Question 1

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-$- 10 + i$

Accepted Answer

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

Question 2

Determine whether or not the equation is linear.
-$6 x - 5 ( x - 9 ) = 12 x$

Accepted Answer

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

Question 3

Solve the equation by the zero-factor property.
-$$x ^ { 2 } + 7 x - 18 = 0$$

Accepted Answer

A)  $\{ - 2,9 \}$ 
B)  $\{ 2,9 \}$ 
C)  $\{ - 9 , - 2 \}$ 
D)  $\{ - 9,2 \}$ 
A)  $\{ - 2,9 \}$ 
B)  $\{ 2,9 \}$ 
C)  $\{ - 9 , - 2 \}$ 
D)  $\{ - 9,2 \}$ D

Question 4

Solve the equation by completing the square.
-$$x ^ { 2 } + 3 x - 9 = 0$$

Accepted Answer

A)  $\left\{ \frac { - 3 - 3 \sqrt { 5 } } { 2 } \right\}$ 
B)  $\{ - 3 \pm 3 \sqrt { 5 } \}$ 
C)  $\left\{ \frac { - 3 + 3 \sqrt { 5 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 3 \pm 3 \sqrt { 5 } } { 2 } \right\}$ 
A)  $\left\{ \frac { - 3 - 3 \sqrt { 5 } } { 2 } \right\}$ 
B)  $\{ - 3 \pm 3 \sqrt { 5 } \}$ 
C)  $\left\{ \frac { - 3 + 3 \sqrt { 5 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 3 \pm 3 \sqrt { 5 } } { 2 } \right\}$

Question 5

The sum of the squares of two consecutive even integers is 52. Find the integers.

Accepted Answer

A)  4,6 
B)  $- 4 , - 6$ 
C)  4,6 or $- 4 , - 6$ 
D)  $5 , - 7$ 
A)  4,6 
B)  $- 4 , - 6$ 
C)  4,6 or $- 4 , - 6$ 
D)  $5 , - 7$

Question 6

Solve the rational inequality. Write the solution set in interval notation.
-$$8 \geq \frac { 1 } { x }$$

Accepted Answer

A)  $( - \infty , 0 ) \cup \left[ \frac { 1 } { 8 } , \infty \right]$ 
B)  $( 0,8 ]$ 
C)  $\left( 0 , \frac { 1 } { 8 } \right)$ 
D)  $( - \infty , 0 ) \cup [ 8 , \infty )$ 
A)  $( - \infty , 0 ) \cup \left[ \frac { 1 } { 8 } , \infty \right]$ 
B)  $( 0,8 ]$ 
C)  $\left( 0 , \frac { 1 } { 8 } \right)$ 
D)  $( - \infty , 0 ) \cup [ 8 , \infty )$

Question 7

Solve the problem.
-Roberto invested some money at 2.5%, and then invested $5000 more than twice this amount at 4%. His total annual income from the two investments was $1565.00. How much was invested at 4%?

Accepted Answer

A)  $31,000 
B)  $15,000 
C)  $26,000 
D)  $3100 
A)  $31,000 
B)  $15,000 
C)  $26,000 
D)  $3100

Question 8

Decide whether the statement is true or false.
-4 is a solution of $2 x = 8$

Accepted Answer

A) True 
 B)False

Question 9

Solve the problem.
-It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 20 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired
Strength?

Accepted Answer

A)  5 L 
B)  6.7 L 
C)  10 L 
D)  8 L 
A)  5 L 
B)  6.7 L 
C)  10 L 
D)  8 L

Question 10

Find the sum or difference. Write the answer in standard form.
-$3 \sqrt { 2 } - ( 7 \sqrt { 2 } + i ) + 9 i - ( - 2 \sqrt { 2 } + 9 i )$

Accepted Answer

A)  $- 2 \sqrt { 2 } - i$ 
B)  $- 2 - 17 i \sqrt { 2 }$ 
C)  $- 2 \sqrt { 2 } + i$ 
D)  $2 - 17 i \sqrt { 2 }$ 
A)  $- 2 \sqrt { 2 } - i$ 
B)  $- 2 - 17 i \sqrt { 2 }$ 
C)  $- 2 \sqrt { 2 } + i$ 
D)  $2 - 17 i \sqrt { 2 }$

Question 11

Solve the problem.
-A chemist needs 130 milliliters of a 72% solution but has only 17% and 82% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

A)  30 mL of 17%; 100 mL of 82% 
B)  20 mL of 17%; 110 mL of 82% 
C)  110 mL of 17%; 20 mL of 82% 
D)  100 mL of 17%; 30 mL of 82% 
A)  30 mL of 17%; 100 mL of 82% 
B)  20 mL of 17%; 110 mL of 82% 
C)  110 mL of 17%; 20 mL of 82% 
D)  100 mL of 17%; 30 mL of 82%

Question 12

Decide what values of the variable cannot possibly be solutions for the equation.
-$6 x ^ { - 2 } - 31 x ^ { - 1 } + 5 = 0$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 6 } , - 5 \right\}$ 
B)  $\left\{ \frac { 1 } { 6 } , 5 \right\}$ 
C)  $\left\{ 6 , \frac { 1 } { 5 } \right\}$ 
D)  $\left\{ - 6 , - \frac { 1 } { 5 } \right\}$ 
A)  $\left\{ - \frac { 1 } { 6 } , - 5 \right\}$ 
B)  $\left\{ \frac { 1 } { 6 } , 5 \right\}$ 
C)  $\left\{ 6 , \frac { 1 } { 5 } \right\}$ 
D)  $\left\{ - 6 , - \frac { 1 } { 5 } \right\}$

Question 13

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

Accepted Answer

A)  $\frac { 29 } { 34 } + \frac { 3 } { 34 } \mathrm { i }$ 
B)  $\frac { 11 } { 34 } - \frac { 27 } { 34 } \mathrm { i }$ 
C)  $\frac { 11 } { 16 } - \frac { 3 } { 16 } \mathrm { i }$ 
D)  $\frac { 29 } { 16 } - \frac { 3 } { 16 } \mathrm { i }$ 
A)  $\frac { 29 } { 34 } + \frac { 3 } { 34 } \mathrm { i }$ 
B)  $\frac { 11 } { 34 } - \frac { 27 } { 34 } \mathrm { i }$ 
C)  $\frac { 11 } { 16 } - \frac { 3 } { 16 } \mathrm { i }$ 
D)  $\frac { 29 } { 16 } - \frac { 3 } { 16 } \mathrm { i }$

Question 14

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.
-$$\mathrm { F } = 229 ^ { \circ }$$

Accepted Answer

A)  $C = 354.6 ^ { \circ }$ 
B)  $C = 123.7 ^ { \circ }$ 
C)  $C = 444.2 ^ { \circ }$ 
D)  $C = 109.4 ^ { \circ }$ 
A)  $C = 354.6 ^ { \circ }$ 
B)  $C = 123.7 ^ { \circ }$ 
C)  $C = 444.2 ^ { \circ }$ 
D)  $C = 109.4 ^ { \circ }$

Question 15

The height of a box is 5 inches. Its length is 5 inches more than its width. Find the length if the volume is 120.

Accepted Answer

A)  8 in. 
B)  5 in. 
C)  24 in. 
D)  3 in. 
A)  8 in. 
B)  5 in. 
C)  24 in. 
D)  3 in.

Question 16

Decide what values of the variable cannot possibly be solutions for the equation.
-$$6 x ^ { 2 / 5 } + 13 x ^ { 1 / 5 } + 5 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 3125 } { 243 } , - \frac { 1 } { 32 } \right\}$ 
B)  $\{ 3,2 \}$ 
C)  $\left\{ \frac { 3125 } { 243 } , \frac { 1 } { 32 } \right\}$ 
D)  $\left\{ - \frac { 5 } { 3 } , - \frac { 1 } { 2 } \right\}$ 
A)  $\left\{ - \frac { 3125 } { 243 } , - \frac { 1 } { 32 } \right\}$ 
B)  $\{ 3,2 \}$ 
C)  $\left\{ \frac { 3125 } { 243 } , \frac { 1 } { 32 } \right\}$ 
D)  $\left\{ - \frac { 5 } { 3 } , - \frac { 1 } { 2 } \right\}$

Question 17

Solve for y.
-$$7 x - 5 y = 4$$

Accepted Answer

A)  $y = 7 x + 9$ 
B)  $y = \frac { 7 x + 4 } { 5 }$ 
C)  $y = 7 x - 9$ 
D)  $y = \frac { 7 x - 4 } { 5 }$ 
A)  $y = 7 x + 9$ 
B)  $y = \frac { 7 x + 4 } { 5 }$ 
C)  $y = 7 x - 9$ 
D)  $y = \frac { 7 x - 4 } { 5 }$

Question 18

Indicate whether the statement is true always, sometimes, or never.
-$$\text { To find the quotient } \frac { 5 + 8 \mathrm { i } } { 5 - 8 \mathrm { i } } \text {, multiply numerator and denominator by } 5 + 8 \mathrm { i } \text {. }$$

Accepted Answer

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

Question 19

Solve for the indicated variable.
-$V = \frac { 1 } { m } \sqrt { 2 V e m }$, for $m$

Accepted Answer

A)  $m = \frac { 2 V ^ { 3 } } { e }$ 
B)  $m = \frac { 2 e } { V }$ 
C)  $\mathrm { m } = \frac { 2 \mathrm {~V} } { \mathrm { e } }$ 
D)  $m = \frac { \pm \sqrt { 2 V e } } { V e }$ 
A)  $m = \frac { 2 V ^ { 3 } } { e }$ 
B)  $m = \frac { 2 e } { V }$ 
C)  $\mathrm { m } = \frac { 2 \mathrm {~V} } { \mathrm { e } }$ 
D)  $m = \frac { \pm \sqrt { 2 V e } } { V e }$

Question 20

Solve the formula for the indicated variable.
-$\mathrm { P } = \mathrm { s } _ { 1 } + \mathrm { s } _ { 2 } + \mathrm { s } _ { 3 }$, for $\mathrm { s } _ { 3 }$

Accepted Answer

A)  $s _ { 3 } = P + s _ { 1 } + s _ { 2 }$ 
B)  $s _ { 3 } = s _ { 1 } + s _ { 2 } - P$ 
C)  $s _ { 3 } = s _ { 1 } + P - s _ { 2 }$ 
D)  $s _ { 3 } = P - s _ { 1 } - s _ { 2 }$ 
A)  $s _ { 3 } = P + s _ { 1 } + s _ { 2 }$ 
B)  $s _ { 3 } = s _ { 1 } + s _ { 2 } - P$ 
C)  $s _ { 3 } = s _ { 1 } + P - s _ { 2 }$ 
D)  $s _ { 3 } = P - s _ { 1 } - s _ { 2 }$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $- 10 + i$

Determine whether or not the equation is linear. - $6 x - 5 ( x - 9 ) = 12 x$

Solve the equation by the zero-factor property. - $x ^ { 2 } + 7 x - 18 = 0$

Solve the equation by completing the square. - $x ^ { 2 } + 3 x - 9 = 0$

The sum of the squares of two consecutive even integers is 52. Find the integers.

Solve the rational inequality. Write the solution set in interval notation. - $8 \geq \frac { 1 } { x }$

Solve the problem. -Roberto invested some money at 2.5%, and then invested $5000 more than twice this amount at 4%. His total annual income from the two investments was $1565.00. How much was invested at 4%?

Decide whether the statement is true or false. -4 is a solution of $2 x = 8$

Solve the problem. -It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 20 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired Strength?

Find the sum or difference. Write the answer in standard form. - $3 \sqrt { 2 } - ( 7 \sqrt { 2 } + i ) + 9 i - ( - 2 \sqrt { 2 } + 9 i )$

Solve the problem. -A chemist needs 130 milliliters of a 72% solution but has only 17% and 82% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Decide what values of the variable cannot possibly be solutions for the equation. - $6 x ^ { - 2 } - 31 x ^ { - 1 } + 5 = 0$

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

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. - $\mathrm { F } = 229 ^ { \circ }$

The height of a box is 5 inches. Its length is 5 inches more than its width. Find the length if the volume is 120.

Decide what values of the variable cannot possibly be solutions for the equation. - $6 x ^ { 2 / 5 } + 13 x ^ { 1 / 5 } + 5 = 0$

Solve for y. - $7 x - 5 y = 4$

Indicate whether the statement is true always, sometimes, or never. - $\text { To find the quotient } \frac { 5 + 8 \mathrm { i } } { 5 - 8 \mathrm { i } } \text {, multiply numerator and denominator by } 5 + 8 \mathrm { i } \text {. }$

Solve for the indicated variable. - $V = \frac { 1 } { m } \sqrt { 2 V e m }$ , for $m$

Solve the formula for the indicated variable. - $\mathrm { P } = \mathrm { s } _ { 1 } + \mathrm { s } _ { 2 } + \mathrm { s } _ { 3 }$ , for $\mathrm { s } _ { 3 }$

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

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - −10+i- 10 + i−10+i

Determine whether or not the equation is linear. - 6x−5(x−9)=12x6 x - 5 ( x - 9 ) = 12 x6x−5(x−9)=12x

Solve the equation by the zero-factor property. - x2+7x−18=0x ^ { 2 } + 7 x - 18 = 0x2+7x−18=0

Solve the equation by completing the square. - x2+3x−9=0x ^ { 2 } + 3 x - 9 = 0x2+3x−9=0

The sum of the squares of two consecutive even integers is 52. Find the integers.

Solve the rational inequality. Write the solution set in interval notation. - 8≥1x8 \geq \frac { 1 } { x }8≥x1​

Solve the problem. -Roberto invested some money at 2.5%, and then invested $5000 more than twice this amount at 4%. His total annual income from the two investments was $1565.00. How much was invested at 4%?

Decide whether the statement is true or false. -4 is a solution of 2x=82 x = 82x=8

Solve the problem. -It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 20 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired Strength?

Find the sum or difference. Write the answer in standard form. - 32−(72+i)+9i−(−22+9i)3 \sqrt { 2 } - ( 7 \sqrt { 2 } + i ) + 9 i - ( - 2 \sqrt { 2 } + 9 i )32​−(72​+i)+9i−(−22​+9i)

Solve the problem. -A chemist needs 130 milliliters of a 72% solution but has only 17% and 82% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Decide what values of the variable cannot possibly be solutions for the equation. - 6x−2−31x−1+5=06 x ^ { - 2 } - 31 x ^ { - 1 } + 5 = 06x−2−31x−1+5=0

Find the quotient. Write the answer in standard form. - 4+3i5+3i\frac { 4 + 3 i } { 5 + 3 i }5+3i4+3i​

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. - F=229∘\mathrm { F } = 229 ^ { \circ }F=229∘

The height of a box is 5 inches. Its length is 5 inches more than its width. Find the length if the volume is 120.

Decide what values of the variable cannot possibly be solutions for the equation. - 6x2/5+13x1/5+5=06 x ^ { 2 / 5 } + 13 x ^ { 1 / 5 } + 5 = 06x2/5+13x1/5+5=0

Solve for y. - 7x−5y=47 x - 5 y = 47x−5y=4

Solve for the indicated variable. - V=1m2VemV = \frac { 1 } { m } \sqrt { 2 V e m }V=m1​2Vem​ , for mmm

Solve the formula for the indicated variable. - P=s1+s2+s3\mathrm { P } = \mathrm { s } _ { 1 } + \mathrm { s } _ { 2 } + \mathrm { s } _ { 3 }P=s1​+s2​+s3​ , for s3\mathrm { s } _ { 3 }s3​

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

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $- 10 + i$

Determine whether or not the equation is linear. - $6 x - 5 ( x - 9 ) = 12 x$

Solve the equation by the zero-factor property. - $x ^ { 2 } + 7 x - 18 = 0$

Solve the equation by completing the square. - $x ^ { 2 } + 3 x - 9 = 0$

Solve the rational inequality. Write the solution set in interval notation. - $8 \geq \frac { 1 } { x }$

Decide whether the statement is true or false. -4 is a solution of $2 x = 8$

Find the sum or difference. Write the answer in standard form. - $3 \sqrt { 2 } - ( 7 \sqrt { 2 } + i ) + 9 i - ( - 2 \sqrt { 2 } + 9 i )$

Decide what values of the variable cannot possibly be solutions for the equation. - $6 x ^ { - 2 } - 31 x ^ { - 1 } + 5 = 0$

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

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. - $\mathrm { F } = 229 ^ { \circ }$

Decide what values of the variable cannot possibly be solutions for the equation. - $6 x ^ { 2 / 5 } + 13 x ^ { 1 / 5 } + 5 = 0$

Solve for y. - $7 x - 5 y = 4$

Solve for the indicated variable. - $V = \frac { 1 } { m } \sqrt { 2 V e m }$ , for $m$

Solve the formula for the indicated variable. - $\mathrm { P } = \mathrm { s } _ { 1 } + \mathrm { s } _ { 2 } + \mathrm { s } _ { 3 }$ , for $\mathrm { s } _ { 3 }$