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

2. Deriv of cot^(-1)x
v3/3
-v3/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
-1/(1+x^2 )

3. derivative
-1
-v3
slope of the tangent line
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

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

5. Deriv of f(x)=cosx is?
0
-sinx
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

6. sin p/2
1
0
undefined
-v2/2

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

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

9. What is the quotient rule?

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

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

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

13. cos 3p/4
-1/2
1/2
-v2/2
1

14. cos 7p/4
-1
v2/2
-v3/2
undefined

15. tan 2p
1
-1
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

16. Deriv of f(x)=csc is?
-cscxcotx
1/u du/dx
undefined
-1/2

17. sin 5p/6
0
1/2
-v2/2
sec^2x

18. tan 2p/3
-v3
-1/v(1-x^2 )
1/(u ln a ) du/dx
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

19. cos 4p/3
-v3
1
-1/2
1/u du/dx

20. Deriv of f(x)=sinx is?
cosx
-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
slope of the tangent line

21. tan 3p/4
0
-1
-sinx
-v3

22. When do derivatives not exist?
-1/(|x| v(x^2-1))
-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
-1/2

23. Deriv of e^x
undefined
-v2/2
v2/2
e^x

24. tan p/3
v3
1/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2

25. cos 5p/6
-v3/2
1
-1/2
-v3/3

26. cos p/2
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
-csc^2x
0

27. cos p/3
1/2
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
1/(1+x^2 )

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

29. cos 2p
1
v3/2
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

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

31. Deriv of ln u
0
1/u du/dx
f(x) = (u)(v) AND f'(x) = u'v + v'u
-1/(|x| v(x^2-1))

32. Deriv of f(x)=tanx 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
1/2
sec^2x

33. tan 7p/4
-1/2
0
1
-1

34. What is the product rule?

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35. Deriv of csc^(-1)x
0
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v2/2
-1/(|x| v(x^2-1))

36. tan 3p/2
1
undefined
-1
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

37. sin 2p
-v3/2
v3/2
0
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

38. cos 3p/2
e^x
-1/2
1/2
0

39. Deriv of log_au=
1/v(1-x^2 )
-v3
-v3/3
1/(u ln a ) du/dx

40. tan p/4
-1/v(1-x^2 )
tanxsecx
1
-csc^2x

41. tan 7p/6
v3/2
v3/3
1/u du/dx
-1/v(1-x^2 )

42. cos 11p/6
v3/2
-v3/3
-v3/2
1/u du/dx

43. tan p
v2/2
1/2
0
-v2/2

44. Implicit differentiation
1/(|x| v(x^2-1))
v3/2
-v2/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

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

46. What is the Chain Rule? When can it be used?
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
v3/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-sinx

47. sin p/6
tanxsecx
cosx
sec^2x
1/2

48. Deriv of cos^(-1)x
-1/v(1-x^2 )
-v3/2
-1
-1/(|x| v(x^2-1))

49. tan 5p/6
a^u lna du/dx
-v3/3
-v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

50. Explicit differentiation
-1/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3
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