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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 csc^(-1)x
-1/(|x| v(x^2-1))
v3
0
1

2. sin 11p/6
-1/(1+x^2 )
v3
1/(1+x^2 )
-1/2

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

4. Deriv of ln u
1/u du/dx
1/2
v2/2
e^x

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

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

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

8. Deriv of f(x)=cosx is?
-v3
-sinx
1
v3

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

10. What is the Chain Rule? When can it be used?
1/(|x| v(x^2-1))
0
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
sec^2x

11. cos 5p/4
-1/(|x| v(x^2-1))
-v2/2
1/(u ln a ) du/dx
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

12. Deriv of a^u
a^u lna du/dx
1/2
-v3/3
1

13. tan 2p/3
tanxsecx
-v2/2
-v3
a^u lna du/dx

14. What is the quotient rule?

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15. cos p/4
-v3/2
0
v2/2
v3/3

16. tan 5p/3
-1/2
undefined
-v3
slope of the tangent line

17. Deriv of e^x
-1/(|x| v(x^2-1))
a^u lna du/dx
-v3
e^x

18. tan 11p/6
-v3/3
v2/2
-1/2
1/2

19. tan 4p/3
v3
f(x) = (u)(v) AND f'(x) = u'v + v'u
1/2
-1

20. cos p/3
-1/2
-1
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

21. sin p/2
undefined
-v3/3
1/u du/dx
1

22. sin 5p/3
-v3/2
0
1
1

23. tan p/4
v3
-csc^2x
v3/2
1

24. What is the Alternate definition of a derivative and what does it find?

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25. cos 7p/6
-v3/3
-v2/2
1
-v3/2

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

27. cos 5p/3
1/2
-v3/2
-v2/2
-v3/2

28. tan 5p/4
1
-v3/3
-1
-1/2

29. Deriv of cot^(-1)x
1
-1/(1+x^2 )
-1
1

30. tan p
-v3/2
1
0
1/2

31. tan 7p/4
-cscxcotx
v3/2
-1
f(x) = (u)(v) AND f'(x) = u'v + v'u

32. tan 2p
-1/2
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
0
-v3

33. cos 3p/4
-v2/2
1/u du/dx
v3/2
-v3/2

34. cos 7p/4
1/(|x| v(x^2-1))
-1/(|x| v(x^2-1))
v2/2
f(x) = (u)(v) AND f'(x) = u'v + v'u

35. derivative
-1/2
1/2
slope of the tangent line
-cscxcotx

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

37. tan 7p/6
v2/2
v3/3
-1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

38. Explicit differentiation
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
cosx
v3/3
slope of the tangent line

39. Deriv of sec^(-1)x
1/(|x| v(x^2-1))
0
-v3/2
-1/2

40. sin p/6
a^u lna du/dx
1/2
slope of the tangent line
-1/2

41. tan 3p/4
-1
v3/2
-v2/2
-1/v(1-x^2 )

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

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43. sin 2p
0
-v3/3
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/(u ln a ) du/dx

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

45. Deriv of f(x)=sinx is?
-v2/2
v3/2
cosx
1/2

46. Deriv of tan^(-1)x
0
1/(1+x^2 )
slope of the tangent line
-1

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

48. sin p/4
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v2/2
slope of the tangent line
undefined

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

50. sin 7p/4
v3/3
-1/2
1/2
-v2/2