Math 095--Review for Final Exam--page 1
Solve.
1.
2a ! 17 = ! 45
2.
7m ! 20 ! m ! 45 = ! 4m + 55
3.
2(3y + 11) = 5(3y + 9)
4.
2(5x + 1) ! (3x ! 7) = 11
5.
6.
7.
8.
9.
Solve and write the solution in interval notation; it’s helpful to graph on a number line.
10.
! 3x + 9 < 48
11.
7 ! 2x $ 23
12.
! 11 < 5 + x < 20
13.
32< 4x + 8 # 56
14.
15.
16.
State the intercepts for 2x + 4y = 4. Graph.
17.
State the intercepts for 6x ! 3y = 24. Graph.
18.
Graph: y = 2x + 3
19.
Graph: 2x + 3y = 12
20.
Graph: 2x ! y = 6
21.
Graph: y =
23.
(4m 2 ! 6m + 14) ! (2m 2 ! 5m ! 11)
Simplify appropriately.
22.
(9z 2 + 21z ! 25) + (6z 2 ! 7z ! 4)
24.
(4m ! 6)(2m + 5)
25.
(4x ! 7) 2
26.
m3 @ m4
27.
9a 3b( ! 2a 5b 2)
28.
(x 3) 5
29.
(x 2) 8(x 3) 9
30.
5x 6y(4x 3y 7) 2
31.
32.
34.
35.
33.
36.
Divide:
37.
Long Divide:
Math 095--Review for Final Exam--page 2
Factor.
38.
x 2 + 25x
39.
16x 3 ! 24x 2
40.
A 2 ! 81
41.
16y 2 ! 25
42.
ax + ay + bx + by
43.
k 2 ! 2k ! 15
44.
z 2 + 10z + 16
45.
x 2 + 3x ! 28
46.
m 2 ! 10m + 24
47.
m 2 ! 10m ! 24
48.
3m 2 + 21m + 18
49.
6x 2 + 17x + 5
50.
8x 2 + 10x ! 7
51.
5x 2 ! 14x ! 3
52.
7x 2 ! 16x + 4
53.
10x 2 + 19x + 6
54.
64x 3 + 125
55.
x 3 ! 7x 2 + 10x
56. .
x 3 + 7x 2 ! 9x ! 63
Solve.
57.
d 2 ! 144 = 0
58.
9m 2 ! 49 = 0
59.
x 2 + 11x + 24 = 0
60.
x 2 + 2x ! 15 = 0
61.
k 2 = 9k ! 18
62.
3b 2 ! 5b = ! 2
63.
6x 2 + 29x + 9 = 0
64.
4y 2 = ! 9y + 9
65.
9x 2 + 4 = ! 12x
66.
z(z ! 3) = 28
67.
8x 2 + 3x ! 7 = 2x 2+ 8x ! 3
Set up and solve.
68.
Four times Friday’s temperature, decreased by 12 degrees, was 56 degrees. What was Friday’s temperature?
69.
A leather jacket costs $105 more than twice a cloth jacket. Together they cost $342. Find the cost of each one.
70.
Use a proportion: On a map, 3 inches represents 180 miles. How many miles are represented by 5 inches?
71.
M olly invested some money at 4% and $4000 more than this at 6% . Her annual interest was $580. How much
was invested at each rate?
72.
A club sold blue shirts for $15 each and red shirts for $18 each. If the club sold 200 shirts and brought in
$3351, how many of each type shirt were sold?
73.
The length of a rectangle is 3 feet more than the width. The area is 40 square feet. Find the length and width.
74.
A 13 foot ladder is leaning against a house. The ladder reaches a height on the wall that is 12 feet above the
ground. Find how far the bottom of the ladder is from the house.
Math 095--Review for Final Exam--page 3
Answer Key.
1.
2a = ! 28
a = ! 14
2.
6m ! 65 = ! 4m + 55
10m = 120
3.
m = 12
4.
10x + 2 ! 3x + 7 = 11
7x + 9 = 11
7x = 2
5.
x=
7.
LCD 28
20x + 18 = 21x + 14
!x = !4
6y + 22 = 15y + 45
! 9y = 23
y=
6.
LCD 24
18x + 48 = 16x + 9
2x = ! 39
9.
LCD 12
3(5x ! 3) + 4(7x + 2) = 2(5)
15x ! 9 + 28x + 8 = 10
x= 4
LCD 36
20x + 6 = ! 27
20x = ! 33
8.
x=
LCD 6 or cross multiply
2(2x + 1) = 3(3x ! 5)
4x + 2 = 9x ! 15
! 5x = ! 17
43x ! 1 = 10
x=
43x = 11
x=
10.
! 3x
< 39
x > ! 13
11.
(! 13, 4 )
13.
24< 4x # 48
6 < x # 12
! 2x $ 16
x#!8
12.
(!4 , ! 8]
14.
x ! 7 # 12 and ! x+ 7 # 12
x # 19 and ! x # 5
x # 19 and x $ ! 5
16.
x intercept is (2, 0)
y intercept is (0, 1)
17.
x intercept is (4, 0)
y intercept is (0, ! 8)
18.
x
0
1
2
19.
x intercept is (6, 0)
y intercept is (0, 4)
y
3
5
7
< x < 15
(! 16, 15)
15.
[ ! 5, 19]
! 5 # x # 19
(6, 12]
! 16
2x+ 5> 17 or ! 2x ! 5> 17
2x > 12 or ! 2x > 22
x > 6 or x < ! 11
( !4 , ! 11) c (6, 4 )
x < ! 11 or x > 6
20.
x-intercept is (3, 0)
y-intercept is (0, ! 6)
Math 095--Review for Final Exam--page 4
using a table
x
y
0
!3
2
!2
4
!1
22.
15z 2 + 14z ! 29
23.
2m 2 ! m + 25
24.
8m 2 + 8m ! 30
25.
16x 2 ! 56x + 49
26.
m7
27.
! 18a b
you could clear fraction
to get 2y = x ! 6
x intercept (6, 0)
y intercept (0, ! 3)
28.
x 15
29.
x 16x 27 Y x 43
30.
5x 6 y @ 16x 6 y 14 Y 80x 12 y 15
31.
32.
x9
34.
35.
21.
36.
4x 2 + 5x ! 2
37.
39.
8x 2(2x ! 3)
40.
42.
(x + y)(a + b)
45.
8 3
33.
38.
x(x + 25)
(A + 9)(A ! 9)
41.
(4y + 5)(4y ! 5)
43.
(k + 3)(k ! 5)
44.
(z + 2)(z + 8)
(x ! 4)(x + 7)
46.
(m ! 4)(m ! 6)
47.
(m + 2)(m ! 12)
48.
3(m 2 + 7m + 6)
3(m + 1)(m + 6)
49.
(3x + 1)(2x + 5)
50.
(4x + 7)(2x ! 1)
51.
(5x + 1)(x ! 3)
52.
(7x ! 2)(x ! 2)
53.
(5x + 2)(2x + 3)
54.
(4x + 5)(16x 2 ! 20x + 25)
55.
x(x 2 ! 7x + 10)
x(x ! 2)(x ! 5)
56.
x 2(x + 7) ! 9(x + 7)
(x + 7)(x 2 ! 9)
(x + 7)(x + 3)(x ! 3)
57.
{! 12, 12}
58.
59.
{! 3, ! 8}
60.
{! 5, 3}
61.
63.
64.
{3, 6}
62.
65.
Math 095--Review for Final Exam--page 5
z 2 ! 3z = 28
z 2 ! 3z ! 28 = 0
(z + 4)(z ! 7) = 0; solve!
{! 4, 7}
68.
Friday’s temperature = x = 17 degrees
4x ! 12 = 56
70.
miles = x = 300 miles
67.
2
8x 2 + 3x ! 7 ! 2x ! 8x + 3 = 0
6x 2 ! 5x ! 4 = 0
6x 2 + 3x ! 8x ! 4 = 0
3x(2x + 1) ! 4(2x + 1) = 0; finish solving!
66.
69.
cost of cloth jacket = x = $79
2x + 105 = cost of leather jacket = $263
cloth + leather = 342
(x) + (2x + 105) = 342
3x + 105 = 342
3x = 180(5)
x = 300
71.
$ invested at 4% = x = $3400
$ invested at 6% = x + 4000 = $7400
0. 04(x) + 0. 06(x + 4000) = 580
0. 04x + 0. 06 + 240 = 580
0. 10x + 240 = 580; solve!
72.
# of blue shirts = x = 83 blue shirts
# of red shirts = 200 ! x = 117 red shirts
15(x) + 18(200 ! x) = 3351
15x + 3600 ! 18x = 3351
! 3x + 3600 = 3351; solve!
73.
width = x =
length = x +
l(w) = A
(x + 3)(x) =
x 2 + 3x ! 40
74.
bottom of ladder to house = x = leg = 5 feet
leg 2 + leg 2 = hypotenuse 2
x 2 + 12 2 = 13 2
x 2 + 144 = 169
x 2 + 144 ! 169 = 0
x 2 ! 25 = 0; solve
5 ft
3=
8 ft
40
= 0; solve