Question 1

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true.
-

Accepted Answer

A) $  \notin$ 
B)  $\in$ 
A) $  \notin$ 
B)  $\in$ B

Question 2

Identify the expression as a polynomial or not a polynomial.
-$15 x - 3$

Accepted Answer

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

Question 3

Evaluate the expression.
-Let $x = 9 , y = - 2$. Evaluate $4 | x | + 5 | y |$.

Accepted Answer

A)  26 
B)  $- 26$ 
C)  46 
D)  $- 46$ 
A)  26 
B)  $- 26$ 
C)  46 
D)  $- 46$ C

Question 4

Evaluate the expression for x $$x = - 2 , y = 3 , \text { and } a = - 4$$
-$$( - 5 x - 3 y ) ( - 8 a )$$

Accepted Answer

A)  $- 32$ 
B)  $- 288$ 
C)  32 
D)  140 
A)  $- 32$ 
B)  $- 288$ 
C)  32 
D)  140

Question 5

Find the distance between two points given their coordinates.
-Find the distance between points $R$ and $S$ on a number line, with coordinates $- 4$ and $- 7$, respectively.

Accepted Answer

A)  $d ( R , S ) = - 11$ 
B)  $d ( R , S ) = 11$ 
C)  $d ( R , S ) = 3$ 
D)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = - 3$ 
A)  $d ( R , S ) = - 11$ 
B)  $d ( R , S ) = 11$ 
C)  $d ( R , S ) = 3$ 
D)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = - 3$

Question 6

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

Question 7

Find the distance between two points given their coordinates.
-Find the distance between points P and Q on a number line, with coordinates 3 and 10, respectively.

Accepted Answer

A)  $d ( P , Q ) = - 13$ 
B)  $d ( P , Q ) = 13$ 
C)  $d ( P , Q ) = - 7$ 
D)  $d ( P , Q ) = 7$ 
A)  $d ( P , Q ) = - 13$ 
B)  $d ( P , Q ) = 13$ 
C)  $d ( P , Q ) = - 7$ 
D)  $d ( P , Q ) = 7$

Question 8

Find the sum or difference.
-16y4 + 24y3 + 6y - 1 4y2 + 1

Accepted Answer

A)  4y2 + 6y - 1 
B)  4y2 - 1 
C)  4y2 + 6y 
D)  4y2 - 6y + 1 
A)  4y2 + 6y - 1 
B)  4y2 - 1 
C)  4y2 + 6y 
D)  4y2 - 6y + 1

Question 9

Find the sum or difference.
-$$( 3 x - 6 y ) ( 5 x + 9 y + 1 )$$

Accepted Answer

A)  $15 x ^ { 2 } - 3 x y - 3 y ^ { 2 }$ 
B)  $15 x ^ { 2 } - 3 x y + 3 x - 54 y ^ { 2 } - 6 y$ 
C)  $15 x ^ { 2 } + 27 x y + 3 x - 54 y ^ { 2 }$ 
D)  $15 x ^ { 2 } - 30 x y + 3 x - 54 y ^ { 2 } - 6 y$ 
A)  $15 x ^ { 2 } - 3 x y - 3 y ^ { 2 }$ 
B)  $15 x ^ { 2 } - 3 x y + 3 x - 54 y ^ { 2 } - 6 y$ 
C)  $15 x ^ { 2 } + 27 x y + 3 x - 54 y ^ { 2 }$ 
D)  $15 x ^ { 2 } - 30 x y + 3 x - 54 y ^ { 2 } - 6 y$

Question 10

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$\left( 2 a ^ { 6 } b ^ { 8 } \right) \left( - 4 a ^ { 7 } b ^ { 4 } \right)$$

Accepted Answer

A)  $8 \ a ^{13}b^{13}$ 
B)  $- 8 a ^ { 42 } b ^ { 8 }$ 
C)  $8 a ^ { 41 } b ^ { 8 }$ 
D)  $- 8 \mathrm { a } ^ { 13 } \mathrm {~b} ^ { 12 }$ 
A)  $8 \ a ^{13}b^{13}$ 
B)  $- 8 a ^ { 42 } b ^ { 8 }$ 
C)  $8 a ^ { 41 } b ^ { 8 }$ 
D)  $- 8 \mathrm { a } ^ { 13 } \mathrm {~b} ^ { 12 }$

Question 11

Factor by any method.
-$4 x ^ { 2 } - 4 y ^ { 2 }$

Accepted Answer

A)  $4 ( x + y ) ( x - y )$ 
B)  $( 2 x + y ) ( 2 x - y )$ 
C)  $2 ( x + y ) ( x - y )$ 
D)  $4 ( x - y ) ^ { 2 }$ 
A)  $4 ( x + y ) ( x - y )$ 
B)  $( 2 x + y ) ( 2 x - y )$ 
C)  $2 ( x + y ) ( x - y )$ 
D)  $4 ( x - y ) ^ { 2 }$

Question 12

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-The radius of a right circular cone is given by the formula $r = \sqrt { \frac { 3 V } { \pi h } }$, where $V$ is the volume and $h$ is the height. If the volume is 552 cubic inches and the height is 13 inches, what is the radius? Use $3.14$ for $\pi$, and round your answer to the nearest tenth of an inch.

Accepted Answer

A)  0.2 in. 
B)  6.4 in. 
C)  3.7 in. 
D)  6.7 in. 
A)  0.2 in. 
B)  6.4 in. 
C)  3.7 in. 
D)  6.7 in.

Question 13

Factor by any method.
-$$x ^ { 3 } - 64$$

Accepted Answer

A)  $( x + 4 ) \left( x ^ { 2 } - 4 x + 16 \right)$ 
B)  $( x - 4 ) \left( x ^ { 2 } + 16 \right)$ 
C)  $( x - 4 ) \left( x ^ { 2 } + 4 x + 16 \right)$ 
D)  $( x + 64 ) \left( x ^ { 2 } - 1 \right)$ 
A)  $( x + 4 ) \left( x ^ { 2 } - 4 x + 16 \right)$ 
B)  $( x - 4 ) \left( x ^ { 2 } + 16 \right)$ 
C)  $( x - 4 ) \left( x ^ { 2 } + 4 x + 16 \right)$ 
D)  $( x + 64 ) \left( x ^ { 2 } - 1 \right)$

Question 14

Find the sum or difference.
-$\frac { 40 x ^ { 7 } + 25 x ^ { 6 } + 10 x ^ { 5 } } { 5 x ^ { 6 } }$

Accepted Answer

A)  $8 x + 5 + \frac { 2 } { x }$ 
B)  $8 x + 25 x ^ { 6 } + \frac { 2 } { x }$ 
C)  $8 x + 5$ 
D)  $10 x + 5$ 
A)  $8 x + 5 + \frac { 2 } { x }$ 
B)  $8 x + 25 x ^ { 6 } + \frac { 2 } { x }$ 
C)  $8 x + 5$ 
D)  $10 x + 5$

Question 15

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { - 4 } { \sqrt [ 3 ] { 2 } } + \frac { 33 } { \sqrt [ 3 ] { 16 } } - \frac { 1 } { \sqrt [ 3 ] { 54 } }$$

Accepted Answer

A)  $\frac { 73 } { 12 } \sqrt [ 3 ] { 4 }$ 
B)  $\frac { 73 } { 4 } \sqrt [ 3 ] { 2 }$ 
C)  $\frac { 19 } { 3 } \sqrt [ 3 ] { 4 }$ 
D)  $\frac { 35 } { 4 } \sqrt [ 3 ] { 2 }$ 
A)  $\frac { 73 } { 12 } \sqrt [ 3 ] { 4 }$ 
B)  $\frac { 73 } { 4 } \sqrt [ 3 ] { 2 }$ 
C)  $\frac { 19 } { 3 } \sqrt [ 3 ] { 4 }$ 
D)  $\frac { 35 } { 4 } \sqrt [ 3 ] { 2 }$

Question 16

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

Accepted Answer

A)  $\frac { 5 ^ { 3 } } { x ^ { 2 } }$ 
B)  $\frac { 1 } { 5 ^ { - 15 } x ^ { 24 } }$ 
C)  $5 ^ { 3 } x ^ { 135 }$ 
D)  $\frac { 5 ^ { 3 } } { x ^ { 24 } }$ 
A)  $\frac { 5 ^ { 3 } } { x ^ { 2 } }$ 
B)  $\frac { 1 } { 5 ^ { - 15 } x ^ { 24 } }$ 
C)  $5 ^ { 3 } x ^ { 135 }$ 
D)  $\frac { 5 ^ { 3 } } { x ^ { 24 } }$

Question 17

Find the sum or difference.
-$$( r - 15 ) ^ { 2 }$$

Accepted Answer

A)  $225 r ^ { 2 } - 30 r + 225$ 
B)  $r ^ { 2 } + 225$ 
C)  $r ^ { 2 } - 30 r + 225$ 
D)  $r + 225$ 
A)  $225 r ^ { 2 } - 30 r + 225$ 
B)  $r ^ { 2 } + 225$ 
C)  $r ^ { 2 } - 30 r + 225$ 
D)  $r + 225$

Question 18

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { a \sqrt { x } - 2 } { a \sqrt { x } + 2 }$

Accepted Answer

A)  $\frac { a ^ { 2 } x - 4 a \sqrt { x } + 4 } { a ^ { 2 } x + 4 }$ 
B)  $\frac { a ^ { 2 } x - 4 a \sqrt { x } - 4 } { a ^ { 2 } x + 4 }$ 
C)  $\frac { a ^ { 2 } x + 4 a \sqrt { x } - 4 } { a ^ { 2 } x - 4 }$ 
D)  $\frac { a ^ { 2 } x - 4 a \sqrt { x } + 4 } { a ^ { 2 } x - 4 }$ 
A)  $\frac { a ^ { 2 } x - 4 a \sqrt { x } + 4 } { a ^ { 2 } x + 4 }$ 
B)  $\frac { a ^ { 2 } x - 4 a \sqrt { x } - 4 } { a ^ { 2 } x + 4 }$ 
C)  $\frac { a ^ { 2 } x + 4 a \sqrt { x } - 4 } { a ^ { 2 } x - 4 }$ 
D)  $\frac { a ^ { 2 } x - 4 a \sqrt { x } + 4 } { a ^ { 2 } x - 4 }$

Question 19

Evaluate the expression.
-Let $x = 2 , y = 5$. Evaluate $| 6 x - 7 y |$.

Accepted Answer

A)  $- 47$ 
B)  23 
C)  47 
D)  $- 23$ 
A)  $- 47$ 
B)  23 
C)  47 
D)  $- 23$

Question 20

Simplify the expression. Assume all variables represent positive real numbers.
-$$8 \sqrt [ 5 ] { m ^ { 11 } p ^ { 7 } } - 2 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$$

Accepted Answer

A)  cannot be simplified 
B)  $6 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$ 
C)  $10 \mathrm { mp } ^ { 2 } \sqrt [ 5 ] { \mathrm { mp } ^ { 2 } }$ 
D)  6 
A)  cannot be simplified 
B)  $6 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$ 
C)  $10 \mathrm { mp } ^ { 2 } \sqrt [ 5 ] { \mathrm { mp } ^ { 2 } }$ 
D)  6

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true. - $Insert \in \mathbf { O r } \notin in the blank to make the statement is true. -$

Identify the expression as a polynomial or not a polynomial. - $15 x - 3$

Evaluate the expression. -Let $x = 9 , y = - 2$ . Evaluate $4 | x | + 5 | y |$ .

Evaluate the expression for x $x = - 2 , y = 3 , \text { and } a = - 4$ - $( - 5 x - 3 y ) ( - 8 a )$

Find the distance between two points given their coordinates. -Find the distance between points $R$ and $S$ on a number line, with coordinates $- 4$ and $- 7$ , respectively.

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

Find the distance between two points given their coordinates. -Find the distance between points P and Q on a number line, with coordinates 3 and 10, respectively.

Find the sum or difference. -16y4 + 24y3 + 6y - 1 4y2 + 1

Find the sum or difference. - $( 3 x - 6 y ) ( 5 x + 9 y + 1 )$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 2 a ^ { 6 } b ^ { 8 } \right) \left( - 4 a ^ { 7 } b ^ { 4 } \right)$

Factor by any method. - $4 x ^ { 2 } - 4 y ^ { 2 }$

Factor by any method. - $x ^ { 3 } - 64$

Find the sum or difference. - $\frac { 40 x ^ { 7 } + 25 x ^ { 6 } + 10 x ^ { 5 } } { 5 x ^ { 6 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { - 4 } { \sqrt [ 3 ] { 2 } } + \frac { 33 } { \sqrt [ 3 ] { 16 } } - \frac { 1 } { \sqrt [ 3 ] { 54 } }$

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

Find the sum or difference. - $( r - 15 ) ^ { 2 }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { a \sqrt { x } - 2 } { a \sqrt { x } + 2 }$

Evaluate the expression. -Let $x = 2 , y = 5$ . Evaluate $| 6 x - 7 y |$ .

Simplify the expression. Assume all variables represent positive real numbers. - $8 \sqrt [ 5 ] { m ^ { 11 } p ^ { 7 } } - 2 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$

Equations and Inequalities

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Arithmetic Sequence: Common Difference and First n Terms

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Exam 1: Review of Basic Concepts

Insert ∈Or∉\in \mathbf { O r } \notin∈Or∈/ in the blank to make the statement is true. -

Identify the expression as a polynomial or not a polynomial. - 15x−315 x - 315x−3

Evaluate the expression. -Let x=9,y=−2x = 9 , y = - 2x=9,y=−2 . Evaluate 4∣x∣+5∣y∣4 | x | + 5 | y |4∣x∣+5∣y∣ .

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 - (−5x−3y)(−8a)( - 5 x - 3 y ) ( - 8 a )(−5x−3y)(−8a)

Find the distance between two points given their coordinates. -Find the distance between points RRR and SSS on a number line, with coordinates −4- 4−4 and −7- 7−7 , respectively.

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