Question 1

Indicate whether the statement is true always, sometimes, or never.
-When i is raised to an even power, the result is -1.

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

The height of a box is 7 inches. The length is three inches more than the width. Find the width if the volume is 126.

Accepted Answer

A)  3 in. 
B)  6 in. 
C)  7 in. 
D)  18 in. 
A)  3 in. 
B)  6 in. 
C)  7 in. 
D)  18 in.

Question 4

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

Accepted Answer

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

Question 5

Solve the equation using the quadratic formula.
-$$\frac { 4 } { 9 } x ^ { 2 } - \frac { 4 } { 3 } x = - 1$$

Accepted Answer

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

Question 6

Decide whether or not the equations are equivalent.
-$\begin{array} { l } 
x = - 2 \
x ^ { 2 } = 4
\end{array}$

Accepted Answer

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

Question 7

Solve the problem.
-On a recent trip, Sarah's car traveled 20 mph faster on the first 110 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Accepted Answer

A)  31 mph 
B)  58 mph 
C)  38 mph 
D)  9 mph 
A)  31 mph 
B)  58 mph 
C)  38 mph 
D)  9 mph

Question 8

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

Accepted Answer

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

Question 9

In a milling operation, the thickness of the metal bars that can be produced satisfies the inequality $| x - 1.97 | \leq 1.38$. What range of thicknesses corresponds to this inequality?

Accepted Answer

A)  $[ 1.38,1.97 ]$ 
B)  $[ 0.59,3.35 ]$ 
C)  $[ 0.59,6.7 ]$ 
D)  $[ 0.3,3.35 ]$ 
A)  $[ 1.38,1.97 ]$ 
B)  $[ 0.59,3.35 ]$ 
C)  $[ 0.59,6.7 ]$ 
D)  $[ 0.3,3.35 ]$

Question 10

Find the quotient. Write the answer in standard form.
-$\frac { - 13 } { - \mathrm { i } }$

Accepted Answer

A)  13 
B)  $13 \mathrm { i }$ 
C)  $- 13$ 
D)  $- 13 \mathrm { i }$ 
A)  13 
B)  $13 \mathrm { i }$ 
C)  $- 13$ 
D)  $- 13 \mathrm { i }$

Question 11

Write the statement as an absolute value inequality.
-m is no more than 7 units from 19

Accepted Answer

A) $| m - 19 | > 7$ B) $| m - 19 | \leq 7$ C) $| m - 19 | < 7$ D) $| m - 7 | < 19$ A) $| m - 19 | > 7$ B) $| m - 19 | \leq 7$ C) $| m - 19 | < 7$ D) $| m - 7 | < 19$

Question 12

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

Accepted Answer

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

Question 13

Write the inequality in interval notation.
-$- 9 < x \leq - 2$

Accepted Answer

A)  $( - 9 , - 2 )$ 
B)  $[ - 9 , - 2 )$ 
C)  $( - 9 , - 2 ]$ 
D)  $[ - 9 , - 2 ]$ 
A)  $( - 9 , - 2 )$ 
B)  $[ - 9 , - 2 )$ 
C)  $( - 9 , - 2 ]$ 
D)  $[ - 9 , - 2 ]$

Question 14

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

Accepted Answer

A)  $\frac { 5 } { 4 } + \frac { 5 } { 16 } \mathrm { i }$ 
B)  $\frac { 10 } { 17 } + \frac { 40 } { 17 } \mathrm { i }$ 
C)  $\frac { 5 } { 8 } + \frac { 5 } { 16 } \mathrm { i }$ 
D)  $\frac { 20 } { 17 } - \frac { 5 } { 17 } \mathrm { i }$ 
A)  $\frac { 5 } { 4 } + \frac { 5 } { 16 } \mathrm { i }$ 
B)  $\frac { 10 } { 17 } + \frac { 40 } { 17 } \mathrm { i }$ 
C)  $\frac { 5 } { 8 } + \frac { 5 } { 16 } \mathrm { i }$ 
D)  $\frac { 20 } { 17 } - \frac { 5 } { 17 } \mathrm { i }$

Question 15

Decide what values of the variable cannot possibly be solutions for the equation.
-Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 4 hours. How long will it take them to do the job working together?

Accepted Answer

A)  $\frac { 8 } { 2 } h r$ 
B)  $\frac { 1 } { 8 } h r$ 
C)  $\frac { 4 } { 3 } \mathrm { hr }$ 
D)  $\frac { 1 } { 6 } \mathrm { hr }$ 
A)  $\frac { 8 } { 2 } h r$ 
B)  $\frac { 1 } { 8 } h r$ 
C)  $\frac { 4 } { 3 } \mathrm { hr }$ 
D)  $\frac { 1 } { 6 } \mathrm { hr }$

Question 16

Find the product. Write the answer in standard form.
-$$( 3 + i ) ( 3 - i ) ( 6 + 7 i )$$

Accepted Answer

A)  $60 + 7 i$ 
B)  $54 - 7 i ^ { 3 }$ 
C)  $48 + 56 i$ 
D)  $60 + 70 \mathrm { i }$ 
A)  $60 + 7 i$ 
B)  $54 - 7 i ^ { 3 }$ 
C)  $48 + 56 i$ 
D)  $60 + 70 \mathrm { i }$

Question 17

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

Accepted Answer

A)  $\{ 5,8 \}$ 
B)  $\varnothing$ 
C)  $\{ - 1 \}$ 
D)  $\{ - 5 , - 8 \}$ 
A)  $\{ 5,8 \}$ 
B)  $\varnothing$ 
C)  $\{ - 1 \}$ 
D)  $\{ - 5 , - 8 \}$

Question 18

Decide what values of the variable cannot possibly be solutions for the equation.
-$$8 x ^ { - 2 / 5 } + 14 x ^ { - 1 / 5 } + 6 = 0$$

Accepted Answer

A)  $\left\{ - 1 , - \frac { 4 } { 3 } \right\}$ 
B)  $\left\{ - 1 , - \frac { 1024 } { 243 } \right\}$ 
C)  $\{ 2,3 \}$ 
D)  $\left\{ 1 , \frac { 1024 } { 243 } \right\}$ 
A)  $\left\{ - 1 , - \frac { 4 } { 3 } \right\}$ 
B)  $\left\{ - 1 , - \frac { 1024 } { 243 } \right\}$ 
C)  $\{ 2,3 \}$ 
D)  $\left\{ 1 , \frac { 1024 } { 243 } \right\}$

Question 19

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

Accepted Answer

A)  $\{ 3,8 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ - 2 \}$ 
D)  $\{ 2,38 \}$ 
A)  $\{ 3,8 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ - 2 \}$ 
D)  $\{ 2,38 \}$

Question 20

Find the quotient. Write the answer in standard form.
-$\frac { 6 } { 7 i }$

Accepted Answer

A)  $- \frac { 6 } { 7 } \mathrm { i }$ 
B)  $\frac { 6 } { 7 }$ 
C)  $- \frac { 6 } { 7 }$ 
D)  $\frac { 6 } { 7 } \mathrm { i }$ 
A)  $- \frac { 6 } { 7 } \mathrm { i }$ 
B)  $\frac { 6 } { 7 }$ 
C)  $- \frac { 6 } { 7 }$ 
D)  $\frac { 6 } { 7 } \mathrm { i }$

Indicate whether the statement is true always, sometimes, or never. -When i is raised to an even power, the result is -1.

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

The height of a box is 7 inches. The length is three inches more than the width. Find the width if the volume is 126.

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

Solve the equation using the quadratic formula. - $\frac { 4 } { 9 } x ^ { 2 } - \frac { 4 } { 3 } x = - 1$

Decide whether or not the equations are equivalent. - x=-2 =4

Solve the problem. -On a recent trip, Sarah's car traveled 20 mph faster on the first 110 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

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

In a milling operation, the thickness of the metal bars that can be produced satisfies the inequality $| x - 1.97 | \leq 1.38$ . What range of thicknesses corresponds to this inequality?

Find the quotient. Write the answer in standard form. - $\frac { - 13 } { - \mathrm { i } }$

Write the statement as an absolute value inequality. -m is no more than 7 units from 19

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

Write the inequality in interval notation. - $- 9 < x \leq - 2$

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

Decide what values of the variable cannot possibly be solutions for the equation. -Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 4 hours. How long will it take them to do the job working together?

Find the product. Write the answer in standard form. - $( 3 + i ) ( 3 - i ) ( 6 + 7 i )$

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

Decide what values of the variable cannot possibly be solutions for the equation. - $8 x ^ { - 2 / 5 } + 14 x ^ { - 1 / 5 } + 6 = 0$

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

Find the quotient. Write the answer in standard form. - $\frac { 6 } { 7 i }$

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

Indicate whether the statement is true always, sometimes, or never. -When i is raised to an even power, the result is -1.

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

The height of a box is 7 inches. The length is three inches more than the width. Find the width if the volume is 126.

Solve the cubic equation using factoring and the quadratic formula. - x3−1=0x ^ { 3 } - 1 = 0x3−1=0

Solve the equation using the quadratic formula. - 49x2−43x=−1\frac { 4 } { 9 } x ^ { 2 } - \frac { 4 } { 3 } x = - 194​x2−34​x=−1

Decide whether or not the equations are equivalent. - x=-2 =4

Solve the problem. -On a recent trip, Sarah's car traveled 20 mph faster on the first 110 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Determine whether or not the equation is linear. - 3x+7=03 x + 7 = 03x+7=0

In a milling operation, the thickness of the metal bars that can be produced satisfies the inequality ∣x−1.97∣≤1.38| x - 1.97 | \leq 1.38∣x−1.97∣≤1.38 . What range of thicknesses corresponds to this inequality?

Find the quotient. Write the answer in standard form. - −13−i\frac { - 13 } { - \mathrm { i } }−i−13​

Write the statement as an absolute value inequality. -m is no more than 7 units from 19

Decide what values of the variable cannot possibly be solutions for the equation. - xx−5=5x−5+5\frac { x } { x - 5 } = \frac { 5 } { x - 5 } + 5x−5x​=x−55​+5

Write the inequality in interval notation. - −9<x≤−2- 9 < x \leq - 2−9<x≤−2

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

Decide what values of the variable cannot possibly be solutions for the equation. -Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 4 hours. How long will it take them to do the job working together?

Find the product. Write the answer in standard form. - (3+i)(3−i)(6+7i)( 3 + i ) ( 3 - i ) ( 6 + 7 i )(3+i)(3−i)(6+7i)

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

Decide what values of the variable cannot possibly be solutions for the equation. - 8x−2/5+14x−1/5+6=08 x ^ { - 2 / 5 } + 14 x ^ { - 1 / 5 } + 6 = 08x−2/5+14x−1/5+6=0

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

Find the quotient. Write the answer in standard form. - 67i\frac { 6 } { 7 i }7i6​

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

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

Solve the equation using the quadratic formula. - $\frac { 4 } { 9 } x ^ { 2 } - \frac { 4 } { 3 } x = - 1$

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

In a milling operation, the thickness of the metal bars that can be produced satisfies the inequality $| x - 1.97 | \leq 1.38$ . What range of thicknesses corresponds to this inequality?

Find the quotient. Write the answer in standard form. - $\frac { - 13 } { - \mathrm { i } }$

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

Write the inequality in interval notation. - $- 9 < x \leq - 2$

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

Find the product. Write the answer in standard form. - $( 3 + i ) ( 3 - i ) ( 6 + 7 i )$

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

Decide what values of the variable cannot possibly be solutions for the equation. - $8 x ^ { - 2 / 5 } + 14 x ^ { - 1 / 5 } + 6 = 0$

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

Find the quotient. Write the answer in standard form. - $\frac { 6 } { 7 i }$