Question 1

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$| 7 - 12 | = | 12 | - | 7 |$$

Accepted Answer

A)  True 
B)  False; $| 7 - 12 | = | 7 | - | 12 |$ 
A)  True 
B)  False; $| 7 - 12 | = | 7 | - | 12 |$

Question 2

Write in radical form. Assume all variables represent positive real numbers.
-$( - 6 x ) ^ { 1 / 5 }$

Accepted Answer

A)  $\sqrt [ 5 ] { - 6 x }$ 
B)  $\frac { 1 } { \sqrt [ 5 ] { - 6 x } }$ 
C)  $\sqrt { - \frac { 6 x } { 5 } }$ 
D)  $\sqrt [ 1 / 5 ] { - 6 x }$ 
A)  $\sqrt [ 5 ] { - 6 x }$ 
B)  $\frac { 1 } { \sqrt [ 5 ] { - 6 x } }$ 
C)  $\sqrt { - \frac { 6 x } { 5 } }$ 
D)  $\sqrt [ 1 / 5 ] { - 6 x }$

Question 3

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$$\frac { \left( x ^ { 2 } + 1 \right) ^ { 4 } ( 4 x ) - x ^ { 2 } ( 16 ) \left( x ^ { 2 } + 1 \right) ^ { 3 } ( 4 x ) } { \left( x ^ { 2 } + 1 \right) ^ { 8 } }$$

Accepted Answer

A)  $\frac { ( 4 x ) \left( 1 + 15 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
B)  $\frac { ( 4 x ) \left( 1 - 15 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
C)  $\frac { ( 4 x ) \left( 1 - 17 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
D)  $\frac { ( 4 x ) \left( 1 + 17 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
A)  $\frac { ( 4 x ) \left( 1 + 15 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
B)  $\frac { ( 4 x ) \left( 1 - 15 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
C)  $\frac { ( 4 x ) \left( 1 - 17 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
D)  $\frac { ( 4 x ) \left( 1 + 17 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$

Question 4

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$13 x ^ { 2 }$

Accepted Answer

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

Question 5

Factor by any method.
-$$( q - 8 ) ^ { 2 } - 25$$

Accepted Answer

A)  $( q - 3 ) ( q - 13 )$ 
B)  $( q + 13 ) ( q - 13 )$ 
C)  $\left[ ( q - 8 ) ^ { 2 } + 5 \right] \left[ ( q - 8 ) ^ { 2 } - 5 \right]$ 
D)  $( q - 3 ) ^ { 2 }$ 
A)  $( q - 3 ) ( q - 13 )$ 
B)  $( q + 13 ) ( q - 13 )$ 
C)  $\left[ ( q - 8 ) ^ { 2 } + 5 \right] \left[ ( q - 8 ) ^ { 2 } - 5 \right]$ 
D)  $( q - 3 ) ^ { 2 }$

Question 6

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$$( 4 a + 7 b ) ( 7 a + 4 b )$$

Accepted Answer

A)  $28 a ^ { 2 } - 33 a b + 28 b ^ { 2 }$ 
B)  $28 a ^ { 2 } - 65 a b + 28 b ^ { 2 }$ 
C)  $28 a ^ { 2 } + 28 b ^ { 2 }$ 
D)  $28 a ^ { 2 } + 65 a b + 28 b ^ { 2 }$ 
A)  $28 a ^ { 2 } - 33 a b + 28 b ^ { 2 }$ 
B)  $28 a ^ { 2 } - 65 a b + 28 b ^ { 2 }$ 
C)  $28 a ^ { 2 } + 28 b ^ { 2 }$ 
D)  $28 a ^ { 2 } + 65 a b + 28 b ^ { 2 }$

Question 7

Simplify the expression. Assume all variables represent positive real numbers.
-$$3 \sqrt [ 5 ] { x ^ { 6 } y } - 2 x \sqrt [ 5 ] { x y }$$

Accepted Answer

A)  $( 3 - 2 x ) \sqrt [ 5 ] { x y }$ 
B)  $x \sqrt [ 5 ] { x y }$ 
C)  $2 x \sqrt [ 5 ] { x y }$ 
D)  cannot be simplified 
A)  $( 3 - 2 x ) \sqrt [ 5 ] { x y }$ 
B)  $x \sqrt [ 5 ] { x y }$ 
C)  $2 x \sqrt [ 5 ] { x y }$ 
D)  cannot be simplified

Question 8

Factor out the greatest common factor. Simplify the factors, if possible.
-$$( x - 3 ) ( x + 7 ) + ( x - 3 ) ( x + 9 )$$

Accepted Answer

A)  $( x - 3 ) ( x + 16 )$ 
B)  $2 ( x - 3 ) ( x + 8 )$ 
C)  $( x - 3 ) ( 2 x + 16 )$ 
D)  $2 ( x - 3 ) ( 2 x + 16 )$ 
A)  $( x - 3 ) ( x + 16 )$ 
B)  $2 ( x - 3 ) ( x + 8 )$ 
C)  $( x - 3 ) ( 2 x + 16 )$ 
D)  $2 ( x - 3 ) ( 2 x + 16 )$

Question 9

Find the sum or difference.
-$$- \left( 6 x ^ { 3 } + x - 7 \right) + \left( 8 x ^ { 3 } + 4 x ^ { 2 } \right) - \left( 9 x ^ { 2 } - 5 x - 1 \right)$$

Accepted Answer

A)  $1 x ^ { 3 } - 3 x ^ { 2 } - 4 x + 8$ 
B)  $2 x ^ { 3 } - 5 x ^ { 2 } + 4 x + 8$ 
C)  $14 x ^ { 3 } - 13 x ^ { 2 } + 4 x - 8$ 
D)  $2 x ^ { 3 } + 5 x ^ { 2 } + 6 x - 8$ 
A)  $1 x ^ { 3 } - 3 x ^ { 2 } - 4 x + 8$ 
B)  $2 x ^ { 3 } - 5 x ^ { 2 } + 4 x + 8$ 
C)  $14 x ^ { 3 } - 13 x ^ { 2 } + 4 x - 8$ 
D)  $2 x ^ { 3 } + 5 x ^ { 2 } + 6 x - 8$

Question 10

Find the domain of the expression.
-$$\frac { y } { y ^ { 2 } - 25 }$$

Accepted Answer

A)  $\{ y \mid y \neq 25$ and $y \neq - 25 \}$ 
B)  $\{ y \mid y \neq 0 \}$ 
C)  $\{ y \mid y \neq 625$ and $y \neq - 625 \}$ 
D)  $\{ y \mid y \neq 5$ and $y \neq - 5 \}$ 
A)  $\{ y \mid y \neq 25$ and $y \neq - 25 \}$ 
B)  $\{ y \mid y \neq 0 \}$ 
C)  $\{ y \mid y \neq 625$ and $y \neq - 625 \}$ 
D)  $\{ y \mid y \neq 5$ and $y \neq - 5 \}$

Question 11

Evaluate the expression for x = -2, y = 3, and a = -4.
-(-7x - 3y)(9a)

Accepted Answer

A)  -756 
B)  -180 
C)  540 
D)  180 
A)  -756 
B)  -180 
C)  540 
D)  180

Question 12

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-A stone is dropped from a tower that is 750 feet high. The formula $h = 750 - 16 t ^ { 2 }$ describes the stone's height above the ground, h, in feet, t seconds after it was dropped. What is the stone's height
5 seconds after it is released?

Accepted Answer

A)  325 ft 
B)  360 ft 
C)  350 ft 
D)  375 ft 
A)  325 ft 
B)  360 ft 
C)  350 ft 
D)  375 ft

Question 13

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { x ^ { 4 } } { x ^ { - 6 } }$$

Accepted Answer

A)  $\frac { 1 } { x ^ { 10 } }$ 
B)  $x ^ { 10 }$ 
C)  $\frac { 1 } { x ^ { 2 } }$ 
D)  $- x ^ { 2 }$ 
A)  $\frac { 1 } { x ^ { 10 } }$ 
B)  $x ^ { 10 }$ 
C)  $\frac { 1 } { x ^ { 2 } }$ 
D)  $- x ^ { 2 }$

Question 14

Factor the trinomial, if possible.
-$$3 x ^ { 3 } + 3 x ^ { 2 } y - 36 x y ^ { 2 }$$

Accepted Answer

A)  $\left( 3 x ^ { 2 } + 9 x y \right) ( x - 4 y )$ 
B)  $( x - 3 y ) \left( 3 x ^ { 2 } + 12 x y \right)$ 
C)  $3 x ( x + 3 y ) ( x - 4 y )$ 
D)  $3 x ( x - 3 y ) ( x + 4 y )$ 
A)  $\left( 3 x ^ { 2 } + 9 x y \right) ( x - 4 y )$ 
B)  $( x - 3 y ) \left( 3 x ^ { 2 } + 12 x y \right)$ 
C)  $3 x ( x + 3 y ) ( x - 4 y )$ 
D)  $3 x ( x - 3 y ) ( x + 4 y )$

Question 15

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
-$- 7 a x ^ { 3 } \left( - 10 a x ^ { 3 } + 5 x ^ { 2 } + 1 \right)$

Accepted Answer

A)  $70 a x ^ { 9 } - 35 a x ^ { 6 } - 7 a x ^ { 3 }$ 
B)  $- 70 a ^ { 2 } x ^ { 6 } + 35 a x ^ { 5 } + 7 a x ^ { 3 }$ 
C)  $70 a ^ { 2 } x ^ { 6 } - 35 a x ^ { 5 } - 7 a x ^ { 3 }$ 
D)  $- 70 a ^ { 2 } x ^ { 9 } + 35 a x ^ { 6 } + 7 a x ^ { 3 }$ 
A)  $70 a x ^ { 9 } - 35 a x ^ { 6 } - 7 a x ^ { 3 }$ 
B)  $- 70 a ^ { 2 } x ^ { 6 } + 35 a x ^ { 5 } + 7 a x ^ { 3 }$ 
C)  $70 a ^ { 2 } x ^ { 6 } - 35 a x ^ { 5 } - 7 a x ^ { 3 }$ 
D)  $- 70 a ^ { 2 } x ^ { 9 } + 35 a x ^ { 6 } + 7 a x ^ { 3 }$

Question 16

Write in radical form. Assume all variables represent positive real numbers.
-$( 6 x ) ^ { 1 / 5 }$

Accepted Answer

A)  $\sqrt [ 5 ] { 6 x }$ 
B)  $\sqrt [ 1 / 5 ] { 6 \mathrm { x } }$ 
C)  $\frac { \sqrt { 6 x } } { 5 }$ 
D)  $- \sqrt [ 5 ] { 6 x }$ 
A)  $\sqrt [ 5 ] { 6 x }$ 
B)  $\sqrt [ 1 / 5 ] { 6 \mathrm { x } }$ 
C)  $\frac { \sqrt { 6 x } } { 5 }$ 
D)  $- \sqrt [ 5 ] { 6 x }$

Question 17

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$$( x - 10 ) ( 4 x + 7 )$$

Accepted Answer

A)  $4 x ^ { 2 } - 35 x - 70$ 
B)  $4 x ^ { 2 } - 33 x - 70$ 
C)  $4 x ^ { 2 } - 33 x - 33$ 
D)  $4 x ^ { 2 } - 70 x - 33$ 
A)  $4 x ^ { 2 } - 35 x - 70$ 
B)  $4 x ^ { 2 } - 33 x - 70$ 
C)  $4 x ^ { 2 } - 33 x - 33$ 
D)  $4 x ^ { 2 } - 70 x - 33$

Question 18

Find the sum or difference.
-$\left( 4 - 3 x ^ { 2 } + 2 x ^ { 4 } + 8 x ^ { 3 } \right) + \left( - 2 x ^ { 3 } - 6 x ^ { 2 } - 9 + 3 x ^ { 4 } \right)$

Accepted Answer

A)  $5 x ^ { 4 } + 6 x ^ { 3 } - 9 x ^ { 2 } - 5$ 
B)  $2 x ^ { 4 } + 2 x ^ { 3 } - 7 x ^ { 2 } + 11$ 
C)  $2 x ^ { 18 } - 5$ 
D)  $5 x ^ { 8 } + 6 x ^ { 6 } - 9 x ^ { 4 } - 5$ 
A)  $5 x ^ { 4 } + 6 x ^ { 3 } - 9 x ^ { 2 } - 5$ 
B)  $2 x ^ { 4 } + 2 x ^ { 3 } - 7 x ^ { 2 } + 11$ 
C)  $2 x ^ { 18 } - 5$ 
D)  $5 x ^ { 8 } + 6 x ^ { 6 } - 9 x ^ { 4 } - 5$

Question 19

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-$$\frac { 1 } { ( a + 2 ) } \cdot ( a + 2 ) = 1 , \text { if } a + 2 \neq 0$$

Accepted Answer

A)  Distributive 
B)  Identity 
C)  Inverse 
D)  Closure 
A)  Distributive 
B)  Identity 
C)  Inverse 
D)  Closure

Question 20

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

Accepted Answer

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

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| 7 - 12 | = | 12 | - | 7 |$

Write in radical form. Assume all variables represent positive real numbers. - $( - 6 x ) ^ { 1 / 5 }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. - $\frac { \left( x ^ { 2 } + 1 \right) ^ { 4 } ( 4 x ) - x ^ { 2 } ( 16 ) \left( x ^ { 2 } + 1 \right) ^ { 3 } ( 4 x ) } { \left( x ^ { 2 } + 1 \right) ^ { 8 } }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $13 x ^ { 2 }$

Factor by any method. - $( q - 8 ) ^ { 2 } - 25$

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $( 4 a + 7 b ) ( 7 a + 4 b )$

Simplify the expression. Assume all variables represent positive real numbers. - $3 \sqrt [ 5 ] { x ^ { 6 } y } - 2 x \sqrt [ 5 ] { x y }$

Factor out the greatest common factor. Simplify the factors, if possible. - $( x - 3 ) ( x + 7 ) + ( x - 3 ) ( x + 9 )$

Find the sum or difference. - $- \left( 6 x ^ { 3 } + x - 7 \right) + \left( 8 x ^ { 3 } + 4 x ^ { 2 } \right) - \left( 9 x ^ { 2 } - 5 x - 1 \right)$

Find the domain of the expression. - $\frac { y } { y ^ { 2 } - 25 }$

Evaluate the expression for x = -2, y = 3, and a = -4. -(-7x - 3y)(9a)

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { 4 } } { x ^ { - 6 } }$

Factor the trinomial, if possible. - $3 x ^ { 3 } + 3 x ^ { 2 } y - 36 x y ^ { 2 }$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $- 7 a x ^ { 3 } \left( - 10 a x ^ { 3 } + 5 x ^ { 2 } + 1 \right)$

Write in radical form. Assume all variables represent positive real numbers. - $( 6 x ) ^ { 1 / 5 }$

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $( x - 10 ) ( 4 x + 7 )$

Find the sum or difference. - $\left( 4 - 3 x ^ { 2 } + 2 x ^ { 4 } + 8 x ^ { 3 } \right) + \left( - 2 x ^ { 3 } - 6 x ^ { 2 } - 9 + 3 x ^ { 4 } \right)$

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $\frac { 1 } { ( a + 2 ) } \cdot ( a + 2 ) = 1 , \text { if } a + 2 \neq 0$

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

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 1: Review of Basic Concepts

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣7−12∣=∣12∣−∣7∣| 7 - 12 | = | 12 | - | 7 |∣7−12∣=∣12∣−∣7∣

Write in radical form. Assume all variables represent positive real numbers. - (−6x)1/5( - 6 x ) ^ { 1 / 5 }(−6x)1/5

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - 13x213 x ^ { 2 }13x2

Factor by any method. - (q−8)2−25( q - 8 ) ^ { 2 } - 25(q−8)2−25

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - (4a+7b)(7a+4b)( 4 a + 7 b ) ( 7 a + 4 b )(4a+7b)(7a+4b)

Simplify the expression. Assume all variables represent positive real numbers. - 3x6y5−2xxy53 \sqrt [ 5 ] { x ^ { 6 } y } - 2 x \sqrt [ 5 ] { x y }35x6y​−2x5xy​

Factor out the greatest common factor. Simplify the factors, if possible. - (x−3)(x+7)+(x−3)(x+9)( x - 3 ) ( x + 7 ) + ( x - 3 ) ( x + 9 )(x−3)(x+7)+(x−3)(x+9)

Find the sum or difference. - −(6x3+x−7)+(8x3+4x2)−(9x2−5x−1)- \left( 6 x ^ { 3 } + x - 7 \right) + \left( 8 x ^ { 3 } + 4 x ^ { 2 } \right) - \left( 9 x ^ { 2 } - 5 x - 1 \right)−(6x3+x−7)+(8x3+4x2)−(9x2−5x−1)

Find the domain of the expression. - yy2−25\frac { y } { y ^ { 2 } - 25 }y2−25y​