Question 1

Solve the inequality. Write the solution set in interval notation.
-$$| - 2 x + 3 | > - 2$$

Accepted Answer

A)  $\left( - \infty , \frac { 5 } { 2 } \right)$ 
B)  $\left( \frac { 1 } { 2 } , \frac { 5 } { 2 } \right)$ 
C)  $( - \infty , \infty )$ 
D)  $\varnothing$ 
A)  $\left( - \infty , \frac { 5 } { 2 } \right)$ 
B)  $\left( \frac { 1 } { 2 } , \frac { 5 } { 2 } \right)$ 
C)  $( - \infty , \infty )$ 
D)  $\varnothing$

Question 2

Solve the quadratic inequality. Write the solution set in interval notation.
-$$( x - 6 ) ( x + 5 ) > 0$$

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( 5 , \infty )$ 
B)  $( - 5,6 )$ 
C)  $( - 5 , \infty )$ 
D)  $( - \infty , - 5 ) \cup ( 6 , \infty )$ 
A)  $( - \infty , - 6 ) \cup ( 5 , \infty )$ 
B)  $( - 5,6 )$ 
C)  $( - 5 , \infty )$ 
D)  $( - \infty , - 5 ) \cup ( 6 , \infty )$

Question 3

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 5 } { x - 1 } - \frac { 6 x } { 1 - x } = 10$$

Accepted Answer

A)  $- 1,1$ 
B)  $- 1,0,1$ 
C)  1 
D)  $- 1,0$ 
A)  $- 1,1$ 
B)  $- 1,0,1$ 
C)  1 
D)  $- 1,0$

Question 4

Solve the problem.
-A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

Accepted Answer

A)  3 ft 
B)  1 ft 
C)  2.2 ft 
D)  1.5 ft 
A)  3 ft 
B)  1 ft 
C)  2.2 ft 
D)  1.5 ft

Question 5

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.
-$$\mathrm { C } = 98 ^ { \circ }$$

Accepted Answer

A)  $\mathrm { F } = 234 ^ { \circ }$ 
B)  $\mathrm { F } = 36.7 ^ { \circ }$ 
C)  $\mathrm { F } = 72.2 ^ { \circ }$ 
D)  $\mathrm { F } = 208.4 ^ { \circ }$ 
A)  $\mathrm { F } = 234 ^ { \circ }$ 
B)  $\mathrm { F } = 36.7 ^ { \circ }$ 
C)  $\mathrm { F } = 72.2 ^ { \circ }$ 
D)  $\mathrm { F } = 208.4 ^ { \circ }$

Question 6

Solve the equation.
-$$\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 1$$

Accepted Answer

A)  $\{ 0 \}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
D)  $\varnothing$ 
A)  $\{ 0 \}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
D)  $\varnothing$

Question 7

Solve the problem.
-From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 14 miles per hour. In how many hours will they be 69 miles apart?

Accepted Answer

A)  5 hr 
B)  1 hr 
C)  3 hr 
D)  4 hr 
A)  5 hr 
B)  1 hr 
C)  3 hr 
D)  4 hr

Question 8

Multiply or divide, as indicated. Simplify the answer.
-$\frac { \sqrt { - 75 } } { \sqrt { 3 } }$

Accepted Answer

A)  $- 5$ 
B)  $5 \mathrm { i }$ 
C)  5 
D)  $- 5 \mathrm { i }$ 
A)  $- 5$ 
B)  $5 \mathrm { i }$ 
C)  5 
D)  $- 5 \mathrm { i }$

Question 9

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$- 0.2 ( x + 9 ) + 0.4 ( x + 9 ) = 0.2 x + 1.8$

Accepted Answer

A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ 0.2 \}$ 
C)  Conditional; $\{ - 9 \}$ 
D)  Identity; {all real numbers } 
A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ 0.2 \}$ 
C)  Conditional; $\{ - 9 \}$ 
D)  Identity; {all real numbers }

Question 10

Solve the problem.
-A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 4 feet longer than the length of a shelf. If 20 feet of lumber is available for the entire unit (including the
Shelves, but NOT the back of the bookcase), find the length and height of the unit.

Accepted Answer

A)  length $= 8.0 \mathrm { ft }$; height $= 9.0 \mathrm { ft }$ 
B)  length $= 2 \mathrm { ft }$; height $= 8 \mathrm { ft }$ 
C)  length $= 2 \mathrm { ft }$; height $= 6 \mathrm { ft }$ 
D)  length $= 3 \mathrm { ft }$; height $= 7 \mathrm { ft }$ 
A)  length $= 8.0 \mathrm { ft }$; height $= 9.0 \mathrm { ft }$ 
B)  length $= 2 \mathrm { ft }$; height $= 8 \mathrm { ft }$ 
C)  length $= 2 \mathrm { ft }$; height $= 6 \mathrm { ft }$ 
D)  length $= 3 \mathrm { ft }$; height $= 7 \mathrm { ft }$

Question 11

Solve the problem.
-Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 18 mi, the distance between the cars was 6 mi more than the distance traveled by the car
Heading east. How far had the east bound car traveled?

Accepted Answer

A)  30 mi 
B)  36 mi 
C)  24 mi 
D)  18 mi 
A)  30 mi 
B)  36 mi 
C)  24 mi 
D)  18 mi

Question 12

Solve the equation.
-$$( 5 x - 9 ) ^ { 2 } = 5 ( 5 x - 9 ) + 14$$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 5 } , - \frac { 16 } { 5 } \right\}$ 
B)  $\{ - 2,7 \}$ 
C)  $\left\{ - \frac { 11 } { 5 } , - \frac { 2 } { 5 } \right\}$ 
D)  $\left\{ \frac { 7 } { 5 } , \frac { 16 } { 5 } \right\}$ 
A)  $\left\{ - \frac { 7 } { 5 } , - \frac { 16 } { 5 } \right\}$ 
B)  $\{ - 2,7 \}$ 
C)  $\left\{ - \frac { 11 } { 5 } , - \frac { 2 } { 5 } \right\}$ 
D)  $\left\{ \frac { 7 } { 5 } , \frac { 16 } { 5 } \right\}$

Question 13

Find the sum or difference. Write the answer in standard form.
-$$( 9 - 4 i ) + ( 6 + 8 i ) + 5 i$$

Accepted Answer

A)  $20 + 9 \mathrm { i }$ 
B)  $15 - 9 \mathrm { i }$ 
C)  $3 + 4 \mathrm { i }$ 
D)  $15 + 9 i$ 
A)  $20 + 9 \mathrm { i }$ 
B)  $15 - 9 \mathrm { i }$ 
C)  $3 + 4 \mathrm { i }$ 
D)  $15 + 9 i$

Question 14

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } + 8 = 0$$

Accepted Answer

A)  $\{ - 2 , - 1 \pm \sqrt { 5 } \}$ 
B)  $\{ - 2,1 \pm \mathrm { i } \sqrt { 3 } \}$ 
C)  $\{ - 2 , \pm 2 \mathrm { i } \}$ 
D)  $\{ - 2,1 \pm i \sqrt { 6 } \}$ 
A)  $\{ - 2 , - 1 \pm \sqrt { 5 } \}$ 
B)  $\{ - 2,1 \pm \mathrm { i } \sqrt { 3 } \}$ 
C)  $\{ - 2 , \pm 2 \mathrm { i } \}$ 
D)  $\{ - 2,1 \pm i \sqrt { 6 } \}$

Question 15

Solve the problem.
-A ball is dropped from a cliff that is 256 feet high. The distance $S$ (in feet) that it falls in $t$ seconds is given by the formula $S = 16 t ^ { 2 }$. How many seconds (to tenths) will it take for the ball to hit the ground?

Accepted Answer

A)  $4 \mathrm { sec }$ 
B)  $4096 \mathrm { sec }$ 
C)  $16 \mathrm { sec }$ 
D)  $15.5 \mathrm { sec }$ 
A)  $4 \mathrm { sec }$ 
B)  $4096 \mathrm { sec }$ 
C)  $16 \mathrm { sec }$ 
D)  $15.5 \mathrm { sec }$

Question 16

Find the product. Write the answer in standard form.
-$$( - 4 - 4 \mathrm { i } ) ( - 4 + 4 \mathrm { i } )$$

Accepted Answer

A)  $16 - 16 \mathrm { i } ^ { 2 }$ 
B)  0 
C)  32 
D)  $16 + 16 \mathrm { i } ^ { 2 }$ 
A)  $16 - 16 \mathrm { i } ^ { 2 }$ 
B)  0 
C)  32 
D)  $16 + 16 \mathrm { i } ^ { 2 }$

Question 17

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
--7 + i

Accepted Answer

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

Question 18

Solve the problem.
-The sum of the squares of two consecutive even integers is 20 . Find the integers.

Accepted Answer

A)  $3 , - 5$ 
B)  $- 2 , - 4$ 
C)  2,4 
D)  2,4 or $- 2 , - 4$ 
A)  $3 , - 5$ 
B)  $- 2 , - 4$ 
C)  2,4 
D)  2,4 or $- 2 , - 4$

Question 19

Solve the inequality. Write the solution set in interval notation.
-$$( x + 7 ) ( x - 4 ) ( x + 3 ) > 0$$

Accepted Answer

A)  $( - \infty , 4 ) \cup ( 3,7 )$ 
B)  $( - 7 , - 4 ) \cup ( 3 , \infty )$ 
C)  $( - 7 , - 3 ) \cup ( 4 , \infty )$ 
D)  $( - \infty , - 7 ) \cup ( 3,4 )$ 
A)  $( - \infty , 4 ) \cup ( 3,7 )$ 
B)  $( - 7 , - 4 ) \cup ( 3 , \infty )$ 
C)  $( - 7 , - 3 ) \cup ( 4 , \infty )$ 
D)  $( - \infty , - 7 ) \cup ( 3,4 )$

Question 20

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 8 } { ( x + 5 ) ^ { 2 } } < 0$$

Accepted Answer

A)  $( - \infty , - 5 )$ 
B)  $( - \infty , \infty )$ 
C)  $\varnothing$ 
D)  $( - 5,0 )$ 
A)  $( - \infty , - 5 )$ 
B)  $( - \infty , \infty )$ 
C)  $\varnothing$ 
D)  $( - 5,0 )$

Solve the inequality. Write the solution set in interval notation. - $| - 2 x + 3 | > - 2$

Solve the quadratic inequality. Write the solution set in interval notation. - $( x - 6 ) ( x + 5 ) > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 5 } { x - 1 } - \frac { 6 x } { 1 - x } = 10$

Solve the problem. -A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

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. - $\mathrm { C } = 98 ^ { \circ }$

Solve the equation. - $\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 1$

Solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 14 miles per hour. In how many hours will they be 69 miles apart?

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 75 } } { \sqrt { 3 } }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $- 0.2 ( x + 9 ) + 0.4 ( x + 9 ) = 0.2 x + 1.8$

Solve the problem. -Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 18 mi, the distance between the cars was 6 mi more than the distance traveled by the car Heading east. How far had the east bound car traveled?

Solve the equation. - $( 5 x - 9 ) ^ { 2 } = 5 ( 5 x - 9 ) + 14$

Find the sum or difference. Write the answer in standard form. - $( 9 - 4 i ) + ( 6 + 8 i ) + 5 i$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } + 8 = 0$

Solve the problem. -A ball is dropped from a cliff that is 256 feet high. The distance $S$ (in feet) that it falls in $t$ seconds is given by the formula $S = 16 t ^ { 2 }$ . How many seconds (to tenths) will it take for the ball to hit the ground?

Find the product. Write the answer in standard form. - $( - 4 - 4 \mathrm { i } ) ( - 4 + 4 \mathrm { i } )$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. --7 + i

Solve the problem. -The sum of the squares of two consecutive even integers is 20 . Find the integers.

Solve the inequality. Write the solution set in interval notation. - $( x + 7 ) ( x - 4 ) ( x + 3 ) > 0$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 8 } { ( x + 5 ) ^ { 2 } } < 0$

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 1: Equations and Inequalities

Solve the inequality. Write the solution set in interval notation. - ∣−2x+3∣>−2| - 2 x + 3 | > - 2∣−2x+3∣>−2

Solve the quadratic inequality. Write the solution set in interval notation. - (x−6)(x+5)>0( x - 6 ) ( x + 5 ) > 0(x−6)(x+5)>0

Decide what values of the variable cannot possibly be solutions for the equation. - 5x−1−6x1−x=10\frac { 5 } { x - 1 } - \frac { 6 x } { 1 - x } = 10x−15​−1−x6x​=10