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Basic Mathematics Flashcards

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1
Q
  1. What is the value of |–7|
A

7

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2
Q
  1. Simplify: (2^3)^4
A

4096

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3
Q
  1. What is the value of 0^0?
A

Undefined

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4
Q
  1. If a^m × a^n = a^k, what is k?
A

m + n

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5
Q
  1. What is the value of log₁₀1?
A

0

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6
Q
  1. What is log(ab)?
A

log a + log b

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7
Q
  1. What is log(a^b)?
A

b log a

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8
Q
  1. What is the base of a common logarithm?
A

10

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9
Q
  1. Evaluate: log₅25
A

2

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10
Q
  1. Simplify: √50
A

5√2

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11
Q
  1. What is the modulus of –12?
A

12

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12
Q
  1. Solve: |x – 3| = 5
A

x = 8 or x = –2

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13
Q
  1. Simplify: √(a^2)
A

|a|

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14
Q
  1. If log a = x and log b = y, what is log(ab)?
A

x + y

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15
Q
  1. Simplify: 4^(3/2)
A

8

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16
Q
  1. Evaluate: log₂(1/8)
A

–3

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17
Q
  1. Solve: |2x – 4| < 6
A

–1 < x < 5

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18
Q
  1. What is the principal square root of 121?
A

11

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19
Q
  1. What is the cube root of –27?
A

–3

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20
Q
  1. What is the value of a number raised to the power zero?
A

1

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21
Q
  1. Simplify: 2^4 × 2^–2
A

4

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22
Q
  1. Rewrite 81 as a power of 3
A

3^4

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23
Q
  1. Solve: x^0 = 1
A

x ≠ 0

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24
Q
  1. Simplify: (x^2)^3
A

x^6

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25
25. Convert 0.0001 into scientific notation
1 × 10^–4
26
26. Solve: log₃(27)
3
27
27. What is the value of √(2 + √3)^2?
5 + 2√3
28
28. Expand: (a + b)^2
a^2 + 2ab + b^2
29
29. Expand: (a – b)^2
a^2 – 2ab + b^2
30
30. Simplify: (x + 1)^2 – (x – 1)^2
4x
31
31. Solve: |x + 2| = 0
x = –2
32
32. Simplify: √72
6√2
33
33. What is the reciprocal of 5/8?
8/5
34
34. Evaluate: (1/3)^–2
9
35
35. Solve: 2^(x + 2) = 32
x = 3
36
36. What is the cube of (a + b)?
a^3 + 3a^2b + 3ab^2 + b^3
37
37. Factor: a^2 – b^2
(a – b)(a + b)
38
38. What is the product of (x – 1)(x + 1)?
x^2 – 1
39
39. What is 1/log_b a equal to?
log_a b
40
40. If log a = 2 and log b = 3, find log(a^2 b^3)
13
41
41. Solve: log₄16 = x
x = 2
42
42. Rewrite 2^(x) = 1/8 in logarithmic form
x = –3
43
43. Solve: 3^x = 81
x = 4
44
44. What is the domain of log x?
x > 0
45
45. What is the value of x if log₅(x) = 0?
x = 1
46
46. Simplify: √(x + 1)^2
|x + 1|
47
47. Evaluate: (27)^(2/3)
9
48
48. Rewrite log 0.01
–2
49
49. Solve the inequality: x^2 – 5x + 6 > 0
x < 2 or x > 3
50
50. Solve: |3x – 1| ≥ 2
x ≤ –1/3 or x ≥ 1
51
51. Simplify: (x – 2)^2 – (x + 2)^2
–8x
52
52. Evaluate: (1/4)^–2
16
53
53. Solve: 2^x = 1
x = 0
54
54. Simplify: (5x)^0
1
55
55. Simplify: (x^3 × y^2)^2
x^6 y^4
56
56. Evaluate: log₁₀(1000)
3
57
57. Simplify: log₁₀(0.1)
–1
58
58. Solve: log₂(x) = 5
x = 32
59
59. Expand: (x + 2)^3
x^3 + 6x^2 + 12x + 8
60
60. Simplify: (x^a)^b
x^(ab)
61
61. Solve: x^2 – 9 = 0
x = 3 or –3
62
62. Solve: |x – 5| > 3
x < 2 or x > 8
63
63. Evaluate: √(a^2 + b^2) if a = 3, b = 4
5
64
64. Convert 0.00032 into scientific notation
3.2 × 10^–4
65
65. Evaluate: (–2)^4
16
66
66. Evaluate: –2^4
–16
67
67. Solve: (1/2)^x = 8
x = –3
68
68. Simplify: √(x^2 – 2x + 1)
|x – 1|
69
69. Factor: x^2 + 5x + 6
(x + 2)(x + 3)
70
70. Solve: log₁₀(x^2) = 2
x = ±10
71
71. What is the range of y = log(x)?
(–∞, ∞)
72
72. Evaluate: 49^(1/2)
7
73
73. Solve: 4^x = 64
x = 3
74
74. Simplify: (x^2 – 4)/(x – 2)
x + 2
75
75. Evaluate: (16)^3/4
128
76
76. Evaluate: (81)^1/4
3
77
77. Solve: |x + 4| ≤ 2
–6 ≤ x ≤ –2
78
78. Expand: (x – y)^3
x^3 – 3x^2y + 3xy^2 – y^3
79
79. Solve: √(x + 1) = 4
x = 15
80
80. Simplify: √(a^4)
a^2
81
81. Evaluate: (3/2)^–2
4/9
82
82. Find x if log₅(x) = –1
x = 1/5
83
83. Simplify: (x^–2)(x^3)
x
84
84. Solve: log₂(2x – 4) = 3
x = 6
85
85. Simplify: log 5 + log 2
log 10 = 1
86
86. Find x: log₄x = 1/2
x = 2
87
87. Simplify: log 25 – log 5
log 5
88
88. Solve: |2x + 3| = 7
x = 2 or x = –5
89
89. Simplify: (3x)^2
9x^2
90
90. Evaluate: 32^(2/5)
4
91
91. Simplify: (x + 3)^2 – 9
x^2 + 6x
92
92. Solve: x^2 – 4x + 4 = 0
x = 2
93
93. Simplify: √(49x^2)
7|x|
94
94. Evaluate: (–8)^(1/3)
–2
95
95. What is the inverse of log base 10?
10^x
96
96. Solve: 10^x = 1000
x = 3
97
97. Simplify: √(x^4)
|x^2|
98
98. Simplify: (4x^3y)^2
16x^6y^2
99
99. Solve: (x – 1)^2 = 0
x = 1
100
100. Simplify: x^0 + x^1
1 + x
101
101. Simplify: (2a^2b)^3
8a^6b^3
102
102. Evaluate: log₉(1/3)
–0.5
103
103. Solve: |x| + 3 = 5
x = 2 or –2
104
104. Simplify: (x^3)^4 × x^2
x^14
105
105. Solve: 9^(x + 1) = 81
x = 1
106
106. Find x: log₁₀x = –2
x = 0.01
107
107. Simplify: (2x + 1)^2 – (2x – 1)^2
8x
108
108. Evaluate: (x^2 – y^2)/(x – y)
x + y
109
109. Evaluate: log₁₀(10^6)
6
110
110. Solve: 5^(x – 1) = 25
x = 3
111
111. Simplify: √(36x^2)
6|x|
112
112. Evaluate: 125^(–2/3)
1/25
113
113. Solve: |3x – 7| = 5
x = 4 or x = 2/3
114
114. Simplify: (3a^2b)^0
1
115
115. Solve: x^2 = 49
x = 7 or –7
116
116. Solve: |x + 4| + 2 = 0
No solution
117
117. Simplify: (a^3b^2)^2
a^6b^4
118
118. Convert 123000 to scientific notation
1.23 × 10^5
119
119. Evaluate: (1/9)^(–1/2)
3
120
120. Solve: log₃(x – 1) = 2
x = 10
121
121. Simplify: (a + b)^2 – (a – b)^2
4ab
122
122. Evaluate: log₂(8) + log₂(4)
5
123
123. Solve: 2x^2 – 8 = 0
x = ±2
124
124. Simplify: (x^2 – 9)/(x – 3)
x + 3
125
125. Evaluate: log₁₀(0.0001)
–4
126
126. Solve: (x + 2)^2 = 0
x = –2
127
127. Find x: 3^(2x – 1) = 1/3
x = 0
128
128. Simplify: (2ab^2)^3
8a^3b^6
129
129. Evaluate: √(x^2 + 6x + 9)
|x + 3|
130
130. Solve: |x – 1| ≤ 4
–3 ≤ x ≤ 5
131
131. Evaluate: 64^(1/3)
4
132
132. Simplify: (5^2 × 5^3) / 5^4
5
133
133. Evaluate: (27x^6)^(1/3)
3x^2
134
134. Solve: 10^x = 0.01
x = –2
135
135. Simplify: (x + y)^3 + (x – y)^3
2x(x^2 + 3y^2)
136
136. Simplify: (a – b)^3 + (b – a)^3
0
137
137. Evaluate: √[(a + b)^2]
|a + b|
138
138. Solve: log₄(2x – 4) = 1
x = 4
139
139. Simplify: √(25a^4b^2)
5a^2|b|
140
140. Solve: 5^(2x) = 625
x = 2
141
141. Evaluate: 100^(–1/2)
0.1
142
142. Simplify: (x^2 + 3x + 2)/(x + 1)
x + 2
143
143. Evaluate: (4/9)^(-1/2)
3/2
144
144. Solve: |x| = –5
No solution
145
145. Simplify: (a^4)^0
1
146
146. Solve: log₅(5x) = 1
x = 1
147
147. Evaluate: (x^2 + y^2 + 2xy)
(x + y)^2
148
148. Simplify: (2x – 1)^2 – 4x^2 + 1
–4x + 2
149
149. Solve: (x – 1)(x + 1) = 0
x = 1 or –1
150
150. Evaluate: (a + b)^2 + (a – b)^2
2a^2 + 2b^2
151
151. Solve: |2x – 5| = 3
x = 4 or x = 1
152
152. Simplify: (3x^2y)^2
9x^4y^2
153
153. Evaluate: (16)^–1/2
1/4
154
154. Simplify: (a^2 – b^2)^2
a^4 – 2a^2b^2 + b^4
155
155. Solve: 7^(x – 2) = 49
x = 4
156
156. Simplify: log a – log b
log(a/b)
157
157. Evaluate: log(1000) – log(10)
2
158
158. Simplify: √(x^2 – 6x + 9)
|x – 3|
159
159. Solve: x^2 + 2x + 1 = 0
x = –1
160
160. Simplify: 1/(x^–2)
x^2
161
161. Evaluate: (x + 2)^3 – (x – 2)^3
24x
162
162. Simplify: √(121x^2)
11|x|
163
163. Solve: log₃(9x) = 4
x = 27
164
164. Simplify: (2x + 3)^2
4x^2 + 12x + 9
165
165. Solve: (x – 3)^2 = 49
x = 10 or –4
166
166. Evaluate: (1/16)^–3/4
8
167
167. Simplify: x^3 – y^3
(x – y)(x^2 + xy + y^2)
168
168. Solve: 2^x = 0
No solution
169
169. Evaluate: (1/1000)^1/3
1/10
170
170. Simplify: √(x^2 + 4x + 4)
|x + 2|
171
171. Solve: 3x^2 = 75
x = ±5
172
172. Evaluate: log(√x)
(1/2) log x
173
173. Simplify: (x + 1)^3 – (x – 1)^3
6x^2 + 2
174
174. Solve: x^2 – 16 = 0
x = ±4
175
175. Evaluate: log₅(125)
3
176
176. Simplify: (2x – 1)^2 – (2x + 1)^2
–8x
177
177. Solve: log₂(x + 2) = 3
x = 6
178
178. Evaluate: 64^(2/3)
16
179
179. Simplify: (a + b)^3 – (a – b)^3
2a(3b^2 + a^2)
180
180. Solve: (x + 4)^2 = 36
x = 2 or –10
181
181. Evaluate: log₁₀(x^3)
3 log x
182
182. Simplify: (x + y)^2 – (x – y)^2
4xy
183
183. Evaluate: (1/27)^–2/3
9
184
184. Solve: x^2 + x – 6 = 0
x = 2 or –3
185
185. Simplify: √(81x^4)
9|x^2|
186
186. Solve: 3^(2x + 1) = 243
x = 2
187
187. Evaluate: log₂(32)
5
188
188. Simplify: (4a^3b^2)^0
1
189
189. Solve: |x – 3| + 2 = 7
x = 8 or –2
190
190. Evaluate: log₁₀(1/100)
–2
191
191. Simplify: (3x – 2)^2
9x^2 – 12x + 4
192
192. Solve: (x – 2)^2 = 0
x = 2
193
193. Evaluate: log₄(1/64)
–3
194
194. Simplify: (x^2 – y^2)/(x – y)
x + y
195
195. Solve: (x – 1)^2 = 9
x = 4 or –2
196
196. Evaluate: 0.00027 in scientific notation
2.7 × 10^–4
197
197. Simplify: √(x^2 – 4x + 4)
|x – 2|
198
198. Solve: x^2 – x – 6 = 0
x = 3 or –2
199
199. Evaluate: log₅(1/125)
–3
200
200. Simplify: x^3 + 3x^2 + 3x + 1
(x + 1)^3
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