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# AB Calculus Question Strategies

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A guide to approaching AB Calculus AP Questions

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### AB Calculus Question Strategies

1. 1. When you see… Find the zeros You think…
2. 2. To find the zeros...
3. 3. You think… When you see… Show that f ( x ) is even
4. 4. Even function
5. 5. You think… When you see… Show that f ( x ) is odd
6. 6. Odd function
7. 7. You think… When you see… Show that exists
8. 8. Show exists <ul><li>Show that </li></ul>
9. 9. You think… When you see…
10. 10. Find Limit with calculator
11. 11. You think… When you see…
12. 12. Find limits, no calculator
13. 13. You think… When you see…
14. 14. Find limit with calculator
15. 15. You think… When you see…
16. 16. Find limit, no calculator
17. 17. You think… When you see… Find horizontal asymptotes of f ( x )
18. 18. Find horizontal asymptotes of f(x)
19. 19. You think… When you see… Find vertical asymptotes of f ( x )
20. 20. Find vertical asymptotes of f(x)
21. 21. You think… When you see… Find the domain of f ( x )
22. 22. Find the domain of f(x)
23. 23. You think… When you see… Show that f ( x ) is continuous
24. 24. . f(x) is continuous
25. 25. You think… When you see… Find the slope of the tangent line to f(x) at x = a
26. 26. Slope of tangent line
27. 27. When you see… Find equation of the line tangent to f ( x ) at ( a , b ) You think…
28. 28. Equation of the tangent line
29. 29. You think… When you see… Find equation of the line normal to f ( x ) at ( a , b )
30. 30. Equation of the normal line
31. 31. You think… When you see… Find the average rate of change of f ( x ) at [ a , b ]
32. 32. Average rate of change of f(x) <ul><li>Find </li></ul><ul><li>f (b) - f ( a) </li></ul><ul><li>b - a </li></ul>
33. 33. You think… When you see…
34. 34. Intermediate Value Theorem (IVT)
35. 35. You think… When you see… Find the interval where f ( x ) is increasing
36. 36. f (x) increasing
37. 37. You think… When you see… Find the interval where the slope of f ( x ) is increasing
38. 38. Slope of f (x) is increasing
39. 39. You think… When you see… Find the instantaneous rate of change of f ( x ) on [ a , b ]
40. 40. Instantaneous rate of change of f(x) <ul><li>Find f ‘ ( a) </li></ul>
41. 41. You think… When you see… Given s ( t ) (position function), find v ( t )
42. 42. Given position s(t), find v(t)
43. 43. You think… When you see… Find f ’ ( x ) by the limit definition
44. 44. Find f ‘ ( x) by definition frequently asked backwards
45. 45. You think… When you see… Find the average velocity of a particle on [ a , b ]
46. 46. Find the average rate of change on [a,b]
47. 47. You think… When you see… Given v ( t ) , determine if a particle is speeding up at t = k
48. 48. Given v(t), determine if the particle is speeding up at t = k
49. 49. You think… When you see… Given a graph of find where f ( x ) is increasing
50. 50. Given a graph of f ‘(x) , find where f(x) is increasing
51. 51. You think… When you see…
52. 53. You think… When you see…
53. 54. Relative maximum
54. 55. You think… When you see…
55. 56. Concave Down
56. 57. You think… When you see…
57. 58. Points of Inflection
58. 59. You think… When you see… Show that a piecewise function is differentiable at the point a where the function rule splits
59. 60. Show a piecewise function is differentiable at x=a
60. 61. You think… When you see…
61. 62. Derivative of Inverse Function
62. 63. You think… When you see…
63. 64. Derivative of the inverse of f(x)
64. 65. You think… When you see…
65. 66. Derivative Rules
66. 67. You think… When you see…
67. 68. Implicit Differentiation
68. 69. You think… When you see… Find the derivative of f ( g ( x ))
69. 70. Chain Rule
70. 71. You think… When you see… Find the minimum value of a function
71. 72. Minimum value of a function
72. 73. You think… When you see… Find the minimum slope of a function
73. 74. Minimum slope of a function
74. 75. You think… When you see… Find critical numbers
75. 76. Find critical numbers
76. 77. You think… When you see… Find the absolute maximum of f ( x )
77. 78. Find the absolute minimum of f(x)
78. 79. You think… When you see…
79. 80. Rolle’s Theorem
80. 81. You think… When you see…
81. 82. Mean Value Theorem
82. 83. You think… When you see… Find the range of f ( x ) on [ a , b ]
83. 84. Find the range of f(x) on [a,b]
84. 85. You think… When you see… Find the range of f ( x ) on
85. 86. Find the range of f(x) on
86. 87. You think… When you see…
87. 88. Second Derivative Test
88. 89. You think… When you see…
89. 90. Find inflection points
90. 91. You think… When you see…
91. 92. . y = mx+b is tangent to f(x) at a point
92. 93. You think… When you see…
93. 94. Horizontal tangent line
94. 95. You think… When you see…
95. 96. Vertical tangent line to f(x)
96. 97. You think… When you see… Approximate the value f (0.1) of by using the tangent line to f at x = 0
97. 98. Approximate f(0.1) using tangent line to f(x) at x = 0
98. 99. You think… When you see… Find rates of change for volume problems
99. 100. Rates of Change of Volumes
100. 101. You think… When you see… Find rates of change for Pythagorean Theorem problems
101. 102. Pythagorean Rates of Change
102. 103. You think… When you see…
103. 104. Average value of the function
104. 105. You think… When you see…
105. 106. Average Rate of Change
106. 107. You think… When you see… Given v ( t ) , find the total distance a particle travels on [ a , b ]
107. 108. Given v(t), find the total distance a particle travels on [a,b]
108. 109. You think… When you see… Given v ( t ) , find the change in position of a particle on [ a , b ]
109. 110. Given v(t), find the change in position of a particle on [a,b]
110. 111. You think… When you see…
111. 112. Given v(t) and the initial position of a particle, find the position at t = a .
112. 113. You think… When you see…
113. 114. Fundamental Theorem
114. 115. You think… When you see…
115. 116. Fundamental Theorem, again Chain Rule, too
116. 117. You think… When you see… Find area using left Riemann sums
117. 118. Area using left Riemann sums
118. 119. You think… When you see… Find area using right Riemann sums
119. 120. Area using right Riemann sums
120. 121. You think… When you see… Find area using midpoint rectangles
121. 122. Area using midpoint rectangles
122. 123. You think… When you see… Find area using trapezoids
123. 124. Area using trapezoids
124. 125. You think… When you see… Describe how you can tell if rectangle or trapezoid approximations over- or under-estimate area.
125. 126. Over- or Under-estimates
126. 127. You think… When you see… Given , find
127. 128. Given area under a curve and vertical shift, find the new area under the curve
128. 129. You think… When you see… Given , draw a slope field
129. 130. Draw a slope field of dy/dx
130. 131. You think… When you see… y is increasing proportionally to y
131. 132. . y is increasing proportionally to y
132. 133. You think… When you see… Solve the differential equation …
133. 134. Solve the differential equation...
134. 135. You think… When you see… Given a base, cross sections perpendicular to the x -axis that are squares
135. 136. Semi-circular cross sections perpendicular to the x-axis
136. 137. You think… When you see… Given the value of F ( a ) and the fact that the anti-derivative of f is F , find F ( b )
137. 138. Given F ( a ) and the that the anti-derivative of f is F , find F ( b )
138. 139. You think… When you see… Meaning of
139. 140. Meaning of the integral of f(t) from a to x
140. 141. You think… When you see… Given v ( t ) and s (0) , find the greatest distance from the origin of a particle on [ a , b ]
141. 142. Given v ( t ) and s (0) , find the greatest distance from the origin of a particle on [ a , b ]
142. 143. When you see…
143. 144. You think… <ul><li>the amount of water in </li></ul><ul><li>the tank at m minutes </li></ul>
144. 145. Amount of water in the tank at t minutes
145. 146. You think… b) the rate the water amount is changing at m
146. 147. Rate the amount of water is changing at t = m
147. 148. You think… c) the time when the water is at a minimum
148. 149. The time when the water is at a minimum
149. 150. You think… When you see…
150. 151. Area between f(x) and g(x) on [a,b]
151. 152. You think… When you see…
152. 153. Volume generated by rotating area between f(x) and g(x) about the x-axis
153. 154. You think… When you see… Given v ( t ) and s (0), find s ( t )
154. 155. Given v(t) and s(0), find s(t)
155. 156. You think… When you see… Find the line x = c that divides the area under f ( x ) on [ a , b ] into two equal areas
156. 157. Find the x=c so the area under f(x) is divided equally OR
157. 158. You think… When you see…
158. 159. Semi-circular cross sections perpendicular to the x-axis