Math 101 Practice Questions
32. A =
33.
1. What is the meaning of x3?
2. Evaluate (x − 3)2 + 5 when x = 10.
1
𝑡
=
4𝑏
,
𝑡
1
𝑚
for b
1
− 𝑛, for m
𝐴
𝜋
34. r = √ , for A
3
3. Find decimal notations of −11.
35. y = ax2 − bx, for x
4. Find the LCM of 15 and 48.
36. x−6 · x2
37.
5. Find the absolute value: |−7|
38. (2y6)2
Compute and simplify.
6. −6 + 12 + (−4) + 7
8. −
3
8
÷
5
2
𝑦3
𝑦 −4
7. 2.8 − (−12.2)
9. 13 · 6 ÷ 3 · 2 ÷ 13
39. Collect like terms and arrange in descending order:
2x − 3 + 5x3 − 2x3 + 7x3 + x.
Compute and simplify.
40. (4x3 + 3x2 − 5) + (3x3 − 5x2 + 4x − 12)
10. Remove parentheses and simplify.
41. (6x2 − 4x + 1) − (−2x2 + 7)
4m + 9 − (6m + 13).
42. −2y2(4y2 − 3y + 1)
Solve.
43. (2t − 3)(3t2 − 4t + 2)
11. 3x = −24
12. 3x + 7 = 2x − 5
1
1
13. 3(y − 1) − 2(y + 2) = 0
44. (𝑡 − 4) (𝑡 + 4)
14. x2 − 8x + 15 = 0
45. (3𝑚 − 2)2
15. y − x = 1,
y = 3 − x
16. x + y = 17,
x − y = 7
17. 4x − 3y = 3,
3x − 2y = 4
18. x2 − x − 6 = 0
19. x2 + 3x = 5
20. 3 − x = √𝑥 2 − 3
21. 5 − 9x ≤ 19 + 5x
23. 0.6x − 1.8 = 1.2x
29.
2𝑥
𝑥+ 1
= 2 −
30.
2𝑥
𝑥+ 3
6
𝑥
+
48. (3𝑝 + 4𝑞 2 )2
4
2𝑥−6
22. −8x + 7 = 8x − 3
50.
3𝑎 4
2𝑎 3
÷
2
2
𝑎 −1
𝑎 −2𝑎+1
24. −3x > 24
51.
3
3𝑥−1
52.
2
𝑥−3
− 𝑥 2 −9𝑥+20
𝑥 2 −16
7
28.
6𝑥 − 2
2𝑥 − 1
5
2𝑥
+ 7 =
47. (𝑥 2 − 0.2𝑦)(𝑥 2 + 0.2𝑦)
49.
3
25. 23 − 19y − 3y ≥ −12 26. 3y2 = 30
27. (x − 3)2 = 6
46. (15𝑥 2 𝑦 3 + 10𝑥𝑦 2 + 5) − (5𝑥𝑦 2 − 𝑥 2 𝑦 2 − 2)
18
𝑥 2 − 3x
31. √𝑥 + 9 = √2𝑥 − 3
Solve the formula for the given letter.
=
9𝑥
3𝑥 +1
·
𝑥−3
𝑥+3
4
+ 5𝑥
Factor.
53. 8𝑥 2 − 4𝑥
54. 25𝑥 2 − 4
55. 6𝑦 2 − 5𝑦 − 6
56. 𝑚2 − 8𝑚 + 16
57. 𝑥 3 − 8𝑥 2 − 5𝑥 + 40
58. 3𝑎4 + 6𝑎2 − 72
59. 16𝑥 4 − 1
1
78. 𝑦 = 3 𝑥 − 2
60. 49𝑎2 𝑏 2 − 4
x
y
61. 9𝑥 2 + 30𝑥𝑦 + 25𝑦 2
62. 2𝑎𝑐 − 6𝑎𝑏 − 3𝑑𝑏 + 𝑑𝑐
63. 15𝑥 2 + 14𝑥𝑦 − 8𝑦 2
79. 𝑦 = −3
Simplify.
3 1
+
𝑥 2𝑥
64. 1 3
−
3𝑥 4𝑥
65. √49
66. −√625
67. √64𝑥 2
x
68. Multiply: √𝑎 + 𝑏 √𝑎 − 𝑏.
y
80. 𝑥 ≥ −3
69. Multiply and simplify: √32𝑎𝑏√6𝑎4 𝑏2 .
x
y
Simplify.
71. √243𝑥 3 𝑦 2
70. √150
100
81
64
𝑥2
72. √
73. √
81. 4𝑥 − 3𝑦 > 12
74. 4√12 + 2√12
x
75. Divide
y
√72
and simplify:
.
√45
76. In a right triangle, where a and b represent the legs
and c represents the hypotenuse, a = 9 and c = 41. Find
b.
82. Graph 𝑦 = 𝑥 2 + 2𝑥 + 1. Label the vertex and the yintercept.
Graph.
1
77. 𝑦 = 3 𝑥 − 2
x
x
y
y
83. Solve 9𝑥 2 − 12𝑥 − 2 = 0 by completing the square.
Show your work.
84. Approximate the solutions of 4𝑥 2 = 4𝑥 + 1 to the
nearest tenth.
Solve.
85. What percent of 52 is 13?
98. Use only the graph below to solve 𝑥 2 + 𝑥 − 6 = 0.
86. 12 is 20% of what?
87. In checking records, a contractor finds that crew A
can resurface a tennis court in 8 hrs. Crew B can do the
same job in 10 hrs. How long would they take if they
worked together?
88. The area of a rectangular movie screen is 96ft2. The
length is 4ft longer than the width. Find the length and
the width of the movie screen.
89. The speed of a boat in still water is 8km/h. It
travels 60km upstream and 60km downstream in a
total time of 16 hours. What is the speed of the stream?
99. Find the x-intercepts of 𝑦 = 𝑥 2 + 4𝑥 + 1.
100. Find the slope and the y-intercept:
−6𝑥 + 3𝑦 = −24
90. The length of a rectangular garage floor is 7m more
than the width. The length of a diagonal is 13m. Find
the length of the garage floor.
101. Determine whether the graphs of the following
equations are parallel, perpendicular, or neither.
91. The sum of the squares of two consecutive odd
integers is 74. Find the integers.
102. Find the slope of the line containing the points
(−5, −6) and (−4,9).
92. Solution A is 75% alcohol and solution B is 50%
alcohol. How much of each is needed in order to make
103. Find an equation of variation in which y varies
directly as x and 𝑦 = 100 when 𝑥 = 10. Then find the
value of y when 𝑥 = 64.
2
60L of a solution that is 663% alcohol?
93. The Eiffel Tower in Paris is 984ft tall. How long
would it take an object to fall to the ground from the
top? (See the formula in Example 11 of Section 9.2.)
94. A student’s paycheck varies directly as the number
of hours worked. The pay was $242.52 for 43 hrs of
work. What would be the pay for 80 hrs of work?
Explain the meaning of the variation constant.
95. Three-fifths of the automobiles entering the city
each morning will be parked in the city parking lots.
There are 3654 such parking spaces filled each
morning. How many cars enter the city each morning?
96. A candy shop wants to mix nuts worth $3.30 per
pound with another variety worth $2.40 per pound in
order to make 42 lbs of a mixture worth $2.70 per
pound. How many pounds of each kind of nuts should
be used?
97. An airplane flew for 3 hrs with a 20-mph tail wind.
The return flight against the same wind took 4 hrs. Find
the speed of the plane in the air.
104. Find an equation of variation in which y varies
inversely as x and 𝑦 = 100 when 𝑥 = 10. Then find the
value of y when 𝑥 = 125.
Determine whether each of the following is the graph of
a function.
105.
106.
A.
Graph the function.
107. 𝑓(𝑥) = 𝑥 2 + 𝑥 − 2
B.
108. 𝑔(𝑥) = |𝑥 + 2|
109. For the function 𝑓 described by 𝑓(𝑥) = 2𝑥 2 +
1
7𝑥 − 4, find 𝑓(0), 𝑓(−4), and𝑓 (2).
110. An airplane flies 408 mi against the wind and 492
mi with the wind in a total time of 3 hrs. The speed
of the airplane in still air is 300 mph. If we assume
there is some wind, the wind is between:
A. 8 and 15 mph. B. 15 and 22 mph.
C. 22 and 29 mph. D. 29 and 26 mph.
C.
111. Solve: 2𝑥 2 + 6𝑥 + 5 = 4.
A. −3 ± √7
B. −3 ± 2√7
C. No real solutions
112. Solve for b: 𝑆 =
D.
−3±√7
2
𝑎+𝑏
.
3𝑏
A. 𝑏 = 3𝑏𝑆 − 𝑎
B. 𝑏 =
𝑎+𝑏
3𝑆
C. 𝑎 = 𝑏(3𝑆 − 1)
D. 𝑏 =
𝑎
3𝑆−1
113. Which of the following is the graph of 3𝑥 − 4𝑦 =
12?
D.
114. Solve: |𝑥| = 12.
115. Simplify: √√√81
116. Find b such that the trinomial 𝑥 2 − 𝑏𝑥 + 225 is a
square
117. Find x.
Determine whether each pair of expressions is
equivalent.
118.
𝑥 2 − 9,
119.
(𝑥 − 3)(𝑥 + 3)
120.
(𝑥 + 5)2 ,
𝑥 2 + 25
122.
√𝑥 2 ,
|𝑥|
𝑥+3
,
3
𝑥
121.
√𝑥 2 + 16,
𝑥+4
Answer Key
1. 𝑥 · 𝑥 · 𝑥
28.
2. 54
2
9
29. −5
3. −0. 27
30. No solution
4. 240
31. 12
5. 7
32. 𝑏 =
6. 9
33.
7. 15
8.
𝐴𝑡
4
𝑡𝑛
𝑡+𝑛
34. 𝐴 = 𝜋𝑟 2
3
− 20
35. 𝑥 =
9. 4
𝑏+√𝑏2 +4𝑎𝑦
2𝑎
1
𝑥4
10. −2𝑚 − 4
36.
11. −8
37. 𝑦 7
12. −12
38. 4𝑦12
13. 7
39. 10𝑥 3 + 3𝑥 − 3
14. 3, 5
40. 7𝑥 3 − 2𝑥 2 + 4𝑥 − 17
15. (1, 2)
41. 8𝑥 2 − 4𝑥 − 6
16. (12, 5)
42. −8𝑦 4 + 6𝑦 3 − 2𝑦 2
17. (6, 7)
43. 6𝑡 3 − 17𝑡 2 + 16𝑡 − 6
18. −2, 3
44. 𝑡 2 − 16
19.
1
−3±√29
2
45. 9𝑚2 − 12𝑚 + 4
20. 2
46. 15𝑥 2 𝑦 3 + 𝑥 2 𝑦 2 + 5𝑥𝑦 2 + 7
21. {𝑥|𝑥 ≥ −1}
47. 𝑥 2 − 0.04𝑦 2
22. 8
48. 9𝑝2 + 24𝑝𝑞 2 + 16𝑞 4
23. −3
49.
2
𝑥+3
50.
3𝑎(𝑎−1)
2(𝑎+1)
51.
27𝑥−4
5𝑥(3𝑥−1)
52.
−(𝑥−2)(𝑥+1)
(𝑥+4)(𝑥−4)(𝑥−5)
24. {𝑥|𝑥 < 8}
35
25. {𝑦|𝑦 ≤ 22}
26. −√10, √10
27. 3 ± √6
53. 4𝑥(2𝑥 − 1)
77.
54. (5𝑥 − 2)(5𝑥 + 2)
55. (3𝑦 + 2)(2𝑦 − 3)
56. (𝑚 − 4)2
57. (𝑥 − 8)(𝑥 2 − 5)
58. 3(𝑎2 + 6)(𝑎 + 2)(𝑎 − 2)
59. (4𝑥 2 + 1)(2𝑥 + 1)(2𝑥 − 1)
60. (7𝑎𝑏 + 2)(7𝑎𝑏 − 2)
78.
61. (3𝑥 + 5𝑦)2
62. (𝑐 − 3𝑏)(2𝑎 + 𝑑)
63. (5𝑥 − 2𝑦)(3𝑥 + 4𝑦)
64. −
42
5
65. 7
66. −25
67. 8𝑥
79.
68. √𝑎2 − 𝑏 2
69. 8𝑎2 𝑏√3𝑎𝑏
70. 5√6
71. 9𝑥𝑦√3𝑥
72.
10
9
73.
8
𝑥
74. 12√3
75.
2√10
5
76. 40
80.
81.
96. $3.30 per pound: 14 lb; $2.40 per pound 28 lb
97. 140 mph
98. −3, 2
99. (−2 − √3, 0), (−2 + √3, 0)
100. Slope: 2; 𝑦-intercept: (0, −8)
101. Neither
102. 15
103. 𝑦 = 10𝑥; 640
82.
104. 𝑦 =
1000
;8
𝑥
105. Yes
106. No
107.
83.
2±√6
3
84. −0.2, 1.2
85. 25%
86. 60
4
87. 4 9 hr
108.
88. Length: 12 ft; width 8 ft
89. 2km/h
90. 12 m
91. 5 and 7; −7 and −5
92. 40 L of A; 20 L of B
93. About 7.8 sec
94. $541.20; the variation constant is the amount
earned per hour
109. −4; 0; 0
95. 6090 cars
111. D
110. C
112. D
113. C
114. −12, 12
115. √3
116. −30, 30
117.
√6
3
118. Yes
119. No
120. No
121. No
122. Yes