Questions and Worked Solutions for AP Calculus AB Multiple Choice 1998.
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AP Calculus AB Multiple Choice 1969 - 1998 Questions - Complete Papers (pdf)
AP Calculus AB Multiple Choice 1998 Questions 1 - 5
1. What is the x-coordinate of the point of inflection on the graph of y = 1/3 x3
2. The graph of a piecewise-linear function f , for −1 ≤ x ≤ 4, is shown above. What is the value of
4. If f is continuous for a ≤ x ≤ b and differentiable for a < x < b , which of the following could be
AP Calculus AB Multiple Choice 1998 Questions 6 - 10
6. If x2
+ xy = 10, then when x = 2, dy/dx =
8. Let f and g be differentiable functions with the following properties:
(i) g(x) > 0 for all x
(ii) f(0) = 1
If h(x) = f(x)g(x) and h'(x) = f(x)g')x) then f(x) =
9. The flow of oil, in barrels per hour, through a pipeline on July 9 is given by the graph shown
above. Of the following, which best approximates the total number of barrels of oil that passed
through the pipeline that day?
10. What is the instantaneous rate of change at x = 2 of the function f given by f(x) = (x2
- 2)/(x - 1)?
AP Calculus AB Multiple Choice 1998 Question 11 - 15
11. If f is a linear function and 0 0 < a < b, then
13. The graph of the function f shown in the figure above has a vertical tangent at the point (2,0) and
horizontal tangents at the points (1, -1) and (3,1). For what values of x, -2 < x < 4, is f not
14. A particle moves along the x-axis so that its position at time t is given by x(t) = t2
- 6t + 5. For what value of t is the velocity of the particle zero?
AP Calculus AB Multiple Choice 1998 Question 16 - 20
16. If f(x) = sin(e-x
), then f'(x) =
17. The graph of a twice-differentiable function f is shown in the figure above. Which of the
following is true?
18. An equation of the line tangent to the graph of y = x + cos x at the point (0,1) is
19. If f"(x) = x(x +1)(x - 2)2
, then the graph of f has inflection points when x =
20. What are all values of k for which
AP Calculus AB Multiple Choice 1998 Question 21 - 25
21. If dy/dt = ky and k is a nonzero constant, then y could be
22. The function f is given by f(x) = x4
- 2. On which of the following intervals is f
23. The graph of f is shown in the figure above. Which of the following could be the graph of the
derivative of f ?
24. The maximum acceleration attained on the interval 0 ≤ t ≤ 3 by the particle whose velocity is given
by v(t) = t3
+ 12t + 4 is
25. What is the area of the region between the graphs of y = xt2
and y = -x from x = 0 to x = 2?
AP Calculus AB Multiple Choice 1998 Question 26 - 28
26. The function f is continuous on the closed interval [0, 2] and has values that are given in the table
above. The equation f(x) = 1/2 must have at least two solutions in the interval [0, 2] if k =
27. What is the average value of y = x2
+ 1) on the interval [0, 2] ?
28. If f(x) = tan(2x), then f'(π/6) =
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