Question 1

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$\frac { x ^ { 3 } } { y } > 0$

Accepted Answer

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

Question 2

Evaluate the expression.
-$- 3 ^ { 5 }$

Accepted Answer

A)  -243 
B)  243 
C)  15 
D)  -15 
A)  -243 
B)  243 
C)  15 
D)  -15

Question 3

Simplify the expression. Assume all variables represent positive real numbers.
-$( \sqrt { 12 } + \sqrt { 10 } ) ( \sqrt { 12 } - \sqrt { 10 } )$

Accepted Answer

A)  22 
B)  2 
C)  $12 + 2 \sqrt { 120 }$ 
D)  $12 - 4 \sqrt { 60 }$ 
A)  22 
B)  2 
C)  $12 + 2 \sqrt { 120 }$ 
D)  $12 - 4 \sqrt { 60 }$

Question 4

Evaluate the expression.
-$( - 27 ) ^ { 1 / 3 }$

Accepted Answer

A)  -27 
B)  3 
C)  not a real number 
D)  -3 
A)  -27 
B)  3 
C)  not a real number 
D)  -3

Question 5

Factor by any method.
-$$a ^ { 6 } + 1$$

Accepted Answer

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

Question 6

Evaluate the expression.
-$14 + 24 \cdot 27 + 28$

Accepted Answer

A)  93 
B)  2090 
C)  690 
D)  1054 
A)  93 
B)  2090 
C)  690 
D)  1054

Question 7

Evaluate the expression.
-$\text { Let } x = - 18 , y = - 1 \text {. Evaluate } | 7 y - 9 x | \text {. }$

Accepted Answer

A)  -169 
B)  -155 
C)  169 
D)  155 
A)  -169 
B)  -155 
C)  169 
D)  155

Question 8

Solve the problem.
-$$[ ( 7 x - 2 ) + 2 y ] ^ { 2 }$$

Accepted Answer

A)  $49 x ^ { 2 } - 28 x + 28 x y - 8 y + 4 y ^ { 2 }$ 
B)  $49 x ^ { 2 } - 14 x + 4 + 14 x y + 4 y + 4 y ^ { 2 }$ 
C)  $49 x ^ { 2 } - 28 x + 4 + 14 x y + 4 y + 4 y ^ { 2 }$ 
D)  $49 x ^ { 2 } - 28 x + 4 + 28 x y - 8 y + 4 y ^ { 2 }$ 
A)  $49 x ^ { 2 } - 28 x + 28 x y - 8 y + 4 y ^ { 2 }$ 
B)  $49 x ^ { 2 } - 14 x + 4 + 14 x y + 4 y + 4 y ^ { 2 }$ 
C)  $49 x ^ { 2 } - 28 x + 4 + 14 x y + 4 y + 4 y ^ { 2 }$ 
D)  $49 x ^ { 2 } - 28 x + 4 + 28 x y - 8 y + 4 y ^ { 2 }$

Question 9

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-The NSC (Not So Consistent) Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss). $$\begin{array} { l r } 
\text { Month } & \text { Profit (Loss) in Dollars } \
\hline \text { January } & - 14,526 \
\text { February } & 1874 \
\text { March } & - 8977 \
\text { April } & - 14,107 \
\text { May } & 14,073 \
\text { June } & 14,632 \
\text { July } & - 13,834 \
\text { August } & - 13,170 \
\text { September } & - 4860 \
\text { October } & 6630 \
\text { November } & - 3338 \
\text { December } & - 974
\end{array}$$ The profit was greatest in

Accepted Answer

A)  January $\underline{ ? }$ 
B)  February 
C)  June 
D)  December 
A)  January $\underline{ ? }$ 
B)  February 
C)  June 
D)  December

Question 10

Find the product. Assume variables represent positive real numbers.
-$$y ^ { 1 / 3 } \left( y ^ { 4 / 9 } - 6 y ^ { 2 / 9 } \right)$$

Accepted Answer

A)  $y ^ { - 1 / 9 } - 6 y ^ { 1 / 9 }$ 
B)  $y ^ { 3 / 4 } - 6 y ^ { 3 / 2 }$ 
C)  $y ^ { 7 / 9 } - 6 y ^ { 5 / 9 }$ 
D)  $y ^ { 4 / 27 } - 6 y ^ { 2 / 27 }$ 
A)  $y ^ { - 1 / 9 } - 6 y ^ { 1 / 9 }$ 
B)  $y ^ { 3 / 4 } - 6 y ^ { 3 / 2 }$ 
C)  $y ^ { 7 / 9 } - 6 y ^ { 5 / 9 }$ 
D)  $y ^ { 4 / 27 } - 6 y ^ { 2 / 27 }$

Question 11

Find the domain of the expression.
-$$\frac { m - 9 } { 2 + m }$$

Accepted Answer

A)  all real numbers 
B)  $\{ \mathrm { m } \mid \mathrm { m } \neq - 2 \}$ 
C)  $\{ \mathrm { m } / \mathrm { m } \neq 2 \}$ 
D)  $\{ \mathrm { m } \mid \mathrm { m } \neq 9 \}$ 
A)  all real numbers 
B)  $\{ \mathrm { m } \mid \mathrm { m } \neq - 2 \}$ 
C)  $\{ \mathrm { m } / \mathrm { m } \neq 2 \}$ 
D)  $\{ \mathrm { m } \mid \mathrm { m } \neq 9 \}$

Question 12

Solve the problem.
-$\left( 2 x ^ { 3 } - x ^ { 2 } + 3 x - 1 \right) ( 2 x + 3 )$

Accepted Answer

A)  $5 x ^ { 4 } - 4 x ^ { 3 } + 2 x ^ { 2 } - 7 x + 3$ 
B)  $3 x ^ { 4 } + 8 x ^ { 3 } + 6 x ^ { 2 } + 9 x - 5$ 
C)  $4 x ^ { 3 } + 4 x ^ { 2 } + 3 x + 7$ 
D)  $4 x ^ { 4 } + 4 x ^ { 3 } + 3 x ^ { 2 } + 7 x - 3$ 
A)  $5 x ^ { 4 } - 4 x ^ { 3 } + 2 x ^ { 2 } - 7 x + 3$ 
B)  $3 x ^ { 4 } + 8 x ^ { 3 } + 6 x ^ { 2 } + 9 x - 5$ 
C)  $4 x ^ { 3 } + 4 x ^ { 2 } + 3 x + 7$ 
D)  $4 x ^ { 4 } + 4 x ^ { 3 } + 3 x ^ { 2 } + 7 x - 3$

Question 13

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$6 ^ { 5 } \cdot 6 ^ { 8 }$$

Accepted Answer

A)  $6^{13}$ 
B)  $36^{40}$ 
C)  $12^{13}$ 
D)  $6^{40}$ 
A)  $6^{13}$ 
B)  $36^{40}$ 
C)  $12^{13}$ 
D)  $6^{40}$

Question 14

Tell whether the statement is true or false.
-$\{ 1,3,4,6 \} \cap \varnothing = \{ 1,3,4,6 \}$

Accepted Answer

A) True 
 B)False

Question 15

Perform the indicated operations.
-$$\frac { 7 } { 2 r ^ { 2 } - 7 r s - 4 s ^ { 2 } } - \frac { 6 } { 6 r ^ { 2 } - 25 r s + 4 s ^ { 2 } } + \frac { 9 } { 12 r ^ { 2 } + 4 r s - s ^ { 2 } }$$

Accepted Answer

A)  $\frac { 39 r - 37 s } { ( 2 r + s ) ( r - 4 s ) ( 6 r - s ) }$ 
B)  $\frac { 63 r - 37 s } { ( 2 r + s ) ( r - 4 s ) ( 6 r - s ) }$ 
C)  $\frac { 63 r - 49 s } { ( 2 r + s ) ( r - 4 s ) ( 6 r - s ) }$ 
D)  $\frac { 39 r - 49 s } { ( 2 r + s ) ( r - 4 s ) ( 6 r - s ) }$ 
A)  $\frac { 39 r - 37 s } { ( 2 r + s ) ( r - 4 s ) ( 6 r - s ) }$ 
B)  $\frac { 63 r - 37 s } { ( 2 r + s ) ( r - 4 s ) ( 6 r - s ) }$ 
C)  $\frac { 63 r - 49 s } { ( 2 r + s ) ( r - 4 s ) ( 6 r - s ) }$ 
D)  $\frac { 39 r - 49 s } { ( 2 r + s ) ( r - 4 s ) ( 6 r - s ) }$

Question 16

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

Accepted Answer

A)  2 
B)  $- 12$ 
C)  $- 2$ 
D)  12 
A)  2 
B)  $- 12$ 
C)  $- 2$ 
D)  12

Question 17

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 8 y ^ { 9 } + 2$

Accepted Answer

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

Question 18

Factor by any method.
-$$( r + s ) ^ { 2 } - 16$$

Accepted Answer

A)  $( \mathrm { r } - \mathrm { s } + 4 ) ( \mathrm { r } - \mathrm { s } - 4 )$ 
B)  $( \mathrm { r } + \mathrm { s } + 4 ) ( \mathrm { r } + \mathrm { s } - 4 )$ 
C)  $\left( r ^ { 2 } + 4 \right) \left( s ^ { 2 } - 4 \right)$ 
D)  $( \mathrm { r } + \mathrm { s } + 4 ) ( \mathrm { r } - \mathrm { s } - 4 )$ 
A)  $( \mathrm { r } - \mathrm { s } + 4 ) ( \mathrm { r } - \mathrm { s } - 4 )$ 
B)  $( \mathrm { r } + \mathrm { s } + 4 ) ( \mathrm { r } + \mathrm { s } - 4 )$ 
C)  $\left( r ^ { 2 } + 4 \right) \left( s ^ { 2 } - 4 \right)$ 
D)  $( \mathrm { r } + \mathrm { s } + 4 ) ( \mathrm { r } - \mathrm { s } - 4 )$

Question 19

Find the domain of the expression.
-$$\frac { x ^ { 2 } - 9 } { x ^ { 2 } + 6 x + 8 }$$

Accepted Answer

A)  $\{ x \mid x \neq 0 \}$ 
B)  $\{ x \mid x \neq 3$ and $x \neq - 3 \}$ 
C)  $\{ x \mid x \neq 4$ and $x \neq 2 \}$ 
D)  $\{ x \mid x \neq - 4$ and $x \neq - 2 \}$ 
A)  $\{ x \mid x \neq 0 \}$ 
B)  $\{ x \mid x \neq 3$ and $x \neq - 3 \}$ 
C)  $\{ x \mid x \neq 4$ and $x \neq 2 \}$ 
D)  $\{ x \mid x \neq - 4$ and $x \neq - 2 \}$

Question 20

Find the product.
-$$\left( 4 m ^ { 4 } \right) \left( 4 m ^ { 4 } \right)$$

Accepted Answer

A)  $16 \mathrm {~m}$ 
B)  $- 16 \mathrm {~m}$ 
C)  $16 m ^ { 8 }$ 
D)  $- 16 m ^ { 8 }$ 
A)  $16 \mathrm {~m}$ 
B)  $- 16 \mathrm {~m}$ 
C)  $16 m ^ { 8 }$ 
D)  $- 16 m ^ { 8 }$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $\frac { x ^ { 3 } } { y } > 0$

Evaluate the expression. - $- 3 ^ { 5 }$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 12 } + \sqrt { 10 } ) ( \sqrt { 12 } - \sqrt { 10 } )$

Evaluate the expression. - $( - 27 ) ^ { 1 / 3 }$

Factor by any method. - $a ^ { 6 } + 1$

Evaluate the expression. - $14 + 24 \cdot 27 + 28$

Evaluate the expression. - $\text { Let } x = - 18 , y = - 1 \text {. Evaluate } | 7 y - 9 x | \text {. }$

Solve the problem. - $[ ( 7 x - 2 ) + 2 y ] ^ { 2 }$

Find the product. Assume variables represent positive real numbers. - $y ^ { 1 / 3 } \left( y ^ { 4 / 9 } - 6 y ^ { 2 / 9 } \right)$

Find the domain of the expression. - $\frac { m - 9 } { 2 + m }$

Solve the problem. - $\left( 2 x ^ { 3 } - x ^ { 2 } + 3 x - 1 \right) ( 2 x + 3 )$

Simplify the expression. Assume all variables represent nonzero real numbers. - $6 ^ { 5 } \cdot 6 ^ { 8 }$

Tell whether the statement is true or false. - $\{ 1,3,4,6 \} \cap \varnothing = \{ 1,3,4,6 \}$

Perform the indicated operations. - $\frac { 7 } { 2 r ^ { 2 } - 7 r s - 4 s ^ { 2 } } - \frac { 6 } { 6 r ^ { 2 } - 25 r s + 4 s ^ { 2 } } + \frac { 9 } { 12 r ^ { 2 } + 4 r s - s ^ { 2 } }$

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

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 8 y ^ { 9 } + 2$

Factor by any method. - $( r + s ) ^ { 2 } - 16$

Find the domain of the expression. - $\frac { x ^ { 2 } - 9 } { x ^ { 2 } + 6 x + 8 }$

Find the product. - $\left( 4 m ^ { 4 } \right) \left( 4 m ^ { 4 } \right)$

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Inverse, Exponential, and Logarithmic Functions

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Exam 1: Review of Basic Concepts

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - x3y>0\frac { x ^ { 3 } } { y } > 0yx3​>0

Evaluate the expression. - −35- 3 ^ { 5 }−35

Simplify the expression. Assume all variables represent positive real numbers. - (12+10)(12−10)( \sqrt { 12 } + \sqrt { 10 } ) ( \sqrt { 12 } - \sqrt { 10 } )(12​+10​)(12​−10​)

Evaluate the expression. - (−27)1/3( - 27 ) ^ { 1 / 3 }(−27)1/3

Factor by any method. - a6+1a ^ { 6 } + 1a6+1

Evaluate the expression. - 14+24⋅27+2814 + 24 \cdot 27 + 2814+24⋅27+28

Evaluate the expression. - Let x=−18,y=−1. Evaluate ∣7y−9x∣. \text { Let } x = - 18 , y = - 1 \text {. Evaluate } | 7 y - 9 x | \text {. } Let x=−18,y=−1. Evaluate ∣7y−9x∣.

Solve the problem. - [(7x−2)+2y]2[ ( 7 x - 2 ) + 2 y ] ^ { 2 }[(7x−2)+2y]2

Find the product. Assume variables represent positive real numbers. - y1/3(y4/9−6y2/9)y ^ { 1 / 3 } \left( y ^ { 4 / 9 } - 6 y ^ { 2 / 9 } \right)y1/3(y4/9−6y2/9)

Find the domain of the expression. - m−92+m\frac { m - 9 } { 2 + m }2+mm−9​

Solve the problem. - (2x3−x2+3x−1)(2x+3)\left( 2 x ^ { 3 } - x ^ { 2 } + 3 x - 1 \right) ( 2 x + 3 )(2x3−x2+3x−1)(2x+3)

Simplify the expression. Assume all variables represent nonzero real numbers. - 65⋅686 ^ { 5 } \cdot 6 ^ { 8 }65⋅68

Tell whether the statement is true or false. - {1,3,4,6}∩∅={1,3,4,6}\{ 1,3,4,6 \} \cap \varnothing = \{ 1,3,4,6 \}{1,3,4,6}∩∅={1,3,4,6}

Perform the indicated operations. - 72r2−7rs−4s2−66r2−25rs+4s2+912r2+4rs−s2\frac { 7 } { 2 r ^ { 2 } - 7 r s - 4 s ^ { 2 } } - \frac { 6 } { 6 r ^ { 2 } - 25 r s + 4 s ^ { 2 } } + \frac { 9 } { 12 r ^ { 2 } + 4 r s - s ^ { 2 } }2r2−7rs−4s27​−6r2−25rs+4s26​+12r2+4rs−s29​

Evaluate the expression. -Let x=−5,y=7x = - 5 , y = 7x=−5,y=7 . Evaluate ∣x∣+∣y∣| x | + | y |∣x∣+∣y∣ .

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - −8y9+2- 8 y ^ { 9 } + 2−8y9+2

Factor by any method. - (r+s)2−16( r + s ) ^ { 2 } - 16(r+s)2−16

Find the domain of the expression. - x2−9x2+6x+8\frac { x ^ { 2 } - 9 } { x ^ { 2 } + 6 x + 8 }x2+6x+8x2−9​

Find the product. - (4m4)(4m4)\left( 4 m ^ { 4 } \right) \left( 4 m ^ { 4 } \right)(4m4)(4m4)