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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. sin 4p/3
-cscxcotx
-v3/2
-1/2
0

2. Deriv of a^u
a^u lna du/dx
-1
-v2/2
slope of the tangent line

3. tan 5p/3
-v3
1/2
1
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

4. sin p/2
1/(|x| v(x^2-1))
v3/2
v2/2
1

5. Deriv of f(x)=csc is?
-cscxcotx
-1
-v3/2
1

6. tan p/4
-1/(1+x^2 )
1
0
-1

7. cos 5p/6
v2/2
-1
0
-v3/2

8. sin 7p/6
-1/2
-v2/2
-sinx
1/2

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

10. sin 11p/6
-1/2
1/2
0
-v3/2

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

12. tan 4p/3
-v3
0
-v3/3
v3

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

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

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

16. cos 5p/3
1
1/2
v3/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

17. tan 2p
v2/2
-v2/2
tanxsecx
0

18. sin p/4
v2/2
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
-v3/3
sec^2x

19. Explicit differentiation
-1/2
-1
1/v(1-x^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

20. cos p
tanxsecx
-csc^2x
-1
1/2

21. cos 3p/2
-1/v(1-x^2 )
1
0
slope of the tangent line

22. tan p/6
e^x
v3/3
-v3
-v3/2

23. Deriv of cos^(-1)x
-1/2
-1/2
v3/3
-1/v(1-x^2 )

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

25. cos 7p/4
-1/2
-v3
v3/3
v2/2

26. Deriv of f(x)=cotx is?
v3
-csc^2x
-1/(|x| v(x^2-1))
-v2/2

27. tan p/3
v2/2
1/u du/dx
-v2/2
v3

28. cos p/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
undefined
0
1/2

29. sin 3p/2
1/(1+x^2 )
1/2
-1
slope of the tangent line

30. Deriv of log_au=
v2/2
-1/v(1-x^2 )
1/(u ln a ) du/dx
e^x

31. sin 7p/4
1/2
-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
0

32. sin 5p/4
-v2/2
0
1/2
0

33. Deriv of e^x
e^x
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v3/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

34. cos 5p/4
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1/2
-v2/2
0

35. tan 3p/2
slope of the tangent line
v3/3
cosx
undefined

36. tan 7p/6
v3/3
-v2/2
undefined
-1/2

37. cos p/4
-v2/2
-1
-1
v2/2

38. Guidelines for implicit differentiation
-csc^2x
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
a^u lna du/dx
-1

39. cos 4p/3
0
-1/2
slope of the tangent line
0

40. tan 5p/4
-v3/2
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
1
f(x) = (u)(v) AND f'(x) = u'v + v'u

41. 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
undefined
-v3/3
-v2/2

42. cos 2p
-1/v(1-x^2 )
1
-1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

43. tan 11p/6
-v3/3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
f(x) = (u)(v) AND f'(x) = u'v + v'u
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

44. Deriv of f(x)=cosx is?
1/(u ln a ) du/dx
-sinx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
1/2

45. tan 3p/4
1/(1+x^2 )
-v2/2
-1
0

46. sin 2p
1/(u ln a ) du/dx
-v2/2
0
1

47. Deriv of sin^(-1)x
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
undefined
1/v(1-x^2 )
1

48. sin p/3
v3/2
v3/3
1
1/2

49. cos p/6
-1
slope of the tangent line
v3/2
1

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