Question 1

Find the product.
-$$( x + 11 ) ( 3 x - 12 )$$

Accepted Answer

A)  $3 x ^ { 2 } + 21 x + 21$ 
B)  $3 x ^ { 2 } + 21 x - 132$ 
C)  $3 x ^ { 2 } - 132 x + 21$ 
D)  $3 x ^ { 2 } + 19 x - 132$ 
A)  $3 x ^ { 2 } + 21 x + 21$ 
B)  $3 x ^ { 2 } + 21 x - 132$ 
C)  $3 x ^ { 2 } - 132 x + 21$ 
D)  $3 x ^ { 2 } + 19 x - 132$ B

Question 2

Solve the problem. Round to two decimal places unless otherwise indicated.
-Suppose a cost-benefit model is given by $\mathrm { y } = \frac { 8.5 \mathrm { x } } { 100 - \mathrm { x } }$, where $\mathrm { y }$ is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing $55 \%$ to the nearest dollar.

Accepted Answer

A)  $\$ 10,389$ 
B)  $\$ 1222$ 
C)  $\$ 4675$ 
D)  $\$ 8500$ 
A)  $\$ 10,389$ 
B)  $\$ 1222$ 
C)  $\$ 4675$ 
D)  $\$ 8500$ A

Question 3

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 5 z + 4$

Accepted Answer

A)  Trinomial 
B)  Monomial 
C)  None of these 
D)  Binomial 
A)  Trinomial 
B)  Monomial 
C)  None of these 
D)  Binomial D

Question 4

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$- 7 ^ { - 4 }$

Accepted Answer

A)  $- 2401$ 
B)  $\frac { 1 } { 2401 }$ 
C)  $- \frac { 1 } { 2401 }$ 
D)  2401 
A)  $- 2401$ 
B)  $\frac { 1 } { 2401 }$ 
C)  $- \frac { 1 } { 2401 }$ 
D)  2401

Question 5

Solve the problem.
-A stone is dropped from a tower that is 730 feet high. The formula $h = 730 - 16 t ^ { 2 }$ describes the stone's height above the ground, $h$, in feet, $t$ seconds after it was dropped. What is the stone's height 3 seconds after it is released?

Accepted Answer

A)  $596 \mathrm { ft }$ 
B)  $611 \mathrm { ft }$ 
C)  $586 \mathrm { ft }$ 
D)  $561 \mathrm { ft }$ 
A)  $596 \mathrm { ft }$ 
B)  $611 \mathrm { ft }$ 
C)  $586 \mathrm { ft }$ 
D)  $561 \mathrm { ft }$

Question 6

Identify the set as finite or infinite.
-$\{ 8,14,20 , \ldots \}$

Accepted Answer

A)  finite 
B)  infinite 
A)  finite 
B)  infinite

Question 7

Factor by grouping.
-$$x ^ { 3 } - 2 x ^ { 2 } + 9 x - 18$$

Accepted Answer

A)  $x \left( x ^ { 2 } - 2 x + 9 \right) - 18$ 
B)  $( x + 9 ) \left( x ^ { 2 } - 2 x \right) ( x - 2 )$ 
C)  $\left( x ^ { 2 } - 2 x \right) + 9 ( x - 2 )$ 
D)  $\left( x ^ { 2 } + 9 \right) ( x - 2 )$ 
A)  $x \left( x ^ { 2 } - 2 x + 9 \right) - 18$ 
B)  $( x + 9 ) \left( x ^ { 2 } - 2 x \right) ( x - 2 )$ 
C)  $\left( x ^ { 2 } - 2 x \right) + 9 ( x - 2 )$ 
D)  $\left( x ^ { 2 } + 9 \right) ( x - 2 )$

Question 8

Factor, using the given factor. Assume all variables represent positive real numbers.
-$8 \mathrm { k } ^ { - 2 } + \mathrm { k } ^ { - 4 } ; \quad \mathrm { k } ^ { - 4 }$

Accepted Answer

A)  $\mathrm { k } ^ { - 4 } \left( 8 \mathrm { k } ^ { 3 } + 1 \right)$ 
B)  $\mathrm { k } ^ { - 4 } \left( 8 \mathrm { k } ^ { 2 } + 1 \right)$ 
C)  $8 \mathrm { k } ^ { - 4 } \left( \mathrm { k } ^ { 2 } + 1 \right)$ 
D)  $\mathrm { k } ^ { - 4 } \left( 8 \mathrm { k } ^ { - 2 } + 1 \right)$ 
A)  $\mathrm { k } ^ { - 4 } \left( 8 \mathrm { k } ^ { 3 } + 1 \right)$ 
B)  $\mathrm { k } ^ { - 4 } \left( 8 \mathrm { k } ^ { 2 } + 1 \right)$ 
C)  $8 \mathrm { k } ^ { - 4 } \left( \mathrm { k } ^ { 2 } + 1 \right)$ 
D)  $\mathrm { k } ^ { - 4 } \left( 8 \mathrm { k } ^ { - 2 } + 1 \right)$

Question 9

Write the expression in lowest terms.
-$$\frac { 6 ( y - 3 ) } { ( y - 3 ) ( y - 4 ) }$$

Accepted Answer

A)  $\frac { y - 3 } { y - 4 }$ 
B)  $\frac { 6 } { y - 3 }$ 
C)  $\frac { 6 } { y - 4 }$ 
D)  $\frac { 1 } { y - 4 }$ 
A)  $\frac { y - 3 } { y - 4 }$ 
B)  $\frac { 6 } { y - 3 }$ 
C)  $\frac { 6 } { y - 4 }$ 
D)  $\frac { 1 } { y - 4 }$

Question 10

Factor the polynomial by substitution.
-$30 z ^ { 6 } - 26 z ^ { 4 } - 40 z ^ { 2 }$

Accepted Answer

A)  $2 z ^ { 2 } \left( 5 z ^ { 2 } - 4 \right) \left( 3 z ^ { 2 } + 5 \right)$ 
B)  $\left( 6 z ^ { 3 } - 10 \right) \left( 5 z ^ { 3 } + 4 \right)$ 
C)  $2 z ^ { 2 } \left( 3 z ^ { 2 } - 5 \right) \left( 5 z ^ { 2 } + 4 \right)$ 
D)  $2 \left( 3 z ^ { 4 } - 5 \right) \left( 5 z ^ { 2 } + 4 \right)$ 
A)  $2 z ^ { 2 } \left( 5 z ^ { 2 } - 4 \right) \left( 3 z ^ { 2 } + 5 \right)$ 
B)  $\left( 6 z ^ { 3 } - 10 \right) \left( 5 z ^ { 3 } + 4 \right)$ 
C)  $2 z ^ { 2 } \left( 3 z ^ { 2 } - 5 \right) \left( 5 z ^ { 2 } + 4 \right)$ 
D)  $2 \left( 3 z ^ { 4 } - 5 \right) \left( 5 z ^ { 2 } + 4 \right)$

Question 11

Divide.
-$$\frac { x ^ { 2 } + 11 x + 19 } { x + 8 }$$

Accepted Answer

A)  $\frac { x + 3 } { x + 8 }$ 
B)  $x + 3 - \frac { 5 } { x + 8 }$ 
C)  $x + 3 + \frac { 5 } { x + 8 }$ 
D)  $x + 4$ 
A)  $\frac { x + 3 } { x + 8 }$ 
B)  $x + 3 - \frac { 5 } { x + 8 }$ 
C)  $x + 3 + \frac { 5 } { x + 8 }$ 
D)  $x + 4$

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { \frac { y ^ { 7 } } { 64 } }$

Accepted Answer

A)  $\frac { y ^ { 2 } \sqrt [ 3 ] { y } } { 4 }$ 
B)  $4 y ^ { 2 } \sqrt [ 3 ] { y }$ 
C)  $y ^ { 2 } - 4 \sqrt [ 3 ] { y }$ 
D)  $\frac { y ^ { 2 } + \sqrt [ 3 ] { y } } { 4 }$ 
A)  $\frac { y ^ { 2 } \sqrt [ 3 ] { y } } { 4 }$ 
B)  $4 y ^ { 2 } \sqrt [ 3 ] { y }$ 
C)  $y ^ { 2 } - 4 \sqrt [ 3 ] { y }$ 
D)  $\frac { y ^ { 2 } + \sqrt [ 3 ] { y } } { 4 }$

Question 13

Simplify the expression. Assume all variables represent positive real numbers.
-$- 8 \sqrt { 5 } + 6 \sqrt { 45 }$

Accepted Answer

A)  $10 \sqrt { 5 }$ 
B)  $26 \sqrt { 5 }$ 
C)  $- 10 \sqrt { 5 }$ 
D)  $- 2 \sqrt { 5 }$ 
A)  $10 \sqrt { 5 }$ 
B)  $26 \sqrt { 5 }$ 
C)  $- 10 \sqrt { 5 }$ 
D)  $- 2 \sqrt { 5 }$

Question 14

Tell whether the statement is true or false.
-$$\{ 6,8,9,11 \} \cup \{ 0,10,8,13,6 \} = \{ 6,8 \}$$

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 15

Solve the problem.
-Find all values of a that will make the polynomial a perfect square trinomial. $9 x ^ { 2 } + a x + 36$

Accepted Answer

A)  $18 , - 18$ 
B)  36 
C)  18 
D)  $36 , - 36$ 
A)  $18 , - 18$ 
B)  36 
C)  18 
D)  $36 , - 36$

Question 16

Use the distributive property to rewrite a sum as a product or the product as a sum.
--(-5y - 7r)

Accepted Answer

A)  5y + 7r 
B)  5y - 7r 
C)  -5y - 7r 
D)  -5y + 7r 
A)  5y + 7r 
B)  5y - 7r 
C)  -5y - 7r 
D)  -5y + 7r

Question 17

Write the expression in lowest terms.
-$$\frac { y ^ { 2 } + 2 y + 1 } { y ^ { 2 } + 6 y + 5 }$$

Accepted Answer

A)  $\frac { y + 1 } { y - 1 }$ 
B)  $\frac { y - 1 } { y - 5 }$ 
C)  $\frac { y + 2 } { y + 6 }$ 
D)  $\frac { y + 1 } { y + 5 }$ 
A)  $\frac { y + 1 } { y - 1 }$ 
B)  $\frac { y - 1 } { y - 5 }$ 
C)  $\frac { y + 2 } { y + 6 }$ 
D)  $\frac { y + 1 } { y + 5 }$

Question 18

Find the product.
-$$[ ( 7 x - 4 ) + 7 y ] ^ { 2 }$$

Accepted Answer

A)  $49 x ^ { 2 } - 28 x + 16 + 49 x y + 28 y + 49 y ^ { 2 }$ 
B)  $49 x ^ { 2 } - 56 x + 16 + 98 x y - 56 y + 49 y ^ { 2 }$ 
C)  $49 x ^ { 2 } - 56 x + 16 + 49 x y + 28 y + 49 y ^ { 2 }$ 
D)  $49 x ^ { 2 } - 56 x + 98 x y - 56 y + 49 y ^ { 2 }$ 
A)  $49 x ^ { 2 } - 28 x + 16 + 49 x y + 28 y + 49 y ^ { 2 }$ 
B)  $49 x ^ { 2 } - 56 x + 16 + 98 x y - 56 y + 49 y ^ { 2 }$ 
C)  $49 x ^ { 2 } - 56 x + 16 + 49 x y + 28 y + 49 y ^ { 2 }$ 
D)  $49 x ^ { 2 } - 56 x + 98 x y - 56 y + 49 y ^ { 2 }$

Question 19

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { 4 } { \sqrt { x + h } - \sqrt { x } }$

Accepted Answer

A)  $\frac { 4 ( \sqrt { x + h } - \sqrt { x } ) } { h }$ 
B)  $\frac { 4 \sqrt { h } } { h }$ 
C)  $\frac { 4 \sqrt { x + h } + \sqrt { x } } { h }$ 
D)  $\frac { 4 ( \sqrt { x + h } + \sqrt { x } ) } { h }$ 
A)  $\frac { 4 ( \sqrt { x + h } - \sqrt { x } ) } { h }$ 
B)  $\frac { 4 \sqrt { h } } { h }$ 
C)  $\frac { 4 \sqrt { x + h } + \sqrt { x } } { h }$ 
D)  $\frac { 4 ( \sqrt { x + h } + \sqrt { x } ) } { h }$

Question 20

Factor the trinomial, if possible.
-$$( m + 2 n ) ^ { 2 } - 6 ( m + 2 n ) + 9$$

Accepted Answer

A)  $( \mathrm { m } + 2 \mathrm { n } + 3 ) ^ { 2 }$ 
B)  $( m - 2 n - 3 ) ^ { 2 }$ 
C)  $( \mathrm { m } + 2 \mathrm { n } - 3 ) ^ { 2 }$ 
D)  $( \mathrm { m } - \mathrm { n } - 6 ) ^ { 2 }$ 
A)  $( \mathrm { m } + 2 \mathrm { n } + 3 ) ^ { 2 }$ 
B)  $( m - 2 n - 3 ) ^ { 2 }$ 
C)  $( \mathrm { m } + 2 \mathrm { n } - 3 ) ^ { 2 }$ 
D)  $( \mathrm { m } - \mathrm { n } - 6 ) ^ { 2 }$

Find the product. - $( x + 11 ) ( 3 x - 12 )$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 5 z + 4$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- 7 ^ { - 4 }$

Solve the problem. -A stone is dropped from a tower that is 730 feet high. The formula $h = 730 - 16 t ^ { 2 }$ describes the stone's height above the ground, $h$ , in feet, $t$ seconds after it was dropped. What is the stone's height 3 seconds after it is released?

Identify the set as finite or infinite. - $\{ 8,14,20 , \ldots \}$

Factor by grouping. - $x ^ { 3 } - 2 x ^ { 2 } + 9 x - 18$

Factor, using the given factor. Assume all variables represent positive real numbers. - $8 \mathrm { k } ^ { - 2 } + \mathrm { k } ^ { - 4 } ; \quad \mathrm { k } ^ { - 4 }$

Write the expression in lowest terms. - $\frac { 6 ( y - 3 ) } { ( y - 3 ) ( y - 4 ) }$

Factor the polynomial by substitution. - $30 z ^ { 6 } - 26 z ^ { 4 } - 40 z ^ { 2 }$

Divide. - $\frac { x ^ { 2 } + 11 x + 19 } { x + 8 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { y ^ { 7 } } { 64 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $- 8 \sqrt { 5 } + 6 \sqrt { 45 }$

Tell whether the statement is true or false. - $\{ 6,8,9,11 \} \cup \{ 0,10,8,13,6 \} = \{ 6,8 \}$

Solve the problem. -Find all values of a that will make the polynomial a perfect square trinomial. $9 x ^ { 2 } + a x + 36$

Use the distributive property to rewrite a sum as a product or the product as a sum. --(-5y - 7r)

Write the expression in lowest terms. - $\frac { y ^ { 2 } + 2 y + 1 } { y ^ { 2 } + 6 y + 5 }$

Find the product. - $[ ( 7 x - 4 ) + 7 y ] ^ { 2 }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { 4 } { \sqrt { x + h } - \sqrt { x } }$

Factor the trinomial, if possible. - $( m + 2 n ) ^ { 2 } - 6 ( m + 2 n ) + 9$

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

Further Topics in Algebra

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Exam 12: Review of Basic Concepts

Find the product. - (x+11)(3x−12)( x + 11 ) ( 3 x - 12 )(x+11)(3x−12)

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - −5z+4- 5 z + 4−5z+4

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −7−4- 7 ^ { - 4 }−7−4

Solve the problem. -A stone is dropped from a tower that is 730 feet high. The formula h=730−16t2h = 730 - 16 t ^ { 2 }h=730−16t2 describes the stone's height above the ground, hhh , in feet, ttt seconds after it was dropped. What is the stone's height 3 seconds after it is released?

Identify the set as finite or infinite. - {8,14,20,…}\{ 8,14,20 , \ldots \}{8,14,20,…}

Factor by grouping. - x3−2x2+9x−18x ^ { 3 } - 2 x ^ { 2 } + 9 x - 18x3−2x2+9x−18

Factor, using the given factor. Assume all variables represent positive real numbers. - 8k−2+k−4;k−48 \mathrm { k } ^ { - 2 } + \mathrm { k } ^ { - 4 } ; \quad \mathrm { k } ^ { - 4 }8k−2+k−4;k−4

Write the expression in lowest terms. - 6(y−3)(y−3)(y−4)\frac { 6 ( y - 3 ) } { ( y - 3 ) ( y - 4 ) }(y−3)(y−4)6(y−3)​

Factor the polynomial by substitution. - 30z6−26z4−40z230 z ^ { 6 } - 26 z ^ { 4 } - 40 z ^ { 2 }30z6−26z4−40z2

Divide. - x2+11x+19x+8\frac { x ^ { 2 } + 11 x + 19 } { x + 8 }x+8x2+11x+19​

Simplify the expression. Assume all variables represent positive real numbers. - y7643\sqrt [ 3 ] { \frac { y ^ { 7 } } { 64 } }364y7​​

Simplify the expression. Assume all variables represent positive real numbers. - −85+645- 8 \sqrt { 5 } + 6 \sqrt { 45 }−85​+645​

Tell whether the statement is true or false. - {6,8,9,11}∪{0,10,8,13,6}={6,8}\{ 6,8,9,11 \} \cup \{ 0,10,8,13,6 \} = \{ 6,8 \}{6,8,9,11}∪{0,10,8,13,6}={6,8}

Solve the problem. -Find all values of a that will make the polynomial a perfect square trinomial. 9x2+ax+369 x ^ { 2 } + a x + 369x2+ax+36