Question 1

Solve the proportion.
-$\frac { x } { 22 } = \frac { 5 } { 11 }$

Accepted Answer

A)  $48 \frac { 2 } { 5 }$ 
B)  10 
C)  20 
D)  $2 \frac { 1 } { 2 }$ 
A)  $48 \frac { 2 } { 5 }$ 
B)  10 
C)  20 
D)  $2 \frac { 1 } { 2 }$

Question 2

Solve.
-Two angles are supplementary if the sum of their measures is $180 ^ { \circ }$. If the measure of one angle is given by $\left( \frac { 31 x } { 18 } \right) ^ { \circ }$ and the measure of its supplement is given by $\left( \frac { 7 x } { 9 } \right) ^ { \circ }$, find the measures of the two angles.

Accepted Answer

A)  $72 ^ { \circ } , 108 ^ { \circ }$ 
B)  $124 ^ { \circ } , 56 ^ { \circ }$ 
C)  $36 ^ { \circ } , 144 ^ { \circ }$ 
D)  $62 ^ { \circ } , 118 ^ { \circ }$ 
A)  $72 ^ { \circ } , 108 ^ { \circ }$ 
B)  $124 ^ { \circ } , 56 ^ { \circ }$ 
C)  $36 ^ { \circ } , 144 ^ { \circ }$ 
D)  $62 ^ { \circ } , 118 ^ { \circ }$

Question 3

Solve the equation.
-$\frac { x } { 4 } - \frac { x } { 9 } = 6$

Accepted Answer

A)  $\frac { 216 } { 5 }$ 
B)  36 
C)  24 
D)  54 
A)  $\frac { 216 } { 5 }$ 
B)  36 
C)  24 
D)  54

Question 4

Simplify.
-$\frac { \frac { 6 } { 7 - x } + \frac { 7 } { x - 7 } } { \frac { 2 } { x } + \frac { 5 } { x - 7 } }$

Accepted Answer

A)  $- \frac { 13 x } { 7 x - 14 }$ 
B)  $- \frac { x } { 7 x - 14 }$ 
C)  $\frac { x } { 7 x - 14 }$ 
D)  $\frac { 13 x } { 7 x - 14 }$ 
A)  $- \frac { 13 x } { 7 x - 14 }$ 
B)  $- \frac { x } { 7 x - 14 }$ 
C)  $\frac { x } { 7 x - 14 }$ 
D)  $\frac { 13 x } { 7 x - 14 }$

Question 5

Find the quotient and simplify.
-$\frac { 6 x ^ { 4 } } { z ^ { 5 } } \div \frac { 9 x ^ { 4 } z ^ { 5 } } { 4 }$

Accepted Answer

A)  $\frac { 27 x ^ { 8 } } { 2 }$ 
B)  $\frac { 8 x ^ { 8 } } { 3 z ^ { 10 } }$ 
C)  $\frac { 8 } { 3 z ^ { 10 } }$ 
D)  $\frac { 8 } { 3 }$ 
A)  $\frac { 27 x ^ { 8 } } { 2 }$ 
B)  $\frac { 8 x ^ { 8 } } { 3 z ^ { 10 } }$ 
C)  $\frac { 8 } { 3 z ^ { 10 } }$ 
D)  $\frac { 8 } { 3 }$

Question 6

Solve.
-Find the perimeter of the trapezoid.

Accepted Answer

A)  $\frac { 2 x + 11 } { x + 5 } i n$. 
B)  $\frac { 4 x + 11 } { x + 5 } \mathrm { in }$. 
C)  $\frac { x + 11 } { x + 5 } i n$. 
D)  $x + 6$ in. 
A)  $\frac { 2 x + 11 } { x + 5 } i n$. 
B)  $\frac { 4 x + 11 } { x + 5 } \mathrm { in }$. 
C)  $\frac { x + 11 } { x + 5 } i n$. 
D)  $x + 6$ in.

Question 7

Find the product and simplify.
-$\frac { x ^ { 2 } + x } { 7 } \cdot \frac { 56 } { x + 1 }$

Accepted Answer

A)  $\frac { 8 x ^ { 2 } + 8 x } { x + 1 }$ 
B)  $8 x ^ { 2 }$ 
C)  $\frac { x } { 8 }$ 
D)  $8 \mathrm { x }$ 
A)  $\frac { 8 x ^ { 2 } + 8 x } { x + 1 }$ 
B)  $8 x ^ { 2 }$ 
C)  $\frac { x } { 8 }$ 
D)  $8 \mathrm { x }$

Question 8

Simplify.
-$\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$

Accepted Answer

A)  1 
B)  $\frac { 16 } { x }$ 
C)  16 
D)  $\frac { \mathrm { x } } { 16 }$ 
A)  1 
B)  $\frac { 16 } { x }$ 
C)  16 
D)  $\frac { \mathrm { x } } { 16 }$

Question 9

Solve.
-On an architect's blueprint, 1 inch corresponds to 12 feet. Find the length of a wall represented by a line $4 \frac { 1 } { 4 }$ inches long on the blueprint. Round to the nearest tenth if necessary.

Accepted Answer

A)  $51 \mathrm { ft }$ 
B)  $28.2 \mathrm { ft }$ 
C)  $35.4 \mathrm { ft }$ 
D)  $4.2 \mathrm { ft }$ 
A)  $51 \mathrm { ft }$ 
B)  $28.2 \mathrm { ft }$ 
C)  $35.4 \mathrm { ft }$ 
D)  $4.2 \mathrm { ft }$

Question 10

Find the least common denominator (LCD).
-$\frac { 1 } { x ^ { 2 } + 4 x + 4 } , \frac { 1 } { x ^ { 2 } + 2 x }$

Accepted Answer

A)  $x ( x + 2 )$ 
B)  $x ( x + 2 ) ^ { 2 }$ 
C)  $( x + 2 ) ^ { 2 }$ 
D)  $x ( x + 1 ) ( x + 2 )$ 
A)  $x ( x + 2 )$ 
B)  $x ( x + 2 ) ^ { 2 }$ 
C)  $( x + 2 ) ^ { 2 }$ 
D)  $x ( x + 1 ) ( x + 2 )$

Question 11

Perform the indicated operation. Simplify if possible.
-$\frac { 3 } { y ^ { 2 } - 3 y + 2 } + \frac { 7 } { y ^ { 2 } - 1 }$

Accepted Answer

A)  $\frac { 42 y - 11 } { ( y - 1 ) ( y + 1 ) ( y - 2 ) }$ 
B)  $\frac { 10 y - 11 } { ( y - 1 ) ( y - 2 ) }$ 
C)  $\frac { 10 y - 11 } { ( y - 1 ) ( y + 1 ) ( y - 2 ) }$ 
D)  $\frac { 11 y - 10 } { ( y - 1 ) ( y + 1 ) ( y - 2 ) }$ 
A)  $\frac { 42 y - 11 } { ( y - 1 ) ( y + 1 ) ( y - 2 ) }$ 
B)  $\frac { 10 y - 11 } { ( y - 1 ) ( y - 2 ) }$ 
C)  $\frac { 10 y - 11 } { ( y - 1 ) ( y + 1 ) ( y - 2 ) }$ 
D)  $\frac { 11 y - 10 } { ( y - 1 ) ( y + 1 ) ( y - 2 ) }$

Question 12

Perform the indicated operation. Simplify if possible.
-$\frac { 3 y } { x ^ { 2 } - y ^ { 2 } } + \frac { 3 x } { y ^ { 2 } - x ^ { 2 } }$

Accepted Answer

A)  $\frac { y - x } { x ^ { 2 } - y ^ { 2 } }$ 
B)  $- \frac { 3 } { x + y }$ 
C)  $\frac { 3 } { x + y }$ 
D)  $\frac { 3 } { x - y }$ 
A)  $\frac { y - x } { x ^ { 2 } - y ^ { 2 } }$ 
B)  $- \frac { 3 } { x + y }$ 
C)  $\frac { 3 } { x + y }$ 
D)  $\frac { 3 } { x - y }$

Question 13

Simplify the expression.
-$\frac { - 2 x - 2 y } { x + y }$

Accepted Answer

A)  $- 2$ 
B)  $- \frac { 1 } { 2 }$ 
C)  2 
D)  $\frac { 1 } { 2 }$ 
A)  $- 2$ 
B)  $- \frac { 1 } { 2 }$ 
C)  2 
D)  $\frac { 1 } { 2 }$

Question 14

Find the product and simplify.
-$\frac { x ^ { 2 } + 10 x + 24 } { x ^ { 2 } + 8 x + 12 } \cdot \frac { x ^ { 2 } + 14 x + 48 } { x ^ { 2 } + 5 x + 4 }$

Accepted Answer

A)  $\frac { ( x + 1 ) ( x + 2 ) } { ( x + 8 ) ( x + 6 ) }$ 
B)  $\frac { ( x + 8 ) ( x + 6 ) } { ( x + 1 ) ( x + 2 ) }$ 
C)  $\frac { 527 } { 45 }$ 
D)  $\frac { ( x + 4 ) ^ { 2 } ( x + 1 ) } { ( x + 8 ) ( x + 6 ) ( x + 2 ) }$ 
A)  $\frac { ( x + 1 ) ( x + 2 ) } { ( x + 8 ) ( x + 6 ) }$ 
B)  $\frac { ( x + 8 ) ( x + 6 ) } { ( x + 1 ) ( x + 2 ) }$ 
C)  $\frac { 527 } { 45 }$ 
D)  $\frac { ( x + 4 ) ^ { 2 } ( x + 1 ) } { ( x + 8 ) ( x + 6 ) ( x + 2 ) }$

Question 15

Find the product and simplify.
-$\frac { ( z - w ) ^ { 2 } } { z + w } \cdot \frac { z } { z ^ { 2 } - z W }$

Accepted Answer

A)  $\frac { z + w } { z - w }$ 
B)  $\frac { z - w } { z + w }$ 
C)  $\frac { w } { z + w }$ 
D)  1 
A)  $\frac { z + w } { z - w }$ 
B)  $\frac { z - w } { z + w }$ 
C)  $\frac { w } { z + w }$ 
D)  1

Question 16

Solve the equation.
-$\frac { 2 } { x ^ { 2 } - 9 } = \frac { 8 } { x + 3 } - \frac { 3 } { x - 3 }$

Accepted Answer

A)  $- 7$ 
B)  no solution 
C)  7 
D)  35 
A)  $- 7$ 
B)  no solution 
C)  7 
D)  35

Question 17

$$\text { Find and simplify the difference quotient } \frac { f ( a + h ) - f ( a ) } { h } , h \neq 0 \text { for the given function. }$$
-$f ( x ) = \frac { 4 } { x }$

Accepted Answer

A)  $\frac { 4 } { a }$ 
B)  $\frac { - 1 } { 4 a ( a + h ) }$ 
C)  $\frac { - 4 } { a ( a + h ) }$ 
D)  $\frac { - 4 } { a }$ 
A)  $\frac { 4 } { a }$ 
B)  $\frac { - 1 } { 4 a ( a + h ) }$ 
C)  $\frac { - 4 } { a ( a + h ) }$ 
D)  $\frac { - 4 } { a }$

Question 18

Perform the indicated operations. Simplify if possible.
-$\frac { 8 } { x ^ { 2 } + 4 x } + \frac { 3 } { x } + \frac { 2 } { x + 4 }$

Accepted Answer

A)  $\frac { 6 } { x }$ 
B)  $\frac { 3 } { x }$ 
C)  $\frac { 2 } { x }$ 
D)  $\frac { 5 } { x }$ 
A)  $\frac { 6 } { x }$ 
B)  $\frac { 3 } { x }$ 
C)  $\frac { 2 } { x }$ 
D)  $\frac { 5 } { x }$

Question 19

Solve.
-It is recommended that there be at least 17 square feet of work space for every person in a conference room. A certain conference room is 18 feet by 18 feet. Find the maximum number of people the room can accommodate.

Accepted Answer

A)  20 people 
B)  39 people 
C)  29 people 
D)  19 people 
A)  20 people 
B)  39 people 
C)  29 people 
D)  19 people

Question 20

Solve.
-Two times the reciprocal of a number equals 48 times the reciprocal of 60 . Find the number.

Accepted Answer

A)  $\frac { 5 } { 2 }$ 
B)  120 
C)  14 
D)  $\frac { 8 } { 5 }$ 
A)  $\frac { 5 } { 2 }$ 
B)  120 
C)  14 
D)  $\frac { 8 } { 5 }$

Solve the proportion. - $\frac { x } { 22 } = \frac { 5 } { 11 }$

Solve the equation. - $\frac { x } { 4 } - \frac { x } { 9 } = 6$

Simplify. - $\frac { \frac { 6 } { 7 - x } + \frac { 7 } { x - 7 } } { \frac { 2 } { x } + \frac { 5 } { x - 7 } }$

Find the quotient and simplify. - $\frac { 6 x ^ { 4 } } { z ^ { 5 } } \div \frac { 9 x ^ { 4 } z ^ { 5 } } { 4 }$

Solve. -Find the perimeter of the trapezoid.

Find the product and simplify. - $\frac { x ^ { 2 } + x } { 7 } \cdot \frac { 56 } { x + 1 }$

Simplify. - $\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$

Solve. -On an architect's blueprint, 1 inch corresponds to 12 feet. Find the length of a wall represented by a line $4 \frac { 1 } { 4 }$ inches long on the blueprint. Round to the nearest tenth if necessary.

Find the least common denominator (LCD). - $\frac { 1 } { x ^ { 2 } + 4 x + 4 } , \frac { 1 } { x ^ { 2 } + 2 x }$

Perform the indicated operation. Simplify if possible. - $\frac { 3 } { y ^ { 2 } - 3 y + 2 } + \frac { 7 } { y ^ { 2 } - 1 }$

Perform the indicated operation. Simplify if possible. - $\frac { 3 y } { x ^ { 2 } - y ^ { 2 } } + \frac { 3 x } { y ^ { 2 } - x ^ { 2 } }$

Simplify the expression. - $\frac { - 2 x - 2 y } { x + y }$

Find the product and simplify. - $\frac { x ^ { 2 } + 10 x + 24 } { x ^ { 2 } + 8 x + 12 } \cdot \frac { x ^ { 2 } + 14 x + 48 } { x ^ { 2 } + 5 x + 4 }$

Find the product and simplify. - $\frac { ( z - w ) ^ { 2 } } { z + w } \cdot \frac { z } { z ^ { 2 } - z W }$

Solve the equation. - $\frac { 2 } { x ^ { 2 } - 9 } = \frac { 8 } { x + 3 } - \frac { 3 } { x - 3 }$

$\text { Find and simplify the difference quotient } \frac { f ( a + h ) - f ( a ) } { h } , h \neq 0 \text { for the given function. }$ - $f ( x ) = \frac { 4 } { x }$

Perform the indicated operations. Simplify if possible. - $\frac { 8 } { x ^ { 2 } + 4 x } + \frac { 3 } { x } + \frac { 2 } { x + 4 }$

Solve. -It is recommended that there be at least 17 square feet of work space for every person in a conference room. A certain conference room is 18 feet by 18 feet. Find the maximum number of people the room can accommodate.

Solve. -Two times the reciprocal of a number equals 48 times the reciprocal of 60 . Find the number.

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Rational Expressions

Solve the proportion. - x22=511\frac { x } { 22 } = \frac { 5 } { 11 }22x​=115​

Solve the equation. - x4−x9=6\frac { x } { 4 } - \frac { x } { 9 } = 64x​−9x​=6

Simplify. - 67−x+7x−72x+5x−7\frac { \frac { 6 } { 7 - x } + \frac { 7 } { x - 7 } } { \frac { 2 } { x } + \frac { 5 } { x - 7 } }x2​+x−75​7−x6​+x−77​​

Find the quotient and simplify. - 6x4z5÷9x4z54\frac { 6 x ^ { 4 } } { z ^ { 5 } } \div \frac { 9 x ^ { 4 } z ^ { 5 } } { 4 }z56x4​÷49x4z5​