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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 5p/3
v3/2
1
1/2
slope of the tangent line

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

3. Deriv of e^x
0
-v3
e^x
v2/2

4. sin p/2
1/2
1
v3
tanxsecx

5. What is the quotient rule?

6. cos 2p
1
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v2/2
undefined

7. 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
0
1
0

8. sin 5p/3
-v3/2
-cscxcotx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
0

9. Deriv of log_au=
undefined
f(x) = (u)(v) AND f'(x) = u'v + v'u
1/(u ln a ) du/dx
-v2/2

10. Deriv of cot^(-1)x
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/(1+x^2 )
e^x
-v3/3

11. Deriv of f(x)=cosx is?
1/(|x| v(x^2-1))
0
0
-sinx

12. Deriv of tan^(-1)x
1/(1+x^2 )
-v2/2
-cscxcotx
-v3/2

13. Deriv of cos^(-1)x
1
-1/v(1-x^2 )
-v2/2
-v3/3

14. sin 2p/3
v3/2
-v2/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3/2

15. cos 5p/6
slope of the tangent line
-v3/2
a^u lna du/dx
v3/3

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

17. sin 7p/4
-v2/2
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
-1
-v3/2

18. tan 11p/6
-v3/3
0
v3/3
sec^2x

19. Deriv of f(x)=csc is?
-v3/2
-cscxcotx
0
0

20. Deriv of sec^(-1)x
-1/v(1-x^2 )
-1
1/(|x| v(x^2-1))
undefined

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

22. cos p/3
a^u lna du/dx
-v2/2
1/2
1/(1+x^2 )

23. cos 3p/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
0
1
sec^2x

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

25. cos p
-1
v3/2
undefined
1/v(1-x^2 )

26. Deriv of f(x)=sinx is?
-v3/3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
cosx
-1/2

27. tan p/4
-cscxcotx
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
e^x

28. cos 7p/4
v3/2
0
v3/3
v2/2

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

30. Deriv of f(x)=secx is?
tanxsecx
-sinx
1
-1

31. tan 5p/6
-v3/3
0
-1
1/(u ln a ) du/dx

32. Deriv of csc^(-1)x
-v3/2
-1/2
-1/(|x| v(x^2-1))
-v2/2

33. cos 2p/3
-1/2
v2/2
undefined
0

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

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

36. What is the product rule?

37. sin 5p/4
-1/2
-v2/2
-cscxcotx
v3

38. tan 4p/3
v2/2
-v2/2
v3
e^x

39. sin 4p/3
-v3/2
0
-1
v3

40. Guidelines for implicit differentiation
cosx
0
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
1/2

41. tan 7p/4
0
-1
v3/3
-1/(1+x^2 )

42. tan 2p
1/(|x| v(x^2-1))
undefined
1/(1+x^2 )
0

43. When do derivatives not exist?
v2/2
1/2
-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

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

45. cos 4p/3
-v2/2
-1/2
-1
v3/3

46. derivative
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1/2
a^u lna du/dx
slope of the tangent line

47. sin 2p
v2/2
0
-v3/3
1

48. sin 7p/6
-v3
-1/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

49. cos 11p/6
-v3/2
1
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v3/2

50. cos 5p/4
-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
-v2/2
1/2