Question 1

Find all solutions.
-$$x ^ { 3 } - 36 x = 0$$

Accepted Answer

A)  $\{ 0,36 \}$ 
B)  $\{ 0,6 \}$ 
C)  $\{ 0,6 , - 6 \}$ 
D)  $\{ 0 , - 6 \}$

Question 2

Solve the problem.
-When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.95. After that, each additional minute or portion of a minute of that call costs $0.25. Use an inequality to find the number of minutes one can call long distance for $4.95.

Accepted Answer

A) 2 minutes or fewer 
B) 11 minutes or fewer 
C) 20 minutes or fewer 
D) 8 minutes or fewer

Question 3

Write the expression in the standard form a + bi.
-$$( 6 + 6 i ) - ( - 7 + i )$$

Accepted Answer

A)  $- 1 + 7 \mathrm { i }$ 
B)  $13 + 5 i$ 
C)  $13 - 5 \mathrm { i }$
$D ) - 13 - 5 i$

Question 4

Solve the equation after making an appropriate substitution.
-$$x ^ { 4 } - 50 x ^ { 2 } + 49 = 0$$

Accepted Answer

A)  $\{ - 49,49 \}$ 
B)  $\{ - 50,50 \}$ 
C)  $\{ - 1,1 , - 7,7 \}$ 
D)  $\{ - 7,7 \}$

Question 5

Solve the equation.
-$- 11 x + 1.1 = - 36.9 - 1.5 x$

Accepted Answer

A)  $\{ - 47 \}$ 
B)  $\{ 4 \}$ 
C)  $\{ 3.6 \}$ 
D)  $\{ 3.5 \}$

Question 6

Solve the radical equation.
-$\sqrt { 3 x + 10 } - \sqrt { x + 2 } = 2$

Accepted Answer

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

Question 7

Solve the linear inequality. Express the solution in set-builder notation.
-$$- \frac { 9 } { 8 } x - \frac { 5 } { 4 } < - \frac { 82 } { 9 }$$

Accepted Answer

A)  $\left\{ x \mid x > \frac { 566 } { 81 } \right\}$ 
B)  $\left\{ x \mid x  - \frac { 82 } { 81 } \right\}$ 
D)  $\left\{ x \mid x > \frac { 566 } { 9 } \right\}$

Question 8

Perform the indicated operations and write the result in standard form.
-$\sqrt { - 7 } - \sqrt { - 144 }$

Accepted Answer

A)  $\sqrt { 7 } i - 12$ 
B)  $\sqrt { 7 \mathrm { i } } - 12 \mathrm { i }$ 
C)  $i ( \sqrt { 7 } + 12 )$ 
D)  $\mathrm { i } ( \sqrt { 7 } - 12 )$

Question 9

Write the expression in the standard form a + bi.
-$\frac { 4 } { 5 - i }$

Accepted Answer

A)  $\frac { 10 } { 13 } - \frac { 2 } { 13 } \mathrm { i }$ 
B)  $\frac { 10 } { 13 } + \frac { 2 } { 13 } \mathrm { i }$ 
C)  $\frac { 5 } { 6 } + \frac { 1 } { 6 } \mathrm { i }$ 
D)  $\frac { 5 } { 6 } - \frac { 1 } { 6 } \mathrm { i }$

Question 10

Write the power of i as i, -1, -i, or 1.
-$$\mathrm { i } ^ { 21 }$$

Accepted Answer

A) 1 
B) i 
C) -1 
D) -i

Question 11

Solve the problem.
-Mary and her brother John collect foreign coins. Mary has four times the number of coins that John has. Together they have 150 foreign coins. Find how many coins Mary has.

Accepted Answer

A) 24 coins 
B) 120 coins 
C) 114 coins 
D) 30 coins

Question 12

Solve the rational inequality. Express the solution in interval notation.
-$$\frac { x - 8 } { x + 1 } < 1$$

Accepted Answer

A)  $( - \infty , - 1 )$ 
B)  $( - 1 , \infty )$ 
C)  $( - \infty , - 1 ) \cup ( 8 , \infty )$ 
D)  $( - 1,8 )$

Question 13

Solve the equation by factoring.
-$$x ^ { 2 } - 6 x - 7 = 0$$

Accepted Answer

A)  $\{ - 1,7 \}$ 
B)  $\{ 1,7 \}$ 
C)  $\{ 1 , - 7 \}$ 
D)  $\{ - 1 , - 7 \}$

Question 14

Solve the radical equation.
-$$\sqrt { 4 x - 3 } = 3$$

Accepted Answer

A)  $\left\{ \frac { 9 } { 4 } \right\}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\{ 9 \}$ 
D)  $\{ 3 \}$

Question 15

Solve the linear inequality. Express the solution in set-builder notation.
-$- 3 x + 1 \geq 7$ or $6 x + 3 \geq - 21$

Accepted Answer

A)  $[ - 4 , - 2 ]$ 
B)  $( - \infty , \infty )$ 
C)  $[ - 4 , \infty )$ 
D)  $[ - 2 , \infty )$

Question 16

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi.
-$\frac { 1 } { 5 } - 2 i$

Accepted Answer

A)  $\frac { 11 } { 5 }$ 
B)  $\frac { 1 } { 25 } + 4 \mathrm { i }$ 
C)  $\frac { 101 } { 25 }$ 
D)  $\frac { 1 } { 25 } - 4 \mathrm { i }$

Question 17

Solve the problem.
-BJ can overhaul a boat's diesel inboard engine in 30 hours. His apprentice takes 60 hours to do the same job. How long would it take them working together assuming no gain or loss in efficiency?

Accepted Answer

A) 12 hr 
B) 90 hr 
C) 20 hr 
D) 8 hr

Question 18

Solve the problem.
-Jim has gotten scores of 98 and 70 on his first two tests. What score must he get on his third test to keep an average of 80 or better?

Accepted Answer

A) at least 84 
B) at least 72 
C) at least 82 
D) at least 70

Question 19

Solve the equation.
-$$\left| x ^ { 2 } - 4 \right| = 0$$

Accepted Answer

A)  $\{ - 2 \}$ 
B)  $\{ - 2,2 \}$ 
C)  $\{ - 16,16 \}$ 
D)  $\{ 2 \}$

Question 20

Write the sentence as an equation. Let the variable x represent the number.
-The sum of twice a number and 5 is 9.

Accepted Answer

A) x + 10 = 9 
B) 2x + 5 = 9 
C) 10x = 9 
D) 2x - 5 = 9

Exam 1: Equations, Inequalities, and Applications

Find all solutions. - $x ^ { 3 } - 36 x = 0$

Solve the problem. -When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.95. After that, each additional minute or portion of a minute of that call costs $0.25. Use an inequality to find the number of minutes one can call long distance for $4.95.

Write the expression in the standard form a + bi. - $( 6 + 6 i ) - ( - 7 + i )$

Solve the equation after making an appropriate substitution. - $x ^ { 4 } - 50 x ^ { 2 } + 49 = 0$

Solve the equation. - $- 11 x + 1.1 = - 36.9 - 1.5 x$

Solve the radical equation. - $\sqrt { 3 x + 10 } - \sqrt { x + 2 } = 2$

Solve the linear inequality. Express the solution in set-builder notation. - $- \frac { 9 } { 8 } x - \frac { 5 } { 4 } < - \frac { 82 } { 9 }$

Perform the indicated operations and write the result in standard form. - $\sqrt { - 7 } - \sqrt { - 144 }$

Write the expression in the standard form a + bi. - $\frac { 4 } { 5 - i }$

Write the power of i as i, -1, -i, or 1. - $\mathrm { i } ^ { 21 }$

Solve the problem. -Mary and her brother John collect foreign coins. Mary has four times the number of coins that John has. Together they have 150 foreign coins. Find how many coins Mary has.

Solve the rational inequality. Express the solution in interval notation. - $\frac { x - 8 } { x + 1 } < 1$

Solve the equation by factoring. - $x ^ { 2 } - 6 x - 7 = 0$

Solve the radical equation. - $\sqrt { 4 x - 3 } = 3$

Solve the linear inequality. Express the solution in set-builder notation. - $- 3 x + 1 \geq 7$ or $6 x + 3 \geq - 21$

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi. - $\frac { 1 } { 5 } - 2 i$

Solve the problem. -BJ can overhaul a boat's diesel inboard engine in 30 hours. His apprentice takes 60 hours to do the same job. How long would it take them working together assuming no gain or loss in efficiency?

Solve the problem. -Jim has gotten scores of 98 and 70 on his first two tests. What score must he get on his third test to keep an average of 80 or better?

Solve the equation. - $\left| x ^ { 2 } - 4 \right| = 0$

Write the sentence as an equation. Let the variable x represent the number. -The sum of twice a number and 5 is 9.

Exam 1: Equations, Inequalities, and Applications

Find all solutions. - x3−36x=0x ^ { 3 } - 36 x = 0x3−36x=0

Solve the problem. -When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.95. After that, each additional minute or portion of a minute of that call costs $0.25. Use an inequality to find the number of minutes one can call long distance for $4.95.

Write the expression in the standard form a + bi. - (6+6i) −(−7+i) ( 6 + 6 i ) - ( - 7 + i ) (6+6i) −(−7+i)

Solve the equation after making an appropriate substitution. - x4−50x2+49=0x ^ { 4 } - 50 x ^ { 2 } + 49 = 0x4−50x2+49=0

Solve the equation. - −11x+1.1=−36.9−1.5x- 11 x + 1.1 = - 36.9 - 1.5 x−11x+1.1=−36.9−1.5x

Solve the radical equation. - 3x+10−x+2=2\sqrt { 3 x + 10 } - \sqrt { x + 2 } = 23x+10​−x+2​=2

Solve the linear inequality. Express the solution in set-builder notation. - −98x−54<−829- \frac { 9 } { 8 } x - \frac { 5 } { 4 } < - \frac { 82 } { 9 }−89​x−45​<−982​

Perform the indicated operations and write the result in standard form. - −7−−144\sqrt { - 7 } - \sqrt { - 144 }−7​−−144​

Write the expression in the standard form a + bi. - 45−i\frac { 4 } { 5 - i }5−i4​

Write the power of i as i, -1, -i, or 1. - i21\mathrm { i } ^ { 21 }i21