Question 1

Solve the quadratic inequality. Write the solution set in interval notation.
-$$( 4 + 3 x ) ^ { 2 } \geq - 9$$

Accepted Answer

A)  $\left[ - \frac { 7 } { 3 } , - \frac { 1 } { 3 } \right]$ 
B)  $\varnothing$ 
C)  $( - \infty , \infty )$ 
D)  $\left( - \infty , - \frac { 7 } { 3 } \right) \cup \left( - \frac { 1 } { 3 } , \infty \right)$ 
A)  $\left[ - \frac { 7 } { 3 } , - \frac { 1 } { 3 } \right]$ 
B)  $\varnothing$ 
C)  $( - \infty , \infty )$ 
D)  $\left( - \infty , - \frac { 7 } { 3 } \right) \cup \left( - \frac { 1 } { 3 } , \infty \right)$

Question 2

Solve the problem.
-The height of a box is 3 inches. The length is three inches more than the width. Find the width if the volume is 264.

Accepted Answer

A)  11 in. 
B)  3 in. 
C)  8 in. 
D)  88 in. 
A)  11 in. 
B)  3 in. 
C)  8 in. 
D)  88 in.

Question 3

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-5 + 8i

Accepted Answer

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

Question 4

Solve the problem.
-Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 7 hours. How long will it take them to do the job working together?

Accepted Answer

A)  $\frac { 1 } { 9 } h r$ 
B)  $\frac { 14 } { 5 } \mathrm { hr }$ 
C)  $\frac { 1 } { 14 } \mathrm { hr }$ 
D)  $\frac { 14 } { 9 } \mathrm { hr }$ 
A)  $\frac { 1 } { 9 } h r$ 
B)  $\frac { 14 } { 5 } \mathrm { hr }$ 
C)  $\frac { 1 } { 14 } \mathrm { hr }$ 
D)  $\frac { 14 } { 9 } \mathrm { hr }$

Question 5

Write the inequality in interval notation.
-$2 < x \leq 7$

Accepted Answer

A)  $( 2,7 ]$ 
B)  $[ 2,7 )$ 
C)  $[ 2,7 ]$ 
D)  $( 2,7 )$ 
A)  $( 2,7 ]$ 
B)  $[ 2,7 )$ 
C)  $[ 2,7 ]$ 
D)  $( 2,7 )$

Question 6

Solve the equation.
-$\sqrt { x + 6 } + \sqrt { 2 - x } = 4$

Accepted Answer

A)  $\{ \sqrt { 31 } , - 2 \}$ 
B)  $\{ 2 , - 2 \}$ 
C)  $\{ - 2 \}$ 
D)  $\{ 0 \}$ 
A)  $\{ \sqrt { 31 } , - 2 \}$ 
B)  $\{ 2 , - 2 \}$ 
C)  $\{ - 2 \}$ 
D)  $\{ 0 \}$

Question 7

Find the sum or difference. Write the answer in standard form.
-$4 \mathrm { i } + ( - 7 - \mathrm { i } )$

Accepted Answer

A)  $- 7 + 3 i$ 
B)  $7 - 5 \mathrm { i }$ 
C)  $7 - 3 \mathrm { i }$ 
D)  $- 7 + 5 i$ 
A)  $- 7 + 3 i$ 
B)  $7 - 5 \mathrm { i }$ 
C)  $7 - 3 \mathrm { i }$ 
D)  $- 7 + 5 i$

Question 8

Solve the formula for the indicated variable.
-$\mathrm { S } = 2 \pi \mathrm { rh } + 2 \pi \mathrm { r } ^ { 2 }$, for $\mathrm { h }$

Accepted Answer

A)  $h = \frac { S } { 2 \pi r } - 1$ 
B)  $h = \frac { S - 2 \pi r ^ { 2 } } { 2 \pi r }$ 
C)  $h = 2 \pi ( S - r )$ 
D)  $h = S - r$ 
A)  $h = \frac { S } { 2 \pi r } - 1$ 
B)  $h = \frac { S - 2 \pi r ^ { 2 } } { 2 \pi r }$ 
C)  $h = 2 \pi ( S - r )$ 
D)  $h = S - r$

Question 9

Solve the equation using the quadratic formula.
-$$( x + 2 ) ( x - 9 ) = 8$$

Accepted Answer

A)  $\left\{ \frac { - 7 \pm 3 \sqrt { 17 } } { 2 } \right\}$ 
B)  $\left\{ - \frac { 7 } { 2 } \pm \frac { 3 \mathrm { i } \sqrt { 17 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 7 } { 2 } \pm \frac { 3 i \sqrt { 17 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 7 \pm 3 \sqrt { 17 } } { 2 } \right\}$ 
A)  $\left\{ \frac { - 7 \pm 3 \sqrt { 17 } } { 2 } \right\}$ 
B)  $\left\{ - \frac { 7 } { 2 } \pm \frac { 3 \mathrm { i } \sqrt { 17 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 7 } { 2 } \pm \frac { 3 i \sqrt { 17 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 7 \pm 3 \sqrt { 17 } } { 2 } \right\}$

Question 10

Solve the equation.
-$$\sqrt [ 3 ] { x + 8 } = 4$$

Accepted Answer

A)  $\{ 8 \}$ 
B)  $\{ - 4 \}$ 
C)  $\{ 56 \}$ 
D)  $\{ 64 \}$ 
A)  $\{ 8 \}$ 
B)  $\{ - 4 \}$ 
C)  $\{ 56 \}$ 
D)  $\{ 64 \}$

Question 11

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 6 x + 5 \geq 0$$

Accepted Answer

A)  $( - \infty , - 5 ] \cup [ - 1 , \infty )$ 
B)  $( - \infty , - 5 ]$ 
C)  $[ - 1 , \infty )$ 
D)  $[ - 5 , - 1 ]$ 
A)  $( - \infty , - 5 ] \cup [ - 1 , \infty )$ 
B)  $( - \infty , - 5 ]$ 
C)  $[ - 1 , \infty )$ 
D)  $[ - 5 , - 1 ]$

Question 12

Solve the equation.
-$$( 2 x - 6 ) ^ { 2 } - 4 ( 2 x - 6 ) + 3 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 6 } , \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ \frac { 7 } { 2 } , \frac { 9 } { 2 } \right\}$ 
C)  $\left\{ \frac { 5 } { 2 } , - \frac { 3 } { 2 } \right\}$ 
D)  $\left\{ \frac { 7 } { 2 } , - \frac { 9 } { 2 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 6 } , \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ \frac { 7 } { 2 } , \frac { 9 } { 2 } \right\}$ 
C)  $\left\{ \frac { 5 } { 2 } , - \frac { 3 } { 2 } \right\}$ 
D)  $\left\{ \frac { 7 } { 2 } , - \frac { 9 } { 2 } \right\}$

Question 13

Solve the equation.
-$$| 5 - 8 x | = 16$$

Accepted Answer

A)  $\left\{ - \frac { 11 } { 8 } \right\}$ 
B)  $\left\{ \frac { 11 } { 8 } , - \frac { 11 } { 8 } \right\}$ 
C)  $\left\{ - \frac { 11 } { 8 } , \frac { 21 } { 8 } \right\}$ 
D)  $\left\{ - \frac { 21 } { 8 } , \frac { 11 } { 8 } \right\}$ 
A)  $\left\{ - \frac { 11 } { 8 } \right\}$ 
B)  $\left\{ \frac { 11 } { 8 } , - \frac { 11 } { 8 } \right\}$ 
C)  $\left\{ - \frac { 11 } { 8 } , \frac { 21 } { 8 } \right\}$ 
D)  $\left\{ - \frac { 21 } { 8 } , \frac { 11 } { 8 } \right\}$

Question 14

Solve the equation.
-$$\sqrt [ 3 ] { 4 + 6 x } - \sqrt [ 3 ] { 1 - 8 x } = 0$$

Accepted Answer

A)  $\left\{ - \frac { 14 } { 3 } \right\}$ 
B)  $\left\{ \frac { 3 } { 14 } \right\}$ 
C)  $\left\{ \frac { 14 } { 3 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 14 } \right\}$ 
A)  $\left\{ - \frac { 14 } { 3 } \right\}$ 
B)  $\left\{ \frac { 3 } { 14 } \right\}$ 
C)  $\left\{ \frac { 14 } { 3 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 14 } \right\}$

Question 15

Solve the equation.
-$\sqrt [ 5 ] { 6 x + 5 } = 3$

Accepted Answer

A)  $\left\{ \frac { 81 } { 2 } \right\}$ 
B)  $\{ 238 \}$ 
C)  $\{ 243 \}$ 
D)  $\left\{ \frac { 119 } { 3 } \right\}$ 
A)  $\left\{ \frac { 81 } { 2 } \right\}$ 
B)  $\{ 238 \}$ 
C)  $\{ 243 \}$ 
D)  $\left\{ \frac { 119 } { 3 } \right\}$

Question 16

Solve the inequality. Write the solution set in interval notation.
-$$| 2 - 3 x | \geq 11$$

Accepted Answer

A)  $( - \infty , - 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
B)  $\left[ - \frac { 13 } { 3 } , 3 \right]$ 
C)  $( - \infty , 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
D)  $\left[ - 3 , \frac { 13 } { 3 } \right]$ 
A)  $( - \infty , - 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
B)  $\left[ - \frac { 13 } { 3 } , 3 \right]$ 
C)  $( - \infty , 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
D)  $\left[ - 3 , \frac { 13 } { 3 } \right]$

Question 17

Solve the equation.
-$$\frac { x } { x - 5 } = \frac { 5 } { x - 5 } + 5$$

Accepted Answer

A)  $\{ - 5 \}$ 
B)  $\{ 5 \}$ 
C)  $\{ 0 \}$ 
D)  $\varnothing$ 
A)  $\{ - 5 \}$ 
B)  $\{ 5 \}$ 
C)  $\{ 0 \}$ 
D)  $\varnothing$

Question 18

Find the values of a, b, and c for which the quadratic equation $$a x ^ { 2 } + b x + c = 0$$ has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$- 5,7$

Accepted Answer

A)  $x ^ { 2 } + 2 x - 35 = 0$ 
B)  $x ^ { 2 } - 35 x + 2 = 0$ 
C)  $x ^ { 2 } - 35 x - 2 = 0$ 
D)  $x ^ { 2 } - 2 x - 35 = 0$ 
A)  $x ^ { 2 } + 2 x - 35 = 0$ 
B)  $x ^ { 2 } - 35 x + 2 = 0$ 
C)  $x ^ { 2 } - 35 x - 2 = 0$ 
D)  $x ^ { 2 } - 2 x - 35 = 0$

Question 19

Solve the equation by completing the square.
-$$x ^ { 2 } = 3 - 8 x$$

Accepted Answer

A)  $\{ 4 + \sqrt { 19 } \}$ 
B)  $\{ - 1 \pm \sqrt { 19 } \}$ 
C)  $\{ - 4 \pm 2 \sqrt { 19 } \}$ 
D)  $\{ - 4 \pm \sqrt { 19 } \}$ 
A)  $\{ 4 + \sqrt { 19 } \}$ 
B)  $\{ - 1 \pm \sqrt { 19 } \}$ 
C)  $\{ - 4 \pm 2 \sqrt { 19 } \}$ 
D)  $\{ - 4 \pm \sqrt { 19 } \}$

Question 20

Solve the equation for the indicated variable. Assume no denominator is 0.
-$\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$, for $\mathrm { r }$

Accepted Answer

A)  $r = \frac { \pm \sqrt { \mathrm { M } \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
B)  $r = \frac { \pm \sqrt { \pi \mathrm { Mhd } } } { \mathrm { hd } }$ 
C)  $r = \pm \sqrt { \pi \mathrm { Mhd } }$ 
D)  $r = \frac { \pm \mathrm { M } \sqrt { \pi h d } } { \pi h d }$ 
A)  $r = \frac { \pm \sqrt { \mathrm { M } \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
B)  $r = \frac { \pm \sqrt { \pi \mathrm { Mhd } } } { \mathrm { hd } }$ 
C)  $r = \pm \sqrt { \pi \mathrm { Mhd } }$ 
D)  $r = \frac { \pm \mathrm { M } \sqrt { \pi h d } } { \pi h d }$

Solve the quadratic inequality. Write the solution set in interval notation. - $( 4 + 3 x ) ^ { 2 } \geq - 9$

Solve the problem. -The height of a box is 3 inches. The length is three inches more than the width. Find the width if the volume is 264.

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. -5 + 8i

Solve the problem. -Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 7 hours. How long will it take them to do the job working together?

Write the inequality in interval notation. - $2 < x \leq 7$

Solve the equation. - $\sqrt { x + 6 } + \sqrt { 2 - x } = 4$

Find the sum or difference. Write the answer in standard form. - $4 \mathrm { i } + ( - 7 - \mathrm { i } )$

Solve the formula for the indicated variable. - $\mathrm { S } = 2 \pi \mathrm { rh } + 2 \pi \mathrm { r } ^ { 2 }$ , for $\mathrm { h }$

Solve the equation using the quadratic formula. - $( x + 2 ) ( x - 9 ) = 8$

Solve the equation. - $\sqrt [ 3 ] { x + 8 } = 4$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } + 6 x + 5 \geq 0$

Solve the equation. - $( 2 x - 6 ) ^ { 2 } - 4 ( 2 x - 6 ) + 3 = 0$

Solve the equation. - $| 5 - 8 x | = 16$

Solve the equation. - $\sqrt [ 3 ] { 4 + 6 x } - \sqrt [ 3 ] { 1 - 8 x } = 0$

Solve the equation. - $\sqrt [ 5 ] { 6 x + 5 } = 3$

Solve the inequality. Write the solution set in interval notation. - $| 2 - 3 x | \geq 11$

Solve the equation. - $\frac { x } { x - 5 } = \frac { 5 } { x - 5 } + 5$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ has the given numbers as solutions. Then use those values to write a quadratic equation. - $- 5,7$

Solve the equation by completing the square. - $x ^ { 2 } = 3 - 8 x$

Solve the equation for the indicated variable. Assume no denominator is 0. - $\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$ , for $\mathrm { r }$

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

Solve the quadratic inequality. Write the solution set in interval notation. - (4+3x)2≥−9( 4 + 3 x ) ^ { 2 } \geq - 9(4+3x)2≥−9

Solve the problem. -The height of a box is 3 inches. The length is three inches more than the width. Find the width if the volume is 264.

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. -5 + 8i

Solve the problem. -Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 7 hours. How long will it take them to do the job working together?

Write the inequality in interval notation. - 2<x≤72 < x \leq 72<x≤7

Solve the equation. - x+6+2−x=4\sqrt { x + 6 } + \sqrt { 2 - x } = 4x+6​+2−x​=4

Find the sum or difference. Write the answer in standard form. - 4i+(−7−i)4 \mathrm { i } + ( - 7 - \mathrm { i } )4i+(−7−i)

Solve the formula for the indicated variable. - S=2πrh+2πr2\mathrm { S } = 2 \pi \mathrm { rh } + 2 \pi \mathrm { r } ^ { 2 }S=2πrh+2πr2 , for h\mathrm { h }h

Solve the equation using the quadratic formula. - (x+2)(x−9)=8( x + 2 ) ( x - 9 ) = 8(x+2)(x−9)=8

Solve the equation. - x+83=4\sqrt [ 3 ] { x + 8 } = 43x+8​=4

Solve the quadratic inequality. Write the solution set in interval notation. - x2+6x+5≥0x ^ { 2 } + 6 x + 5 \geq 0x2+6x+5≥0

Solve the equation. - (2x−6)2−4(2x−6)+3=0( 2 x - 6 ) ^ { 2 } - 4 ( 2 x - 6 ) + 3 = 0(2x−6)2−4(2x−6)+3=0

Solve the equation. - ∣5−8x∣=16| 5 - 8 x | = 16∣5−8x∣=16

Solve the equation. - 4+6x3−1−8x3=0\sqrt [ 3 ] { 4 + 6 x } - \sqrt [ 3 ] { 1 - 8 x } = 034+6x​−31−8x​=0

Solve the equation. - 6x+55=3\sqrt [ 5 ] { 6 x + 5 } = 356x+5​=3

Solve the inequality. Write the solution set in interval notation. - ∣2−3x∣≥11| 2 - 3 x | \geq 11∣2−3x∣≥11

Solve the equation. - xx−5=5x−5+5\frac { x } { x - 5 } = \frac { 5 } { x - 5 } + 5x−5x​=x−55​+5

Find the values of a, b, and c for which the quadratic equation ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0 has the given numbers as solutions. Then use those values to write a quadratic equation. - −5,7- 5,7−5,7

Solve the equation by completing the square. - x2=3−8xx ^ { 2 } = 3 - 8 xx2=3−8x

Solve the equation for the indicated variable. Assume no denominator is 0. - M=πr2hd\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }M=πr2hd , for r\mathrm { r }r