MATH 100 Review Sheet for Test #1
15) A biologist collected 317 fern and moss
samples. There were 37 fewer ferns than moss
samples. How many fern samples did the
biologist collect?
Solve the equation.
1) 8x + 2 = 14
2) 37t - 34 = 2t - 9
Solve the percent problem.
16) If Gloria received a 6 percent raise and is now
making $26,500 a year, what was her salary
before the raise?
3) (y - 7) - (y + 2) = 8y
4) -[6x + (5x + 1)] = 2 - (9x + 7)
5)
2x x
- = 3
3
5
6)
a 1
- = -6
5 5
7)
b
- 5 = -2
5
17) Stevie bought a stereo for $200 and put it on
sale at his store at a 65% markup rate. What
was the retail price of the stereo?
18) At the end of the day, a storekeeper had $1339
in the cash register, counting both the sale of
goods and the sales tax of 3%. Find the
amount that is the tax.
Solve the mixture problem.
19) How many liters of a 20% alcohol solution
must be mixed with 40 liters of a 90% solution
to get a 40% solution?
7x
4x + 3 5
+ = - 8)
2
4
2
Solve.
20) In a chemistry class, 5 liters of a 4% silver
iodide solution must be mixed with a 10%
solution to get a 6% solution. How many liters
of the 10% solution are needed?
9) 0.08x + 0.1(x + 7000) = 1960
10) 0.01y + 0.12(9000 - y) = 0.39y
Use the variable x for the unknown. Write an equation
representing the verbal sentence and solve the problem.
11) Four times a number added to 8 times the
number equals 36.
21) A merchant has coffee worth $6 a pound that
she wishes to mix with 30 pounds of coffee
worth $9 a pound to get a mixture that can be
sold for $7 a pound. How many pounds of the
$6 coffee should be used?
12) If 6 times a number is added to -6, the result is
equal to 12 times the number.
Solve the investment problem.
22) Mardi received an inheritance of $50,000. She
invested part at 11% and deposited the
remainder in tax-free bonds at 12%. Her total
annual income from the investments was
$5600. Find the amount invested at 11%.
1
13) When of a number is added to 24, the result
4
is 38.
Solve the problem.
14) Gloria collected 26 fantail and comet goldfish.
There were 6 fewer fantails than comets. How
many comets did Gloria have?
23) Walt made an extra $8000 last year from a
part-time job. He invested part of the money
at 6% and the rest at 9%. He made a total of
$570 in interest. How much was invested at
9%?
1
Solve the inequality, giving its solution set in both
interval and graph forms.
24) 7x - 2 > -51
Let A = {q, s, u, v, w, x, y, z}, B = {q, s, y, z},
C = {v, w, x, y, z}, and D = {s}. List the elements in the
following set.
33) A ∩ B
34) A ∩ D
25) 4x + 6 ≤ 3x - 2
35) B ∪ C
36) C ∪ D
26)
2x + 9
1
< - 4
2
37) C ∩ D
For the compound inequality, give the solution set in both
interval and graph forms.
38) x ≥ 2 and x ≤ 7
27) m - 2(m + 4) < 3m
-8
28)
-6
-4
-2
0
2
39) x < -2 and x < 7
4
2
1
(3k + 4) > (3k - 5)
3
6
-8
-6
-4
40) 4x - 4 ≥ 8 and 4x - 4 ≤ 24
-2
0
2
4
-7 -6 -5 -4 -3 -2 -1 0
29) -6 < x + 6 < 4
-14
-12 -10
-8
-6
-4
-2
0
2
4
-2
0
42) x ≤ 3 or x ≥ 5
2
4
6
8
10
12
14
43) x ≥ -3 or x ≥ 7
31) 4 < -2z ≤ 12
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
32) 6 ≤ 3
4
5
6
7
1
2
3
4
5
6
7
6
30) -18 ≤ 6(x - 4) ≤ 6
-4
2
41) 5x + 9 ≥ -1 and 3x + 6 ≥ 18
-7 -6 -5 -4 -3 -2 -1 0
-6
1
44) x > 2 or x < 2
3x - 1
≤ 12
7
2
59) |2y - 6| > -9
45) 6x - 4 < 2x or -2x ≤ -6
-10
-8
-6
-4
-2
0
2
4
6
8
10
60) g - 6 < 7
Express the set in simplest interval form.
46) (-∞, 3) ∩ (-7, ∞)
-20
-15
-10
-5
0
5
47) (-5, 6] ∩ (-3, ∞)
61) 5x - 2 ≤ 9
48) (-5, 4) ∪ [0, 9]
-8
-6
-4
-2
0
2
4
6
Solve.
49) 3m + 8 = 9
62) 7 - x ≤ 13
50) |6 - 3p|= 18
-35
1
51) 8 - x = 3
2
-30
-25
-20
-15
-10
-5
0
5
63) -3x - 3 ≤ 5
-8
Solve the equation or inequality.
52) 4f + 8 = -3
-6
-4
-2
0
2
4
6
64) m - 1 < 0
53) 2x - 4 = 0
-10
Solve the given equation or inequality. If an equation is
given, then write the solution set in set notation. If an
inequality is given, then write the solution set in interval
notation.
54) x + 7 = 14
66) (-5, -17)
67) (-2, 0)
Solve the inequality and graph the solution set.
56) x - 1 ≥ 8
2 4 6
8 10 12 14 1
57) 2x - 5 ≥ 8
-14 -12 -10 -8
-6
-4
-2
0
2
4
6
8
10
1
58) 5 - x ≥ 8
-18 -16 -14 -12 -10 -8 -6 -4 -2 0
2 4 6
0
Name the quadrant, if any, in which the point is located.
65) (20, 20)
55) |x + 3| + 8 = 13
-18 -16 -14 -12 -10 -8 -6 -4 -2 0
-5
8 10 12 14 1
3
72) y - x = -1; (4, ), ( , 6), (3, )
Locate the point on the rectangular coordinate system.
6
A
B
y
D
y
10
4
E
2 C
G
-6
-4
5
F
-2
H
2
-10
-2
J
I
6 x
4
-5
K
-4
5
10
x
-5
L
-6
-10
68) (0, 2)
69) (-3, 4)
73) x + 2y = 8; (0, ), ( , 0), (3, ), ( , 3)
70) (3, 5)
y
10
Graph the equation by determining the missing values
needed to plot the ordered pairs.
71) y + x = 3; (1, ), (3, ), (2, )
5
y
-10
10
-5
5
10
x
-5
5
-10
-10
-5
5
10
x
-5
Find the x- and y-intercepts. Then graph the equation.
74) 2x - 10y = 10
-10
y
10
5
-10
-5
5
-5
-10
4
10
x
75) -6x - 12y = 24
80) (-4, -8) and (-4, 1)
y
10
Find the slope of the line.
81)
y
5
10
-10
-5
5
10
x
5
-5
-10
-5
5
10
x
5
10
x
-10
-5
76) x = -7
-10
y
10
82)
y
5
10
-10
-5
5
10
x
5
-5
-10
-5
-10
-5
77) x - 4y = 0
-10
y
10
Find the slope of the line, and sketch the graph.
83) x + 5y = -5
5
y
10
-10
-5
5
10
x
5
-5
-10
-5
5
-10
-5
Find the slope of the line through the pair of points.
78) (1, -4) and (6, -5)
-10
79) (3, -8) and (-4, -3)
5
10
x
84) x + y = 1
88) 6x + 2y = 8 and 24x + 8y = 34
y
10
89) 3x - 2y = -15 and 2x + 3y = -10
5
-10
90) 9x + 3y = 12 and 15x + 5y = 23
-5
5
10
Write the equation in standard form of the line satisfying
the given conditions.
2
91) Through (2, 5); m = - 3
x
-5
-10
92) Through (0, 5); m = 85) x + 4 = 0
4
5
93) Through (-2, 6); horizontal
y
10
Write the equation in standard form of the line through
the given points.
94) (-3, 3) and (0, 5)
5
-10
-5
5
10
95) (6, -4) and (-7, 6)
x
-5
96)
-10
1 2
3 5
, and , 3 3
4 4
Find the equation in slope-intercept form of the line
satisfying the conditions.
97) m = 9; b = -16
86) y = 3x
y
49
9
98) m = - ; y-intercept 0, 2
2
10
5
-10
-5
1
99) m = ; through (0, 1)
2
5
10
x
Find an equation of the line satisfying the conditions.
Write the equation in slope-intercept form.
100) Through (-6, 5); parallel to -7x + 5y = 57
-5
-10
101) Through (-3, 8); perpendicular to -3x + 4y =
-23
Decide whether the pair of lines is parallel,
perpendicular, or neither.
87) The line through (3, -5) and (-1, 7) and the line
through (6, -13) and (-2, 11)
102) Through (1, 9); perpendicular to x = 5
6
106) x + 3y ≥ -5
Graph the linear inequality in two variables.
103) x + y ≤ 7
y
10
y
10
5
5
-10
-10
-5
5
10
-5
5
10
x
5
10
x
x
-5
-5
-10
-10
107) x - 4y ≥ 0
104) x - y < -4
y
y
10
10
5
5
-10
-10
-5
5
10
-5
x
-5
-5
-10
-10
Graph the compound inequality.
108) x + y ≥ 2 and y ≤ 2
105) 5x - y ≤ -4
y
10
y
4
5
2
-10
-5
5
10
x
-5
-4
-2
2
-2
-10
-4
-6
7
4
6x
109) 2x + y ≤ 4 and x - 1 > 0
112) 3x + y ≥ 3 or x - 4y ≤ 1
y
y
10
4
5
2
-10
-4
-2
2
-5
10
x
5
10
x
5
10
x
5
6x
4
-5
-2
-10
-4
-6
113) 2x + 2y > 1 or 3x + 4y > 2
110) x + 2y ≤ 2 and x + y ≥ 0
y
10
y
5
4
2
-4
-10
-2
2
-5
-5
6x
4
-2
-10
-4
114) 3x + 5y ≥ 3 or y ≥ 3
-6
y
111) 2x + y < 6 or 3x - 2y > 5
10
y
5
10
-10
5
-5
-5
-10
-5
5
10
x
-10
-5
-10
8
Answer Key
Testname: 100REVTEST1
1)
3
2
2)
5
7
3) - 9
8
4)
5)
6)
7)
2
{45}
{-29}
{15}
16
8) - 15
9) {7000}
10) {2160}
11) 4x + 8x = 36; 3
12) 6x + (-6) = 12x; -1
1
13) x + 24 = 38; 56
4
14) 16 comets
15) 140 fern samples
16) $25,000
17) $330.00
18) $39
19) 100 liters
20) 2.5 liters
21) 60 lb
22) $40,000
23) $3000
24) (-7, ∞)
-10
-5
0
5
10
25) (-∞, -8]
-15 -14 -13 -12 -11 -10 -9
26) -∞, - -8
-7
-6
-5
-4
-3
-2
-1
11
2
- 11
2
27) (-2, ∞)
-10
-8
-6
-4
-2
0
2
4
6
9
Answer Key
Testname: 100REVTEST1
7
28) - , ∞
3
-10
-8
-6
-4
-2
0
2
4
-12 -10
-8
-6
-4
-2
0
2
4
6
-4
0
2
4
6
8
10
12
14
6
29) (-12, -2)
-14
30) [1, 5]
-6
-2
31) [-6, -2)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
32) 43 85
,
3 3
43
3
85
3
33) {q, s, y, z}
34) {s} or D
35) {q, s, v, w, x, y, z}
36) {s, v, w, x, y, z}
37) ∅
38) [2, 7]
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
39) (-∞, -2)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
3
4
5
6
7
6
7
8
9 10
40) [3, 7]
-7
41) [4, ∞)
-6 -5 -4 -3 -2 -1 0
-7 -6 -5 -4 -3 -2 -1 0
1
1
2
2
3
4
5
6
7
42) (-∞, 3] ∪ [5,∞)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
10
Answer Key
Testname: 100REVTEST1
43) [-3, ∞)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
44) (-∞, 2) ∪ (2,∞)
-7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
45) (-∞, 1) ∪ [3, ∞)
-7 -6 -5 -4 -3 -2 -1 0
46) (-7, 3)
47) (-3, 6]
48) (-5, 9]
17
1
, - 49)
3
3
50) - 4, 8
51) {10, 22}
52) ∅
53) 2
54) {-7, 7}
55) -8, 2
56) (-∞, -7] ∪ [9, ∞)
-18 -16 -14 -12 -10 -8 -6 -4 -2 0
57) -∞, - 2 4 6
8 10 12 14 16 18
3
13
∪ , ∞
2
2
-14 -12 -10 -8
-6
-4
-2
0
2
4
6
8
10
12 14
58) (-∞, -3] ∪ [13, ∞)
-18 -16 -14 -12 -10 -8 -6 -4 -2 0
2 4 6
8 10 12 14 16 18
59) (-∞, ∞)
-10
-8
-6
-4
-2
0
2
4
6
8
10
60) (-1, 13)
-20
-15
-10
-5
0
5
10
15
20
7 11
61) - , 5 5
-8
-6
-4
-2
0
2
4
6
8
62) [-6, 20]
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
11
20
25
30
35
Answer Key
Testname: 100REVTEST1
8 2
63) - , 3 3
-8
-6
-4
-2
0
2
4
6
8
64) ∅
65) I
66) III
67) None
68) C
69) B
70) D
71)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
72)
y
10
5
-10
-5
-5
-10
12
Answer Key
Testname: 100REVTEST1
73)
y
10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
74) (5, 0); (0, -1)
y
10
5
-10
-5
-5
-10
75) (-4, 0); (0, -2)
y
10
5
-10
-5
-5
-10
13
Answer Key
Testname: 100REVTEST1
76) (-7, 0); none
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
77) (0, 0); (0, 0)
y
10
5
-10
-5
-5
-10
78) - 1
5
79) - 5
7
80) Undefined
81) -1
82) 3
14
Answer Key
Testname: 100REVTEST1
83) Slope: - 1
5
y
10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
84) Slope: -1
y
10
5
-10
-5
-5
-10
85) Slope: Undefined
y
10
5
-10
-5
-5
-10
15
Answer Key
Testname: 100REVTEST1
86) Slope: 3
y
10
5
-10
-5
5
10
x
-5
-10
87) Parallel
88) Parallel
89) Perpendicular
90) Parallel
91) 2x + 3y = 19
92) 4x - 5y = -25
93) y = 6
94) 2x - 3y = -15
95) 10x + 13y = 8
96) 7x - 5y = -1
97) y = 9x - 16
49
9
98) y = - x + 2
2
1
99) y = x + 1
2
67
7
100) y = x + 5
5
4
101) y = - x + 4
3
102) y = 9
103)
y
10
5
-10
-5
5
10
x
-5
-10
16
Answer Key
Testname: 100REVTEST1
104)
y
10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
105)
y
10
5
-10
-5
-5
-10
106)
y
10
5
-10
-5
-5
-10
17
Answer Key
Testname: 100REVTEST1
107)
y
10
5
-10
-5
5
10
x
-5
-10
108)
y
4
2
-4
-2
2
4
6x
2
4
6x
-2
-4
-6
109)
y
4
2
-4
-2
-2
-4
-6
18
Answer Key
Testname: 100REVTEST1
110)
y
4
2
-4
-2
2
6x
4
-2
-4
-6
111)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
112)
y
10
5
-10
-5
-5
-10
19
Answer Key
Testname: 100REVTEST1
113)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
114)
y
10
5
-10
-5
-5
-10
20