question 8

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
- The easiest way to simplify the expression   is to multiply both the numerator and denominator by

Accepted Answer

A) True 
 B)False

Question 9

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the equation.
-  = 6

Accepted Answer

A)  { 38} 
B)  { 34} 
C)  { 36} 
D)  { 64} 
A)  { 38} 
B)  { 34} 
C)  { 36} 
D)  { 64}

Question 10

Simplify the radical. Assume that all variables represent nonnegative real numbers.
-

Accepted Answer

A)    
B)      
C)      
D)    
A)    
B)      
C)      
D)

Question 11

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-Summarize the guidelines to follow when simplifying radical expressions.

Accepted Answer

Answers will vary. A sample answer might

Question 12

Find the perimeter of the figure.
-

Accepted Answer

A)  24   
B)  24   
C)  12   
D)  12   
A)  24   
B)  24   
C)  12   
D)  12

Question 13

Simplify and add or subtract wherever possible.
--5   - 7

Accepted Answer

A)  -12   
B)  2   
C)  35   
D)  -12   
A)  -12   
B)  2   
C)  35   
D)  -12

Question 14

Simplify the radical.
-

Accepted Answer

A)  -   
B)    
C)  -   
D)    
A)  -   
B)    
C)  -   
D)

Question 15

Solve the problem. Give the answer to the nearest thousandth if necessary.
-The diagram below shows the side view of a plan for a slanted roof. Find the unknown length in this roof plan.

Accepted Answer

A)  4 ft 
B)  8 ft 
C)  7.325 ft 
D)  6.325 ft 
A)  4 ft 
B)  8 ft 
C)  7.325 ft 
D)  6.325 ft

Question 16

Simplify the radical expression. Assume that all variables represent nonnegative real numbers.
-( 2   +   )( 5   -   )

Accepted Answer

A)  10t + 5   + 2   + 5   
B)  10t + 5   - 2   - 5   
C)  10   + 5   + 2   + 5   
D)  10   + 5   - 2   - 5   
A)  10t + 5   + 2   + 5   
B)  10t + 5   - 2   - 5   
C)  10   + 5   + 2   + 5   
D)  10   + 5   - 2   - 5

Question 17

Find the length of the unknown side of a right triangle with legs a and b and hypotenuse c. Round to the nearest thousandth, if necessary.
-a = 10, b = 24

Accepted Answer

A)  c = 26 
B)  c = 18 
C)  c = 22 
D)  c = 25 
A)  c = 26 
B)  c = 18 
C)  c = 22 
D)  c = 25

Question 18

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the equation.
-  + 1 = 5

Accepted Answer

A)  { 16} 
B)  { 36} 
C)  { 24} 
D)    
A)  { 16} 
B)  { 36} 
C)  { 24} 
D)

Question 19

Simplify the radical.
-7

Accepted Answer

A)  27 
B)  105 
C)  7   
D)  15   
A)  27 
B)  105 
C)  7   
D)  15

Question 20

Choose the one alternative that best completes the statement or answers the question. 
 
Solve the equation.
-  = 3 +

Accepted Answer

A)  {-1} 
B)  {-5, -8} 
C)  {5, 8} 
D)    
A)  {-1} 
B)  {-5, -8} 
C)  {5, 8} 
D)

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - = -9

Find the length of the unknown side of a right triangle with legs a and b and hypotenuse c. Round to the nearest thousandth, if necessary. -a = 6, c = 10

Solve the problem. Give the answer to the nearest thousandth if necessary. -A long-distance runner runs 2 miles south and then 10 miles east. How far is the runner from the starting point?

Rationalize the denominator. Assume that all variables represent positive real numbers. -

Find all square roots of the number -100

Perform the indicated operations and express the result in simplest form. -

Solve the problem. -Fill in the blank.13 + 7 cannot be simplified because the _________ are not the same.

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - The easiest way to simplify the expression is to multiply both the numerator and denominator by

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - = 6

Simplify the radical. Assume that all variables represent nonnegative real numbers. -

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Summarize the guidelines to follow when simplifying radical expressions.

Find the perimeter of the figure. -

Simplify and add or subtract wherever possible. --5 - 7

Simplify the radical. -

Solve the problem. Give the answer to the nearest thousandth if necessary. -The diagram below shows the side view of a plan for a slanted roof. Find the unknown length in this roof plan.

Simplify the radical expression. Assume that all variables represent nonnegative real numbers. -( 2 + )( 5 - )

Find the length of the unknown side of a right triangle with legs a and b and hypotenuse c. Round to the nearest thousandth, if necessary. -a = 10, b = 24

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - + 1 = 5

Simplify the radical. -7

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - = 3 +

The Real Number System

Linear Equations and Inequalities in One Variable

Linear Equations and Inequalities in Two Variables; Functions

Systems of Linear Equations and Inequalities

Exponents and Polynomials

Factoring and Applications

Rational Expressions and Applications

Roots and Radicals

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Exam 9: Quadratic Equations