Question 1

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-45   = 21 + 96x

Accepted Answer

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

Question 2

Solve the problem.
-The table shows the population of a city for five years.
 
This data was used to develop the quadratic equation   , which models the population of the city y in millions in the year x, where x = 0 represents 2007, x = 1 represents 2008, and so on. Use the model to find the estimated population in the year 2009.

Accepted Answer

A)  1,490,000,000,000 
B)  1,490,000 
C)  65,538,000 
D)  66,822,000 
A)  1,490,000,000,000 
B)  1,490,000 
C)  65,538,000 
D)  66,822,000

Question 3

Find the greatest common factor of the numbers
-8, 32, 36, 40

Accepted Answer

A)  8 
B)  1 
C)  2 
D)  4 
A)  8 
B)  1 
C)  2 
D)  4

Question 4

Factor completely.
-x2 + 9x - 22

Accepted Answer

A)  (x - 11)(x + 1) 
B)  Prime 
C)  (x + 11)(x - 2) 
D)  (x - 11)(x + 2) 
A)  (x - 11)(x + 1) 
B)  Prime 
C)  (x + 11)(x - 2) 
D)  (x - 11)(x + 2)

Question 5

Find the pair of numbers whose product and sum are given.
-Product: 18 Sum: -11

Accepted Answer

A)  2 and 9 
B)  -2 and -9 
C)  -2 and 9 
D)  2 and -9 
A)  2 and 9 
B)  -2 and -9 
C)  -2 and 9 
D)  2 and -9

Question 6

Solve the problem.
-A parallelogram has a base of length x + 7 and a height of x + 2 and has an area of 50 square units. Find the base and height of the parallelogram. (A = bh)

Accepted Answer

A)  height = 2 units; base = 25 units 
B)  height = 5 units; base = 10 units 
C)  height = 6.25 units; base = 8 units 
D)  height = 1 unit; base = 50 units 
A)  height = 2 units; base = 25 units 
B)  height = 5 units; base = 10 units 
C)  height = 6.25 units; base = 8 units 
D)  height = 1 unit; base = 50 units

Question 7

Solve the problem.
-The product of two consecutive integers is 41 more than their sum. Find the integers.

Accepted Answer

A)  7, 8 
B)  -6, -5 
C)  7, 8 or -6, -5 
D)  6, 7 or -6, -5 
A)  7, 8 
B)  -6, -5 
C)  7, 8 or -6, -5 
D)  6, 7 or -6, -5

Question 8

Factor completely. If the polynomial is prime, say so.
-  - 216

Accepted Answer

A)  (y - 6)(   + 6y - 36) 
B)  (y - 6)(   + 6y + 36) 
C)  (y + 6)(   - 6y - 36) 
D)  (y - 6)(   - 36) 
A)  (y - 6)(   + 6y - 36) 
B)  (y - 6)(   + 6y + 36) 
C)  (y + 6)(   - 6y - 36) 
D)  (y - 6)(   - 36)

Question 9

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-A student was trying to solve the problem   . The student knew that he or she should set   but was confused about whether or not he or she should set   , or   and   . How would you advise this student?

Accepted Answer

Setting 9x

Question 10

Factor the binomial completely. If it is prime, say so.
-147a4b - 108b3

Accepted Answer

A)  3b( 7a2 + 6b)( 7a2 - 6b) 
B)  3b( 7a + 6b)2  
C)  3b( 7a - 6b)2  
D)  Prime 
A)  3b( 7a2 + 6b)( 7a2 - 6b) 
B)  3b( 7a + 6b)2  
C)  3b( 7a - 6b)2  
D)  Prime

Question 11

Factor by grouping.
-40   + 25ry - 8xr - 5xy

Accepted Answer

A)  ( 8r + 5y)(x - 5r) 
B)  ( 8r + 5y)( 5x - r) 
C)  ( 5r + 8y)( 5r - x) 
D)  ( 8r + 5y)( 5r - x) 
A)  ( 8r + 5y)(x - 5r) 
B)  ( 8r + 5y)( 5x - r) 
C)  ( 5r + 8y)( 5r - x) 
D)  ( 8r + 5y)( 5r - x)

Question 12

Factor completely.
--   - 5x + 36

Accepted Answer

A)  (x + 9)(x - 4) 
B)  -1(x - 9)(x + 4) 
C)  -1(x - 9)(x - 4) 
D)  -1(x + 9)(x - 4) 
A)  (x + 9)(x - 4) 
B)  -1(x - 9)(x + 4) 
C)  -1(x - 9)(x - 4) 
D)  -1(x + 9)(x - 4)

Question 13

Complete the factoring.
-x2 + 16x + 64 = (x + 8)( )

Accepted Answer

A)  x + 56 
B)  x - 24 
C)  x2 + 8 
D)  x + 8 
A)  x + 56 
B)  x - 24 
C)  x2 + 8 
D)  x + 8

Question 14

Factor out the greatest common factor.
-

Accepted Answer

A)    
B)  No common factor (except 1) 
C)    
D)    
A)    
B)  No common factor (except 1) 
C)    
D)

Question 15

Factor by grouping.
-20x2 + 15x - 24x - 18

Accepted Answer

A)  ( 20x - 6)(x + 3) 
B)  ( 5x + 6)( 4x - 3) 
C)  ( 20x + 6)(x - 3) 
D)  ( 5x - 6)( 4x + 3) 
A)  ( 20x - 6)(x + 3) 
B)  ( 5x + 6)( 4x - 3) 
C)  ( 20x + 6)(x - 3) 
D)  ( 5x - 6)( 4x + 3)

Question 16

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-3x(x - 9) = ( 2x - 4)(x - 9)

Accepted Answer

A)  { 9, -4} 
B)  { 4} 
C)  { -4} 
D)  { -9, 4} 
A)  { 9, -4} 
B)  { 4} 
C)  { -4} 
D)  { -9, 4}

Question 17

Factor completely.
-

Accepted Answer

A)      
B)      
C)    ( 5p + 6q)( 5p - 6q) 
D)      
A)      
B)      
C)    ( 5p + 6q)( 5p - 6q) 
D)

Question 18

Factor the binomial completely. If it is prime, say so.
-80   - 125

Accepted Answer

A)  ( 20x + 25)( 4x - 5) 
B)  5( 4x + 5)( 4x - 5) 
C)  ( 4x + 5)( 20x - 25) 
D)  5( 4x - 5)2  
A)  ( 20x + 25)( 4x - 5) 
B)  5( 4x + 5)( 4x - 5) 
C)  ( 4x + 5)( 20x - 25) 
D)  5( 4x - 5)2

Question 19

Factor completely.
-x2 - 10xy + 25y2

Accepted Answer

A)  (x + 5y)2  
B)  (x - 5y)(x + 5y) 
C)  (x - 5y)2  
D)  Prime 
A)  (x + 5y)2  
B)  (x - 5y)(x + 5y) 
C)  (x - 5y)2  
D)  Prime

Question 20

Factor the polynomial completely.
-  + 1

Accepted Answer

A)  (   + 1)(   -   + 1) 
B)  ( b + 1)( b - 1)(   -   + 1) 
C)  (   + 1)(   - 1) 
D)  ( b + 1)( b - 1)(   + b + 1)(   - b + 1) 
A)  (   + 1)(   -   + 1) 
B)  ( b + 1)( b - 1)(   -   + 1) 
C)  (   + 1)(   - 1) 
D)  ( b + 1)( b - 1)(   + b + 1)(   - b + 1)

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -45 = 21 + 96x

Find the greatest common factor of the numbers -8, 32, 36, 40

Factor completely. -x² + 9x - 22

Find the pair of numbers whose product and sum are given. -Product: 18 Sum: -11

Solve the problem. -A parallelogram has a base of length x + 7 and a height of x + 2 and has an area of 50 square units. Find the base and height of the parallelogram. (A = bh)

Solve the problem. -The product of two consecutive integers is 41 more than their sum. Find the integers.

Factor completely. If the polynomial is prime, say so. - - 216

Factor the binomial completely. If it is prime, say so. -147a⁴b - 108b³

Factor by grouping. -40 + 25ry - 8xr - 5xy

Factor completely. -- - 5x + 36

Complete the factoring. -x² + 16x + 64 = (x + 8)( )

Factor out the greatest common factor. -

Factor by grouping. -20x² + 15x - 24x - 18

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -3x(x - 9) = ( 2x - 4)(x - 9)

Factor completely. -

Factor the binomial completely. If it is prime, say so. -80 - 125

Factor completely. -x² - 10xy + 25y²

Factor the polynomial completely. - + 1

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

Roots and Radicals

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Exam 7: Rational Expressions and Applications