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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 7p/4
-csc^2x
-v3
0
-1

2. tan 11p/6
-v3/3
v3/2
v3/3
v2/2

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

4. Deriv of sin^(-1)x
1/v(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
a^u lna du/dx
v3/2

5. cos p/6
v3/2
-csc^2x
0
1/v(1-x^2 )

6. sin 4p/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
0
v2/2
-v3/2

7. cos 5p/4
v2/2
-v2/2
undefined
1/(u ln a ) du/dx

8. derivative
-v3
1
slope of the tangent line
-1

9. tan 2p/3
-v3
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
slope of the tangent line

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

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

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

13. cos 2p/3
-csc^2x
1/2
1/2
-1/2

14. Deriv of a^u
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
undefined
-sinx
a^u lna du/dx

15. Guidelines for implicit differentiation
v2/2
1/u du/dx
v3/2
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

16. tan 4p/3
v3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
undefined
sec^2x

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

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

19. What is the product rule?

20. sin 5p/6
1/2
0
-1
-v2/2

21. tan p/6
v3/3
undefined
v3/2
v2/2

22. When do derivatives not exist?
-v3
v3
-v3/3
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

23. cos 2p
-1/2
-cscxcotx
1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

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

25. tan 5p/3
-v3
-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
0

26. Implicit differentiation
1
slope of the tangent line
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-cscxcotx

27. tan 5p/6
-v3/3
v2/2
-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

28. Deriv of sec^(-1)x
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
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1/(|x| v(x^2-1))
-1/2

29. sin p/4
-sinx
v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

30. Deriv of f(x)=cosx is?
-v2/2
-sinx
1
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

31. Deriv of ln u
0
-v2/2
-csc^2x
1/u du/dx

32. Deriv of tan^(-1)x
1/(1+x^2 )
v2/2
1
1/(u ln a ) du/dx

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

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

35. What is the Chain Rule? When can it be used?
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1/(1+x^2 )
1/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

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

37. sin p
undefined
e^x
0
-1

38. sin 2p
0
-1/(|x| v(x^2-1))
v3/2
1/u du/dx

39. cos 3p/4
v2/2
-csc^2x
1/(|x| v(x^2-1))
-v2/2

40. cos 7p/6
-v2/2
1/u du/dx
-v3/2
-sinx

41. cos p/4
1
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

42. sin 11p/6
-sinx
-v2/2
v3
-1/2

43. Deriv of f(x)=sinx is?
cosx
0
1/(1+x^2 )
-1

44. cos 4p/3
-1/(1+x^2 )
-1/2
v3/2
-v3/3

45. Deriv of f(x)=csc is?
v2/2
-v3/2
-cscxcotx
-v2/2

46. Deriv of log_au=
-v3
0
1/(u ln a ) du/dx
-v2/2

47. sin 7p/4
-1
1
-v2/2
undefined

48. tan p/2
slope of the tangent line
0
1/u du/dx
undefined

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

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