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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. Deriv of csc^(-1)x
-cscxcotx
1/v(1-x^2 )
-v3/3
-1/(|x| v(x^2-1))

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

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

4. tan 2p
1/2
undefined
1/2
0

5. Guidelines for implicit differentiation
-v3/3
v2/2
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
-1/2

6. tan p/4
1
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3
-v3

7. sin p/4
v2/2
1/(|x| v(x^2-1))
e^x
-1

8. Deriv of e^x
-1/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v2/2
e^x

9. tan 2p/3
0
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v3
-1/2

10. Deriv of ln u
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
v3/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1/u du/dx

11. Deriv of f(x)=tanx is?
v3/3
-v2/2
sec^2x
-v2/2

12. Implicit differentiation
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v3/3
1/u du/dx
0

13. When do derivatives not exist?
v2/2
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
tanxsecx

14. Deriv of log_au=
-1
v3/3
1/(u ln a ) du/dx
1/(1+x^2 )

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

16. tan p/3
v3
-1/2
v3/3
-1/2

17. tan 7p/4
slope of the tangent line
-cscxcotx
1
-1

18. tan 5p/3
-v3
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-cscxcotx

19. sin p/6
1/2
v3/3
v3/2
v3/2

20. Deriv of cot^(-1)x
-v2/2
-1/(1+x^2 )
v2/2
v3

21. sin 7p/4
-1/2
-v2/2
undefined
-cscxcotx

22. sin 5p/3
v3/2
-csc^2x
-sinx
-v3/2

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

24. tan 3p/2
-1
a^u lna du/dx
-v3/2
undefined

25. cos 5p/4
f(x) = (u)(v) AND f'(x) = u'v + v'u
tanxsecx
-v2/2
-v3/3

26. cos p
-1
f(x) = (u)(v) AND f'(x) = u'v + v'u
undefined
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

27. tan 4p/3
v3
0
-1/(|x| v(x^2-1))
-v2/2

28. sin 7p/6
v2/2
-1/2
-v3
-1/(1+x^2 )

29. What is the product rule?

30. cos 2p/3
-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
-1/2
0

31. tan p/2
undefined
0
v2/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

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

33. tan 7p/6
v3/3
-v3
-v3/2
-v3/2

34. cos 3p/4
v3
1/2
-v2/2
0

35. Deriv of f(x)=cotx is?
-csc^2x
-v3/2
1/u du/dx
-1

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

37. Deriv of a^u
undefined
-v3/3
a^u lna du/dx
-1/(|x| v(x^2-1))

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

39. cos 11p/6
v3/2
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
-1
-v2/2

40. sin p/3
v2/2
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
v3/2
-v2/2

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

42. tan 11p/6
1/(u ln a ) du/dx
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
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

43. tan 5p/4
-1/2
1
v3/2
undefined

44. sin 3p/2
sec^2x
1/(u ln a ) du/dx
0
-1

45. Explicit differentiation
-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/(1+x^2 )
v2/2

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

47. Deriv of f(x)=secx is?
tanxsecx
v3/2
v2/2
-v2/2

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

49. sin 11p/6
-1/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/2
-1/(1+x^2 )

50. cos p/4
v2/2
-csc^2x
-1/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?