Question 1

Decide whether or not the equations are equivalent.
-$$\begin{array} { l } 
\frac { x + 1 } { 5 } = \frac { 4 } { 5 } \
x + 2 = 5
\end{array}$$

Accepted Answer

A)  Equivalent 
B)  Not equivalent 
A)  Equivalent 
B)  Not equivalent

Question 2

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-$$\sqrt { 9 }$$

Accepted Answer

A)  Nonreal complex 
B)  Complex, pure imaginary, nonreal complex 
C)  Real, complex 
D)  Complex 
A)  Nonreal complex 
B)  Complex, pure imaginary, nonreal complex 
C)  Real, complex 
D)  Complex

Question 3

Write the number as the product of a real number and i.
-$\sqrt { - 49 }$

Accepted Answer

A)  $- \mathrm { i } \sqrt { 49 }$ 
B)  $7 \sqrt { \mathrm { i } }$ 
C)  $- 7 \mathrm { i }$ 
D)  $7 \mathrm { i }$ 
A)  $- \mathrm { i } \sqrt { 49 }$ 
B)  $7 \sqrt { \mathrm { i } }$ 
C)  $- 7 \mathrm { i }$ 
D)  $7 \mathrm { i }$

Question 4

Solve the equation by completing the square.
-$$x ^ { 2 } + 10 x = - 21$$

Accepted Answer

A)  $\{ - 3 , - 7 \}$ 
B)  $\{ 3 , - 7 \}$ 
C)  $\{ - 3,7 \}$ 
D)  $\{ 3,7 \}$ 
A)  $\{ - 3 , - 7 \}$ 
B)  $\{ 3 , - 7 \}$ 
C)  $\{ - 3,7 \}$ 
D)  $\{ 3,7 \}$

Question 5

Solve the equation.
-$$| 7 x + 6 | + 7 = - 1$$

Accepted Answer

A)  $\{ - 2 \}$ 
B)  $\varnothing$ 
C)  $\left\{ - \frac { 2 } { 7 } , - 2 \right\}$ 
D)  $\left\{ \frac { 2 } { 7 } , 2 \right\}$ 
A)  $\{ - 2 \}$ 
B)  $\varnothing$ 
C)  $\left\{ - \frac { 2 } { 7 } , - 2 \right\}$ 
D)  $\left\{ \frac { 2 } { 7 } , 2 \right\}$

Question 6

Solve for the indicated variable.
-$\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$, for $\mathrm { v }$

Accepted Answer

A)  $v = \frac { \pm \sqrt { 2 \mathrm { mVe } } } { \mathrm { m } }$ 
B)  $v = \pm 2 \frac { \sqrt { \mathrm { Ve } } } { \mathrm { m } }$ 
C)  $\mathrm { v } = \pm \sqrt { 2 \mathrm { Ve } }$ 
D)  $v = \pm \sqrt { \frac { V e } { 2 m } }$ 
A)  $v = \frac { \pm \sqrt { 2 \mathrm { mVe } } } { \mathrm { m } }$ 
B)  $v = \pm 2 \frac { \sqrt { \mathrm { Ve } } } { \mathrm { m } }$ 
C)  $\mathrm { v } = \pm \sqrt { 2 \mathrm { Ve } }$ 
D)  $v = \pm \sqrt { \frac { V e } { 2 m } }$

Question 7

Simplify the power of i.
-$$\mathrm { i } ^ { - 22 }$$

Accepted Answer

A)  $- 1$ 
B)  - $\mathrm { i }$ 
C)  $\mathrm { i }$ 
D)  1 
A)  $- 1$ 
B)  - $\mathrm { i }$ 
C)  $\mathrm { i }$ 
D)  1

Question 8

Solve the equation.
-$$- 2.9 x + 1.3 = - 10.7 - 1.4 x$$

Accepted Answer

A)  $\{ 4.6 \}$ 
B)  $\{ 4.1 \}$ 
C)  $\{ - 13 \}$ 
D)  $\{ 8 \}$ 
A)  $\{ 4.6 \}$ 
B)  $\{ 4.1 \}$ 
C)  $\{ - 13 \}$ 
D)  $\{ 8 \}$

Question 9

Simplify the power of i.
-$\mathrm { i } ^ { - 11 }$

Accepted Answer

A)  $- \mathrm { i }$ 
B)  $i$ 
C)  $- 1$ 
D)  1 
A)  $- \mathrm { i }$ 
B)  $i$ 
C)  $- 1$ 
D)  1

Question 10

Solve the equation.
-$$| x + 8 | + 4 = 6$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ - 6 , - 10 \}$ 
C)  $\{ - 6 \}$ 
D)  $\{ 6,10 \}$ 
A)  $\varnothing$ 
B)  $\{ - 6 , - 10 \}$ 
C)  $\{ - 6 \}$ 
D)  $\{ 6,10 \}$

Question 11

Solve the equation.
-$$\sqrt { 2 x + 15 } - x = 6$$

Accepted Answer

A)  $\{ - 7 \}$ 
B)  $\{ - 3 \}$ 
C)  $\{ - 7 , - 3 \}$ 
D)  $\varnothing$ 
A)  $\{ - 7 \}$ 
B)  $\{ - 3 \}$ 
C)  $\{ - 7 , - 3 \}$ 
D)  $\varnothing$

Question 12

Solve for the indicated variable.
-$\frac { 1 } { A } = \frac { 1 } { B } + \frac { 1 } { C ^ { \prime } }$, for $A$

Accepted Answer

A)  $A = \frac { B } { B + C }$ 
B)  $A = \frac { B C } { B + C }$ 
C)  $\mathrm { A } = \frac { \mathrm { B } - \mathrm { C } } { \mathrm { BC } }$ 
D)  $\mathrm { A } = 4 + \mathrm { B } + \mathrm { C }$ 
A)  $A = \frac { B } { B + C }$ 
B)  $A = \frac { B C } { B + C }$ 
C)  $\mathrm { A } = \frac { \mathrm { B } - \mathrm { C } } { \mathrm { BC } }$ 
D)  $\mathrm { A } = 4 + \mathrm { B } + \mathrm { C }$

Question 13

Solve the equation by the square root property.
-$$( x - 1 ) ^ { 2 } = 5$$

Accepted Answer

A)  $\{ \sqrt { 5 } - 1 , - \sqrt { 5 - 1 } \}$ 
B)  $\{ 1 + \sqrt { 5 } \}$ 
C)  $\{ \sqrt { 5 } - \sqrt { - 1 } \}$ 
D)  $\{ 1 \pm \sqrt { 5 } \}$ 
A)  $\{ \sqrt { 5 } - 1 , - \sqrt { 5 - 1 } \}$ 
B)  $\{ 1 + \sqrt { 5 } \}$ 
C)  $\{ \sqrt { 5 } - \sqrt { - 1 } \}$ 
D)  $\{ 1 \pm \sqrt { 5 } \}$

Question 14

Solve the problem.
-In the morning, May drove to an appointment at $50 \mathrm { mph }$. Her average speed on the return trip in the afternoon was $40 \mathrm { mph }$. The return trip took $\frac { 1 } { 5 }$ hour longer. How far did she travel to the appointment?

Accepted Answer

A)  $40 \mathrm { mi }$ 
B)  $12 \mathrm { mi }$ 
C)  $0.8 \mathrm { mi }$ 
D)  $32 \mathrm { mi }$ 
A)  $40 \mathrm { mi }$ 
B)  $12 \mathrm { mi }$ 
C)  $0.8 \mathrm { mi }$ 
D)  $32 \mathrm { mi }$

Question 15

Simplify the power of i.
-$$\frac { 1 } { \mathrm { i } ^ { 51 } }$$

Accepted Answer

A)  $- \mathrm { i }$ 
B)  $\mathrm { i }$ 
C)  1 
D)  $- 1$ 
A)  $- \mathrm { i }$ 
B)  $\mathrm { i }$ 
C)  1 
D)  $- 1$

Question 16

Solve the problem.
-A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall.

Accepted Answer

A)  8 ft 
B)  10 ft 
C)  6 ft 
D)  12 ft 
A)  8 ft 
B)  10 ft 
C)  6 ft 
D)  12 ft

Question 17

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 7 x \leq - 12$$

Accepted Answer

A)  $( - \infty , 3 ] \cup [ 4 , \infty )$ 
B)  $[ 3,4 ]$ 
C)  $[ - 4 , - 3 ]$ 
D)  $( 3,4 )$ 
A)  $( - \infty , 3 ] \cup [ 4 , \infty )$ 
B)  $[ 3,4 ]$ 
C)  $[ - 4 , - 3 ]$ 
D)  $( 3,4 )$

Question 18

Solve the problem.
-Levi borrowed $\$ 5073$ at $4 \%$ simple interest for 5 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 5 months? Round answers to the nearest cent if necessary.

Accepted Answer

A)  $\$ 85.26 ; \$ 5158.26$ 
B)  $\$ 84.55 ; \$ 5157.55$ 
C)  $\$ 67.64 ; \$ 5140.64$ 
D)  $\$ 101.46 ; \$ 5174.46$ 
A)  $\$ 85.26 ; \$ 5158.26$ 
B)  $\$ 84.55 ; \$ 5157.55$ 
C)  $\$ 67.64 ; \$ 5140.64$ 
D)  $\$ 101.46 ; \$ 5174.46$

Question 19

Solve the equation.
-$$36 x ^ { 4 } - 85 x ^ { 2 } + 49 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 6 } , - 1,1 , \frac { 7 } { 6 } \right\}$ 
B)  $\left\{ - 1 , - \frac { 6 } { 7 } \right\}$ 
C)  $\left\{ - 1 , - \frac { 6 } { 7 } , \frac { 6 } { 7 } , 1 \right\}$ 
D)  $\left\{ 1 , \frac { 7 } { 6 } \right\}$ 
A)  $\left\{ - \frac { 7 } { 6 } , - 1,1 , \frac { 7 } { 6 } \right\}$ 
B)  $\left\{ - 1 , - \frac { 6 } { 7 } \right\}$ 
C)  $\left\{ - 1 , - \frac { 6 } { 7 } , \frac { 6 } { 7 } , 1 \right\}$ 
D)  $\left\{ 1 , \frac { 7 } { 6 } \right\}$

Question 20

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } - 8 = 0$$

Accepted Answer

A)  $\{ 2,1 \pm \mathrm { i } \sqrt { 6 } \}$ 
B)  $\{ 2 , \pm 2 \mathrm { i } \}$ 
C)  $\{ 2 , - 1 \pm \mathrm { i } \sqrt { 3 } \}$ 
D)  $\{ 2 , - 1 \pm \sqrt { 5 } \}$ 
A)  $\{ 2,1 \pm \mathrm { i } \sqrt { 6 } \}$ 
B)  $\{ 2 , \pm 2 \mathrm { i } \}$ 
C)  $\{ 2 , - 1 \pm \mathrm { i } \sqrt { 3 } \}$ 
D)  $\{ 2 , - 1 \pm \sqrt { 5 } \}$

Decide whether or not the equations are equivalent. - = x+2=5

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $\sqrt { 9 }$

Write the number as the product of a real number and i. - $\sqrt { - 49 }$

Solve the equation by completing the square. - $x ^ { 2 } + 10 x = - 21$

Solve the equation. - $| 7 x + 6 | + 7 = - 1$

Solve for the indicated variable. - $\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$ , for $\mathrm { v }$

Simplify the power of i. - $\mathrm { i } ^ { - 22 }$

Solve the equation. - $- 2.9 x + 1.3 = - 10.7 - 1.4 x$

Simplify the power of i. - $\mathrm { i } ^ { - 11 }$

Solve the equation. - $| x + 8 | + 4 = 6$

Solve the equation. - $\sqrt { 2 x + 15 } - x = 6$

Solve for the indicated variable. - $\frac { 1 } { A } = \frac { 1 } { B } + \frac { 1 } { C ^ { \prime } }$ , for $A$

Solve the equation by the square root property. - $( x - 1 ) ^ { 2 } = 5$

Solve the problem. -In the morning, May drove to an appointment at $50 \mathrm { mph }$ . Her average speed on the return trip in the afternoon was $40 \mathrm { mph }$ . The return trip took $\frac { 1 } { 5 }$ hour longer. How far did she travel to the appointment?

Simplify the power of i. - $\frac { 1 } { \mathrm { i } ^ { 51 } }$

Solve the problem. -A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall.

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } + 7 x \leq - 12$

Solve the problem. -Levi borrowed $\$ 5073$ at $4 \%$ simple interest for 5 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 5 months? Round answers to the nearest cent if necessary.

Solve the equation. - $36 x ^ { 4 } - 85 x ^ { 2 } + 49 = 0$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } - 8 = 0$

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

Decide whether or not the equations are equivalent. - = x+2=5

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - 9\sqrt { 9 }9​

Write the number as the product of a real number and i. - −49\sqrt { - 49 }−49​

Solve the equation by completing the square. - x2+10x=−21x ^ { 2 } + 10 x = - 21x2+10x=−21

Solve the equation. - ∣7x+6∣+7=−1| 7 x + 6 | + 7 = - 1∣7x+6∣+7=−1

Solve for the indicated variable. - Ve=12mv2\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }Ve=21​mv2 , for v\mathrm { v }v

Simplify the power of i. - i−22\mathrm { i } ^ { - 22 }i−22

Solve the equation. - −2.9x+1.3=−10.7−1.4x- 2.9 x + 1.3 = - 10.7 - 1.4 x−2.9x+1.3=−10.7−1.4x

Simplify the power of i. - i−11\mathrm { i } ^ { - 11 }i−11

Solve the equation. - ∣x+8∣+4=6| x + 8 | + 4 = 6∣x+8∣+4=6

Solve the equation. - 2x+15−x=6\sqrt { 2 x + 15 } - x = 62x+15​−x=6

Solve for the indicated variable. - 1A=1B+1C′\frac { 1 } { A } = \frac { 1 } { B } + \frac { 1 } { C ^ { \prime } }A1​=B1​+C′1​ , for AAA

Solve the equation by the square root property. - (x−1)2=5( x - 1 ) ^ { 2 } = 5(x−1)2=5

Solve the problem. -In the morning, May drove to an appointment at 50mph50 \mathrm { mph }50mph . Her average speed on the return trip in the afternoon was 40mph40 \mathrm { mph }40mph . The return trip took 15\frac { 1 } { 5 }51​ hour longer. How far did she travel to the appointment?

Simplify the power of i. - 1i51\frac { 1 } { \mathrm { i } ^ { 51 } }i511​