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AP Calculus 2

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. tan 5p/4
1
-1/(1+x^2 )
1/v(1-x^2 )
1/u du/dx

2. sin p/6
1
1/2
-v3/3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

3. Implicit differentiation
-sinx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
0
-1/(|x| v(x^2-1))

4. sin 4p/3
1/2
-v3/2
v3/2
-v3/3

5. What is the quotient rule?

6. tan 2p/3
-v3
cosx
-1
v3/3

7. What is the Chain Rule? When can it be used?
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
1/2
-1/(1+x^2 )

8. Explicit differentiation
-v3/2
v3/2
-1/2
very clear; the variable y is explicitly written as a function of x and it only works when you can solve for the function explicitly E.g. y=3x^2-5

9. tan p/3
v3
-cscxcotx
v3/2
1/v(1-x^2 )

10. tan 7p/6
v3/3
-v3/2
0
0

11. sin 5p/6
-v3/2
-1/2
-v3/3
1/2

12. What is the product rule?

13. cos 7p/6
-v3/2
-1
very clear; the variable y is explicitly written as a function of x and it only works when you can solve for the function explicitly E.g. y=3x^2-5
v2/2

14. tan 7p/4
-1/v(1-x^2 )
v3/2
-1
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

15. tan p/4
1
0
-v3
1/2

16. cos 2p
1
1)At a "spot" of discontinuity (pt.(hole) - infinite(VA) - jump) 2)At a corner 3)At a cusp(sharp pt.) 4)At a vertical tangent line
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-1/2

17. Deriv of cot^(-1)x
v3/2
0
v3/3
-1/(1+x^2 )

18. Deriv of f(x)=secx is?
a^u lna du/dx
tanxsecx
-1/2
f(x) = (u)(v) AND f'(x) = u'v + v'u

19. Deriv of e^x
1/(u ln a ) du/dx
e^x
-v2/2
v3

20. What is the Alternate definition of a derivative and what does it find?

21. tan p/6
-1
-v3/2
-1
v3/3

22. Deriv of sec^(-1)x
1/(|x| v(x^2-1))
0
-1
-v3/3

23. cos 3p/2
-1
1/(u ln a ) du/dx
tanxsecx
0

24. cos p/4
-v3
1/2
slope of the tangent line
v2/2

25. cos 5p/6
v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v3/2
v3/2

26. cos 2p/3
v3/2
-v3/3
-1/2
-v3/2

27. sin p/3
cosx
-v2/2
-v3/3
v3/2

28. tan 11p/6
0
1/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v3/3

29. sin 7p/6
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1
-1/2
sec^2x

30. cos 11p/6
-cscxcotx
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/2
v2/2

31. sin p/4
undefined
v2/2
-1/(|x| v(x^2-1))
1) find the derivative of both sides of the function 2) put all terms with a y prime on the same side (y prime aka derivative of y) 3) factor out a y 4) solve for y prime

32. tan 4p/3
1/(|x| v(x^2-1))
1/2
undefined
v3

33. Deriv of a^u
a^u lna du/dx
-v3
v2/2
-v3

34. sin p
1
-1/v(1-x^2 )
-1/2
0

35. tan 5p/3
e^x
-1
1) find the derivative of both sides of the function 2) put all terms with a y prime on the same side (y prime aka derivative of y) 3) factor out a y 4) solve for y prime
-v3

36. Deriv of tan^(-1)x
1/(1+x^2 )
1/2
slope of the tangent line
-1/2

37. derivative
slope of the tangent line
0
e^x
cosx

38. sin 3p/2
undefined
1/2
-1/v(1-x^2 )
-1

39. Deriv of f(x)=cotx is?
undefined
-csc^2x
v3/2
v2/2

40. tan p/2
v2/2
-v2/2
undefined
1

41. Deriv of sin^(-1)x
-1
0
1/v(1-x^2 )
-v2/2

42. Deriv of f(x)=cosx is?
-sinx
1/(u ln a ) du/dx
0
v3/2

43. sin 2p/3
v3/2
v3
-v3/3
1/2

44. tan 5p/6
1/(1+x^2 )
1
-v3/2
-v3/3

45. sin 5p/3
v3
-v3/2
-1
v2/2

46. tan 2p
tanxsecx
v2/2
1/2
0

47. cos 4p/3
-v3
1
-1/2
-v2/2

48. cos p/2
-sinx
1
1) find the derivative of both sides of the function 2) put all terms with a y prime on the same side (y prime aka derivative of y) 3) factor out a y 4) solve for y prime
0

49. cos p
-1
-v2/2
slope of the tangent line
0

50. Deriv of cos^(-1)x
slope of the tangent line
-1/v(1-x^2 )
1/(1+x^2 )
v3/2