Question 1

Solve the inequality. Write the solution set in interval notation.
-$$( x + 8 ) ( x + 6 ) ( x - 9 ) > 0$$

Accepted Answer

A)  $( - 8 , - 6 ) \cup ( 9 , \infty )$ 
B)  $( 9 , \infty )$ 
C)  $( - \infty , - 8 ) \cup ( - 6,9 )$ 
D)  $( - \infty , - 6 )$ 
A)  $( - 8 , - 6 ) \cup ( 9 , \infty )$ 
B)  $( 9 , \infty )$ 
C)  $( - \infty , - 8 ) \cup ( - 6,9 )$ 
D)  $( - \infty , - 6 )$

Question 2

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { - 5 } { x - 2 } + \frac { 2 } { x + 2 } = \frac { - 20 } { x ^ { 2 } - 4 }$$

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\{ - 2 \}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 8 } { 3 } \right\}$ 
A)  $\{ 2 \}$ 
B)  $\{ - 2 \}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 8 } { 3 } \right\}$

Question 3

Solve the equation by the zero-factor property.
-$$x ^ { 2 } + 14 x + 40 = 0$$

Accepted Answer

A)  $\{ 2 \sqrt { 10 } , - 2 \sqrt { 10 } \}$ 
B)  $\{ - 20 , - 8 \}$ 
C)  $\{ - 10 , - 4 \}$ 
D)  $\{ 4,10 \}$ 
A)  $\{ 2 \sqrt { 10 } , - 2 \sqrt { 10 } \}$ 
B)  $\{ - 20 , - 8 \}$ 
C)  $\{ - 10 , - 4 \}$ 
D)  $\{ 4,10 \}$

Question 4

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

Accepted Answer

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

Question 5

Solve the problem.
-In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 35° less than that of angle C. Find the measure of the angles.

Accepted Answer

A)  $86 ^ { \circ } , 8 ^ { \circ }$ and $43 ^ { \circ }$ 
B)  $86 ^ { \circ } , 8 ^ { \circ }$ and $86 ^ { \circ }$ 
C)  $129 ^ { \circ } , 8 ^ { \circ }$ and $86 ^ { \circ }$ 
D)  $129 ^ { \circ } , 8 ^ { \circ }$ and $43 ^ { \circ }$ 
A)  $86 ^ { \circ } , 8 ^ { \circ }$ and $43 ^ { \circ }$ 
B)  $86 ^ { \circ } , 8 ^ { \circ }$ and $86 ^ { \circ }$ 
C)  $129 ^ { \circ } , 8 ^ { \circ }$ and $86 ^ { \circ }$ 
D)  $129 ^ { \circ } , 8 ^ { \circ }$ and $43 ^ { \circ }$

Question 6

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 3 x - 28 \leq 0$$

Accepted Answer

A)  $[ 7 , \infty )$ 
B)  $( - \infty , - 4 ] \cup [ 7 , \infty )$ 
C)  $( - \infty , - 4 ]$ 
D)  $[ - 4,7 ]$ 
A)  $[ 7 , \infty )$ 
B)  $( - \infty , - 4 ] \cup [ 7 , \infty )$ 
C)  $( - \infty , - 4 ]$ 
D)  $[ - 4,7 ]$

Question 7

Solve the problem.
-Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 5 miles per hour, and Delvis is traveling at a speed of 10 miles per hour. In 3 hours what is the distance between them (assuming
That they began at the same point and time)?

Accepted Answer

A)  24 mi 
B)  15 mi 
C)  12 mi 
D)  16 mi 
A)  24 mi 
B)  15 mi 
C)  12 mi 
D)  16 mi

Question 8

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt [ 4 ] { x + 9 } = \sqrt [ 4 ] { 5 x }$$

Accepted Answer

A)  $\left\{ \frac { 4 } { 9 } \right\}$ 
B)  $\left\{ \frac { 9 } { 4 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 9 } { 5 } \right\}$ 
A)  $\left\{ \frac { 4 } { 9 } \right\}$ 
B)  $\left\{ \frac { 9 } { 4 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \frac { 9 } { 5 } \right\}$

Question 9

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { - 4 } { - 3 x - 5 } > 0$$

Accepted Answer

A)  $\left( - \frac { 5 } { 3 } , \infty \right)$ 
B)  $\left( - \infty , \frac { 5 } { 3 } \right)$ 
C)  $( 0 , \infty )$ 
D)  $\left( - \infty , - \frac { 3 } { 5 } \right)$ 
A)  $\left( - \frac { 5 } { 3 } , \infty \right)$ 
B)  $\left( - \infty , \frac { 5 } { 3 } \right)$ 
C)  $( 0 , \infty )$ 
D)  $\left( - \infty , - \frac { 3 } { 5 } \right)$

Question 10

Multiply or divide, as indicated. Simplify the answer.
-$$\frac { \sqrt { - 10 } \cdot \sqrt { - 2 } } { \sqrt { 5 } }$$

Accepted Answer

A)  $2 \mathrm { i }$ 
B)  $- 2$ 
C)  $- 2 \mathrm { i }$ 
D)  2 
A)  $2 \mathrm { i }$ 
B)  $- 2$ 
C)  $- 2 \mathrm { i }$ 
D)  2

Question 11

The difference of the squares of two positive consecutive even integers is 108. Find the integers.

Accepted Answer

A)  24, 22 
B)  28, 30 
C)  26, 24 
D)  26, 28 
A)  24, 22 
B)  28, 30 
C)  26, 24 
D)  26, 28

Question 12

Simplify the power of i.
-$$\frac { 1 } { \mathrm { i } ^ { - 11 } }$$

Accepted Answer

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

Question 13

Solve the inequality. Write the solution set in interval notation.
-| $$3 x - 9 \mid \leq - 6$$

Accepted Answer

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

Question 14

A coin is tossed upward from a balcony $228 \mathrm { ft }$ high with an initial velocity of $32 \mathrm { ft } / \mathrm { sec }$. During what interval of

Accepted Answer

A)  $4 \leq t \leq 8$ 
B)  $0 \leq t \leq 4$ 
C)  $3 \leq t \leq 4$ 
D)  $0 \leq t \leq 1$ 
A)  $4 \leq t \leq 8$ 
B)  $0 \leq t \leq 4$ 
C)  $3 \leq t \leq 4$ 
D)  $0 \leq t \leq 1$

Question 15

Determine whether or not the equation is linear.
-$0.04 x ^ { 2 } + 0.05 x = 0.20$

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

A rock falls from a tower that is $117.6 \mathrm {~m}$ high. As it is falling, its height is given by the formula $h = 117.6 = 4.9 \mathrm { t } 2$, with $t$ in seconds. How many seconds will it take for the rock to hit the ground $( h = 0 )$ ?

Accepted Answer

A)  10.8 sec 
B)  2822.4 sec 
C)  10.6 sec 
D)  4.9 sec 
A)  10.8 sec 
B)  2822.4 sec 
C)  10.6 sec 
D)  4.9 sec

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.
-$4 + 7 z ^ { 2 } = 8 z$

Accepted Answer

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

Question 19

Find the quotient. Write the answer in standard form.
-$$\frac { 9 - 4 i } { 5 + 3 i }$$

Accepted Answer

A)  $\frac { 57 } { 16 } + \frac { 47 } { 16 } \mathrm { i }$ 
B)  $\frac { 33 } { 16 } + \frac { 47 } { 16 } \mathrm { i }$ 
C)  $\frac { 57 } { 34 } - \frac { 7 } { 34 } \mathrm { i }$ 
D)  $\frac { 33 } { 34 } - \frac { 47 } { 34 } \mathrm { i }$ 
A)  $\frac { 57 } { 16 } + \frac { 47 } { 16 } \mathrm { i }$ 
B)  $\frac { 33 } { 16 } + \frac { 47 } { 16 } \mathrm { i }$ 
C)  $\frac { 57 } { 34 } - \frac { 7 } { 34 } \mathrm { i }$ 
D)  $\frac { 33 } { 34 } - \frac { 47 } { 34 } \mathrm { i }$

Question 20

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$24 ( x - 3 ) = 2 ( 12 x - 1 ) - 70$$

Accepted Answer

A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ - 72 \}$ 
C)  Identity; {all real numbers } 
D)  Conditional; $\{ 0 \}$ 
A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ - 72 \}$ 
C)  Identity; {all real numbers } 
D)  Conditional; $\{ 0 \}$

Solve the inequality. Write the solution set in interval notation. - $( x + 8 ) ( x + 6 ) ( x - 9 ) > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { - 5 } { x - 2 } + \frac { 2 } { x + 2 } = \frac { - 20 } { x ^ { 2 } - 4 }$

Solve the equation by the zero-factor property. - $x ^ { 2 } + 14 x + 40 = 0$

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

Solve the problem. -In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 35° less than that of angle C. Find the measure of the angles.

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 3 x - 28 \leq 0$

Solve the problem. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 5 miles per hour, and Delvis is traveling at a speed of 10 miles per hour. In 3 hours what is the distance between them (assuming That they began at the same point and time)?

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 4 ] { x + 9 } = \sqrt [ 4 ] { 5 x }$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { - 4 } { - 3 x - 5 } > 0$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 10 } \cdot \sqrt { - 2 } } { \sqrt { 5 } }$

The difference of the squares of two positive consecutive even integers is 108. Find the integers.

Simplify the power of i. - $\frac { 1 } { \mathrm { i } ^ { - 11 } }$

Solve the inequality. Write the solution set in interval notation. -| $3 x - 9 \mid \leq - 6$

A coin is tossed upward from a balcony $228 \mathrm { ft }$ high with an initial velocity of $32 \mathrm { ft } / \mathrm { sec }$ . During what interval of

Determine whether or not the equation is linear. - $0.04 x ^ { 2 } + 0.05 x = 0.20$

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

A rock falls from a tower that is $117.6 \mathrm {~m}$ high. As it is falling, its height is given by the formula $h = 117.6 = 4.9 \mathrm { t } 2$ , with $t$ in seconds. How many seconds will it take for the rock to hit the ground $( h = 0 )$ ?

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. - $4 + 7 z ^ { 2 } = 8 z$

Find the quotient. Write the answer in standard form. - $\frac { 9 - 4 i } { 5 + 3 i }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $24 ( x - 3 ) = 2 ( 12 x - 1 ) - 70$

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

Solve the inequality. Write the solution set in interval notation. - (x+8)(x+6)(x−9)>0( x + 8 ) ( x + 6 ) ( x - 9 ) > 0(x+8)(x+6)(x−9)>0

Decide what values of the variable cannot possibly be solutions for the equation. - −5x−2+2x+2=−20x2−4\frac { - 5 } { x - 2 } + \frac { 2 } { x + 2 } = \frac { - 20 } { x ^ { 2 } - 4 }x−2−5​+x+22​=x2−4−20​

Solve the equation by the zero-factor property. - x2+14x+40=0x ^ { 2 } + 14 x + 40 = 0x2+14x+40=0

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - π\piπ

Solve the problem. -In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 35° less than that of angle C. Find the measure of the angles.

Solve the quadratic inequality. Write the solution set in interval notation. - x2−3x−28≤0x ^ { 2 } - 3 x - 28 \leq 0x2−3x−28≤0

Solve the problem. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 5 miles per hour, and Delvis is traveling at a speed of 10 miles per hour. In 3 hours what is the distance between them (assuming That they began at the same point and time)?

Decide what values of the variable cannot possibly be solutions for the equation. - x+94=5x4\sqrt [ 4 ] { x + 9 } = \sqrt [ 4 ] { 5 x }4x+9​=45x​

Solve the rational inequality. Write the solution set in interval notation. - −4−3x−5>0\frac { - 4 } { - 3 x - 5 } > 0−3x−5−4​>0

Multiply or divide, as indicated. Simplify the answer. - −10⋅−25\frac { \sqrt { - 10 } \cdot \sqrt { - 2 } } { \sqrt { 5 } }5​−10​⋅−2​​

The difference of the squares of two positive consecutive even integers is 108. Find the integers.

Simplify the power of i. - 1i−11\frac { 1 } { \mathrm { i } ^ { - 11 } }i−111​

Solve the inequality. Write the solution set in interval notation. -| 3x−9∣≤−63 x - 9 \mid \leq - 63x−9∣≤−6

A coin is tossed upward from a balcony 228ft228 \mathrm { ft }228ft high with an initial velocity of 32ft/sec32 \mathrm { ft } / \mathrm { sec }32ft/sec . During what interval of

Determine whether or not the equation is linear. - 0.04x2+0.05x=0.200.04 x ^ { 2 } + 0.05 x = 0.200.04x2+0.05x=0.20

Solve the formula for the indicated variable. - I=nEnr+R′I = \frac { n E } { n r + R ^ { \prime } }I=nr+R′nE​ , for nnn

A rock falls from a tower that is 117.6 m117.6 \mathrm {~m}117.6 m high. As it is falling, its height is given by the formula h=117.6=4.9t2h = 117.6 = 4.9 \mathrm { t } 2h=117.6=4.9t2 , with ttt in seconds. How many seconds will it take for the rock to hit the ground (h=0)( h = 0 )(h=0) ?

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. - 4+7z2=8z4 + 7 z ^ { 2 } = 8 z4+7z2=8z

Find the quotient. Write the answer in standard form. - 9−4i5+3i\frac { 9 - 4 i } { 5 + 3 i }5+3i9−4i​

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 24(x−3)=2(12x−1)−7024 ( x - 3 ) = 2 ( 12 x - 1 ) - 7024(x−3)=2(12x−1)−70

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

Solve the inequality. Write the solution set in interval notation. - $( x + 8 ) ( x + 6 ) ( x - 9 ) > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { - 5 } { x - 2 } + \frac { 2 } { x + 2 } = \frac { - 20 } { x ^ { 2 } - 4 }$

Solve the equation by the zero-factor property. - $x ^ { 2 } + 14 x + 40 = 0$

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

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 3 x - 28 \leq 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 4 ] { x + 9 } = \sqrt [ 4 ] { 5 x }$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { - 4 } { - 3 x - 5 } > 0$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 10 } \cdot \sqrt { - 2 } } { \sqrt { 5 } }$

Simplify the power of i. - $\frac { 1 } { \mathrm { i } ^ { - 11 } }$

Solve the inequality. Write the solution set in interval notation. -| $3 x - 9 \mid \leq - 6$

A coin is tossed upward from a balcony $228 \mathrm { ft }$ high with an initial velocity of $32 \mathrm { ft } / \mathrm { sec }$ . During what interval of

Determine whether or not the equation is linear. - $0.04 x ^ { 2 } + 0.05 x = 0.20$

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

A rock falls from a tower that is $117.6 \mathrm {~m}$ high. As it is falling, its height is given by the formula $h = 117.6 = 4.9 \mathrm { t } 2$ , with $t$ in seconds. How many seconds will it take for the rock to hit the ground $( h = 0 )$ ?

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. - $4 + 7 z ^ { 2 } = 8 z$

Find the quotient. Write the answer in standard form. - $\frac { 9 - 4 i } { 5 + 3 i }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $24 ( x - 3 ) = 2 ( 12 x - 1 ) - 70$