Question 1

Determine whether or not the equation is linear.
-7x - 2x = 0

Accepted Answer

A)  Linear 
B)  Not linear 
A)  Linear 
B)  Not linear

Question 2

Solve the equation.
-$5 x ^ { - 2 } - 11 x ^ { - 1 } - 12 = 0$

Accepted Answer

A)  $\left\{ \frac { 5 } { 4 } , - \frac { 1 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 4 } { 5 } , 3 \right\}$ 
C)  $\left\{ \frac { 4 } { 5 } , - 3 \right\}$ 
D)  $\left\{ - \frac { 5 } { 4 } , \frac { 1 } { 3 } \right\}$ 
A)  $\left\{ \frac { 5 } { 4 } , - \frac { 1 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 4 } { 5 } , 3 \right\}$ 
C)  $\left\{ \frac { 4 } { 5 } , - 3 \right\}$ 
D)  $\left\{ - \frac { 5 } { 4 } , \frac { 1 } { 3 } \right\}$

Question 3

Solve the equation.
-$$| 2 x - 8 | = - 4$$

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\{ - 2,2 \}$ 
C)  $\varnothing$ 
D)  $\{ 6 , - 2 \}$ 
A)  $\{ 2 \}$ 
B)  $\{ - 2,2 \}$ 
C)  $\varnothing$ 
D)  $\{ 6 , - 2 \}$

Question 4

Multiply or divide, as indicated. Simplify the answer.
-$\frac { \sqrt { - 128 } } { \sqrt { - 8 } }$

Accepted Answer

A)  $- 4$ 
B)  $- 4 \mathrm { i }$ 
C)  4 
D)  $4 \mathrm { i }$ 
A)  $- 4$ 
B)  $- 4 \mathrm { i }$ 
C)  4 
D)  $4 \mathrm { i }$

Question 5

Solve the equation by the zero-factor property.
-$$28 x ^ { 2 } + 41 x + 15 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 7 } , - \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { 7 } { 5 } , \frac { 4 } { 3 } \right\}$ 
C)  $\left\{ \frac { 5 } { 7 } , \frac { 3 } { 4 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 5 } , - \frac { 3 } { 4 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 7 } , - \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { 7 } { 5 } , \frac { 4 } { 3 } \right\}$ 
C)  $\left\{ \frac { 5 } { 7 } , \frac { 3 } { 4 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 5 } , - \frac { 3 } { 4 } \right\}$

Question 6

Solve the problem.
-The temperatures in a freeze-dry process in degrees Celsius roughly satisfy the inequality $\mid \mathrm { C }$ $+ 80 \mid \leq 57$. What range of temperatures corresponds to this inequality?

Accepted Answer

A)  $\left[ - 23 ^ { \circ } \mathrm { C } , 23 ^ { \circ } \mathrm { C } \right]$ 
B)  $\left[ - 137 ^ { \circ } \mathrm { C } , - 23 ^ { \circ } \mathrm { C } \right]$ 
C)  $\left[ - 137 ^ { \circ } \mathrm { C } , 137 ^ { \circ } \mathrm { C } \right]$ 
D)  $\left[ - 23 ^ { \circ } \mathrm { C } , 137 ^ { \circ } \mathrm { C } \right]$ 
A)  $\left[ - 23 ^ { \circ } \mathrm { C } , 23 ^ { \circ } \mathrm { C } \right]$ 
B)  $\left[ - 137 ^ { \circ } \mathrm { C } , - 23 ^ { \circ } \mathrm { C } \right]$ 
C)  $\left[ - 137 ^ { \circ } \mathrm { C } , 137 ^ { \circ } \mathrm { C } \right]$ 
D)  $\left[ - 23 ^ { \circ } \mathrm { C } , 137 ^ { \circ } \mathrm { C } \right]$

Question 7

Solve the equation using the quadratic formula.
-$$x ^ { 2 } + x + 4 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } \pm \frac { \sqrt { 15 } } { 2 } \mathrm { i } \right\}$ 
B)  $\left\{ \frac { - 1 \pm \sqrt { 15 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 \pm \sqrt { 15 } } { 2 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } \pm \frac { \sqrt { 15 } } { 2 } \mathrm { i } \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } \pm \frac { \sqrt { 15 } } { 2 } \mathrm { i } \right\}$ 
B)  $\left\{ \frac { - 1 \pm \sqrt { 15 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 \pm \sqrt { 15 } } { 2 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } \pm \frac { \sqrt { 15 } } { 2 } \mathrm { i } \right\}$

Question 8

Find the product. Write the answer in standard form.
-$( 2 + i ) ( 2 - i ) ( 6 + 4 i )$

Accepted Answer

A)  $18 + 12 \mathrm { i }$ 
B)  $30 + 4 \mathrm { i }$ 
C)  $30 + 20 \mathrm { i }$ 
D)  $24 - 4 i ^ { 3 }$ 
A)  $18 + 12 \mathrm { i }$ 
B)  $30 + 4 \mathrm { i }$ 
C)  $30 + 20 \mathrm { i }$ 
D)  $24 - 4 i ^ { 3 }$

Question 9

Solve the equation by the zero-factor property.
-$$2 x ^ { 2 } = - 12 x - 16$$

Accepted Answer

A)  $\{ - 2 , - 4 \}$ 
B)  $\{ - 4 , - 8 \}$ 
C)  $\{ 4 , - 2 \}$ 
D)  $\{ 4,2 \}$ 
A)  $\{ - 2 , - 4 \}$ 
B)  $\{ - 4 , - 8 \}$ 
C)  $\{ 4 , - 2 \}$ 
D)  $\{ 4,2 \}$

Question 10

Find the quotient. Write the answer in standard form.
-$\frac { 7 - 9 i } { 5 + 3 i }$

Accepted Answer

A)  $\frac { 62 } { 17 } + \frac { 24 } { 17 } \mathrm { i }$ 
B)  $\frac { 31 } { 8 } + \frac { 33 } { 16 } \mathrm { i }$ 
C)  $\frac { 4 } { 17 } - \frac { 33 } { 17 } \mathrm { i }$ 
D)  $\frac { 1 } { 4 } + \frac { 33 } { 16 } \mathrm { i }$ 
A)  $\frac { 62 } { 17 } + \frac { 24 } { 17 } \mathrm { i }$ 
B)  $\frac { 31 } { 8 } + \frac { 33 } { 16 } \mathrm { i }$ 
C)  $\frac { 4 } { 17 } - \frac { 33 } { 17 } \mathrm { i }$ 
D)  $\frac { 1 } { 4 } + \frac { 33 } { 16 } \mathrm { i }$

Question 11

Write the number as the product of a real number and i.
-$\sqrt { - 99 }$

Accepted Answer

A)  $3 \mathrm { i } \sqrt { 11 }$ 
B)  $- 3 \sqrt { 11 \mathrm { i } }$ 
C)  $3 \sqrt { 11 i }$ 
D)  $- 3 \mathrm { i } \sqrt { 11 }$ 
A)  $3 \mathrm { i } \sqrt { 11 }$ 
B)  $- 3 \sqrt { 11 \mathrm { i } }$ 
C)  $3 \sqrt { 11 i }$ 
D)  $- 3 \mathrm { i } \sqrt { 11 }$

Question 12

Answer the question.
-To solve for the lengths of the right triangle sides, which equation is correct?

Accepted Answer

A)  $( 2 x - 10 ) ^ { 2 } + x ^ { 2 } = ( 3 x ) ^ { 2 }$ 
B)  $x ^ { 2 } + ( 3 x ) ^ { 2 } = ( 2 x - 10 ) ^ { 2 }$ 
C)  $x ^ { 2 } = ( 3 x ) ^ { 2 } + ( 2 x - 10 ) ^ { 2 }$ 
D)  $( 2 x - 10 ) ^ { 2 } = x ^ { 2 } + ( 3 x ) ^ { 2 }$ 
A)  $( 2 x - 10 ) ^ { 2 } + x ^ { 2 } = ( 3 x ) ^ { 2 }$ 
B)  $x ^ { 2 } + ( 3 x ) ^ { 2 } = ( 2 x - 10 ) ^ { 2 }$ 
C)  $x ^ { 2 } = ( 3 x ) ^ { 2 } + ( 2 x - 10 ) ^ { 2 }$ 
D)  $( 2 x - 10 ) ^ { 2 } = x ^ { 2 } + ( 3 x ) ^ { 2 }$

Question 13

Solve the equation by the square root property.
-$$( 2 x + 3 ) ^ { 2 } = 14$$

Accepted Answer

A)  $\{ - 3 \pm \sqrt { 14 } \}$ 
B)  $\left\{ \frac { - 3 \pm \sqrt { 14 } } { 2 } \right\}$ 
C)  $\left\{ \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$ 
D)  $\left\{ \frac { - 3 + \sqrt { 14 } } { 2 } \right\}$ 
A)  $\{ - 3 \pm \sqrt { 14 } \}$ 
B)  $\left\{ \frac { - 3 \pm \sqrt { 14 } } { 2 } \right\}$ 
C)  $\left\{ \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$ 
D)  $\left\{ \frac { - 3 + \sqrt { 14 } } { 2 } \right\}$

Question 14

Solve the equation for the indicated variable. Assume no denominator is 0.
-$$2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1 , \text { for } x$$

Accepted Answer

A)  $x = \frac { 2 y \pm \sqrt { 2 - 2 y ^ { 2 } } } { 2 }$ 
B)  $x = y \pm ( 1 - y )$ 
C)  $x = - y \pm \sqrt { 1 - y ^ { 2 } }$ 
D)  $x = - y \pm 2 \sqrt { 1 - y ^ { 2 } }$ 
A)  $x = \frac { 2 y \pm \sqrt { 2 - 2 y ^ { 2 } } } { 2 }$ 
B)  $x = y \pm ( 1 - y )$ 
C)  $x = - y \pm \sqrt { 1 - y ^ { 2 } }$ 
D)  $x = - y \pm 2 \sqrt { 1 - y ^ { 2 } }$

Question 15

Solve the problem.
-Find the height of a moving box if its length is 32 in., its width is 26 in., and its surface area is 2940 in $^ { 2 }$. Assume that the surface area includes the top of the moving box.

Accepted Answer

A)  $11 \mathrm { in }$. 
B)  $26 \mathrm { in }$. 
C)  $32 \mathrm { in }$. 
D)  $9152 \mathrm { in }$. 
A)  $11 \mathrm { in }$. 
B)  $26 \mathrm { in }$. 
C)  $32 \mathrm { in }$. 
D)  $9152 \mathrm { in }$.

Question 16

Solve the problem.
-In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 44° greater than that of angle A. Find the measure of the angles.

Accepted Answer

A)  $17 ^ { \circ } , 78 ^ { \circ }$ and $102 ^ { \circ }$ 
B)  $17 ^ { \circ } , 78 ^ { \circ }$ and $85 ^ { \circ }$ 
C)  $17 ^ { \circ } , 61 ^ { \circ }$ and $102 ^ { \circ }$ 
D)  $17 ^ { \circ } , 61 ^ { \circ }$ and $119 ^ { \circ }$ 
A)  $17 ^ { \circ } , 78 ^ { \circ }$ and $102 ^ { \circ }$ 
B)  $17 ^ { \circ } , 78 ^ { \circ }$ and $85 ^ { \circ }$ 
C)  $17 ^ { \circ } , 61 ^ { \circ }$ and $102 ^ { \circ }$ 
D)  $17 ^ { \circ } , 61 ^ { \circ }$ and $119 ^ { \circ }$

Question 17

Find the product. Write the answer in standard form.
-$$( 1 + 3 i ) ^ { 3 }$$

Accepted Answer

A)  $i ^ { 3 } + 27 i ^ { 2 } + 9 i + a ^ { 3 }$ 
B)  $- 26 + 26 i$ 
C)  $- 26 + 9 i + i ^ { 3 }$ 
D)  $- 26 - 18 \mathrm { i }$ 
A)  $i ^ { 3 } + 27 i ^ { 2 } + 9 i + a ^ { 3 }$ 
B)  $- 26 + 26 i$ 
C)  $- 26 + 9 i + i ^ { 3 }$ 
D)  $- 26 - 18 \mathrm { i }$

Question 18

Solve the inequality. Write the solution set in interval notation.
-$$| - 9 + 9 x | > 6$$

Accepted Answer

A)  $\left( - \infty , - \frac { 13 } { 9 } \right) \cup \left( - \frac { 1 } { 9 } , \infty \right)$ 
B)  $\left( - \infty , \frac { 1 } { 3 } \right) \cup \left( \frac { 5 } { 3 } , \infty \right)$ 
C)  $\left( \frac { 1 } { 3 } , \frac { 5 } { 3 } \right)$ 
D)  $\left( \frac { 5 } { 3 } , - \frac { 1 } { 3 } \right)$ 
A)  $\left( - \infty , - \frac { 13 } { 9 } \right) \cup \left( - \frac { 1 } { 9 } , \infty \right)$ 
B)  $\left( - \infty , \frac { 1 } { 3 } \right) \cup \left( \frac { 5 } { 3 } , \infty \right)$ 
C)  $\left( \frac { 1 } { 3 } , \frac { 5 } { 3 } \right)$ 
D)  $\left( \frac { 5 } { 3 } , - \frac { 1 } { 3 } \right)$

Question 19

Solve the equation.
-$$| 2 x - 4 | = 5$$

Accepted Answer

A)  $\left\{ \frac { 9 } { 2 } \right\}$ 
B)  $\left\{ \frac { 9 } { 2 } , - \frac { 1 } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , - \frac { 9 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } , - \frac { 9 } { 2 } \right\}$ 
A)  $\left\{ \frac { 9 } { 2 } \right\}$ 
B)  $\left\{ \frac { 9 } { 2 } , - \frac { 1 } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , - \frac { 9 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 2 } , - \frac { 9 } { 2 } \right\}$

Question 20

Solve for y.
-$$10 x ^ { 2 } - y + 6 x = 0$$

Accepted Answer

A)  $y = 10 x ^ { 2 } - 6 x$ 
B)  $y = - 10 x ^ { 2 } - 6 x$ 
C)  $y = - 10 x ^ { 2 } + 6 x$ 
D)  $y = 10 x ^ { 2 } + 6 x$ 
A)  $y = 10 x ^ { 2 } - 6 x$ 
B)  $y = - 10 x ^ { 2 } - 6 x$ 
C)  $y = - 10 x ^ { 2 } + 6 x$ 
D)  $y = 10 x ^ { 2 } + 6 x$

Determine whether or not the equation is linear. -7x - 2x = 0

Solve the equation. - $5 x ^ { - 2 } - 11 x ^ { - 1 } - 12 = 0$

Solve the equation. - $| 2 x - 8 | = - 4$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 128 } } { \sqrt { - 8 } }$

Solve the equation by the zero-factor property. - $28 x ^ { 2 } + 41 x + 15 = 0$

Solve the problem. -The temperatures in a freeze-dry process in degrees Celsius roughly satisfy the inequality $\mid \mathrm { C }$ $+ 80 \mid \leq 57$ . What range of temperatures corresponds to this inequality?

Solve the equation using the quadratic formula. - $x ^ { 2 } + x + 4 = 0$

Find the product. Write the answer in standard form. - $( 2 + i ) ( 2 - i ) ( 6 + 4 i )$

Solve the equation by the zero-factor property. - $2 x ^ { 2 } = - 12 x - 16$

Find the quotient. Write the answer in standard form. - $\frac { 7 - 9 i } { 5 + 3 i }$

Write the number as the product of a real number and i. - $\sqrt { - 99 }$

Answer the question. -To solve for the lengths of the right triangle sides, which equation is correct?

Solve the equation by the square root property. - $( 2 x + 3 ) ^ { 2 } = 14$

Solve the equation for the indicated variable. Assume no denominator is 0. - $2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1 , \text { for } x$

Solve the problem. -Find the height of a moving box if its length is 32 in., its width is 26 in., and its surface area is 2940 in $^ { 2 }$ . Assume that the surface area includes the top of the moving box.

Solve the problem. -In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 44° greater than that of angle A. Find the measure of the angles.

Find the product. Write the answer in standard form. - $( 1 + 3 i ) ^ { 3 }$

Solve the inequality. Write the solution set in interval notation. - $| - 9 + 9 x | > 6$

Solve the equation. - $| 2 x - 4 | = 5$

Solve for y. - $10 x ^ { 2 } - y + 6 x = 0$

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

Review of Basic Concepts

Filters

Exam 1: Equations and Inequalities

Determine whether or not the equation is linear. -7x - 2x = 0

Solve the equation. - 5x−2−11x−1−12=05 x ^ { - 2 } - 11 x ^ { - 1 } - 12 = 05x−2−11x−1−12=0

Solve the equation. - ∣2x−8∣=−4| 2 x - 8 | = - 4∣2x−8∣=−4

Multiply or divide, as indicated. Simplify the answer. - −128−8\frac { \sqrt { - 128 } } { \sqrt { - 8 } }−8​−128​​

Solve the equation by the zero-factor property. - 28x2+41x+15=028 x ^ { 2 } + 41 x + 15 = 028x2+41x+15=0

Solve the problem. -The temperatures in a freeze-dry process in degrees Celsius roughly satisfy the inequality ∣C\mid \mathrm { C }∣C +80∣≤57+ 80 \mid \leq 57+80∣≤57 . What range of temperatures corresponds to this inequality?

Solve the equation using the quadratic formula. - x2+x+4=0x ^ { 2 } + x + 4 = 0x2+x+4=0

Find the product. Write the answer in standard form. - (2+i)(2−i)(6+4i)( 2 + i ) ( 2 - i ) ( 6 + 4 i )(2+i)(2−i)(6+4i)

Solve the equation by the zero-factor property. - 2x2=−12x−162 x ^ { 2 } = - 12 x - 162x2=−12x−16

Find the quotient. Write the answer in standard form. - 7−9i5+3i\frac { 7 - 9 i } { 5 + 3 i }5+3i7−9i​

Write the number as the product of a real number and i. - −99\sqrt { - 99 }−99​