Question 1

Find the sum or difference.
-$$\frac { 9 m ^ { 2 } + 74 m - 63 } { m + 9 }$$

Accepted Answer

A)  $9 m + 7$ 
B)  $m - 7$ 
C)  $9 m - 7 + \frac { 5 } { m - 7 }$ 
D)  $9 m - 7$ 
A)  $9 m + 7$ 
B)  $m - 7$ 
C)  $9 m - 7 + \frac { 5 } { m - 7 }$ 
D)  $9 m - 7$

Question 2

Evaluate the expression.
-$$\frac { - 7 \cdot 5 + 3 - ( - 1 + 6 ) } { - 7 \cdot 8 + 2 }$$

Accepted Answer

A)  $\frac { 61 } { 70 }$ 
B)  $\frac { 59 } { 54 }$ 
C)  $\frac { 37 } { 54 }$ 
D)  $\frac { 37 } { 70 }$ 
A)  $\frac { 61 } { 70 }$ 
B)  $\frac { 59 } { 54 }$ 
C)  $\frac { 37 } { 54 }$ 
D)  $\frac { 37 } { 70 }$

Question 3

Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { m ^ { - 1 } - n ^ { - 1 } } { m ^ { - 1 } + n ^ { - 1 } } \cdot \frac { m + n } { m - n }$$

Accepted Answer

A)  $- 1$ 
B)  $\frac { m n } { m + n }$ 
C)  1 
D)  $\frac { \mathrm { m } - \mathrm { n } } { \mathrm { m } }$ 
A)  $- 1$ 
B)  $\frac { m n } { m + n }$ 
C)  1 
D)  $\frac { \mathrm { m } - \mathrm { n } } { \mathrm { m } }$

Question 4

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-A formula for calculating the distance, d, one can see from an airplane to the horizon on a clear day is $\mathrm { d } = 1.22 \mathrm { x } ^ { 1 / 2 }$ , where x is the altitude of the plane in feet and d is given in miles. How far can one see in a plane flying at 28,000 feet? Round your answer to the nearest tenth mile, if necessary.

Accepted Answer

A)  204.1 mi 
B)  1708 mi 
C)  184.8 mi 
D)  17,080 mi 
A)  204.1 mi 
B)  1708 mi 
C)  184.8 mi 
D)  17,080 mi

Question 5

Write in radical form. Assume all variables represent positive real numbers.
-$( \mathrm { mn } ) ^ { 1 / 6 }$

Accepted Answer

A)  $\sqrt [ 6 ] { m n }$ 
B)  $( \sqrt { \mathrm { mn } } ) ^ { 6 }$ 
C)  $( \mathrm { mn } ) ^ { - 6 }$ 
D)  $\frac { 1 } { \sqrt [ 6 ] { m n } }$ 
A)  $\sqrt [ 6 ] { m n }$ 
B)  $( \sqrt { \mathrm { mn } } ) ^ { 6 }$ 
C)  $( \mathrm { mn } ) ^ { - 6 }$ 
D)  $\frac { 1 } { \sqrt [ 6 ] { m n } }$

Question 6

Insert   in the blank to make the statement true.
-

Accepted Answer

A)  $\subseteq$ 
B)  $\nsubseteq$ 
A)  $\subseteq$ 
B)  $\nsubseteq$

Question 7

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
-$3 ^ { 0 }$

Accepted Answer

A)  $- 1$ 
B)  0 
C)  1 
D)  3 
A)  $- 1$ 
B)  0 
C)  1 
D)  3

Question 8

Solve the problem. Round to two decimal places unless otherwise indicated.
-In the following formula, $y$ is the minimum number of hours of studying required to attain a test score of $x$ : $y =$ $\frac { 0.47 x } { 100.5 - x }$. How many hours of study are needed to score $97 ?$

Accepted Answer

A)  13.03 hr 
B)  27.85 hr 
C)  100.02 hr 
D)  130.30 hr 
A)  13.03 hr 
B)  27.85 hr 
C)  100.02 hr 
D)  130.30 hr

Question 9

Evaluate the expression.
-Let $x = - 18 , y = 12$.
Evaluate $| 4 y - 5 x | - | 4 y |$.

Accepted Answer

A)  90 
B)  60 
C)  84 
D)  36 
A)  90 
B)  60 
C)  84 
D)  36

Question 10

Evaluate the expression.
-Let $x = - 9 , y = 13$. Evaluate $| 9 y - 2 x |$.

Accepted Answer

A)  $- 99$ 
B)  $- 135$ 
C)  135 
D)  99 
A)  $- 99$ 
B)  $- 135$ 
C)  135 
D)  99

Question 11

Evaluate the expression.
-$( - 4 ) ^ { 3 }$

Accepted Answer

A)  $- 64$ 
B)  64 
C)  144 
D)  $- 12$ 
A)  $- 64$ 
B)  64 
C)  144 
D)  $- 12$

Question 12

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 5 } { 4 } ( 16 y - 16 x + 20 z )$$

Accepted Answer

A)  $20 y - 20 x - 25 z$ 
B)  $20 y + 20 x + 25 z$ 
C)  $20 y + 20 x - 25 z$ 
D)  $20 y - 20 x + 25 z$ 
A)  $20 y - 20 x - 25 z$ 
B)  $20 y + 20 x + 25 z$ 
C)  $20 y + 20 x - 25 z$ 
D)  $20 y - 20 x + 25 z$

Question 13

Tell whether the statement is true or false.
-$11 \notin \{ 0,9,10,12,14 \}$

Accepted Answer

A) True 
 B)False

Question 14

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { x ^ { 17 } } { x ^ { 2 } }$$

Accepted Answer

A)  $\frac { 1 } { x }$ 
B)  $- x ^ { 15 }$ 
C)  $x ^ { 19 }$ 
D)  $x ^ { 15 }$ 
A)  $\frac { 1 } { x }$ 
B)  $- x ^ { 15 }$ 
C)  $x ^ { 19 }$ 
D)  $x ^ { 15 }$

Question 15

Perform the indicated operations.
-$$\frac { 64 x } { 3 ( 8 x + 1 ) } - \frac { 1 } { 3 x ( 8 x + 1 ) } + \frac { 19 } { x }$$

Accepted Answer

A)  $\frac { 64 x ^ { 2 } + 456 x + 56 } { 24 x ^ { 2 } + 3 x }$ 
B)  $\frac { 8 ( x + 7 ) } { 24 x ^ { 2 } + 3 x }$ 
C)  $\frac { 8 ( x + 7 ) } { 3 x }$ 
D)  $\frac { 64 x ^ { 2 } + 456 x + 56 } { 3 x }$ 
A)  $\frac { 64 x ^ { 2 } + 456 x + 56 } { 24 x ^ { 2 } + 3 x }$ 
B)  $\frac { 8 ( x + 7 ) } { 24 x ^ { 2 } + 3 x }$ 
C)  $\frac { 8 ( x + 7 ) } { 3 x }$ 
D)  $\frac { 64 x ^ { 2 } + 456 x + 56 } { 3 x }$

Question 16

Factor the trinomial, if possible.
-$$u ^ { 2 } - 2 u v - 48 v ^ { 2 }$$

Accepted Answer

A)  $( u - 6 v ) ( u + v )$ 
B)  prime 
C)  $( u + 6 v ) ( u - 8 v )$ 
D)  $( u - 6 v ) ( u + 8 v )$ 
A)  $( u - 6 v ) ( u + v )$ 
B)  prime 
C)  $( u + 6 v ) ( u - 8 v )$ 
D)  $( u - 6 v ) ( u + 8 v )$

Question 17

Factor out the greatest common factor. Simplify the factors, if possible.
-$$( x - 4 ) ( x + 9 ) + ( x - 4 ) ( x + 5 )$$

Accepted Answer

A)  $( x - 4 ) ( x + 14 )$ 
B)  $2 ( x - 4 ) ( 2 x + 14 )$ 
C)  $2 ( x - 4 ) ( x + 7 )$ 
D)  $( x - 4 ) ( 2 x + 14 )$ 
A)  $( x - 4 ) ( x + 14 )$ 
B)  $2 ( x - 4 ) ( 2 x + 14 )$ 
C)  $2 ( x - 4 ) ( x + 7 )$ 
D)  $( x - 4 ) ( 2 x + 14 )$

Question 18

Factor by any method.
-$27 c ^ { 3 } + 125$

Accepted Answer

A)  $( 3 c + 5 ) \left( 9 c ^ { 2 } + 25 \right)$ 
B)  $( 27 c + 5 ) \left( c ^ { 2 } - 15 c + 25 \right)$ 
C)  $( 3 c + 5 ) \left( 9 c ^ { 2 } - 15 c + 25 \right)$ 
D)  $( 3 c - 5 ) \left( 9 c ^ { 2 } + 15 c + 25 \right)$ 
A)  $( 3 c + 5 ) \left( 9 c ^ { 2 } + 25 \right)$ 
B)  $( 27 c + 5 ) \left( c ^ { 2 } - 15 c + 25 \right)$ 
C)  $( 3 c + 5 ) \left( 9 c ^ { 2 } - 15 c + 25 \right)$ 
D)  $( 3 c - 5 ) \left( 9 c ^ { 2 } + 15 c + 25 \right)$

Question 19

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-The cost of manufacturing clocks is given by c $c = 25 ( n + 49 ) ^ { 1 / 2 }$ , where c is the cost in dollars and n is the number produced. What is the cost when no clocks are produced?

Accepted Answer

A)  $1225 
B)  $175 
C)  $35 
D)  $25 
A)  $1225 
B)  $175 
C)  $35 
D)  $25

Question 20

Evaluate the expression for x $$x = - 2 , y = 3 , \text { and } a = - 4$$
-$- 4 a - 6 y - 3 x$

Accepted Answer

A)  8 
B)  19 
C)  23 
D)  4 
A)  8 
B)  19 
C)  23 
D)  4

Find the sum or difference. - $\frac { 9 m ^ { 2 } + 74 m - 63 } { m + 9 }$

Evaluate the expression. - $\frac { - 7 \cdot 5 + 3 - ( - 1 + 6 ) } { - 7 \cdot 8 + 2 }$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { m ^ { - 1 } - n ^ { - 1 } } { m ^ { - 1 } + n ^ { - 1 } } \cdot \frac { m + n } { m - n }$

Write in radical form. Assume all variables represent positive real numbers. - $( \mathrm { mn } ) ^ { 1 / 6 }$

Insert in the blank to make the statement true. -

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $3 ^ { 0 }$

Solve the problem. Round to two decimal places unless otherwise indicated. -In the following formula, $y$ is the minimum number of hours of studying required to attain a test score of $x$ : $y =$ $\frac { 0.47 x } { 100.5 - x }$ . How many hours of study are needed to score $97 ?$

Evaluate the expression. -Let $x = - 18 , y = 12$ . Evaluate $| 4 y - 5 x | - | 4 y |$ .

Evaluate the expression. -Let $x = - 9 , y = 13$ . Evaluate $| 9 y - 2 x |$ .

Evaluate the expression. - $( - 4 ) ^ { 3 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 5 } { 4 } ( 16 y - 16 x + 20 z )$

Tell whether the statement is true or false. - $11 \notin \{ 0,9,10,12,14 \}$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { 17 } } { x ^ { 2 } }$

Perform the indicated operations. - $\frac { 64 x } { 3 ( 8 x + 1 ) } - \frac { 1 } { 3 x ( 8 x + 1 ) } + \frac { 19 } { x }$

Factor the trinomial, if possible. - $u ^ { 2 } - 2 u v - 48 v ^ { 2 }$

Factor out the greatest common factor. Simplify the factors, if possible. - $( x - 4 ) ( x + 9 ) + ( x - 4 ) ( x + 5 )$

Factor by any method. - $27 c ^ { 3 } + 125$

Evaluate the expression for x $x = - 2 , y = 3 , \text { and } a = - 4$ - $- 4 a - 6 y - 3 x$

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 1: Review of Basic Concepts

Find the sum or difference. - 9m2+74m−63m+9\frac { 9 m ^ { 2 } + 74 m - 63 } { m + 9 }m+99m2+74m−63​

Evaluate the expression. - −7⋅5+3−(−1+6)−7⋅8+2\frac { - 7 \cdot 5 + 3 - ( - 1 + 6 ) } { - 7 \cdot 8 + 2 }−7⋅8+2−7⋅5+3−(−1+6)​

Perform the indicated operation and write your answer with positive integer exponents. - m−1−n−1m−1+n−1⋅m+nm−n\frac { m ^ { - 1 } - n ^ { - 1 } } { m ^ { - 1 } + n ^ { - 1 } } \cdot \frac { m + n } { m - n }m−1+n−1m−1−n−1​⋅m−nm+n​

Write in radical form. Assume all variables represent positive real numbers. - (mn)1/6( \mathrm { mn } ) ^ { 1 / 6 }(mn)1/6

Insert in the blank to make the statement true. -

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 303 ^ { 0 }30

Evaluate the expression. -Let x=−18,y=12x = - 18 , y = 12x=−18,y=12 . Evaluate ∣4y−5x∣−∣4y∣| 4 y - 5 x | - | 4 y |∣4y−5x∣−∣4y∣ .

Evaluate the expression. -Let x=−9,y=13x = - 9 , y = 13x=−9,y=13 . Evaluate ∣9y−2x∣| 9 y - 2 x |∣9y−2x∣ .

Evaluate the expression. - (−4)3( - 4 ) ^ { 3 }(−4)3

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 54(16y−16x+20z)\frac { 5 } { 4 } ( 16 y - 16 x + 20 z )45​(16y−16x+20z)

Tell whether the statement is true or false. - 11∉{0,9,10,12,14}11 \notin \{ 0,9,10,12,14 \}11∈/{0,9,10,12,14}

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - x17x2\frac { x ^ { 17 } } { x ^ { 2 } }x2x17​

Perform the indicated operations. - 64x3(8x+1)−13x(8x+1)+19x\frac { 64 x } { 3 ( 8 x + 1 ) } - \frac { 1 } { 3 x ( 8 x + 1 ) } + \frac { 19 } { x }3(8x+1)64x​−3x(8x+1)1​+x19​

Factor the trinomial, if possible. - u2−2uv−48v2u ^ { 2 } - 2 u v - 48 v ^ { 2 }u2−2uv−48v2

Factor out the greatest common factor. Simplify the factors, if possible. - (x−4)(x+9)+(x−4)(x+5)( x - 4 ) ( x + 9 ) + ( x - 4 ) ( x + 5 )(x−4)(x+9)+(x−4)(x+5)

Factor by any method. - 27c3+12527 c ^ { 3 } + 12527c3+125

Evaluate the expression for x x=−2,y=3, and a=−4x = - 2 , y = 3 , \text { and } a = - 4x=−2,y=3, and a=−4 - −4a−6y−3x- 4 a - 6 y - 3 x−4a−6y−3x