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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 3p/2
0
v3/3
v3/2
v3/3

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

3. sin 2p/3
-v3/2
-1/(1+x^2 )
v2/2
v3/2

4. cos p/2
0
cosx
v3/2
-1/(|x| v(x^2-1))

5. derivative
-v3/2
slope of the tangent line
-1
-v2/2

6. sin p
1
v3/3
0
v2/2

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

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8. tan p/4
1
v2/2
-1
0

9. sin p/2
undefined
1/(u ln a ) du/dx
-1
1

10. cos 5p/6
-v3/2
v3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
0

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

12. sin 7p/6
-1/(1+x^2 )
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
1
-1/2

13. tan 3p/2
v2/2
undefined
f(x) = (u)(v) AND f'(x) = u'v + v'u
-1

14. cos 5p/3
0
1/2
-v2/2
-v3/3

15. sin 11p/6
1/u du/dx
-v3
-v2/2
-1/2

16. sin p/4
undefined
-v2/2
0
v2/2

17. Deriv of cos^(-1)x
0
-v3/2
0
-1/v(1-x^2 )

18. tan 2p
a^u lna du/dx
0
-1/(|x| v(x^2-1))
-v3/2

19. Deriv of csc^(-1)x
-1/(|x| v(x^2-1))
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3/3
1/(1+x^2 )

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

21. cos 5p/4
-v3
-v2/2
1/v(1-x^2 )
undefined

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

23. tan 7p/4
-1
1
v3
v3

24. cos 7p/6
undefined
-v3/2
0
v2/2

25. tan 5p/4
-1/(|x| v(x^2-1))
1
v3/2
1/2

26. What is the Chain Rule? When can it be used?
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
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
undefined
-1

27. Guidelines for implicit differentiation
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
1/(u ln a ) du/dx
1/2
1/2

28. What is the product rule?

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29. cos 4p/3
1/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-1/2
slope of the tangent line

30. cos 11p/6
1/(1+x^2 )
v3/2
0
v2/2

31. sin 3p/4
v2/2
-v3/3
undefined
-1

32. tan p
1/2
v2/2
0
sec^2x

33. cos p/3
-1
-v3
undefined
1/2

34. cos p/4
slope of the tangent line
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2
-1/2

35. cos p
-1
1
slope of the tangent line
v3/3

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

37. tan p/6
v3/3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
undefined
-v3/3

38. What is the quotient rule?

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

40. sin 4p/3
v3/3
-v3/2
0
-v2/2

41. tan 7p/6
0
-cscxcotx
v2/2
v3/3

42. When do derivatives not exist?
-1
-cscxcotx
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

43. Deriv of tan^(-1)x
v2/2
1/(1+x^2 )
-v2/2
1/(u ln a ) du/dx

44. cos 7p/4
v3
1/2
-csc^2x
v2/2

45. Implicit differentiation
1/2
a^u lna du/dx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
tanxsecx

46. Deriv of f(x)=tanx is?
-v3/2
-v2/2
sec^2x
-v3/3

47. tan p/2
1/v(1-x^2 )
v3/2
undefined
0

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

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49. Deriv of cot^(-1)x
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
0
-1/(1+x^2 )

50. sin p/6
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
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
v3/3