3.
MATH 096 STUDY GUIDE FOR FINAL EXAM
Please note that this study guide does not necessarily represent all of the information you need to know for the final. In addition, it is strongly recommended that you also review the past test reviews, tests, and quizzes.
Evaluate.
1. 24

[ 6

(

13 )] 2.
(

6
2

6 )
2
5

2
4
4. 7

4 ( 5

7 )
5. 33

[ 28

(

22 )] 6. 9
 
2
7.

6

5

(

4 ) 8.
20
4


3
4
( 5

5

8

9 )
11.
Simplify.
9. 8

( x

3 )

7 y

8

15 y

14
Evaluate for
13. a b
 a
 c d
 
2 , b a 2  b 2
15.

3 , c
 
1 , and d

6 .
10.
12.
14.
26

4 ( 3 w

7 )
6 ( c

2 d )

2 ( 7 c
 d ) a
 d
 c
MTH 096 Final Exam Review – Last Revised Fall 2015 1

16.
7
Find the Least Common Denominator of
10
8
and
15
.
Solve.
17. The lowest recorded temperature for January 1 st in a particular city is 28 degrees below zero in Fahrenheit. The difference between the highest recorded temperature and the lowest recorded temperature for January 1 st in this same city is 81 degrees. What is the record high?
18.
Solve.
Calculate the total cost of dinner if the meal costs $54.50 and you leave an 18% tip.
19. 2 ( x

3 )

7

9 20. 3 ( x

4 )

7 x

12

4 x
21. 12 x

3

6 x

15 22. 2 ( 2 x

2 )

5 x

9

4
23. 2 ( y

4 )

3 ( y

7 )
 
2 ( 3 y

1 )

6 y 24.
11 y
12
 
121
25.
1
4 x

1

3 26. x

2
 x
3
27.
4 x

1

5 x
2
28.
3
5
 x
2

4 x

1
10
MTH 096 Final Exam Review – Last Revised Fall 2015 2

35.
34.
Solve.
29.

3
4 n

3

2 n
3

1
30. Solve for C given the following equation: 𝐹 =
9
5
𝐶 + 32
32.
33.
Set up an equation or equations and solve.
31. Seven more than twice a number is 175. Find the number.
Find three consecutive integers whose sum is 45.
A collection of 60 dimes and nickels is worth $5.50. How many nickels are there?
You bought a shirt for $22.50. If the shirt was on sale for 35% off, what was the original price of the shirt?
The length of a rectangle is twice the width. The perimeter is 72 meters. Find the dimensions of the rectangle.
Solve and graph on a number line. Write your final answers in interval notation.
36.

5 ( x

2 )

10 37.

3 ( x

1 )

4

4 ( x

2 )
MTH 096 Final Exam Review – Last Revised Fall 2015 3

52.
Solve and graph on a number line. Write your final answers in interval notation.
38. 1

2 x

3

5
Simplify.
39. ( 4 x

2 y

8 )

( 3 x

6 y

10 ) 40. ( 4 a
2 
2 ab

3 b
2
)

( 2 a
2 
5 ab
 b
2
)
41. ( 8 x
2 y
2 
4 x
2 y

3 xy )

( 7 y
2  x
2 y
2 
3 x
2 y ) 42. 6 ( x
 y )

2 ( 4 x

2 y )

( x
 y )
43. Subtract 3𝑥 − 5 from 10𝑥 − 1 .
For 44 - 50, simplify. Final answers should be expressed with positive exponents only.
44. a 2  a 3  a 4
45. (

2 x
2 y
3
)( 3 x
3 y
4
)(
 y
5
) 46.
(

3 s
2 t
3
)
3
( 9 s
2 t )
2
47.
 

2 a
2 b
4
3 c
2


2
48. x
4 x

5 xx

4
49.
 m
4 n

4


3
50.
( x
3 y

2
)

2
( 2 x
2 y

1
)
2
51. Evaluate a

1  b

2
for a

4 and b

3
(a) Write 0.00000489 in scientific notation. (b) Write 1 .
37

10 5 in standard notation.
MTH 096 Final Exam Review – Last Revised Fall 2015 4

53.
54.
What is the slope of the line that goes through the points (2, –4) and (3, 1)?
What is the slope of the line y = –3 x + 4?
55.
57.
What is the slope of a horizontal line? 56. What is the slope of a vertical line?
What are the x and y intercepts of the line 3 x – 2 y = 6?
58. Find the slope of the line below. Then give the equation of the line in slope intercept form.
y
3
-2
61.
For 59-62, graph the lines.
59. y

2
3 x

4
4 x

8 y

16
x
MTH 096 Final Exam Review – Last Revised Fall 2015
60. 2 y
 
4 x

6
62. Graph the linear
inequality:
2 x

5 y

10
5

65.
63. In a particular neighborhood, the equation 𝑦 = 100𝑥 + 40,000 roughly estimates the home price (y), where x is the square footage of the home. Find and interpret the slope and y-intercept.
Find the equations of the lines. Write final answers in slope-intercept form.
The line that has slope of –2 and passes through the point (5, –1). 64.
66.
The line that goes through the points (4, 3) and (2, –5).
The line that goes through (1,2) and is perpendicular to the line y = 5.
Solve the following systems.
67. x
2 x

 y y


3
3
68.

3 x x
 y
 y

3
 
5
69. Draw an example of a system of equations that satisfies each condition: a. It has no solution b. It has exactly one solution. c. It has infinitely many solutions.
Multiply and simplify.
70. ( x

4 )( x

6 ) 71. ( 2 x

4 )( x

5 )
72. ( x

4 )( x
2 
2 x

3 ) 73. ( x

1 )
2
MTH 096 Final Exam Review – Last Revised Fall 2015 6

80.
78.
76.
Factor completely.
74. 6 y
3 
8 y
2 
30 y x
2 
36
2 x
2 
2 x

4 x
4 
8 x
82. Divide and simplify.

2 x
3 y

3 x
2 y
2 
6 xy
.
6 xy
83. Find the quotient when 2𝑥 2 + 13𝑥 + 15 is divided by 𝑥 + 5 .
84. Divide (using long division).
5 x
2 x


3 x
4

6
MTH 096 Final Exam Review – Last Revised Fall 2015
75. x
2 
6 x

9
77. x
2 
2 x

15
79. 4 x
2 
18 x

10
81. 2 x
2 
50
7

Solve.
87.
85.
86.
88.
2 x
3 ( x
( x x
3 
50 x



2 )
2 )


48
48
0
Find the x and y intercepts of y

2 x
3 
7 x
2 
3 x
MTH 096 Final Exam Review – Last Revised Fall 2015 8