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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 p/6
v3/3
-1/2
sec^2x
0

2. cos 3p/4
-v2/2
a^u lna du/dx
v2/2
-1/2

3. sin p
sec^2x
0
1/2
undefined

4. tan p/2
undefined
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
cosx
1

5. tan 11p/6
-v3/3
-v3/2
-v2/2
-1

6. derivative
-csc^2x
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
0
slope of the tangent line

7. tan 3p/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
undefined
0
-1/2

8. sin 11p/6
1/(u ln a ) du/dx
1/2
-1
-1/2

9. cos 5p/4
-v3/2
-v2/2
0
v3

10. sin 5p/4
v3/2
v2/2
-v2/2
0

11. Deriv of cot^(-1)x
a^u lna du/dx
v3
-v3/2
-1/(1+x^2 )

12. cos 3p/2
1
0
1/u du/dx
-csc^2x

13. Deriv of ln u
v3
undefined
v2/2
1/u du/dx

14. Deriv of f(x)=tanx is?
sec^2x
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
1/2
1/(1+x^2 )

15. sin 3p/4
1/(1+x^2 )
-1/2
1
v2/2

16. sin 2p
1/v(1-x^2 )
0
v2/2
cosx

17. sin p/6
1/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
tanxsecx
v2/2

18. tan p/3
-v3
v3
v2/2
-1

19. Deriv of f(x)=sinx is?
cosx
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-v2/2
v3

20. tan 5p/6
1/2
v2/2
v3/2
-v3/3

21. What is the quotient rule?

22. sin p/3
v3/2
1/2
v2/2
-v2/2

23. tan 2p
f(x) = (u)(v) AND f'(x) = u'v + v'u
v3/3
-1/(|x| v(x^2-1))
0

24. sin 5p/3
-v3/2
a^u lna du/dx
-v3
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

25. cos p/4
1/(u ln a ) du/dx
-v3/2
a^u lna du/dx
v2/2

26. cos p/3
v3/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1/2

27. tan 5p/4
1/(1+x^2 )
-1
-v3/2
1

28. tan 7p/4
-1
-1/2
undefined
-1/v(1-x^2 )

29. Implicit differentiation
-v3/2
-1/(|x| v(x^2-1))
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
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

30. sin 4p/3
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
-v3/2
sec^2x
undefined

31. Deriv of tan^(-1)x
v3/2
1/(1+x^2 )
-csc^2x
-sinx

32. cos 5p/6
-v3/2
v3/3
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v2/2

33. Deriv of sec^(-1)x
1/2
-cscxcotx
1/(|x| v(x^2-1))
-v3

34. Deriv of f(x)=cosx is?
sec^2x
-1
-sinx
v2/2

35. When do derivatives not exist?
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
sec^2x
1
1/2

36. cos p/6
v3/2
-v3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v3/3

37. sin 7p/4
-v3/2
-v2/2
-v3/2
v2/2

38. cos 2p
1/(1+x^2 )
-1
1
e^x

39. tan 2p/3
-v3
1
a^u lna du/dx
1/2

40. Deriv of sin^(-1)x
v3
-v3/3
1/(1+x^2 )
1/v(1-x^2 )

41. what is the the limit definition of a derivative and what does it find?

42. sin p/2
0
v3/2
1
-v2/2

43. tan p
-v2/2
v3/3
-1/(|x| v(x^2-1))
0

44. tan 5p/3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v3
1/u du/dx
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

45. tan 3p/4
-1
1/v(1-x^2 )
0
v3/3

46. cos 2p/3
-1/(1+x^2 )
-1/2
0
f^' (a)=lim-(x?a)??(f(x)-f(a))/(x-a)? - It is finding the slope of the tangent line at a particular x-value

47. Deriv of a^u
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v2/2
-v3/3
a^u lna du/dx

48. tan 7p/6
-1
v3/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3/2

49. Deriv of e^x
-csc^2x
e^x
-v2/2
0

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