Question 1

Solve the equation for the indicated variable. Assume no denominator is 0.
-$\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$, for $\mathrm { v }$

Accepted Answer

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

Question 2

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 1 } { x + 9 } > 0$$

Accepted Answer

A)  $( 9 , - \infty )$ 
B)  $( - \infty , 9 )$ 
C)  $[ 9 , \infty ]$ 
D)  $( - 9 , \infty )$ 
A)  $( 9 , - \infty )$ 
B)  $( - \infty , 9 )$ 
C)  $[ 9 , \infty ]$ 
D)  $( - 9 , \infty )$

Question 3

Solve the equation.
-$$| 5 x + 1 | = | x - 9 |$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 2 } , \frac { 4 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 5 } { 2 } , - \frac { 4 } { 3 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 2 } , \frac { 4 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 5 } { 2 } , - \frac { 4 } { 3 } \right\}$

Question 4

Solve the equation.
-$\left| 3 x ^ { 3 } - 3 x ^ { 2 } - 6 x \right| = 0$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } , 1,0 \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } , - 1 \right\}$ 
C)  $\{ 2 , - 1,0 \}$ 
D)  $\left\{ \frac { 1 } { 2 } , 0 \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } , 1,0 \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } , - 1 \right\}$ 
C)  $\{ 2 , - 1,0 \}$ 
D)  $\left\{ \frac { 1 } { 2 } , 0 \right\}$

Question 5

Determine whether or not the equation is linear.
-4x + 7x(x - 2) = 16x

Accepted Answer

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

Question 6

Solve the problem.
-The high temperature on December 12 in Tampa, FL ranges from $36 ^ { \circ } \mathrm { F }$ to $84 ^ { \circ } \mathrm { F }$. Using $\mathrm { F }$ as the variable, write an absolute value inequality that corresponds to this range.

Accepted Answer

A)  $| F - 36 | \leq 48$ 
B)  $| F - 24 | \leq 60$ 
C)  $| F - 48 | \leq 36$ 
D)  $| F - 60 | \leq 24$ 
A)  $| F - 36 | \leq 48$ 
B)  $| F - 24 | \leq 60$ 
C)  $| F - 48 | \leq 36$ 
D)  $| F - 60 | \leq 24$

Question 7

Solve the inequality. Write the solution set in interval notation.
-$$| 4 - x | \geq 1$$

Accepted Answer

A)  $[ 3,5 ]$ 
B)  $[ 5 , \infty )$ 
C)  $[ 3 , \infty )$ 
D)  $( - \infty , 3 ] \cup [ 5 , \infty )$ 
A)  $[ 3,5 ]$ 
B)  $[ 5 , \infty )$ 
C)  $[ 3 , \infty )$ 
D)  $( - \infty , 3 ] \cup [ 5 , \infty )$

Question 8

Solve the equation by the zero-factor property.
-$$x ^ { 2 } + 3 x - 10 = 0$$

Accepted Answer

A)  $\{ - 5 , - 2 \}$ 
B)  $\{ - 2,5 \}$ 
C)  $\{ - 5,2 \}$ 
D)  $\{ 2,5 \}$ 
A)  $\{ - 5 , - 2 \}$ 
B)  $\{ - 2,5 \}$ 
C)  $\{ - 5,2 \}$ 
D)  $\{ 2,5 \}$

Question 9

Solve the problem.
-A building needs a ramp to make it handicap accessible. By law, the ramp must run 10 inches horizontally for every 1 inch of rise. If the surface of the ramp is 73 inches long how far above the
Ground is the inclined end of the ramp? Round to the nearest tenth of an inch.

Accepted Answer

A)  7.3 in. 
B)  24.3 in. 
C)  4.8 in. 
D)  6.6 in. 
A)  7.3 in. 
B)  24.3 in. 
C)  4.8 in. 
D)  6.6 in.

Question 10

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } + 1 = 0$$

Accepted Answer

A)  $\left\{ - 1 , \frac { 1 } { 2 } \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$ 
B)  $\{ - 1 , \pm i \}$ 
C)  $\{ - 1,1 \pm \mathrm { i } \sqrt { 3 } \}$ 
D)  $\{ - 1 , - 1 \pm \mathrm { i } \sqrt { 3 } \}$ 
A)  $\left\{ - 1 , \frac { 1 } { 2 } \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$ 
B)  $\{ - 1 , \pm i \}$ 
C)  $\{ - 1,1 \pm \mathrm { i } \sqrt { 3 } \}$ 
D)  $\{ - 1 , - 1 \pm \mathrm { i } \sqrt { 3 } \}$

Question 11

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$3 ( 28 x + 16 ) = 12 ( 5 x + 12 )$$

Accepted Answer

A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ - 8 \}$ 
C)  Conditional; $\{ 4 \}$ 
D)  Identity;{all real numbers} 
A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ - 8 \}$ 
C)  Conditional; $\{ 4 \}$ 
D)  Identity;{all real numbers}

Question 12

Solve the formula for the indicated variable.
-$I = \frac { n E } { n r + R }$, for $n$

Accepted Answer

A)  $n = \operatorname { IR } ( \operatorname { Ir } - \mathrm { E } )$ 
B)  $n = \frac { I R } { I r + E }$ 
C)  $n = \frac { R } { E - I r }$ 
D)  $n = \frac { I R } { E - I r }$ 
A)  $n = \operatorname { IR } ( \operatorname { Ir } - \mathrm { E } )$ 
B)  $n = \frac { I R } { I r + E }$ 
C)  $n = \frac { R } { E - I r }$ 
D)  $n = \frac { I R } { E - I r }$

Question 13

Solve for the indicated variable.
-$\mathrm { Z } = \mathrm { A } ( 1 + \mathrm { x } ) ^ { 1 / 2 }$, for $\mathrm { x }$

Accepted Answer

A)  $x = \left( \frac { Z } { A } \right) ^ { 2 } - 1$ 
B)  $x = \left( \frac { Z } { A } \right) ^ { 2 }$ 
C)  $x = \left( \frac { A } { Z } \right) ^ { 2 }$ 
D)  $x = \left( \frac { Z } { A } \right) ^ { 2 } + 1$ 
A)  $x = \left( \frac { Z } { A } \right) ^ { 2 } - 1$ 
B)  $x = \left( \frac { Z } { A } \right) ^ { 2 }$ 
C)  $x = \left( \frac { A } { Z } \right) ^ { 2 }$ 
D)  $x = \left( \frac { Z } { A } \right) ^ { 2 } + 1$

Question 14

Find the product. Write the answer in standard form.
-$$( 6 - 5 i ) ( 2 + 8 i )$$

Accepted Answer

A)  $52 - 38 \mathrm { i }$ 
B)  $52 + 38 \mathrm { i }$ 
C)  $- 28 - 58 \mathrm { i }$ 
D)  $- 40 \mathrm { i } ^ { 2 } + 38 \mathrm { i } - 12$ 
A)  $52 - 38 \mathrm { i }$ 
B)  $52 + 38 \mathrm { i }$ 
C)  $- 28 - 58 \mathrm { i }$ 
D)  $- 40 \mathrm { i } ^ { 2 } + 38 \mathrm { i } - 12$

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.
-$- 5 - 5 a ^ { 2 } = - 7 a - 7$

Accepted Answer

A)  Two distinct nonreal complex solutions 
B)  Two distinct rational solutions 
C)  One rational solution (a double solution) 
D)  Two distinct irrational solutions 
A)  Two distinct nonreal complex solutions 
B)  Two distinct rational solutions 
C)  One rational solution (a double solution) 
D)  Two distinct irrational solutions

Question 16

Decide whether or not the equations are equivalent.
-$$\begin{array} { l } 
\mathrm { z } ^ { 2 } = 25 \
\mathrm { z } = 5
\end{array}$$

Accepted Answer

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

Question 17

Find the sum or difference. Write the answer in standard form.
-$$( 8 - 9 i ) + ( 7 + 5 i )$$

Accepted Answer

A)  $15 + 4 \mathrm { i }$ 
B)  $1 + 14 \mathrm { i }$ 
C)  $- 15 + 4 i$ 
D)  $15 - 4 \mathrm { i }$ 
A)  $15 + 4 \mathrm { i }$ 
B)  $1 + 14 \mathrm { i }$ 
C)  $- 15 + 4 i$ 
D)  $15 - 4 \mathrm { i }$

Question 18

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.
-$$s ^ { 2 } - 6 s + 5 = 0$$

Accepted Answer

A)  One rational solution (a double solution) 
B)  Two distinct nonreal complex solutions 
C)  Two distinct irrational solutions 
D)  Two distinct rational solutions 
A)  One rational solution (a double solution) 
B)  Two distinct nonreal complex solutions 
C)  Two distinct irrational solutions 
D)  Two distinct rational solutions

Question 19

Determine whether or not the equation is linear.
-3x + 7 = 0

Accepted Answer

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

Question 20

Solve the formula for the indicated variable.
-$\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32$, for $\mathrm { C }$

Accepted Answer

A)  $C = \frac { 5 } { 9 } ( F - 32 )$ 
B)  $C = \frac { F - 32 } { 9 }$ 
C)  $C = \frac { 9 } { 5 } ( F - 32 )$ 
D)  $C = \frac { 5 } { F - 32 }$ 
A)  $C = \frac { 5 } { 9 } ( F - 32 )$ 
B)  $C = \frac { F - 32 } { 9 }$ 
C)  $C = \frac { 9 } { 5 } ( F - 32 )$ 
D)  $C = \frac { 5 } { F - 32 }$

Solve the equation for the indicated variable. Assume no denominator is 0. - $\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$ , for $\mathrm { v }$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 1 } { x + 9 } > 0$

Solve the equation. - $| 5 x + 1 | = | x - 9 |$

Solve the equation. - $\left| 3 x ^ { 3 } - 3 x ^ { 2 } - 6 x \right| = 0$

Determine whether or not the equation is linear. -4x + 7x(x - 2) = 16x

Solve the problem. -The high temperature on December 12 in Tampa, FL ranges from $36 ^ { \circ } \mathrm { F }$ to $84 ^ { \circ } \mathrm { F }$ . Using $\mathrm { F }$ as the variable, write an absolute value inequality that corresponds to this range.

Solve the inequality. Write the solution set in interval notation. - $| 4 - x | \geq 1$

Solve the equation by the zero-factor property. - $x ^ { 2 } + 3 x - 10 = 0$

Solve the problem. -A building needs a ramp to make it handicap accessible. By law, the ramp must run 10 inches horizontally for every 1 inch of rise. If the surface of the ramp is 73 inches long how far above the Ground is the inclined end of the ramp? Round to the nearest tenth of an inch.

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } + 1 = 0$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $3 ( 28 x + 16 ) = 12 ( 5 x + 12 )$

Solve the formula for the indicated variable. - $I = \frac { n E } { n r + R }$ , for $n$

Solve for the indicated variable. - $\mathrm { Z } = \mathrm { A } ( 1 + \mathrm { x } ) ^ { 1 / 2 }$ , for $\mathrm { x }$

Find the product. Write the answer in standard form. - $( 6 - 5 i ) ( 2 + 8 i )$

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. - $- 5 - 5 a ^ { 2 } = - 7 a - 7$

Decide whether or not the equations are equivalent. - =25 =5

Find the sum or difference. Write the answer in standard form. - $( 8 - 9 i ) + ( 7 + 5 i )$

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. - $s ^ { 2 } - 6 s + 5 = 0$

Determine whether or not the equation is linear. -3x + 7 = 0

Solve the formula for the indicated variable. - $\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32$ , for $\mathrm { C }$

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 equation for the indicated variable. Assume no denominator is 0. - Ve=12mv2\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }Ve=21​mv2 , for v\mathrm { v }v

Solve the rational inequality. Write the solution set in interval notation. - 1x+9>0\frac { 1 } { x + 9 } > 0x+91​>0

Solve the equation. - ∣5x+1∣=∣x−9∣| 5 x + 1 | = | x - 9 |∣5x+1∣=∣x−9∣

Solve the equation. - ∣3x3−3x2−6x∣=0\left| 3 x ^ { 3 } - 3 x ^ { 2 } - 6 x \right| = 0​3x3−3x2−6x​=0