AP Calculus - Chapter 2 Practice Test

1.
Find an equation of the line that is tangent to the graph of f and parallel to the given line.

 A.
 B.
 C.
 D.
 E. None of the above

2.
Find the derivative of the function.

 A.
 B.
 C.
 D.
 E. None of the above

3.
Find the derivative of the function.

 A.
 B.
 C.
 D.
 E. None of the above

4.
Find the slope of the graph of the function at the given value.

when
 A.
 B.
 C.
 D.
 E.

5.
Find the slope of the graph of the function at the given value.

when
 A.
 B.
 C.
 D.
 E.

6.
Find the slope of the graph of the function at the given value.

when
 A.
 B.
 C.
 D.
 E.

7.
Find the slope of the graph of the function at the given value.

when
 A.
 B.
 C.
 D.
 E.

8.
Determine the point(s), (if any), at which the graph of the function has a horizontal tangent.

 A.
 B. and
 C. and
 D.
 E. There are no points at which the graph has a horizontal tangent.

9.
Determine the point(s), (if any), at which the graph of the function has a horizontal tangent.

 A.
 B. and
 C. and
 D.
 E. There are no points at which the graph has a horizontal tangent.

10.
Find the derivative of the algebraic function..

 A.
 B.
 C.
 D.
 E. None of the above

11.
Use the product rule to differentiate.

 A.
 B.
 C.
 D.
 E.

12.
Find the derivative of the algebraic function.

 A.
 B.
 C.
 D.
 E.

13.
Find the derivative of the algebraic function.

 A.
 B.
 C.
 D.
 E.

14.
Find the derivative of the trigonometric function.

 A.
 B.
 C.
 D.
 E. None of the above

15.
Find the derivative of the function.

 A.
 B.
 C.
 D.
 E.

16.
Find the derivative of the function.

 A.
 B.
 C.
 D.
 E.

17.
Find an equation of the tangent line to the graph of f at the given point.

at
 A.
 B.
 C.
 D.
 E.

18.
The radius of a right circular cylinder is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time.
 A. cubic inches/second
 B. square inches/second
 C. cubic inches/second
 D. cubic inches/second
 E. inches/second

19.
Find the second derivative of the function.

 A.
 B.
 C.
 D.
 E. None of the above

20.
Find the second derivative of the function.

 A.
 B.
 C.
 D.
 E.

21.
Find the derivative of the function.

 A.
 B.
 C.
 D.
 E.

22.
Find the derivative of the function.

 A.
 B.
 C.
 D.
 E.

23.
Find the derivative of the function.

 A.
 B.
 C.
 D.
 E.

24.
Find the derivative of the function.

 A.
 B.
 C.
 D.
 E.

25.
Find the derivative of the function.

 A.
 B.
 C.
 D.
 E.

26.
Find the derivative of the function.

 A.
 B.
 C.
 D.
 E.

27.
Evaluate the derivative of the function at the given point.

,
 A.
 B.
 C.
 D.
 E.

28.
Evaluate the derivative of the function at the given point.

,
 A.
 B.
 C.
 D.
 E.

29.
Find an equation to the tangent line for the graph of f at the given point.

,
 A.
 B.
 C.
 D.
 E.

30.
Find the second derivative of the function.

 A.
 B.
 C.
 D.
 E.

31.
Find the second derivative of the function.

 A.
 B.
 C.
 D.
 E.

32.
Find dy/dx by implicit differentiation.

 A.
 B.
 C.
 D.
 E.

33.
Find dy/dx by implicit differentiation.

 A.
 B.
 C.
 D.
 E.

34.
Find d2y/dx2 in terms of x and y.

 A.
 B.
 C.
 D.
 E. None of the above

35.
Find the points at which the graph of the equation has a vertical or horizontal tangent line.

 A. There is a horizontal tangent at but no vertical tangents.
 B. There is a horizontal tangent at and a vertical tangent at .
 C. There is a vertical tangent at but no horizontal tangents.
 D. There is a horizontal tangent at and a vertical tangent at .
 E. There are no horizontal or vertical tangent lines.

36.
Area The radius, r, of a circle is increasing at a rate of 4 centimeters per minute.

Find the rate of change of area, A, when the radius is
 A.
 B.
 C.
 D.
 E.

37.
Depth A conical tank (with vertex down) is 10 ft across the top and 16 ft deep. If water is flowing into the tank at a rate of 11 cubic ft per minute, find the rate of change of depth of water when the water is 4 ft deep.
 A. ft per minute
 B. ft per minute
 C. ft per minute
 D. ft per minute
 E. None of the above

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