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

2. tan p/4
-1/2
e^x
1
f(x) = (u)(v) AND f'(x) = u'v + v'u

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

4. sin p/2
1
-cscxcotx
v3/2
-v2/2

5. derivative
1/2
0
1
slope of the tangent line

6. When do derivatives not exist?
1
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
-1/2

7. tan p/2
undefined
-cscxcotx
1/(u ln a ) du/dx
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

8. sin p/4
-csc^2x
-v2/2
1
v2/2

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

10. Deriv of log_au=
v2/2
sec^2x
-1/2
1/(u ln a ) du/dx

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

12. tan 11p/6
1
-v3/2
-v3/3
-1

13. sin p
0
-sinx
-1
-v3/2

14. tan 5p/3
-v2/2
-v3
e^x
1

15. cos 5p/4
-1/2
-v2/2
-1
v3

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

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17. What is the product rule?

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

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

20. cos 3p/4
-v2/2
-v3/2
v3/3
v3/2

21. tan 5p/6
-1/2
-v3/3
v3/2
1

22. Deriv of f(x)=tanx is?
-1/2
-1/2
1
sec^2x

23. tan 3p/4
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
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
-1
v2/2

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

25. tan 4p/3
v3
1/2
v2/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

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

27. Deriv of cos^(-1)x
1
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1/v(1-x^2 )
-v3/3

28. cos p/4
v2/2
-1/2
-1/2
-csc^2x

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

30. cos 7p/6
-v3/2
v2/2
-v3
0

31. tan p
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
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
-v2/2
0

32. sin p/3
-cscxcotx
1
v3/2
v2/2

33. sin 3p/4
1/2
v3/2
v2/2
-csc^2x

34. sin 11p/6
-1/2
0
-1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

35. tan 2p/3
-1/(1+x^2 )
-v3
-v2/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

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

37. tan 7p/6
-v3/2
-v3/2
v3/3
v3/2

38. sin 5p/6
1/2
v3
0
1/(|x| v(x^2-1))

39. cos 2p
v3/3
-sinx
v3/2
1

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

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

42. cos p
-1
-v3/3
-v3
0

43. Deriv of a^u
0
-1/(1+x^2 )
v3
a^u lna du/dx

44. Deriv of sin^(-1)x
-v2/2
-v3/3
1/(1+x^2 )
1/v(1-x^2 )

45. Guidelines for implicit differentiation
-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
v3/3
-1

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

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

48. cos 7p/4
v2/2
1/2
1/u du/dx
0

49. sin 2p
undefined
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/2
0

50. Deriv of e^x
e^x
1
1/2
v2/2