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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
-v3/2
-v2/2
-1
v3/2

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

3. Deriv of ln u
0
1/u du/dx
-v3/2
cosx

4. Deriv of log_au=
1/2
1/(u ln a ) du/dx
-1/2
-1

5. tan 5p/4
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1
-v3/2
slope of the tangent line

6. sin 11p/6
1
v3/3
-1/2
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

7. tan 11p/6
-v3/3
v3/2
-v3
-cscxcotx

8. cos 2p
undefined
0
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1

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

10. sin p/6
1/2
v3/3
1/(1+x^2 )
f(x) = (u)(v) AND f'(x) = u'v + v'u

11. sin 3p/4
v2/2
-v3/2
1/(|x| v(x^2-1))
-v2/2

12. cos 4p/3
1/(|x| v(x^2-1))
-1
v3/2
-1/2

13. sin 2p
0
v3/2
-1/2
v2/2

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

15. cos 2p/3
-1/2
-cscxcotx
-v3/3
-1/v(1-x^2 )

16. Guidelines for implicit differentiation
undefined
v3/2
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

17. sin 5p/3
1
-v3/2
1/(u ln a ) du/dx
-v2/2

18. Deriv of cot^(-1)x
-1/(1+x^2 )
1/2
v3/2
-1/2

19. sin 5p/4
0
1/2
-cscxcotx
-v2/2

20. cos p/2
0
1/(1+x^2 )
sec^2x
undefined

21. Deriv of sin^(-1)x
sec^2x
v3/3
1/v(1-x^2 )
v3/2

22. cos 5p/4
tanxsecx
v3/2
-v2/2
-1/2

23. sin 7p/6
1/(1+x^2 )
-1/2
tanxsecx
a^u lna du/dx

24. sin 3p/2
1/2
v2/2
1/2
-1

25. cos 3p/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
cosx
-1

26. Deriv of f(x)=secx is?
0
tanxsecx
e^x
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

27. sin p/3
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
v3/2
0

28. sin 5p/6
v3/3
1/2
-v3/2
v2/2

29. tan p/2
v2/2
undefined
sec^2x
1/v(1-x^2 )

30. Deriv of a^u
a^u lna du/dx
-cscxcotx
v3/2
-v3/2

31. sin 4p/3
-v2/2
1/u du/dx
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
-v3/2

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

33. cos 7p/4
v2/2
-1/2
-v3/3
-v3/3

34. cos p/4
1
undefined
0
v2/2

35. Deriv of tan^(-1)x
-1/(1+x^2 )
1/(1+x^2 )
-1/v(1-x^2 )
-cscxcotx

36. tan 5p/6
-1/2
-v3/3
slope of the tangent line
-1

37. cos 11p/6
-v3/3
-1/2
-v2/2
v3/2

38. tan 7p/6
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-1
v3/3
0

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

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

41. tan p/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
-sinx
v3
1/2

42. What is the product rule?
v3/2
1/u du/dx
f(x) = (u)(v) AND f'(x) = u'v + v'u
0

43. Deriv of f(x)=csc is?
-sinx
-1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-cscxcotx

44. tan 3p/4
1
-1
-v3/2
v3/3

45. tan p
0
v3/3
-1
-sinx

46. Deriv of e^x
-v2/2
e^x
-1
1/u du/dx

47. sin p
-v3/2
1/2
0
undefined

48. derivative
v3
v3/2
slope of the tangent line
v2/2

49. Deriv of f(x)=sinx is?
v2/2
0
cosx
-v2/2

50. tan p/4
-sinx
1
v3/2
0

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