Question 1

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 14 s ^ { 5 } + 9 s + 8$

Accepted Answer

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

Question 2

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$6 x ^ { 3 } + 9 w ^ { 2 } + 3 w - 4 y ^ { 4 } - 2$

Accepted Answer

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

Question 3

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 4 + \frac { 2 } { x } } { \frac { x } { 3 } + \frac { 1 } { 6 } }$$

Accepted Answer

A)  $\frac { 12 } { x }$ 
B)  12 
C)  $\frac { x } { 12 }$ 
D)  1 
A)  $\frac { 12 } { x }$ 
B)  12 
C)  $\frac { x } { 12 }$ 
D)  1

Question 4

Tell whether the statement is true or false.
-{8, 13, 11, 14} = {11, 8, 13}

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

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

Question 6

Simplify the expression. Assume all variables represent nonzero real numbers.
-$( 8 \mathrm { t } ) ^ { 5 }$

Accepted Answer

A)  $8 t ^ { 5 }$ 
B)  $40 t ^ { 5 }$ 
C)  $85 \mathrm { t } 5$ 
D)  $85 ^ { t }$ 
A)  $8 t ^ { 5 }$ 
B)  $40 t ^ { 5 }$ 
C)  $85 \mathrm { t } 5$ 
D)  $85 ^ { t }$

Question 7

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$x ^ { 2 } y < 0$

Accepted Answer

A)  x and y must be negative. 
B)  x must be negative. 
C)  y must be negative. 
D)  x and y have different signs. 
A)  x and y must be negative. 
B)  x must be negative. 
C)  y must be negative. 
D)  x and y have different signs.

Question 8

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\left( \frac { 2 } { 3 } \right) ^ { - 4 }$$

Accepted Answer

A)  $\frac { 81 } { 16 }$ 
B)  $\frac { 16 } { 81 }$ 
C)  $- \frac { 81 } { 16 }$ 
D)  $- \frac { 16 } { 81 }$ 
A)  $\frac { 81 } { 16 }$ 
B)  $\frac { 16 } { 81 }$ 
C)  $- \frac { 81 } { 16 }$ 
D)  $- \frac { 16 } { 81 }$

Question 9

Write the expression in lowest terms.
-$$\frac { 18 \mathrm { k } ^ { 2 } } { 15 \mathrm { k } }$$

Accepted Answer

A)  $\frac { 6 } { 5 } \mathrm { k }$ 
B)  $\frac { 9 } { 7 }$ 
C)  $\frac { 6 } { 5 }$ 
D)  $\frac { 9 } { 7 } \mathrm { k }$ 
A)  $\frac { 6 } { 5 } \mathrm { k }$ 
B)  $\frac { 9 } { 7 }$ 
C)  $\frac { 6 } { 5 }$ 
D)  $\frac { 9 } { 7 } \mathrm { k }$

Question 10

Find the product. Assume variables represent positive real numbers.
-$$\left( - 4 p ^ { 3 / 5 } - 9 p ^ { 4 / 5 } \right) ^ { 2 }$$

Accepted Answer

A)  $16 p ^ { 9 / 25} + 7 p$ 
B)  $- 8 p ^ { 6 / 5 } + 36 p ^ { - 18 / 5 } - 18 p ^ { 8 / 5 }$ 
C)  $16 p ^ { 6 / 5 } + 36 p ^ { 7 / 5 } + 81 p ^ { 8 / 5 }$ 
D)  $16 p ^ { 6 / 5 } + 72 p ^ { 7 / 5 } + 81 p ^ { 8 / 5 }$ 
A)  $16 p ^ { 9 / 25} + 7 p$ 
B)  $- 8 p ^ { 6 / 5 } + 36 p ^ { - 18 / 5 } - 18 p ^ { 8 / 5 }$ 
C)  $16 p ^ { 6 / 5 } + 36 p ^ { 7 / 5 } + 81 p ^ { 8 / 5 }$ 
D)  $16 p ^ { 6 / 5 } + 72 p ^ { 7 / 5 } + 81 p ^ { 8 / 5 }$

Question 11

Evaluate the expression.
-$- 4 \cdot 5 ^ { 2 }$

Accepted Answer

A)  -100 
B)  400 
C)  -400 
D)  100 
A)  -100 
B)  400 
C)  -400 
D)  100

Question 12

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 4,5,6,7,8,9,10,11,12,13,14 \} , \mathrm { M } = \{ 4,6,8,10 \} , \mathrm { N } = \{ 5,7,9,11,13 \} , \mathrm { Q } = \{ 4,6,8,10,12,14 \}$, and $R = \{ 4,5,6,7 \}$.

$( \mathrm { U } \cup \varnothing ) \cap \mathrm { R } ^ { \prime }$

Accepted Answer

A)  $\{ 8,9,10,11,12,13,14 \}$ 
B)  $\varnothing ; \mathrm { R } ^ { \prime }$ and $( \mathrm { U } \cup \varnothing )$ are disjoint sets. 
C)  R, or $\{ 4,5,6,7 \}$ 
D)  U, or $\{ 4,5,6,7,8,9,10,11,12,13,14 \}$ 
A)  $\{ 8,9,10,11,12,13,14 \}$ 
B)  $\varnothing ; \mathrm { R } ^ { \prime }$ and $( \mathrm { U } \cup \varnothing )$ are disjoint sets. 
C)  R, or $\{ 4,5,6,7 \}$ 
D)  U, or $\{ 4,5,6,7,8,9,10,11,12,13,14 \}$

Question 13

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }$$

Accepted Answer

A)  $10 \sqrt [ 3 ] { 15 }$ 
B)  $10 \sqrt [ 3 ] { 35 }$ 
C)  $5 \sqrt [ 3 ] { 35 }$ 
D)  $5 \sqrt [ 3 ] { 25 }$ 
A)  $10 \sqrt [ 3 ] { 15 }$ 
B)  $10 \sqrt [ 3 ] { 35 }$ 
C)  $5 \sqrt [ 3 ] { 35 }$ 
D)  $5 \sqrt [ 3 ] { 25 }$

Question 14

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-Use the formula $$\text { Passing Rating } \approx 85.68 \left( \frac { \mathrm { C } } { \mathrm { A } } \right) + 4.31 \left( \frac { \mathrm { Y } } { \mathrm { A } } \right) + 326.42 \left( \frac { \mathrm { T } } { \mathrm { A } } \right) - 419.06 \left( \frac { \mathrm { I } } { \mathrm { A } } \right) \text {, where } \mathrm { A } = \text { number of passes }$$ attempted, C= number of passes completed, Y = total number of yards gained passing, T = number of touchdown passes, and I = number of interceptions, to approximate the passing rating for C. Felix.
Round to the nearest tenth. $$\begin{array} { l r r r r c } 
\hline \text { Quarterback } & \text { A } & \text { C } & \text { Y } & \text { T } & \text { I } \
\hline \text { A. Smith } & 438 & 237 & 3062 & 21 & 7 \
\text { B. Jones } & 477 & 270 & 3157 & 25 & 10 \
\text { C. Felix } & 696 & 342 & 4331 & 24 & 15 \
\hline
\end{array}$$

Accepted Answer

A)  85.3 
B)  71.1 
C)  71.4 
D)  85.4 
A)  85.3 
B)  71.1 
C)  71.4 
D)  85.4

Question 15

Evaluate the expression.
-$$\left( - \frac { 1 } { 64 } \right) ^ { - 2 / 3 }$$

Accepted Answer

A)  262,144 
B)  $\frac { 1 } { 16 }$ 
C)  16 
D)  not a real number 
A)  262,144 
B)  $\frac { 1 } { 16 }$ 
C)  16 
D)  not a real number

Question 16

Evaluate the expression for x = -2, y = 3, and a = -4.
-$5 x - 6 y - 3 a$

Accepted Answer

A)  -32 
B)  39 
C)  5 
D)  -16 
A)  -32 
B)  39 
C)  5 
D)  -16

Question 17

Factor by any method.
-$$125 a ^ { 3 } - 27 b ^ { 3 }$$

Accepted Answer

A)  $( 5 a - 3 b ) \left( 25 a ^ { 2 } + 15 a b + 9 b ^ { 2 } \right)$ 
B)  $( 125 a - 3 b ) \left( a ^ { 2 } + 15 a b + 9 b ^ { 2 } \right)$ 
C)  $\left( 5 a + 3 b ^ { 2 } \right) \left( 25 a ^ { 2 } - 15 a b + 9 b ^ { 2 } \right)$ 
D)  $( 5 a - 3 b ) \left( 25 a ^ { 2 } + 9 b ^ { 2 } \right)$ 
A)  $( 5 a - 3 b ) \left( 25 a ^ { 2 } + 15 a b + 9 b ^ { 2 } \right)$ 
B)  $( 125 a - 3 b ) \left( a ^ { 2 } + 15 a b + 9 b ^ { 2 } \right)$ 
C)  $\left( 5 a + 3 b ^ { 2 } \right) \left( 25 a ^ { 2 } - 15 a b + 9 b ^ { 2 } \right)$ 
D)  $( 5 a - 3 b ) \left( 25 a ^ { 2 } + 9 b ^ { 2 } \right)$

Question 18

Solve the problem.
-$$( r - 15 ) ^ { 2 }$$

Accepted Answer

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

Question 19

Find the product.
-$$8 x ^ { 2 } \left( 3 x ^ { 5 } + 7 x ^ { 3 } \right)$$

Accepted Answer

A)  $24 x ^ { 7 } - 56 x ^ { 5 }$ 
B)  $24 x ^ { 10 } + 56 x ^ { 6 }$ 
C)  $24 x ^ { 7 } + 56 x ^ { 5 }$ 
D)  $24 x ^ { 7 } + 7 x ^ { 3 }$ 
A)  $24 x ^ { 7 } - 56 x ^ { 5 }$ 
B)  $24 x ^ { 10 } + 56 x ^ { 6 }$ 
C)  $24 x ^ { 7 } + 56 x ^ { 5 }$ 
D)  $24 x ^ { 7 } + 7 x ^ { 3 }$

Question 20

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

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 14 s ^ { 5 } + 9 s + 8$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $6 x ^ { 3 } + 9 w ^ { 2 } + 3 w - 4 y ^ { 4 } - 2$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 4 + \frac { 2 } { x } } { \frac { x } { 3 } + \frac { 1 } { 6 } }$

Tell whether the statement is true or false. -{8, 13, 11, 14} = {11, 8, 13}

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

Simplify the expression. Assume all variables represent nonzero real numbers. - $( 8 \mathrm { t } ) ^ { 5 }$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $x ^ { 2 } y < 0$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\left( \frac { 2 } { 3 } \right) ^ { - 4 }$

Write the expression in lowest terms. - $\frac { 18 \mathrm { k } ^ { 2 } } { 15 \mathrm { k } }$

Find the product. Assume variables represent positive real numbers. - $\left( - 4 p ^ { 3 / 5 } - 9 p ^ { 4 / 5 } \right) ^ { 2 }$

Evaluate the expression. - $- 4 \cdot 5 ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }$

Evaluate the expression. - $\left( - \frac { 1 } { 64 } \right) ^ { - 2 / 3 }$

Evaluate the expression for x = -2, y = 3, and a = -4. - $5 x - 6 y - 3 a$

Factor by any method. - $125 a ^ { 3 } - 27 b ^ { 3 }$

Solve the problem. - $( r - 15 ) ^ { 2 }$

Find the product. - $8 x ^ { 2 } \left( 3 x ^ { 5 } + 7 x ^ { 3 } \right)$

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

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

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Exam 1: Review of Basic Concepts

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - −14s5+9s+8- 14 s ^ { 5 } + 9 s + 8−14s5+9s+8

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - 6x3+9w2+3w−4y4−26 x ^ { 3 } + 9 w ^ { 2 } + 3 w - 4 y ^ { 4 } - 26x3+9w2+3w−4y4−2

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 4+2xx3+16\frac { 4 + \frac { 2 } { x } } { \frac { x } { 3 } + \frac { 1 } { 6 } }3x​+61​4+x2​​

Tell whether the statement is true or false. -{8, 13, 11, 14} = {11, 8, 13}

Factor by any method. - x6−1x ^ { 6 } - 1x6−1

Simplify the expression. Assume all variables represent nonzero real numbers. - (8t)5( 8 \mathrm { t } ) ^ { 5 }(8t)5

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - x2y<0x ^ { 2 } y < 0x2y<0

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (23)−4\left( \frac { 2 } { 3 } \right) ^ { - 4 }(32​)−4

Write the expression in lowest terms. - 18k215k\frac { 18 \mathrm { k } ^ { 2 } } { 15 \mathrm { k } }15k18k2​

Find the product. Assume variables represent positive real numbers. - (−4p3/5−9p4/5)2\left( - 4 p ^ { 3 / 5 } - 9 p ^ { 4 / 5 } \right) ^ { 2 }(−4p3/5−9p4/5)2

Evaluate the expression. - −4⋅52- 4 \cdot 5 ^ { 2 }−4⋅52

Simplify the expression. Assume all variables represent positive real numbers. - 1753⋅253\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }3175​⋅325​

Evaluate the expression. - (−164)−2/3\left( - \frac { 1 } { 64 } \right) ^ { - 2 / 3 }(−641​)−2/3

Evaluate the expression for x = -2, y = 3, and a = -4. - 5x−6y−3a5 x - 6 y - 3 a5x−6y−3a

Factor by any method. - 125a3−27b3125 a ^ { 3 } - 27 b ^ { 3 }125a3−27b3

Solve the problem. - (r−15)2( r - 15 ) ^ { 2 }(r−15)2

Find the product. - 8x2(3x5+7x3)8 x ^ { 2 } \left( 3 x ^ { 5 } + 7 x ^ { 3 } \right)8x2(3x5+7x3)

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