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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 5p/3
-v3
v3/2
1
1/2

2. Deriv of f(x)=cotx is?
-csc^2x
v2/2
-1
-sinx

3. tan 5p/4
1
v3/2
0
v2/2

4. Deriv of a^u
v3/2
v3
cosx
a^u lna du/dx

5. tan 3p/2
undefined
-v3/2
v2/2
-v3/2

6. sin 5p/6
1/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v2/2
0

7. sin 5p/4
-v2/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3/2
v2/2

8. sin 2p
-v3
v3/3
-v2/2
0

9. cos 2p
1
0
-1/2
-csc^2x

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

11. sin 2p/3
1
v3/2
1/2
-v2/2

12. cos p/2
-v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
0
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

13. sin p/3
1/2
0
v3/2
-1

14. tan 2p
0
v2/2
v2/2
-1/v(1-x^2 )

15. Guidelines for implicit differentiation
1
e^x
-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

16. sin p/2
-v3/2
0
1
1/v(1-x^2 )

17. Deriv of sec^(-1)x
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3
-1/2
1/(|x| v(x^2-1))

18. tan p/4
1
-v3/3
v2/2
v3

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

20. Deriv of cot^(-1)x
-v2/2
1/(|x| v(x^2-1))
-1/(1+x^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

21. tan 2p/3
-1/2
-v3/2
-v2/2
-v3

22. cos 7p/6
-v3/2
1/u du/dx
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/2

23. tan p/2
undefined
-v2/2
v3
tanxsecx

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

25. Deriv of f(x)=tanx is?
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3/3
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
sec^2x

26. sin 4p/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
-1/2
-v3/2
-v2/2

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

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

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

30. cos 11p/6
1/(1+x^2 )
0
-cscxcotx
v3/2

31. sin 7p/4
1
-1
-v2/2
-v3/2

32. Deriv of log_au=
0
1/v(1-x^2 )
1/(u ln a ) du/dx
0

33. cos p/6
-v3
sec^2x
1/2
v3/2

34. cos 5p/6
-v3/2
-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
0

35. sin 11p/6
-1/2
1/(|x| v(x^2-1))
f(x) = (u)(v) AND f'(x) = u'v + v'u
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

36. Deriv of ln u
-1/(|x| v(x^2-1))
0
1/u du/dx
v2/2

37. Deriv of e^x
-1
v2/2
e^x
undefined

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

39. Explicit differentiation
tanxsecx
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
-sinx
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

40. cos p
-1
v2/2
-1/2
0

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

42. tan 5p/6
-v3/3
1/2
-1/(1+x^2 )
slope of the tangent line

43. cos 7p/4
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
1/2
v2/2
-1

44. What is the quotient rule?

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45. tan 7p/4
e^x
-1
1
1/u du/dx

46. sin 7p/6
0
v3
-1/2
-v3/2

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

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48. cos 5p/4
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
-v2/2
-1/v(1-x^2 )

49. What is the product rule?

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50. sin 3p/2
v3/3
-v3
-v3/2
-1