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

2. sin 5p/4
-v3/2
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
-v2/2

3. sin p/2
1
1/2
v3
v3/3

4. Deriv of sec^(-1)x
0
1/(|x| v(x^2-1))
1
-v3

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

6. sin p/6
1/2
1/(1+x^2 )
-1
-v3

7. cos p/6
1/v(1-x^2 )
v3/2
-v2/2
-v2/2

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

9. cos 2p/3
sec^2x
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
-1/2
-v3/2

10. tan 5p/4
v2/2
v3/2
1
-v2/2

11. cos 5p/3
1/(1+x^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
-v2/2
1/2

12. sin 4p/3
sec^2x
-csc^2x
-v3/2
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

13. sin 2p/3
v3/2
tanxsecx
e^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

14. Deriv of f(x)=secx is?
tanxsecx
-v3/3
0
slope of the tangent line

15. cos 5p/4
-v2/2
0
v3/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

16. Explicit differentiation
-1
1/(u ln a ) 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
1

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

18. Deriv of e^x
e^x
-1/2
1
v2/2

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

20. sin 3p/2
v3/2
-cscxcotx
-1
0

21. sin 7p/6
0
-1/(1+x^2 )
1/2
-1/2

22. tan 7p/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
v3/3
0
a^u lna du/dx

23. Deriv of cot^(-1)x
-1/2
-1/(1+x^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
-cscxcotx

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

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

26. tan 3p/2
-1/2
0
undefined
-1

27. tan p
0
-1/2
1
-v3

28. sin p
f(x) = (u)(v) AND f'(x) = u'v + v'u
tanxsecx
0
v3/2

29. cos p/4
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
v2/2
-1/v(1-x^2 )

30. derivative
-v3
-csc^2x
slope of the tangent line
-1/2

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

32. sin p/4
v2/2
a^u lna du/dx
f(x) = (u)(v) AND f'(x) = u'v + v'u
-1/v(1-x^2 )

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

34. Deriv of a^u
v2/2
-1/v(1-x^2 )
a^u lna du/dx
-v2/2

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

36. Deriv of f(x)=cosx is?
e^x
-sinx
v3/2
-v2/2

37. Deriv of f(x)=csc is?
-v2/2
-cscxcotx
-1/v(1-x^2 )
-v3

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

39. Deriv of log_au=
1/(u ln a ) du/dx
-csc^2x
-v2/2
v2/2

40. tan p/6
-v3/2
1/(u ln a ) du/dx
0
v3/3

41. cos 11p/6
-1/(|x| v(x^2-1))
-v2/2
v3/2
1

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

43. What is the quotient rule?

44. cos 7p/4
v2/2
slope of the tangent line
-sinx
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

45. cos p/3
v3
1
1/2
slope of the tangent line

46. Deriv of sin^(-1)x
1
-1/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
1/v(1-x^2 )

47. Deriv of csc^(-1)x
-1/(1+x^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/(|x| v(x^2-1))
v3/2

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

49. sin 11p/6
-1/2
-v2/2
1/2
1

50. When do derivatives not exist?
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
-1/(1+x^2 )
1/(|x| v(x^2-1))