Question 1

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

Accepted Answer

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

Question 2

Solve the inequality. Write the solution set in interval notation.
-$$| 7 x + 9 | - 3 < 3$$

Accepted Answer

A)  $\left( - \frac { 15 } { 7 } , - \frac { 3 } { 7 } \right)$ 
B)  $\varnothing$ 
C)  $\left\{ - \infty , - \frac { 15 } { 7 } \right) \cup \left( - \frac { 3 } { 7 } , \infty \right)$ 
D)  $\left( - \infty , - \frac { 15 } { 7 } \right)$ 
A)  $\left( - \frac { 15 } { 7 } , - \frac { 3 } { 7 } \right)$ 
B)  $\varnothing$ 
C)  $\left\{ - \infty , - \frac { 15 } { 7 } \right) \cup \left( - \frac { 3 } { 7 } , \infty \right)$ 
D)  $\left( - \infty , - \frac { 15 } { 7 } \right)$

Question 3

Decide whether the statement is true or false.
-$- 11 \text { is a solution of } - 3 x + 9 = 37$

Accepted Answer

A) True 
 B)False

Question 4

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } + 64 = 0$$

Accepted Answer

A)  $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 5 } \}$ 
B)  $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 3 } \}$ 
C)  $\{ - 4 , - 2 \pm 2 \mathrm { i } \}$ 
D)  $\{ - 4 , - 2 \pm 2 \mathrm { i } \sqrt { 6 } \}$ 
A)  $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 5 } \}$ 
B)  $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 3 } \}$ 
C)  $\{ - 4 , - 2 \pm 2 \mathrm { i } \}$ 
D)  $\{ - 4 , - 2 \pm 2 \mathrm { i } \sqrt { 6 } \}$

Question 5

Graph the solution set.
-$$| 5 x + 4 | = | 8 x + 1 |$$

Accepted Answer

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

Question 6

Solve the equation by completing the square.
-$$x ^ { 2 } = 3 - 4 x$$

Accepted Answer

A)  $\{ 2 + \sqrt { 7 } \}$ 
B)  $\{ - 2 \pm \sqrt { 7 } \}$ 
C)  $\{ - 1 \pm \sqrt { 7 } \}$ 
D)  $\{ - 2 \pm 2 \sqrt { 7 } \}$ 
A)  $\{ 2 + \sqrt { 7 } \}$ 
B)  $\{ - 2 \pm \sqrt { 7 } \}$ 
C)  $\{ - 1 \pm \sqrt { 7 } \}$ 
D)  $\{ - 2 \pm 2 \sqrt { 7 } \}$

Question 7

The average annual growth rate of Cyprus trees in inches satisfies the inequality |x - 3.25| 2.69. What range of growth corresponds to this inequality?

Accepted Answer

A)  [0.56, 11.88] 
B)  [0.56, 5.94] 
C)  [2.69, 3.25] 
D)  [0.28, 5.94] 
A)  [0.56, 11.88] 
B)  [0.56, 5.94] 
C)  [2.69, 3.25] 
D)  [0.28, 5.94]

Question 8

Graph the solution set.
-$| x | > 9$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Solve the cubic equation using factoring and the quadratic formula.
-$$x - 5 = 0$$

Accepted Answer

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

Question 10

Solve for the indicated variable.
-$\frac { 1 } { \mathrm { Q } } = \frac { 1 } { \mathrm {~T} _ { 1 } } + \frac { 1 } { \mathrm {~T} _ { 2 } }$, for $\mathrm { T } _ { 2 }$

Accepted Answer

A)  $\mathrm { T } _ { 2 } = \frac { \mathrm { Q } - \mathrm { T } _ { 1 } } { \mathrm {~T} _ { 1 } \mathrm { Q } }$ 
B)  $\mathrm { T } _ { 2 } = \frac { \mathrm { T } _ { 1 } - \mathrm { Q } } { \mathrm { T } _ { 1 } \mathrm { Q } }$ 
C)  $\mathrm { T } _ { 2 } = \frac { \mathrm { QT } _ { 1 } } { \mathrm {~T} _ { 1 } - \mathrm { Q } }$ 
D)  $\mathrm { T } _ { 2 } = \frac { \mathrm { QT } _ { 1 } } { \mathrm {~T} _ { 1 } + 4 \mathrm { Q } }$ 
A)  $\mathrm { T } _ { 2 } = \frac { \mathrm { Q } - \mathrm { T } _ { 1 } } { \mathrm {~T} _ { 1 } \mathrm { Q } }$ 
B)  $\mathrm { T } _ { 2 } = \frac { \mathrm { T } _ { 1 } - \mathrm { Q } } { \mathrm { T } _ { 1 } \mathrm { Q } }$ 
C)  $\mathrm { T } _ { 2 } = \frac { \mathrm { QT } _ { 1 } } { \mathrm {~T} _ { 1 } - \mathrm { Q } }$ 
D)  $\mathrm { T } _ { 2 } = \frac { \mathrm { QT } _ { 1 } } { \mathrm {~T} _ { 1 } + 4 \mathrm { Q } }$

Question 11

Indicate whether the statement is true always, sometimes, or never.
-The product of a pair of complex conjugates (with b  0) is the difference of the squares of the real and imaginary parts.

Accepted Answer

A)  Always 
B)  Never 
C)  Sometimes 
A)  Always 
B)  Never 
C)  Sometimes

Question 12

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

Accepted Answer

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

Question 13

Decide what values of the variable cannot possibly be solutions for the equation.
-$\sqrt { 2 x + 3 } + \sqrt { 4 - x } = 4$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ - 3 \}$ 
C)  $\left\{ 3 , \frac { 11 } { 9 } \right\}$ 
D)  $\{ 3 \}$ 
A)  $\varnothing$ 
B)  $\{ - 3 \}$ 
C)  $\left\{ 3 , \frac { 11 } { 9 } \right\}$ 
D)  $\{ 3 \}$

Question 14

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$2 [ 3 - ( 3 - 5 x ) ] - x = - 6 + 3 ( 2 + 3 x )$$

Accepted Answer

A)  Conditional; $\{ 6 \}$ 
B)  Conditional; $\{ - 3 \}$ 
C)  Contradiction; $\varnothing$ 
D)  Identity; {all real numbers\} 
A)  Conditional; $\{ 6 \}$ 
B)  Conditional; $\{ - 3 \}$ 
C)  Contradiction; $\varnothing$ 
D)  Identity; {all real numbers\}

Question 15

Solve and graph the inequality. Give answer in interval notation.
-$$0 < - 3 x \leq 12$$

Accepted Answer

A)  $[ - 4,0 )$
  
B)  $[ - 4,0 ]$
  
C)  $( 0,4 ]$
  
D)  $[ 0,4 )$
  
A)  $[ - 4,0 )$
  
B)  $[ - 4,0 ]$
  
C)  $( 0,4 ]$
  
D)  $[ 0,4 )$

Question 16

The length of a rectangle is 4 inches more than its width. If 2 inches are taken from the length and added to the width, the figure becomes a square with an area of 169 square inches. What are the dimensions of the original
Figure?

Accepted Answer

A)  13 in. by 13 in. 
B)  11 in. by 13 in. 
C)  11 in. by 15 in. 
D)  9 in. by 13 in. 
A)  13 in. by 13 in. 
B)  11 in. by 13 in. 
C)  11 in. by 15 in. 
D)  9 in. by 13 in.

Question 17

Solve the problem.
-A triangular shaped lake-front lot has a perimeter of 1500 ft. One side is 100 ft longer than the shortest side, while the third side is 200 ft longer than the shortest side. Find the lengths of all three sides.

Accepted Answer

A)  100 ft, 200 ft, 300 ft 
B)  500 ft, 600 ft, 700 ft 
C)  500 ft, 500 ft, 500 ft 
D)  400 ft, 500 ft, 600 ft 
A)  100 ft, 200 ft, 300 ft 
B)  500 ft, 600 ft, 700 ft 
C)  500 ft, 500 ft, 500 ft 
D)  400 ft, 500 ft, 600 ft

Question 18

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( x + 5 ) ^ { 2 / 3 } + 4 ( x + 5 ) ^ { 1 / 3 } + 3 = 0$$

Accepted Answer

A)  $\{ 32 , - 6 \}$ 
B)  $\{ - 1,1 \}$ 
C)  $\varnothing$ 
D)  $\{ - 32 , - 6 \}$ 
A)  $\{ 32 , - 6 \}$ 
B)  $\{ - 1,1 \}$ 
C)  $\varnothing$ 
D)  $\{ - 32 , - 6 \}$

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

Solve the inequality. Write the solution set in interval notation. - $| 7 x + 9 | - 3 < 3$

Decide whether the statement is true or false. - $- 11 \text { is a solution of } - 3 x + 9 = 37$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } + 64 = 0$

Graph the solution set. - $| 5 x + 4 | = | 8 x + 1 |$

Solve the equation by completing the square. - $x ^ { 2 } = 3 - 4 x$

The average annual growth rate of Cyprus trees in inches satisfies the inequality |x - 3.25| 2.69. What range of growth corresponds to this inequality?

Graph the solution set. - $| x | > 9$

Solve the cubic equation using factoring and the quadratic formula. - $x - 5 = 0$

Solve for the indicated variable. - $\frac { 1 } { \mathrm { Q } } = \frac { 1 } { \mathrm {~T} _ { 1 } } + \frac { 1 } { \mathrm {~T} _ { 2 } }$ , for $\mathrm { T } _ { 2 }$

Indicate whether the statement is true always, sometimes, or never. -The product of a pair of complex conjugates (with b  0) is the difference of the squares of the real and imaginary parts.

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

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 2 x + 3 } + \sqrt { 4 - x } = 4$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $2 [ 3 - ( 3 - 5 x ) ] - x = - 6 + 3 ( 2 + 3 x )$

Solve and graph the inequality. Give answer in interval notation. - $0 < - 3 x \leq 12$ $Solve and graph the inequality. Give answer in interval notation. - 0 < - 3 x \leq 12$

The length of a rectangle is 4 inches more than its width. If 2 inches are taken from the length and added to the width, the figure becomes a square with an area of 169 square inches. What are the dimensions of the original Figure?

Solve the problem. -A triangular shaped lake-front lot has a perimeter of 1500 ft. One side is 100 ft longer than the shortest side, while the third side is 200 ft longer than the shortest side. Find the lengths of all three sides.

Decide what values of the variable cannot possibly be solutions for the equation. - $( x + 5 ) ^ { 2 / 3 } + 4 ( x + 5 ) ^ { 1 / 3 } + 3 = 0$

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

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

Solve the inequality. Write the solution set in interval notation. - ∣7x+9∣−3<3| 7 x + 9 | - 3 < 3∣7x+9∣−3<3

Decide whether the statement is true or false. - −11 is a solution of −3x+9=37- 11 \text { is a solution of } - 3 x + 9 = 37−11 is a solution of −3x+9=37

Solve the cubic equation using factoring and the quadratic formula. - x3+64=0x ^ { 3 } + 64 = 0x3+64=0

Graph the solution set. - ∣5x+4∣=∣8x+1∣| 5 x + 4 | = | 8 x + 1 |∣5x+4∣=∣8x+1∣

Solve the equation by completing the square. - x2=3−4xx ^ { 2 } = 3 - 4 xx2=3−4x

The average annual growth rate of Cyprus trees in inches satisfies the inequality |x - 3.25| 2.69. What range of growth corresponds to this inequality?

Graph the solution set. - ∣x∣>9| x | > 9∣x∣>9

Solve the cubic equation using factoring and the quadratic formula. - x−5=0x - 5 = 0x−5=0

Solve for the indicated variable. - 1Q=1 T1+1 T2\frac { 1 } { \mathrm { Q } } = \frac { 1 } { \mathrm {~T} _ { 1 } } + \frac { 1 } { \mathrm {~T} _ { 2 } }Q1​= T1​1​+ T2​1​ , for T2\mathrm { T } _ { 2 }T2​

Indicate whether the statement is true always, sometimes, or never. -The product of a pair of complex conjugates (with b  0) is the difference of the squares of the real and imaginary parts.

Solve the formula for the indicated variable. - F=95C+32, for C\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \text {, for } \mathrm { C }F=59​C+32, for C

Decide what values of the variable cannot possibly be solutions for the equation. - 2x+3+4−x=4\sqrt { 2 x + 3 } + \sqrt { 4 - x } = 42x+3​+4−x​=4

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 2[3−(3−5x)]−x=−6+3(2+3x)2 [ 3 - ( 3 - 5 x ) ] - x = - 6 + 3 ( 2 + 3 x )2[3−(3−5x)]−x=−6+3(2+3x)

Solve and graph the inequality. Give answer in interval notation. - 0<−3x≤120 < - 3 x \leq 120<−3x≤12

The length of a rectangle is 4 inches more than its width. If 2 inches are taken from the length and added to the width, the figure becomes a square with an area of 169 square inches. What are the dimensions of the original Figure?

Solve the problem. -A triangular shaped lake-front lot has a perimeter of 1500 ft. One side is 100 ft longer than the shortest side, while the third side is 200 ft longer than the shortest side. Find the lengths of all three sides.

Decide what values of the variable cannot possibly be solutions for the equation. - (x+5)2/3+4(x+5)1/3+3=0( x + 5 ) ^ { 2 / 3 } + 4 ( x + 5 ) ^ { 1 / 3 } + 3 = 0(x+5)2/3+4(x+5)1/3+3=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

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

Solve the inequality. Write the solution set in interval notation. - $| 7 x + 9 | - 3 < 3$

Decide whether the statement is true or false. - $- 11 \text { is a solution of } - 3 x + 9 = 37$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } + 64 = 0$

Graph the solution set. - $| 5 x + 4 | = | 8 x + 1 |$

Solve the equation by completing the square. - $x ^ { 2 } = 3 - 4 x$

Graph the solution set. - $| x | > 9$

Solve the cubic equation using factoring and the quadratic formula. - $x - 5 = 0$

Solve for the indicated variable. - $\frac { 1 } { \mathrm { Q } } = \frac { 1 } { \mathrm {~T} _ { 1 } } + \frac { 1 } { \mathrm {~T} _ { 2 } }$ , for $\mathrm { T } _ { 2 }$

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

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 2 x + 3 } + \sqrt { 4 - x } = 4$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $2 [ 3 - ( 3 - 5 x ) ] - x = - 6 + 3 ( 2 + 3 x )$

Solve and graph the inequality. Give answer in interval notation. - $0 < - 3 x \leq 12$ $Solve and graph the inequality. Give answer in interval notation. - 0 < - 3 x \leq 12$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x + 5 ) ^ { 2 / 3 } + 4 ( x + 5 ) ^ { 1 / 3 } + 3 = 0$