**AP Physics C Calculus Review**

You should be able to:

1. Given a drawing of a linear function, write the function in the form y = mx + b

2. Understand what is meant by *one radian*

3. Convert between polar
coordinates (radius and angle) and Cartesian coordinates (x and y)

4. Define the six basic trigonometric functions in terms of x, y, and r.

5. Prove sin^{2}θ + cos^{2}θ = 1
and what dividing this by sin^{2}θ or cos^{2}θ
yields.

6. Given the three sides of a right triangle, define the six trigonometric functions for either acute angle in terms of the sides.

7. Graph the six trigonometric functions from x = 0 to x = 2π.

8. Know the exact value of each of the six trigonometric functions for angles of 0, 30, 45, 60, 90, etc. degrees.

9. Solve basic problems using properties of exponents and logs.

10. Determine the limit of a function like [(1 + x)^{2} – 1] / x as x approaches zero.

11. Given a position versus time curve, approximate the instantaneous velocity at any time and find the average velocity between two times.

12. Use limits to show something like that if s = t^{2},
then v = 2t.

13. Given a position versus time curve, sketch an approximate graph for velocity versus time which matches.

14. Differentiate functions like y = 5, y = 10x, y = 4x^{2},
y = -3x^{2} + 10x – 6, y = 2x^{-5}, y = 4x^{1/2}, y = 1
/ x^{3}.

15. Use the product rule to differentiate functions like y =
(x^{3} – 4)(12x^{2} – 5x + 2)

16. Use the quotient rule to differentiate functions like y
= (5x^{2} + 10x)/(8x^{3})

17. Use the chain rule to differentiate functions like y =
(4x^{2} – 8)^{5} or y = 1/(x^{3} + 5)

18. Differentiate the six trigonometric functions.

19. Differentiate functions like y = 6cos(12x).

20. Differentiate functions
like y = ln x, y = ln x^{2}, y = ln (10x) and y = 5^{x}, y = e^{10x},
y = e^{-3x}

21. Find the second derivatives of functions

22. Find the minimum or maximum of a give function like y =
x^{2} + 6 and state if it is a minimum or maximum.

23. For a given graph, find the area under the curve between two boundaries.

24. Integrate functions like y = 5, y = 6x, y = cos x, y = x^{3},
y = e^{x}, y = 12x^{2} + 4x, y = 1/x, y = e^{6x}

25. Use change of variables to integrate functions like ∫ sin(4x)dx

26. Use integration by parts to integrate functions like ∫ θsin(θ)dθ

27. Find the area under a curve of a given function between two boundaries using integral notation.

28. Integrate functions like ∫ sin(θ)dθ from 0 to 2π or ∫ 2e^{x} from 0
to x.

29. Given an acceleration function, find the corresponding velocity function or given a velocity function, find the corresponding position function.

30. Use integral notation to find the area of a circle, the volume of a cone, the volume of a cube, or the volume of a sphere.