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AP Calculus 2

Instructions:

Answer 50 questions in 15 minutes.
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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 7p/6
1/(|x| v(x^2-1))
-v3/2
v3/2
v2/2

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

3. sin p
a^u lna du/dx
0
1
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

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

5. tan p/3
1/2
-v3/2
v3
undefined

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

7. derivative
-1/v(1-x^2 )
v3/3
-csc^2x
slope of the tangent line

8. What is the product rule?

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

10. tan 7p/6
v3/3
1/(|x| v(x^2-1))
1
slope of the tangent line

11. tan p/2
1/2
-1
-v3/3
undefined

12. cos p/3
1/(1+x^2 )
undefined
1/(|x| v(x^2-1))
1/2

13. cos 2p/3
undefined
-1/2
-1/(|x| v(x^2-1))
cosx

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

15. Guidelines for implicit differentiation
-1
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
-v3

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

17. tan 7p/4
-1
cosx
0
1/v(1-x^2 )

18. sin 7p/6
v3/3
-v2/2
v3
-1/2

19. cos p/6
v3/3
v2/2
v3/2
-v3/3

20. sin 5p/3
-v3/2
-v3/3
slope of the tangent line
v2/2

21. Deriv of cot^(-1)x
v3/3
-1/(1+x^2 )
undefined
-1/(|x| v(x^2-1))

22. Implicit differentiation
v2/2
1/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
a^u lna du/dx

23. sin p/6
0
1/2
v3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

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

25. sin 11p/6
-1/2
0
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

26. tan 5p/3
1/(u ln a ) du/dx
-v2/2
-v3
0

27. sin 7p/4
-1
-v2/2
1/2
1

28. What is the quotient rule?

29. sin 2p
0
1
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
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

30. cos 3p/4
1/2
1/(u ln a ) du/dx
-v2/2
v3/3

31. tan 2p/3
-v3
-cscxcotx
0
sec^2x

32. What is the Chain Rule? When can it be used?
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-cscxcotx
v2/2
1

33. Deriv of f(x)=cosx is?
tanxsecx
-1
-1/(|x| v(x^2-1))
-sinx

34. Deriv of f(x)=tanx is?
a^u lna du/dx
sec^2x
-csc^2x
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

35. tan 5p/4
-v2/2
1
1/(1+x^2 )
v3/3

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

37. cos 7p/4
1
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v2/2
-v3

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

39. tan p/4
0
1
-cscxcotx
-1

40. Deriv of f(x)=secx is?
e^x
tanxsecx
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v2/2

41. cos p/4
v2/2
-v3/2
a^u lna du/dx
-cscxcotx

42. cos p/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
f(x) = (u)(v) AND f'(x) = u'v + v'u
slope of the tangent line
0

43. Deriv of ln u
-1/2
v3/3
-v2/2
1/u du/dx

44. cos 5p/3
-v2/2
-v2/2
undefined
1/2

45. cos 11p/6
-sinx
v3/2
-v3/2
v3/3

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

47. Deriv of a^u
v2/2
undefined
f(x) = (u)(v) AND f'(x) = u'v + v'u
a^u lna du/dx

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

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

50. sin p/4
-1
-csc^2x
v3/2
v2/2