Math 093–Review for Final Exam–page 1
Simplify.
1.
30 + (! 16)
2.
! 24
4.
! 55
5.
7.
! 43 ! (! 38)
8.
+ 17 + (! 39) + 29
+ (! 48)
3.
! 49
+ 21
17 ! 50
6.
! 32 !
! 59 ! (! 68)
9.
12 ! (! 25)
49
10.
63 ! 78 + (! 3) ! (! 12)
11.
8(! 6)
12.
! 3(! 6)
13.
3(! 5)(4)
14.
! 9(10)(! 2)
15.
5(! 2)(! 3)(! 4)
16.
17.
÷ 2 + 7(10 ! 12)
20.
18.
8(! 3) + 2(7 ! 10)2
! 14
22.
48 ! 2(5 ! 72) + 18 ÷ (! 2)
23.
8z + 13 ! 12z + 6
24.
! 4m !
25.
6(4m + 5) ! 2(3m ! 8)
26.
7(5y ! 6) ! (8y ! 9)
27.
!
16 + 3m + 5 ! m ! 3
21.
24 ! (! 9 + 1) ! 42
19.
31x ! (19x ! 25) + 16 + 9(x + 3)
Solve.
28.
m + 25 = 32
29.
z ! 11 = 28
30.
5y = 40
31.
y + 18 = 2
32.
x ! 15 = ! 2
33.
a + 28 = ! 9
34.
! 4k
= ! 20
35.
8z = 24 + 2z
36.
! 6y
37.
! 3m
+ 39 = 57
38.
5z ! 20 = ! 55
39.
9a + 16 = 5a + 40
40.
2y + 6 = 8y ! 42
41.
5a + 2 + 3a + 22 = 8
42.
3(2x+ 4) ! 4(4x ! 5) = 2
43.
9(2m ! 4) = 5(4m ! 6)
44.
2m + 5 = 12
45.
4k + 12 = ! 2k ! 5
46.
3(4w + 5) = 1
47.
6(5m + 3) = 3(3m + 5)
48.
49.
52.
50.
8k + 30 + 2k ! 45 = 17 + 14k ! 60 ! 5k
= 48 ! 2y
51.
53.
0.04z + 1.04 = 8.2
Math 093–Review for Final Exam–page 2
Simplify.
54.
3x2 + 9x ! 17 + 2x2 ! 7x + 3
55.
(10m2 + 3m ! 11) + (4m2 ! 8m ! 6)
56.
(6a2 ! 7a + 11) ! (4a2 ! 6a ! 3)
57.
(x + 3)(x + 7)
58.
(2x + 7)(x ! 9)
59.
(4x ! 2)(5x ! 1)
60.
x2 @ x3
61.
y4(y2)
62.
m3 @ m2 @ m @ m8
63.
4y2(7y5)
64.
2m3(! 5m4)
65.
(! 8a9)(4a3b4)
66.
(7x3y5)(! 5x2y7)
67.
(x5)4
68.
(x2y3)4
69.
(3x4 y z3)2
70.
(x3)4 (x2)5
71.
(2x4)3(3x5)2
Simplify.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
Evaluate.
87.
6m + 25 when m = ! 7
88.
2x2 + 5x + 11 for x = 3
Math 093–Review for Final Exam–page 3
Choose the appropriate formula and find the answer.
89.
A rectangle has a length 10 feet and width 7 feet.
a.
find the perimeter
b.
find the area
90.
Find the area of a triangle with base 12 cm and height 9 cm.
91.
A circle has a radius of 4 inches.
a.
find the circumference
92.
b.
find the area
Find the volume of a rectangular solid with length 9 inches, width 7 inches, and height 4 inches.
Plot the following points.
Show your table of values. Graph.
93.
94.
95.
96.
97.
98.
99.
100.
(5, 4)
(! 3, 2)
(1, ! 6)
(! 5, ! 3)
y=
y=
y=
y=
2x + 3
3x ! 4
!x + 4
! 2x
Set up and solve.
101.
Joe’s bank balance increased by $1235 is $3948. Find Joe’s bank balance.
102.
If Glenn owns 14 trees more than Mary does, and together they own 52 trees, how many does each
one own?
103.
Gary earns $24 less than twice what Mike does. Together, they earn $1200. How much does each
one earn?
104.
In November, 200 people bought tickets to a play. Then 16 people had to return the tickets for a
refund. What percent of the people returned their tickets for a refund?
105.
A test had 25 questions, and a student had 80% correct. How many questions were correct?
106.
In a theater, 20 seats had to be replaced. If this represents 2% of the seats, how many seats are there
in the theater?
Answer Key.
1.
14
2.
! 72
3.
! 28
4.
! 48
5.
! 33
6.
! 81
7.
!5
8.
9
9.
37
10.
!6
11.
! 48
12.
18
13.
! 60
14.
180
15.
! 120
Math 093–Review for Final Exam–page 4
16.
!9
17.
!5
18.
3
19.
! 21
20.
!6
21.
16
22.
127
23.
! 4z
24.
! 2m !
25.
18m + 46
26.
27y ! 33
27.
! 41x
28.
m= 7
29.
z = 39
30.
y= 8
31.
y = ! 16
32.
x = 13
33.
a = ! 37
34.
k= 5
35.
z= 4
36.
y = ! 12
37.
m = !6
38.
z = !7
39.
a= 6
40.
y= 8
41.
a = !2
42.
x= 3
43.
m = !3
44.
45.
47.
48.
51.
y = ! 20
46.
+ 19
14
+ 68
49.
x=
50.
52.
k = ! 28
53.
z = 179
54.
5x2 + 2x ! 14
55.
14m2 ! 5m ! 17
56.
2a2 ! a + 14
57.
x2 + 10x + 21
58.
2x2 ! 11x ! 63
59.
20x2 ! 14x + 2
60.
x5
61.
y6
62.
m14
63.
28y7
64.
! 10m
65.
! 32a
66.
! 35x
67.
x20
68.
x8y12
69.
9x8 y2 z6
70.
x22
71.
72x22
72.
73.
7
74.
12 4
b
75.
5 12
x
y
Math 093–Review for Final Exam–page 5
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
! 17
90.
A = 54 sq cm
88.
44
89a.
89b.
P = 34 feet
A = 70 square feet
91a.
91b.
C = 25.12 in
A = 50.24 square inches
93.
(5, 4) move 5 right and then 4 up; located in 1st quadrant
94.
(! 3, 2) move 3 left and then 2 up; located in 2nd quadrant
95.
(1, ! 6) move 1 right and then 6 down; located in 4th quadrant
96.
(! 5, ! 3) move 5 left and then 3 down; located in 3rd quadrant
92.
V = 252 cu in
Math 093–Review for Final Exam–page 6
On the table of values, I chose to use x = 0, 1, 2. You can choose different x numbers. As long as you do
the arithmetic correctly, your graph and my graph should look the same (if we each draw the line longer).
97.
y = 2x + 3
x
y
0
3
1
5
2
7
98.
100.
y = ! 2x
x
y
0
0
1
!2
2
!4
101.
Joe’s bank balance = x
x + 1235 = 3948
solve!
x = 2713
Joe’s bank balance is $2713.
y = 3x ! 4
x
y
0
!4
1
!1
2
2
99.
102.
y = !x + 4
x
y
0
4
1
3
2
2
Mary’s trees = x
Glenn’s trees = x + 14
Mary + Glenn = 52
(x) + (x + 14) = 52
solve!
x = 19
Mary owns 19 trees;
Glenn owns 33 trees.
Math 093–Review for Final Exam–page 7
103.
Mike = x
Gary = 2x ! 24
Mike + Gary = 1200
(x) + (2x ! 24) = 1200
solve!
x = 408
Mike earns $408; Gary earns $792.
104.
percent = x
whole = 200
part = 16
percent (whole) = part
x(200) = 16
200x = 16
solve!
x = 0.08 = 8%
8% of the people returned their tickets
for a refund.
105.
percent = 80% = 0.80
whole = 25
part = x
percent (whole) = part
0.80(25) = x
solve!
x = 20
The student had 20 questions correct.
106.
percent = 2% = 0.02
whole = x
part = 20
percent (whole) = part
0.02 (x) = 20
solve!
x = 1000
There are 1000 seats in the theater.