Question 1

Factor by any method.
-$$x ^ { 3 } - 8$$

Accepted Answer

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

Question 2

Simplify the expression.
-$\sqrt { ( - 4 ) ^ { 2 } }$

Accepted Answer

A)  2 
B)  4 
C)  $- 4$ 
D)  $- 2$ 
A)  2 
B)  4 
C)  $- 4$ 
D)  $- 2$

Question 3

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$\frac { 25 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 125 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 625 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$

Accepted Answer

A)  $\frac { 1 + 5 x ^ { 3 } - 15 x } { 25 }$ 
B)  $\frac { 1 - 5 x ^ { 3 } - 15 x } { 125 }$ 
C)  $\frac { 1 + 5 x ^ { 3 } + 15 x } { 25 }$ 
D)  $\frac { 1 - 5 x ^ { 3 } + 15 x } { 125 }$ 
A)  $\frac { 1 + 5 x ^ { 3 } - 15 x } { 25 }$ 
B)  $\frac { 1 - 5 x ^ { 3 } - 15 x } { 125 }$ 
C)  $\frac { 1 + 5 x ^ { 3 } + 15 x } { 25 }$ 
D)  $\frac { 1 - 5 x ^ { 3 } + 15 x } { 125 }$

Question 4

Find the distance between two points given their coordinates.
-Find the distance between points $\mathrm { P }$ and $\mathrm { Q }$ on a number line, with coordinates 5 and 12 , respectively.

Accepted Answer

A)  $d ( P , Q ) = - 7$ 
B)  $d ( P , Q ) = 7$ 
C)  $d ( P , Q ) = - 17$ 
D)  $d ( P , Q ) = 17$ 
A)  $d ( P , Q ) = - 7$ 
B)  $d ( P , Q ) = 7$ 
C)  $d ( P , Q ) = - 17$ 
D)  $d ( P , Q ) = 17$

Question 5

Factor the trinomial, if possible.
-$$( x - 5 y ) ^ { 2 } + 4 ( x - 5 y ) + 4$$

Accepted Answer

A)  $( x + 5 y + 2 ) ^ { 2 }$ 
B)  $( x - 5 y - 2 ) ^ { 2 }$ 
C)  $( x - 5 y + 2 ) ^ { 2 }$ 
D)  $( x + 5 y - 2 ) ( x - 5 y + 2 )$ 
A)  $( x + 5 y + 2 ) ^ { 2 }$ 
B)  $( x - 5 y - 2 ) ^ { 2 }$ 
C)  $( x - 5 y + 2 ) ^ { 2 }$ 
D)  $( x + 5 y - 2 ) ( x - 5 y + 2 )$

Question 6

Factor by any method.
-$25 z ^ { 4 } + 5 z ^ { 2 } - 12$

Accepted Answer

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

Question 7

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$( - 3 x ) ^ { 3 }$$

Accepted Answer

A)  $9 x ^ { 3 }$ 
B)  $- 9 x$ 
C)  $27 x$ 
D)  $- 27 x ^ { 3 }$ 
A)  $9 x ^ { 3 }$ 
B)  $- 9 x$ 
C)  $27 x$ 
D)  $- 27 x ^ { 3 }$

Question 8

Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { m n ^ { - 1 } - n m ^ { - 1 } } { m ^ { 2 } - n ^ { 2 } }$$

Accepted Answer

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

Question 9

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { 64 \mathrm { k } ^ { 15 } }$$

Accepted Answer

A)  $4 \mathrm { k } ^ { 18 }$ 
B)  $64 \mathrm { k } ^ { 5 }$ 
C)  $- 4 \mathrm { k } ^ { 5 }$ 
D)  $4 \mathrm { k } ^ { 5 }$ 
A)  $4 \mathrm { k } ^ { 18 }$ 
B)  $64 \mathrm { k } ^ { 5 }$ 
C)  $- 4 \mathrm { k } ^ { 5 }$ 
D)  $4 \mathrm { k } ^ { 5 }$

Question 10

Solve the problem.
-During a certain football game, a player gained 94 yards rushing and -2 yards returning fumbles. Find his total yardage. Is this the same as the sum of the absolute values of the two categories?
Why or why not?

Accepted Answer

A)  92 yards; Yes, it is the same. 
B)  -92; yards; No, it is not the same because the sum of the absolute values is -96. 
C)  96 yards; No, it is not the same because the sum of the absolute values is 92 . 
D)  92 yards; No, it is not the same because the sum of the absolute values is 96. 
A)  92 yards; Yes, it is the same. 
B)  -92; yards; No, it is not the same because the sum of the absolute values is -96. 
C)  96 yards; No, it is not the same because the sum of the absolute values is 92 . 
D)  92 yards; No, it is not the same because the sum of the absolute values is 96.

Question 11

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$- \frac { x } { y } > 0$$

Accepted Answer

A)  x and y must be negative. 
B)  x and y must be positive. 
C)  x and y have the same sign. 
D)  x and y have different signs. 
A)  x and y must be negative. 
B)  x and y must be positive. 
C)  x and y have the same sign. 
D)  x and y have different signs.

Question 12

Solve the problem. 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 $C ( x ) = \frac { 300 } { x + 10 }$, what is the unit cost for 40 units?

Accepted Answer

A)  $\$ 7.50$ 
B)  $\$ - 2.50$ 
C)  $\$ 0.75$ 
D)  $\$ 6.00$ 
A)  $\$ 7.50$ 
B)  $\$ - 2.50$ 
C)  $\$ 0.75$ 
D)  $\$ 6.00$

Question 13

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\left( x ^ { - 7 } y ^ { 9 } \right) \left( x ^ { - 2 } y ^ { 7 } \right) ^ { - 1 }$$

Accepted Answer

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

Question 14

Factor by any method.
-$$81 x ^ { 2 } - 16$$

Accepted Answer

A)  $( 9 x - 4 ) ^ { 2 }$ 
B)  $( 9 x + 4 ) ^ { 2 }$ 
C)  $( 81 x + 1 ) ( x - 16 )$ 
D)  $( 9 x + 4 ) ( 9 x - 4 )$ 
A)  $( 9 x - 4 ) ^ { 2 }$ 
B)  $( 9 x + 4 ) ^ { 2 }$ 
C)  $( 81 x + 1 ) ( x - 16 )$ 
D)  $( 9 x + 4 ) ( 9 x - 4 )$

Question 15

Determine the degree of the polynomial.
-$6 a ^ { 2 } + 14 a ^ { 5 } - 9 a$

Accepted Answer

A)  5 
B)  8 
C)  3 
D)  7 
A)  5 
B)  8 
C)  3 
D)  7

Question 16

Factor out the greatest common factor. Simplify the factors, if possible.
-$7 \mathrm {~m} ( 9 - \mathrm { m } ) + 3 \mathrm { n } ( 9 - \mathrm { m } )$

Accepted Answer

A)  $7 ( \mathrm {~m} + \mathrm { n } ) ( 9 - \mathrm { m } )$ 
B)  $( 7 m + 3 n ) ( 9 - m )$ 
C)  $m ( 7 + 3 n ) ( 9 - m )$ 
D)  $( 7 m - 3 n ) ( 9 - m )$ 
A)  $7 ( \mathrm {~m} + \mathrm { n } ) ( 9 - \mathrm { m } )$ 
B)  $( 7 m + 3 n ) ( 9 - m )$ 
C)  $m ( 7 + 3 n ) ( 9 - m )$ 
D)  $( 7 m - 3 n ) ( 9 - m )$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 112 a ^ { 2 } b } { c ^ { 2 } } }$

Accepted Answer

A)  $\frac { 16 a \sqrt { 7 b } } { c }$ 
B)  $\frac { a \sqrt { 112 b } } { c }$ 
C)  $\frac { 4 \sqrt { 7 a ^ { 2 } b } } { c }$ 
D)  $\frac { 4 a \sqrt { 7 b } } { c }$ 
A)  $\frac { 16 a \sqrt { 7 b } } { c }$ 
B)  $\frac { a \sqrt { 112 b } } { c }$ 
C)  $\frac { 4 \sqrt { 7 a ^ { 2 } b } } { c }$ 
D)  $\frac { 4 a \sqrt { 7 b } } { c }$

Question 18

Factor the trinomial, if possible.
-$$9 x ^ { 2 } + 10 x y + y ^ { 2 }$$

Accepted Answer

A)  $( 9 x + y ) ( x + 9 y )$ 
B)  $( 9 x + y ) ( x + y )$ 
C)  prime 
D)  $( 9 x - y ) ( x - y )$ 
A)  $( 9 x + y ) ( x + 9 y )$ 
B)  $( 9 x + y ) ( x + y )$ 
C)  prime 
D)  $( 9 x - y ) ( x - y )$

Question 19

Calculate the value mentally.
-$0.1 ^ { 1 / 2 } \cdot 1000 ^ { 1 / 2 }$

Accepted Answer

A)  40 
B)  10 
C)  20 
D)  5 
A)  40 
B)  10 
C)  20 
D)  5

Question 20

Divide.
-$$\frac { y ^ { 2 } + 8 y + 16 } { y + 4 }$$

Accepted Answer

A)  $y + \frac { 4 } { y + 4 }$ 
B)  $\mathrm { y } - 4$ 
C)  $\mathrm { y } + 4$ 
D)  $\mathrm { y } ^ { 2 } + 4$ 
A)  $y + \frac { 4 } { y + 4 }$ 
B)  $\mathrm { y } - 4$ 
C)  $\mathrm { y } + 4$ 
D)  $\mathrm { y } ^ { 2 } + 4$

Factor by any method. - $x ^ { 3 } - 8$

Simplify the expression. - $\sqrt { ( - 4 ) ^ { 2 } }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. - $\frac { 25 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 125 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 625 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$

Find the distance between two points given their coordinates. -Find the distance between points $\mathrm { P }$ and $\mathrm { Q }$ on a number line, with coordinates 5 and 12 , respectively.

Factor the trinomial, if possible. - $( x - 5 y ) ^ { 2 } + 4 ( x - 5 y ) + 4$

Factor by any method. - $25 z ^ { 4 } + 5 z ^ { 2 } - 12$

Simplify the expression. Assume all variables represent nonzero real numbers. - $( - 3 x ) ^ { 3 }$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { m n ^ { - 1 } - n m ^ { - 1 } } { m ^ { 2 } - n ^ { 2 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 64 \mathrm { k } ^ { 15 } }$

Solve the problem. -During a certain football game, a player gained 94 yards rushing and -2 yards returning fumbles. Find his total yardage. Is this the same as the sum of the absolute values of the two categories? Why or why not?

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $- \frac { x } { y } > 0$

Solve the problem. 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 $C ( x ) = \frac { 300 } { x + 10 }$ , what is the unit cost for 40 units?

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\left( x ^ { - 7 } y ^ { 9 } \right) \left( x ^ { - 2 } y ^ { 7 } \right) ^ { - 1 }$

Factor by any method. - $81 x ^ { 2 } - 16$

Determine the degree of the polynomial. - $6 a ^ { 2 } + 14 a ^ { 5 } - 9 a$

Factor out the greatest common factor. Simplify the factors, if possible. - $7 \mathrm {~m} ( 9 - \mathrm { m } ) + 3 \mathrm { n } ( 9 - \mathrm { m } )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 112 a ^ { 2 } b } { c ^ { 2 } } }$

Factor the trinomial, if possible. - $9 x ^ { 2 } + 10 x y + y ^ { 2 }$

Calculate the value mentally. - $0.1 ^ { 1 / 2 } \cdot 1000 ^ { 1 / 2 }$

Divide. - $\frac { y ^ { 2 } + 8 y + 16 } { y + 4 }$

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

Filters

Exam 12: Review of Basic Concepts

Factor by any method. - x3−8x ^ { 3 } - 8x3−8

Simplify the expression. - (−4)2\sqrt { ( - 4 ) ^ { 2 } }(−4)2​

Find the distance between two points given their coordinates. -Find the distance between points P\mathrm { P }P and Q\mathrm { Q }Q on a number line, with coordinates 5 and 12 , respectively.

Factor the trinomial, if possible. - (x−5y)2+4(x−5y)+4( x - 5 y ) ^ { 2 } + 4 ( x - 5 y ) + 4(x−5y)2+4(x−5y)+4

Factor by any method. - 25z4+5z2−1225 z ^ { 4 } + 5 z ^ { 2 } - 1225z4+5z2−12

Simplify the expression. Assume all variables represent nonzero real numbers. - (−3x)3( - 3 x ) ^ { 3 }(−3x)3

Perform the indicated operation and write your answer with positive integer exponents. - mn−1−nm−1m2−n2\frac { m n ^ { - 1 } - n m ^ { - 1 } } { m ^ { 2 } - n ^ { 2 } }m2−n2mn−1−nm−1​

Simplify the expression. Assume all variables represent positive real numbers. - 64k153\sqrt [ 3 ] { 64 \mathrm { k } ^ { 15 } }364k15​