AP Calculus AB Questions

AP Calculus AB Questions

 

1.  Find  . (5 points)
 
·         5x2 + h2 + 7
·         10x
·         3x2 – 2
·         10x – 2

 

2.  Given  find f ‘(x) and give its domain. (5 points)
 
·          Domain: All real numbers, x ≠ 2, 4.
·          Domain: All real numbers.
·          Domain: All real numbers, x ≠ 2.
·          Domain: All real numbers, x ≠ 4.

 

3.  Use a graphing calculator to graph  and then select the response which is true. (5 points)
 
·         f increases without bound
·         f has no tangent line
·         f has a horizontal tangent line
·         none of these responses

 

4.  Find  for y = 3cos(x) + sec(x). (5 points)
 
·         -3sin(x) + sec(x)tan(x)
·         3cos(x) – sec(x)tan(x)
·         3sin(x) – sec2(x)
·         3cos(x) – sec(x)

 

5.  Differentiate  . (5 points)
 
·         -1
·         -2csc(x)
·         2csc(x)
·

 

6.  Which one of the following statements is true? (5 points)
 
·         If f and g are differentiable, then  .
·
·         If f and g are differentiable, then  .
·         None of these statements are true.

 

7.  Is the following true or false?

(5 points)

 
·         True
·         False
 

 

 

 

 

 

 

8.  FREE RESPONSE If h(x) = f[g(x)], use the table of values for f, g, f ‘ and g ‘ to find the value of h ‘(1). (5 points)

x f(x) g(x) f ‘(x) g ‘(x)
1 3 2 2 6
2 1 8 5 7
3 7 2 7 9

#8 (answer)___________________________

 

 

9.  Determine the slope of the graph of x4 = ln(xy) at the point (1, e). (5 points)
·         3e
·         e4
·         1
·         4

 

10.  Find y’ if x = sin(x + y). (5 points)
 
·
·         1
·         0
·         cos(x + y)
11.  Use the graph of f(x) below to estimate the value of f ‘(3):

(4 points)

 
·         -5
·         -1
·         0
·         1

 

12.  Given the graph of f ‘(x), the derivative of f(x), which of the following statements are true about the graph of f(x)? (4 points)

I.The graph of f is decreasing on the interval (0, 2).
II.The graph of f is increasing on the interval (1, infinity).
III.The graph of f has point of inflection at x = 0.

 
·         I only
·         II only
·         III only
·         None of these are true

 

13.  Find the critical point of the function f(x) = x2 – 2x + 7. (4 points)
 
·         (-1, 10)
·         (-1, 6)
·         (1, 0)
·         (1, 6)

 

14.  For what values of x is the graph of  concave upward? (4 points)
 
·         No values of x
·         x < 6
·         x > -6
·         x > 6

 

15.  At what value(s) of x does f(x) = x4 – 18x2 have a critical point where the graph changes from decreasing to increasing? (4 points)
 
·         0 and -3 only
·         0 and 3 only
·         -3, and 3 only
·         0 only

 

16.  The maximum value of f(x) = 2x3 – 18x2 + 48x – 1 on the interval [0, 3] is (4 points)
 
·         -1
·         39
·         35
·         71

 

17.  In which interval is the function f(x) =  – 4x2 + 12x + 1 increasing? (4 points)
 
·         (-∞, 2) only
·         (-∞, 2) U (6, ∞)
·         (6, ∞) only
·         (2, 6) only

 

18.  What are the critical values on the graph of y = x3 – 12x + 1? (4 points)
 
·         x = -2, 0, 2
·         x = -2, 2
·         x = -4, 4
·         x = -3.42, 0, 3.42

 

19.  Find the x-coordinate of the point(s) of inflection on the graph of y = x3 – 12x2 – 5. (4 points)
 
·         x = -2
·         x = 4
·         x = 2
·         x = 12

 

20.  Which one of the following statements is true? (4 points)
 
·         If f “(x) > 0 on the interval (a, b) then f(x) is concave down on the interval (a, b).
·         If f ‘(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b).
·         If f ‘(c) = 0, then x = c is a relative maximum on the graph of f(x).
·         None of these are true.

 

 

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