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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 3p/2
0
v2/2
-v3/2
undefined

2. Deriv of f(x)=cotx is?
1/(1+x^2 )
-csc^2x
v3
-v3/3

3. tan 7p/6
v3/3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1
e^x

4. Deriv of f(x)=cosx is?
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
-sinx
-1
1/2

5. Deriv of e^x
e^x
-v3/2
1/2
1

6. Deriv of tan^(-1)x
1/(1+x^2 )
tanxsecx
-v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

7. tan 7p/4
-v3/2
-1
v3/3
undefined

8. Deriv of log_au=
-v3/3
1/(u ln a ) du/dx
-v3
-1/2

9. Explicit differentiation
0
v2/2
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

10. sin p/6
-v3/2
-1/2
1/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

11. Implicit differentiation
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
-v3

12. tan 2p
-v3/3
a^u lna du/dx
0
-1

13. sin 4p/3
-v3/2
cosx
v2/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

14. sin p/4
-v2/2
v2/2
cosx
v3/2

15. tan 3p/4
0
-1
slope of the tangent line
-v2/2

16. cos p/3
v2/2
-v2/2
1/2
-1/2

17. cos 3p/4
1/2
-v2/2
-1/2
-1/(1+x^2 )

18. Deriv of f(x)=sinx is?
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
f(x) = (u)(v) AND f'(x) = u'v + v'u
cosx
v3/2

19. Deriv of csc^(-1)x
1/2
v3/3
-1/2
-1/(|x| v(x^2-1))

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

21. Guidelines for implicit differentiation
-v3/2
1/v(1-x^2 )
-v2/2
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

22. sin 11p/6
v3/3
-1/(1+x^2 )
-1/2
1

23. tan 11p/6
-v3/3
-1
sec^2x
-csc^2x

24. What is the Chain Rule? When can it be used?
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3/3
1
v3/2

25. sin 5p/4
-v2/2
-1/2
-v3/2
-v3/3

26. cos p/6
-v3/2
v3/2
-v3/3
0

27. Deriv of f(x)=tanx is?
sec^2x
1/(1+x^2 )
v3
-1/(|x| v(x^2-1))

28. Deriv of ln u
v3/3
-1
1/u du/dx
v3/3

29. cos 5p/6
undefined
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
-v3/2
v3/2

30. tan p
undefined
-1/2
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
0

31. cos p
-1
v2/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
1/u du/dx

32. Deriv of sec^(-1)x
v2/2
-sinx
1/(|x| v(x^2-1))
-1

33. Deriv of cot^(-1)x
1
-v3/2
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
-1/(1+x^2 )

34. tan 5p/4
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
a^u lna du/dx
1
-v2/2

35. cos 4p/3
-1/2
0
v3
f(x) = (u)(v) AND f'(x) = u'v + v'u

36. tan 5p/6
1/(u ln a ) du/dx
-v3/3
0
1

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

38. sin 7p/4
-1
-1/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v2/2

39. tan p/6
-v3/2
v3/3
0
1/(|x| v(x^2-1))

40. Deriv of f(x)=secx is?
v3/2
-1/(|x| v(x^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
tanxsecx

41. tan 4p/3
0
-1
v3/2
v3

42. sin 7p/6
-v2/2
-cscxcotx
-v2/2
-1/2

43. cos 2p/3
-v3/3
-1/2
0
v2/2

44. cos 7p/6
-v3/2
v3
undefined
v3

45. cos 11p/6
undefined
0
-v2/2
v3/2

46. Deriv of sin^(-1)x
-1/(|x| v(x^2-1))
-v3/3
1/(|x| v(x^2-1))
1/v(1-x^2 )

47. sin p/3
tanxsecx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
1/(1+x^2 )
v3/2

48. derivative
slope of the tangent line
-1/v(1-x^2 )
v2/2
-1

49. cos 5p/3
v3/2
tanxsecx
1/2
-v3

50. cos 5p/4
tanxsecx
-v2/2
-1/2
-csc^2x