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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. Deriv of f(x)=cotx is?
-v3/2
slope of the tangent line
-csc^2x
-1

2. Deriv of f(x)=secx is?
-1
0
tanxsecx
v3/2

3. Deriv of f(x)=cosx is?
-1/2
-sinx
0
-1

4. cos 3p/2
undefined
-1/(|x| v(x^2-1))
0
v3/3

5. Deriv of cot^(-1)x
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1/(1+x^2 )
1/2
a^u lna du/dx

6. cos 2p/3
-1/2
-v3/3
0
1/2

7. sin p/4
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2
-v3/3
-v2/2

8. Deriv of cos^(-1)x
-1/v(1-x^2 )
-v2/2
-1
-v2/2

9. cos p/3
1/2
e^x
v3/2
-v3/2

10. tan 4p/3
v2/2
0
-1
v3

11. cos p/4
-csc^2x
v2/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1/2

12. sin 3p/4
1/2
v2/2
1
-v3/2

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

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

15. tan 11p/6
-v3/2
-v2/2
-v3/3
-v2/2

16. Deriv of f(x)=tanx is?
sec^2x
v2/2
v3/3
-v2/2

17. cos p
-1
1/v(1-x^2 )
1/(u ln a ) du/dx
-v2/2

18. What is the quotient rule?

19. sin p/3
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
1/v(1-x^2 )
v3/2

20. What is the product rule?

21. cos 2p
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
-v2/2
-v3/2
1

22. cos 7p/4
1/(u ln a ) du/dx
v3/2
1/u du/dx
v2/2

23. cos 7p/6
-v3/2
1/v(1-x^2 )
-sinx
-1/2

24. sin 5p/4
-v2/2
-1/2
0
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

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

26. tan 3p/4
cosx
1
-1
tanxsecx

27. Deriv of tan^(-1)x
e^x
0
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
1/(1+x^2 )

28. tan 3p/2
0
undefined
-1/2
-v2/2

29. tan 2p
-v3/3
0
-1/2
-v2/2

30. tan p/2
undefined
v3/2
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
-1

31. Deriv of f(x)=sinx is?
cosx
-cscxcotx
-v3
-1/(1+x^2 )

32. cos 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
-v2/2
1/2
v2/2

33. cos 11p/6
v3/2
-1
-v2/2
1/2

34. Guidelines for implicit differentiation
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
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

35. sin p/6
cosx
1/2
v3/3
1

36. tan 5p/4
v2/2
-1
-v3/3
1

37. tan 5p/3
-v3
-1/2
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
sec^2x

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

39. tan p/3
v3/2
v3
cosx
0

40. sin 4p/3
-csc^2x
0
undefined
-v3/2

41. derivative
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
slope of the tangent line
-1
v3/2

42. Deriv of e^x
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
v3
e^x
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

43. sin 5p/6
-v2/2
1/2
-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

44. Deriv of log_au=
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1/2
-1/2
1/(u ln a ) du/dx

45. tan p/6
v3/2
v3/3
v2/2
-v3/2

46. sin 2p
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
-v3/3
-v3
0

47. cos 5p/3
1/2
-csc^2x
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
cosx

48. cos 5p/6
1
-v3/2
-v2/2
v3/2

49. tan p
undefined
1/2
1/(|x| v(x^2-1))
0

50. tan 7p/4
1/(1+x^2 )
-1
-1/v(1-x^2 )
-v3/2