Question 1

Determine whether or not the equation is linear.
-$$\frac { x + 2 } { 3 } = \frac { x - 8 } { 4 }$$

Accepted Answer

A)  $\{ - 32 \}$ 
B)  $\{ - 16 \}$ 
C)  $\left\{ - \frac { 32 } { 7 } \right\}$ 
D)  $\{ - 26 \}$ 
A)  $\{ - 32 \}$ 
B)  $\{ - 16 \}$ 
C)  $\left\{ - \frac { 32 } { 7 } \right\}$ 
D)  $\{ - 26 \}$

Question 2

Solve the inequality. Write the solution set in interval notation.
-$$| x + 1 | - 9 > 13$$

Accepted Answer

A)  $( - \infty , - 23 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 23 ) \cup ( 21 , \infty )$ 
C)  $( - 23,21 )$ 
D)  $( - \infty , - 3 ) \cup ( 23 , \infty )$ 
A)  $( - \infty , - 23 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 23 ) \cup ( 21 , \infty )$ 
C)  $( - 23,21 )$ 
D)  $( - \infty , - 3 ) \cup ( 23 , \infty )$

Question 3

Solve the inequality. Write the solution set in interval notation.
-$$| 4 - x | \leq 9$$

Accepted Answer

A)  $[ - 5 , \infty )$ 
B)  $[ 13 , \infty )$ 
C)  $[ - 5,13 ]$ 
D)  $( - \infty , - 5 ] \cup [ 13 , \infty )$ 
A)  $[ - 5 , \infty )$ 
B)  $[ 13 , \infty )$ 
C)  $[ - 5,13 ]$ 
D)  $( - \infty , - 5 ] \cup [ 13 , \infty )$

Question 4

Determine whether or not the equation is linear.
-$$1 - \frac { 3 } { 4 x } = \frac { 9 } { 6 }$$

Accepted Answer

A)  $\left\{ \frac { 3 } { 2 } \right\}$ 
B)  $\{ 6 \rangle$ 
C)  $\left\{ - \frac { 9 } { 4 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
A)  $\left\{ \frac { 3 } { 2 } \right\}$ 
B)  $\{ 6 \rangle$ 
C)  $\left\{ - \frac { 9 } { 4 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 2 } \right\}$

Question 5

Solve the inequality. Write the solution set in interval notation.
-$( x - 4 ) ( x - 10 ) ( x + 5 ) < 0$

Accepted Answer

A)  $( - 10 , - 4 ) \cup ( 5 , \infty )$ 
B)  $( - \infty , - 5 ) \cup ( 4,10 )$ 
C)  $( - \infty , - 4 ) \cup ( 5,10 )$ 
D)  $( - 4 , - 5 ) \cup ( 10 , \infty )$ 
A)  $( - 10 , - 4 ) \cup ( 5 , \infty )$ 
B)  $( - \infty , - 5 ) \cup ( 4,10 )$ 
C)  $( - \infty , - 4 ) \cup ( 5,10 )$ 
D)  $( - 4 , - 5 ) \cup ( 10 , \infty )$

Question 6

Write the statement as an absolute value inequality.
-p is 5 units from 8

Accepted Answer

A)  $| p - 5 | = 8$ 
B)  $| p - 8 | < 5$ 
C)  $| \mathrm { p } | = 3$ 
D)  $| p - 8 | = 5$ 
A)  $| p - 5 | = 8$ 
B)  $| p - 8 | < 5$ 
C)  $| \mathrm { p } | = 3$ 
D)  $| p - 8 | = 5$

Question 7

Solve the formula for the indicated variable.
-$V = \frac { 1 } { 3 } B h$, for $B$

Accepted Answer

A)  $\mathrm { B } = \frac { \mathrm { h } } { 3 \mathrm {~V} }$ 
B)  $B = \frac { 3 V } { h }$ 
C)  $\mathrm { B } = \frac { \mathrm { V } } { 3 \mathrm {~h} }$ 
D)  $B = \frac { 3 h } { V }$ 
A)  $\mathrm { B } = \frac { \mathrm { h } } { 3 \mathrm {~V} }$ 
B)  $B = \frac { 3 V } { h }$ 
C)  $\mathrm { B } = \frac { \mathrm { V } } { 3 \mathrm {~h} }$ 
D)  $B = \frac { 3 h } { V }$

Question 8

Solve the inequality. Write the solution set in interval notation.
-$$\left| \frac { 5 } { 8 } - \frac { 1 } { 5 } x \right| < \frac { 2 } { 7 }$$

Accepted Answer

A)  $\left( - \infty , \frac { 95 } { 56 } \right) \cup \left( \frac { 255 } { 56 } , \infty \right)$ 
B)  $\left( \frac { 95 } { 56 } , \frac { 255 } { 56 } \right)$ 
C)  $( - \infty , \infty )$ 
D)  $\left( - \infty , - \frac { 255 } { 56 } \right) \cup \left( \frac { 95 } { 56 } , \infty \right)$ 
A)  $\left( - \infty , \frac { 95 } { 56 } \right) \cup \left( \frac { 255 } { 56 } , \infty \right)$ 
B)  $\left( \frac { 95 } { 56 } , \frac { 255 } { 56 } \right)$ 
C)  $( - \infty , \infty )$ 
D)  $\left( - \infty , - \frac { 255 } { 56 } \right) \cup \left( \frac { 95 } { 56 } , \infty \right)$

Question 9

A retailer knows that $\mathrm { n }$ games can be sold in a month if the price is $20 - 0.2 \mathrm { n }$ dollars per game. If he buys each game for $\$ 10$, and if he wishes to make a profit of at least $\$ 120$ per month on sales of this game, how many games must he sell each month?

Accepted Answer

A)  $20 \leq n \leq 30$ 
B)  $15 \leq n \leq 20$ 
C)  $15 \leq n \leq 25$ 
D)  $20 \leq n \leq 50$ 
A)  $20 \leq n \leq 30$ 
B)  $15 \leq n \leq 20$ 
C)  $15 \leq n \leq 25$ 
D)  $20 \leq n \leq 50$

Question 10

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary.
-$C = 76 ^ { \circ }$

Accepted Answer

A)  $\mathrm { F } = 60 ^ { \circ }$ 
B)  $\mathrm { F } = 194.4 ^ { \circ }$ 
C)  $\mathrm { F } = 168.8 ^ { \circ }$ 
D)  $\mathrm { F } = 24.4 ^ { \circ }$ 
A)  $\mathrm { F } = 60 ^ { \circ }$ 
B)  $\mathrm { F } = 194.4 ^ { \circ }$ 
C)  $\mathrm { F } = 168.8 ^ { \circ }$ 
D)  $\mathrm { F } = 24.4 ^ { \circ }$

Question 11

Multiply or divide, as indicated. Simplify the answer.
-$\frac { \sqrt { - 18 } } { \sqrt { - 2 } }$

Accepted Answer

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

Question 12

Simplify the power of i.
-$\frac { 1 } { i ^ { 43 } }$

Accepted Answer

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

Question 13

A real estate development consists of home sites that range in width from 59 to 115 feet and in depth from 135 to 191 feet. Using $x$ as the variable in both cases, write absolute value inequalities that correspond to these ranges.

Accepted Answer

A)  $| \mathrm { B } - 56 | \leq 59 , | x - 56 | \leq 135$ 
B)  $| \mathrm { B } - 59 | \leq 56 , | \mathrm { x } - 135 | \leq 56$ 
C)  $| x - 87 | \leq 28 , | x - 163 | \leq 28$ 
D)  $| x - 28 | \leq 87 , | x - 28 | \leq 163$ 
A)  $| \mathrm { B } - 56 | \leq 59 , | x - 56 | \leq 135$ 
B)  $| \mathrm { B } - 59 | \leq 56 , | \mathrm { x } - 135 | \leq 56$ 
C)  $| x - 87 | \leq 28 , | x - 163 | \leq 28$ 
D)  $| x - 28 | \leq 87 , | x - 28 | \leq 163$

Question 14

Determine whether or not the equation is linear.
-$3 x = 5 x - 9 x$

Accepted Answer

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

Question 15

Decide what values of the variable cannot possibly be solutions for the equation.
-$( x - 1 ) ^ { 4 } - 5 ( x - 1 ) ^ { 2 } + 4 = 0$

Accepted Answer

A)  $\{ - 1 , - 4 \}$ 
B)  $\{ - 2 , - 1,1,2 \}$ 
C)  $\{ 1,4 \}$ 
D)  $\{ - 1,0,2,3 \}$ 
A)  $\{ - 1 , - 4 \}$ 
B)  $\{ - 2 , - 1,1,2 \}$ 
C)  $\{ 1,4 \}$ 
D)  $\{ - 1,0,2,3 \}$

Question 16

Graph the solution set.
-$| 3 - 9 x | = 4$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 9 } , - \frac { 1 } { 9 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 9 } , \frac { 7 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 9 } , \frac { 1 } { 9 } \right\}$ 
A)  $\left\{ - \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 9 } , - \frac { 1 } { 9 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 9 } , \frac { 7 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 9 } , \frac { 1 } { 9 } \right\}$

Question 17

Find the product. Write the answer in standard form.
-$$( 8 - 5 i ) ^ { 2 }$$

Accepted Answer

A)  $89 + 80 \mathrm { i }$ 
B)  $39 - 80 \mathrm { i }$ 
C)  $89 - 80 \mathrm { i }$ 
D)  $39 + 80 i$ 
A)  $89 + 80 \mathrm { i }$ 
B)  $39 - 80 \mathrm { i }$ 
C)  $89 - 80 \mathrm { i }$ 
D)  $39 + 80 i$

Question 18

Find the product. Write the answer in standard form.
-$$- 8 \mathrm { i } ( - 4 - 8 \mathrm { i } ) ^ { 2 }$$

Accepted Answer

A)  $512 i - 512 i ^ { 2 } - 512 i ^ { 3 }$ 
B)  $384 - 512 \mathrm { i }$ 
C)  $384 \mathrm { i }$ 
D)  $512 + 384 \mathrm { i }$ 
A)  $512 i - 512 i ^ { 2 } - 512 i ^ { 3 }$ 
B)  $384 - 512 \mathrm { i }$ 
C)  $384 \mathrm { i }$ 
D)  $512 + 384 \mathrm { i }$

Question 19

Solve the cubic equation using factoring and the quadratic formula.
-$$\mathrm { x } ^ { 2 } - 3 = 0$$

Accepted Answer

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

Question 20

Solve the inequality. Write the solution set in interval notation.
-$| x + 2 | \geq 0$

Accepted Answer

A)  $[ - 2,2 ]$ 
B)  $\varnothing$ 
C)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $[ - 2,2 ]$ 
B)  $\varnothing$ 
C)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  $( - \infty , \infty )$

Determine whether or not the equation is linear. - $\frac { x + 2 } { 3 } = \frac { x - 8 } { 4 }$

Solve the inequality. Write the solution set in interval notation. - $| x + 1 | - 9 > 13$

Solve the inequality. Write the solution set in interval notation. - $| 4 - x | \leq 9$

Determine whether or not the equation is linear. - $1 - \frac { 3 } { 4 x } = \frac { 9 } { 6 }$

Solve the inequality. Write the solution set in interval notation. - $( x - 4 ) ( x - 10 ) ( x + 5 ) < 0$

Write the statement as an absolute value inequality. -p is 5 units from 8

Solve the formula for the indicated variable. - $V = \frac { 1 } { 3 } B h$ , for $B$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 5 } { 8 } - \frac { 1 } { 5 } x \right| < \frac { 2 } { 7 }$

A retailer knows that $\mathrm { n }$ games can be sold in a month if the price is $20 - 0.2 \mathrm { n }$ dollars per game. If he buys each game for $\$ 10$ , and if he wishes to make a profit of at least $\$ 120$ per month on sales of this game, how many games must he sell each month?

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. - $C = 76 ^ { \circ }$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 18 } } { \sqrt { - 2 } }$

Simplify the power of i. - $\frac { 1 } { i ^ { 43 } }$

A real estate development consists of home sites that range in width from 59 to 115 feet and in depth from 135 to 191 feet. Using $x$ as the variable in both cases, write absolute value inequalities that correspond to these ranges.

Determine whether or not the equation is linear. - $3 x = 5 x - 9 x$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x - 1 ) ^ { 4 } - 5 ( x - 1 ) ^ { 2 } + 4 = 0$

Graph the solution set. - $| 3 - 9 x | = 4$

Find the product. Write the answer in standard form. - $( 8 - 5 i ) ^ { 2 }$

Find the product. Write the answer in standard form. - $- 8 \mathrm { i } ( - 4 - 8 \mathrm { i } ) ^ { 2 }$

Solve the cubic equation using factoring and the quadratic formula. - $\mathrm { x } ^ { 2 } - 3 = 0$

Solve the inequality. Write the solution set in interval notation. - $| x + 2 | \geq 0$

Review of Basic Concepts

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 2: Equations and Inequalities

Determine whether or not the equation is linear. - x+23=x−84\frac { x + 2 } { 3 } = \frac { x - 8 } { 4 }3x+2​=4x−8​

Solve the inequality. Write the solution set in interval notation. - ∣x+1∣−9>13| x + 1 | - 9 > 13∣x+1∣−9>13

Solve the inequality. Write the solution set in interval notation. - ∣4−x∣≤9| 4 - x | \leq 9∣4−x∣≤9

Determine whether or not the equation is linear. - 1−34x=961 - \frac { 3 } { 4 x } = \frac { 9 } { 6 }1−4x3​=69​

Solve the inequality. Write the solution set in interval notation. - (x−4)(x−10)(x+5)<0( x - 4 ) ( x - 10 ) ( x + 5 ) < 0(x−4)(x−10)(x+5)<0

Write the statement as an absolute value inequality. -p is 5 units from 8

Solve the formula for the indicated variable. - V=13BhV = \frac { 1 } { 3 } B hV=31​Bh , for BBB

Solve the inequality. Write the solution set in interval notation. - ∣58−15x∣<27\left| \frac { 5 } { 8 } - \frac { 1 } { 5 } x \right| < \frac { 2 } { 7 }​85​−51​x​<72​

Use these equations to convert between the two systems. C=59(F−32)F=95C+32C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32C=95​(F−32)F=59​C+32 Round answer to the nearest tenth of a degree if necessary. - C=76∘C = 76 ^ { \circ }C=76∘

Multiply or divide, as indicated. Simplify the answer. - −18−2\frac { \sqrt { - 18 } } { \sqrt { - 2 } }−2​−18​​

Simplify the power of i. - 1i43\frac { 1 } { i ^ { 43 } }i431​

A real estate development consists of home sites that range in width from 59 to 115 feet and in depth from 135 to 191 feet. Using xxx as the variable in both cases, write absolute value inequalities that correspond to these ranges.

Determine whether or not the equation is linear. - 3x=5x−9x3 x = 5 x - 9 x3x=5x−9x

Decide what values of the variable cannot possibly be solutions for the equation. - (x−1)4−5(x−1)2+4=0( x - 1 ) ^ { 4 } - 5 ( x - 1 ) ^ { 2 } + 4 = 0(x−1)4−5(x−1)2+4=0

Graph the solution set. - ∣3−9x∣=4| 3 - 9 x | = 4∣3−9x∣=4

Find the product. Write the answer in standard form. - (8−5i)2( 8 - 5 i ) ^ { 2 }(8−5i)2

Find the product. Write the answer in standard form. - −8i(−4−8i)2- 8 \mathrm { i } ( - 4 - 8 \mathrm { i } ) ^ { 2 }−8i(−4−8i)2

Solve the cubic equation using factoring and the quadratic formula. - x2−3=0\mathrm { x } ^ { 2 } - 3 = 0x2−3=0

Solve the inequality. Write the solution set in interval notation. - ∣x+2∣≥0| x + 2 | \geq 0∣x+2∣≥0

Review of Basic Concepts

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Determine whether or not the equation is linear. - $\frac { x + 2 } { 3 } = \frac { x - 8 } { 4 }$

Solve the inequality. Write the solution set in interval notation. - $| x + 1 | - 9 > 13$

Solve the inequality. Write the solution set in interval notation. - $| 4 - x | \leq 9$

Determine whether or not the equation is linear. - $1 - \frac { 3 } { 4 x } = \frac { 9 } { 6 }$

Solve the inequality. Write the solution set in interval notation. - $( x - 4 ) ( x - 10 ) ( x + 5 ) < 0$

Solve the formula for the indicated variable. - $V = \frac { 1 } { 3 } B h$ , for $B$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 5 } { 8 } - \frac { 1 } { 5 } x \right| < \frac { 2 } { 7 }$

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. - $C = 76 ^ { \circ }$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 18 } } { \sqrt { - 2 } }$

Simplify the power of i. - $\frac { 1 } { i ^ { 43 } }$

A real estate development consists of home sites that range in width from 59 to 115 feet and in depth from 135 to 191 feet. Using $x$ as the variable in both cases, write absolute value inequalities that correspond to these ranges.

Determine whether or not the equation is linear. - $3 x = 5 x - 9 x$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x - 1 ) ^ { 4 } - 5 ( x - 1 ) ^ { 2 } + 4 = 0$

Graph the solution set. - $| 3 - 9 x | = 4$

Find the product. Write the answer in standard form. - $( 8 - 5 i ) ^ { 2 }$

Find the product. Write the answer in standard form. - $- 8 \mathrm { i } ( - 4 - 8 \mathrm { i } ) ^ { 2 }$

Solve the cubic equation using factoring and the quadratic formula. - $\mathrm { x } ^ { 2 } - 3 = 0$

Solve the inequality. Write the solution set in interval notation. - $| x + 2 | \geq 0$