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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 p/2
-1/2
0
undefined
1/(u ln a ) du/dx

2. cos 5p/6
-v3/2
-v3
-v2/2
-cscxcotx

3. tan 4p/3
1
v3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1/2

4. When do derivatives not exist?
1/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
-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

5. What is the quotient rule?

6. tan 7p/6
1/(|x| v(x^2-1))
v3/3
-1
-v3/2

7. sin p/6
1/2
1
v2/2
v2/2

8. cos 5p/4
-v2/2
v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1

9. cos 7p/4
v2/2
undefined
0
0

10. Deriv of cos^(-1)x
-sinx
-cscxcotx
-v3
-1/v(1-x^2 )

11. cos 4p/3
undefined
cosx
1/2
-1/2

12. sin 11p/6
0
1/(|x| v(x^2-1))
-1/2
v3/2

13. sin 2p/3
v3/2
1
v2/2
1/2

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

15. sin 3p/2
-v3/3
e^x
-1
0

16. Deriv of tan^(-1)x
-v2/2
1/2
1/(1+x^2 )
-1

17. What is the product rule?

18. Deriv of f(x)=cosx is?
-1/2
-sinx
f(x) = (u)(v) AND f'(x) = u'v + v'u
1/(|x| v(x^2-1))

19. derivative
-1
-v2/2
slope of the tangent line
v2/2

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

21. Deriv of f(x)=tanx is?
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
-1

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

23. Deriv of f(x)=secx is?
-1/v(1-x^2 )
slope of the tangent line
tanxsecx
-1/2

24. cos 5p/3
1/2
-v3/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1/2

25. Deriv of a^u
v3
a^u lna du/dx
-v3/3
-sinx

26. tan 7p/4
-1
-1/2
undefined
0

27. Deriv of csc^(-1)x
1
-1/(|x| v(x^2-1))
-v2/2
cosx

28. Deriv of sec^(-1)x
v2/2
1/(|x| v(x^2-1))
slope of the tangent line
-1/2

29. sin p/2
0
-v2/2
1
1/v(1-x^2 )

30. tan p
-v2/2
v2/2
-csc^2x
0

31. Guidelines for implicit differentiation
-v3/3
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
v3

32. cos p/6
v3/2
-1
-1/2
0

33. Deriv of f(x)=cotx is?
-sinx
-v3/3
-csc^2x
-1

34. tan p/6
1/2
v3/3
-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

35. sin 7p/6
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
undefined

36. cos 7p/6
v3
undefined
-v3/2
slope of the tangent line

37. sin 4p/3
v3/3
v2/2
-v3/2
e^x

38. tan 5p/4
v2/2
0
v2/2
1

39. tan p/4
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
cosx
-v2/2
1

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

41. sin p
-v3
v3
undefined
0

42. sin 5p/4
-v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-v3/3
0

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

44. sin 5p/6
-1
-1/2
1/2
v3/2

45. cos p
e^x
0
-v3/3
-1

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

47. sin 7p/4
0
v2/2
1/u du/dx
-v2/2

48. sin 5p/3
-v3/2
slope of the tangent line
1/2
0

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

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