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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.
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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 f(x)=secx is?
-1/2
tanxsecx
v3/3
-1/(|x| v(x^2-1))

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

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

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

5. Deriv of f(x)=cotx is?
-v2/2
-csc^2x
v3
e^x

6. Deriv of a^u
a^u lna du/dx
-v3
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
slope of the tangent line

7. sin p/2
1
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1/(u ln a ) du/dx
v3/2

8. sin 5p/6
1/2
v2/2
sec^2x
-v3/2

9. tan 2p
cosx
-1/2
undefined
0

10. sin 7p/4
v3/3
-v2/2
0
undefined

11. cos 7p/6
-v3
-v3/2
-1/2
-1

12. tan p
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
0
-v2/2

13. What is the product rule?

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14. Explicit differentiation
-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
1/2
v3/2

15. cos 5p/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
1/2
1/(u ln a ) du/dx
-1

16. Deriv of csc^(-1)x
undefined
v2/2
-1/(|x| v(x^2-1))
1/2

17. Deriv of ln u
v2/2
-1
-v2/2
1/u du/dx

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

19. sin 2p
-1
0
v2/2
1/2

20. sin p/4
1/2
v2/2
-1/(|x| v(x^2-1))
0

21. sin 7p/6
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
e^x
-1/2
-1/(1+x^2 )

22. sin 5p/4
e^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
1
-v2/2

23. cos 3p/2
v2/2
-v3/2
v2/2
0

24. cos p/4
-1/2
v2/2
slope of the tangent line
-cscxcotx

25. tan 5p/6
-1/2
-v3/3
v3/3
1/(u ln a ) du/dx

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

27. sin p/3
undefined
1
v3/2
-v3

28. Deriv of f(x)=tanx is?
-1/2
cosx
-1
sec^2x

29. cos 4p/3
-1/2
a^u lna du/dx
v3/2
-v2/2

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

31. cos 2p/3
v3/2
1/v(1-x^2 )
-1/2
0

32. cos 3p/4
v3/2
-1/v(1-x^2 )
-v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

33. What is the quotient rule?

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

35. tan p/6
-1/v(1-x^2 )
v3/3
-v2/2
cosx

36. 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
-v3/2
-v2/2
-v2/2

37. sin p
-1
1/(1+x^2 )
-v3/2
0

38. tan 7p/4
1/u du/dx
-1
1/2
a^u lna du/dx

39. tan 7p/6
v3/3
-1/(1+x^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

40. Deriv of f(x)=csc is?
1/u du/dx
-cscxcotx
0
1/2

41. Deriv of cos^(-1)x
v2/2
-1/v(1-x^2 )
v2/2
1/u du/dx

42. tan p/4
-1
1
-v3/2
v2/2

43. tan 4p/3
-1
0
v3
1/2

44. tan 11p/6
-1/2
-v3/3
-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

45. cos 7p/4
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
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

46. tan 5p/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
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
-1/v(1-x^2 )
-v3

47. cos 2p
e^x
-v3/3
-v2/2
1

48. Deriv of log_au=
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
1/(u ln a ) du/dx
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

49. cos p/2
1/(u ln a ) du/dx
-sinx
0
-csc^2x

50. Deriv of sin^(-1)x
sec^2x
1/v(1-x^2 )
1/(1+x^2 )
v3/2