Question 1

Decide whether the expression has been simplified correctly.
-$x ^ { 4 } \cdot x ^ { 2 } = x ^ { 6 }$

Accepted Answer

A)  Not simplified correctly 
B)  Simplified correctly 
A)  Not simplified correctly 
B)  Simplified correctly

Question 2

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { x ^ { 15 } } { x ^ { 4 } }$$

Accepted Answer

A)  $\frac { 1 } { x ^ { 11 } }$ 
B)  $x ^ { 19 }$ 
C)  $- x ^ { 11 }$ 
D)  $x ^ { 11 }$ 
A)  $\frac { 1 } { x ^ { 11 } }$ 
B)  $x ^ { 19 }$ 
C)  $- x ^ { 11 }$ 
D)  $x ^ { 11 }$

Question 3

Factor the polynomial by substitution.
-$$6 ( p + 1 ) ^ { 2 } + 11 ( p + 1 ) + 4$$

Accepted Answer

A)  $( 2 p + 1 ) ( 3 p + 4 )$ 
B)  $( 2 p + 6 ) ( 3 p + 4 )$ 
C)  $( 2 p + 2 ) ( 3 p + 5 )$ 
D)  $( 2 p + 3 ) ( 3 p + 7 )$ 
A)  $( 2 p + 1 ) ( 3 p + 4 )$ 
B)  $( 2 p + 6 ) ( 3 p + 4 )$ 
C)  $( 2 p + 2 ) ( 3 p + 5 )$ 
D)  $( 2 p + 3 ) ( 3 p + 7 )$

Question 4

Evaluate the expression for x = -2, y = 3, and a = -4.
-$$\frac { \frac { 6 } { y } - \frac { a } { 2 } } { \frac { x } { 2 } + \frac { 12 } { y } }$$

Accepted Answer

A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 4 } { 3 }$ 
C)  0 
D)  1 
A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 4 } { 3 }$ 
C)  0 
D)  1

Question 5

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { \left( 3 x ^ { 4 } y ^ { 6 } \right) ^ { 5 } } { 9 x y ^ { 2 } }$$

Accepted Answer

A)  $27 x ^ { 8 } y ^ { 9 }$ 
B)  $\frac { x ^ { 19 } y ^ { 28 } } { 3 }$ 
C)  $27 x ^ { 19 } y ^ { 28 }$ 
D)  $\frac { x ^ { 8 } y ^ { 9 } } { 3 }$ 
A)  $27 x ^ { 8 } y ^ { 9 }$ 
B)  $\frac { x ^ { 19 } y ^ { 28 } } { 3 }$ 
C)  $27 x ^ { 19 } y ^ { 28 }$ 
D)  $\frac { x ^ { 8 } y ^ { 9 } } { 3 }$

Question 6

Solve the problem.
-The length of the diagonal of a rectangle is given by $D = \sqrt { L ^ { 2 } + W ^ { 2 } }$ where $L$ and $W$ are the length and width of the rectangle. What is the length of the diagonal, D, of a rectangle that is 68 inches long and 41 inches wide? Round your answer to the nearest tenth of an inch, if necessary.

Accepted Answer

A)  $52.8 \mathrm { in }$. 
B)  $54.2 \mathrm { in }$. 
C)  $10.4 \mathrm { in }$. 
D)  $79.4 \mathrm { in }$. 
A)  $52.8 \mathrm { in }$. 
B)  $54.2 \mathrm { in }$. 
C)  $10.4 \mathrm { in }$. 
D)  $79.4 \mathrm { in }$.

Question 7

Find the product or quotient.
-$$\frac { z ^ { 2 } + 6 z + 8 } { z ^ { 2 } + 10 z + 16 } \div \frac { z ^ { 2 } + 4 z } { z ^ { 2 } + 10 z + 16 }$$

Accepted Answer

A)  $\frac { z } { z ^ { 2 } + 10 z + 16 }$ 
B)  $\frac { z + 2 } { z }$ 
C)  $z + 2$ 
D)  $\frac { z + 2 } { z ^ { 2 } + 8 z }$ 
A)  $\frac { z } { z ^ { 2 } + 10 z + 16 }$ 
B)  $\frac { z + 2 } { z }$ 
C)  $z + 2$ 
D)  $\frac { z + 2 } { z ^ { 2 } + 8 z }$

Question 8

Round to two decimal places unless otherwise indicated.
If the average cost per unit C(x) to produce x units of plywood is given by C(x) , what is the
-
C ( x ) = $\frac {  900} { x+30^{\prime} }$
 unit cost for 20 units?

Accepted Answer

A)  $45.00 
B)  $1.50 
C)  $18.00 
D)  $15.00 
A)  $45.00 
B)  $1.50 
C)  $18.00 
D)  $15.00

Question 9

Use set notation, and list all the elements of the set.
-{10, 17, 24, . . ., 59}

Accepted Answer

A)  {10, 17, 24, 32, 39, 46, 53, 60} 
B)  {10, 17, 23, 30, 37, 44, 51, 58} 
C)  {10, 17, 24, 31, 38, 45, 52, 59} 
D)  {10, 17, 24, 31, 38} 
A)  {10, 17, 24, 32, 39, 46, 53, 60} 
B)  {10, 17, 23, 30, 37, 44, 51, 58} 
C)  {10, 17, 24, 31, 38, 45, 52, 59} 
D)  {10, 17, 24, 31, 38}

Question 10

Solve the problem.
-$$( 7 m + 3 ) ^ { 2 }$$

Accepted Answer

A)  $7 m ^ { 2 } + 9$ 
B)  $49 m ^ { 2 } + 42 m + 9$ 
C)  $7 m ^ { 2 } + 42 m + 9$ 
D)  $49 m ^ { 2 } + 9$ 
A)  $7 m ^ { 2 } + 9$ 
B)  $49 m ^ { 2 } + 42 m + 9$ 
C)  $7 m ^ { 2 } + 42 m + 9$ 
D)  $49 m ^ { 2 } + 9$

Question 11

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$- 2 ^ { 0 }$

Accepted Answer

A)  -2 
B)  1 
C)  -1 
D)  0 
A)  -2 
B)  1 
C)  -1 
D)  0

Question 12

Tell whether the statement is true or false.
-$\{ 4,6,7,9 \} \cup \{ 0,8,6,11,4 \} = \{ 4,6 \}$

Accepted Answer

A) True 
 B)False

Question 13

Evaluate the expression.
-$( - 8 ) ^ { 2 / 3 }$

Accepted Answer

A)  not a real number 
B)  -4 
C)  4 
D)  -2 
A)  not a real number 
B)  -4 
C)  4 
D)  -2

Question 14

Solve the equation
-$$\frac { x ^ { 2 } + 9 x + 20 } { x + 5 }$$

Accepted Answer

A)  $x ^ { 2 } + 4$ 
B)  $x ^ { 3 } - 15$ 
C)  $x - 15$ 
D)  $x + 4$ 
A)  $x ^ { 2 } + 4$ 
B)  $x ^ { 3 } - 15$ 
C)  $x - 15$ 
D)  $x + 4$

Question 15

Evaluate the expression.
-$$- \left| - \frac { 8 } { 3 } \right|$$

Accepted Answer

A)  $\pm \frac { 8 } { 3 }$ 
B)  $- \frac { 8 } { 3 }$ 
C)  $\frac { 8 } { 3 }$ 
D)  0 
A)  $\pm \frac { 8 } { 3 }$ 
B)  $- \frac { 8 } { 3 }$ 
C)  $\frac { 8 } { 3 }$ 
D)  0

Question 16

Determine the degree of the polynomial.
-$- 5 a ^ { 4 } - 14 a ^ { 2 } + 7 a + 6 a ^ { 6 }$

Accepted Answer

A)  6 
B)  13 
C)  12 
D)  4 
A)  6 
B)  13 
C)  12 
D)  4

Question 17

Identify the expression as a polynomial or not a polynomial.
-$0.6 x ^ { 4 } - 7.4$

Accepted Answer

A)  Polynomial 
B)  Not a polynomial 
A)  Polynomial 
B)  Not a polynomial

Question 18

Find the product or quotient.
-$$\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 10 z + 24 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } - 2 z - 24 }$$

Accepted Answer

A)  $z - 6$ 
B)  $\frac { z } { z ^ { 2 } + 10 z + 24 }$ 
C)  $\frac { z - 6 } { z ^ { 2 } + 4 z }$ 
D)  $\frac { z - 6 } { z }$ 
A)  $z - 6$ 
B)  $\frac { z } { z ^ { 2 } + 10 z + 24 }$ 
C)  $\frac { z - 6 } { z ^ { 2 } + 4 z }$ 
D)  $\frac { z - 6 } { z }$

Question 19

Solve the problem.
-$$( 6 x - 5 y + 7 ) ( 6 x - 5 y - 7 )$$

Accepted Answer

A)  $36 x ^ { 2 } - 60 x y + 25 y ^ { 2 } - 49$ 
B)  $- 60 x y - 42 x + - 35 y - 49$ 
C)  $12 x ^ { 2 } - 10 y ^ { 2 } - 98$ 
D)  $36 x ^ { 2 } + 60 x y - 25 y ^ { 2 } - 98$ 
A)  $36 x ^ { 2 } - 60 x y + 25 y ^ { 2 } - 49$ 
B)  $- 60 x y - 42 x + - 35 y - 49$ 
C)  $12 x ^ { 2 } - 10 y ^ { 2 } - 98$ 
D)  $36 x ^ { 2 } + 60 x y - 25 y ^ { 2 } - 98$

Question 20

Factor by any method.
-$$8 s ^ { 3 } + 1$$

Accepted Answer

A)  $( 2 s - 1 ) \left( 4 s ^ { 2 } + 2 s + 1 \right)$ 
B)  $( 2 s + 1 ) \left( 4 s ^ { 2 } - 2 s + 1 \right)$ 
C)  $( 2 \mathrm {~s} + 1 ) \left( 4 \mathrm {~s} ^ { 2 } + 1 \right)$ 
D)  $( 8 s + 1 ) \left( s ^ { 2 } - 2 s + 1 \right)$ 
A)  $( 2 s - 1 ) \left( 4 s ^ { 2 } + 2 s + 1 \right)$ 
B)  $( 2 s + 1 ) \left( 4 s ^ { 2 } - 2 s + 1 \right)$ 
C)  $( 2 \mathrm {~s} + 1 ) \left( 4 \mathrm {~s} ^ { 2 } + 1 \right)$ 
D)  $( 8 s + 1 ) \left( s ^ { 2 } - 2 s + 1 \right)$

Decide whether the expression has been simplified correctly. - $x ^ { 4 } \cdot x ^ { 2 } = x ^ { 6 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { 15 } } { x ^ { 4 } }$

Factor the polynomial by substitution. - $6 ( p + 1 ) ^ { 2 } + 11 ( p + 1 ) + 4$

Evaluate the expression for x = -2, y = 3, and a = -4. - $\frac { \frac { 6 } { y } - \frac { a } { 2 } } { \frac { x } { 2 } + \frac { 12 } { y } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { \left( 3 x ^ { 4 } y ^ { 6 } \right) ^ { 5 } } { 9 x y ^ { 2 } }$

Find the product or quotient. - $\frac { z ^ { 2 } + 6 z + 8 } { z ^ { 2 } + 10 z + 16 } \div \frac { z ^ { 2 } + 4 z } { z ^ { 2 } + 10 z + 16 }$

Round to two decimal places unless otherwise indicated. If the average cost per unit C(x) to produce x units of plywood is given by C(x) , what is the - C ( x ) = $\frac { 900} { x+30^{\prime} }$ unit cost for 20 units?

Use set notation, and list all the elements of the set. -{10, 17, 24, . . ., 59}

Solve the problem. - $( 7 m + 3 ) ^ { 2 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- 2 ^ { 0 }$

Tell whether the statement is true or false. - $\{ 4,6,7,9 \} \cup \{ 0,8,6,11,4 \} = \{ 4,6 \}$

Evaluate the expression. - $( - 8 ) ^ { 2 / 3 }$

Solve the equation - $\frac { x ^ { 2 } + 9 x + 20 } { x + 5 }$

Evaluate the expression. - $- \left| - \frac { 8 } { 3 } \right|$

Determine the degree of the polynomial. - $- 5 a ^ { 4 } - 14 a ^ { 2 } + 7 a + 6 a ^ { 6 }$

Identify the expression as a polynomial or not a polynomial. - $0.6 x ^ { 4 } - 7.4$

Find the product or quotient. - $\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 10 z + 24 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } - 2 z - 24 }$

Solve the problem. - $( 6 x - 5 y + 7 ) ( 6 x - 5 y - 7 )$

Factor by any method. - $8 s ^ { 3 } + 1$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

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Exam 1: Review of Basic Concepts

Decide whether the expression has been simplified correctly. - x4⋅x2=x6x ^ { 4 } \cdot x ^ { 2 } = x ^ { 6 }x4⋅x2=x6

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - x15x4\frac { x ^ { 15 } } { x ^ { 4 } }x4x15​

Factor the polynomial by substitution. - 6(p+1)2+11(p+1)+46 ( p + 1 ) ^ { 2 } + 11 ( p + 1 ) + 46(p+1)2+11(p+1)+4

Evaluate the expression for x = -2, y = 3, and a = -4. - 6y−a2x2+12y\frac { \frac { 6 } { y } - \frac { a } { 2 } } { \frac { x } { 2 } + \frac { 12 } { y } }2x​+y12​y6​−2a​​

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - (3x4y6)59xy2\frac { \left( 3 x ^ { 4 } y ^ { 6 } \right) ^ { 5 } } { 9 x y ^ { 2 } }9xy2(3x4y6)5​

Find the product or quotient. - z2+6z+8z2+10z+16÷z2+4zz2+10z+16\frac { z ^ { 2 } + 6 z + 8 } { z ^ { 2 } + 10 z + 16 } \div \frac { z ^ { 2 } + 4 z } { z ^ { 2 } + 10 z + 16 }z2+10z+16z2+6z+8​÷z2+10z+16z2+4z​

Round to two decimal places unless otherwise indicated. If the average cost per unit C(x) to produce x units of plywood is given by C(x) , what is the - C ( x ) = 900x+30′\frac { 900} { x+30^{\prime} }x+30′900​ unit cost for 20 units?