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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/4
1
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/2
a^u lna du/dx

2. cos p
v2/2
-1
0
-v2/2

3. sin p
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
0
sec^2x

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

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5. sin 11p/6
-1/2
0
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
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

6. tan 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
v3/3
1
-cscxcotx

7. tan 2p/3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v3/3
-v3
-v2/2

8. tan 11p/6
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v3/2
v2/2
-v3/3

9. derivative
-v3/2
v2/2
-v3
slope of the tangent line

10. Deriv of tan^(-1)x
-v3/2
1/(1+x^2 )
1/(|x| v(x^2-1))
-1/(1+x^2 )

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

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

13. sin 7p/6
1
-1/2
-1
v3/2

14. tan p/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3
-cscxcotx
0

15. sin 5p/3
e^x
-v3/2
1/u du/dx
1/2

16. sin 5p/4
-1/v(1-x^2 )
1/u du/dx
-v2/2
v3

17. tan p/6
v2/2
0
v3/3
1

18. cos 5p/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
-1
-1/v(1-x^2 )

19. Explicit differentiation
-v2/2
-v3/2
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

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

21. tan p/2
-v3/2
e^x
undefined
v2/2

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

23. tan 5p/4
1
slope of the tangent line
0
undefined

24. sin 7p/4
slope of the tangent line
-v2/2
sec^2x
-v3/3

25. tan 5p/3
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
-v3
v2/2

26. Deriv of e^x
-v2/2
e^x
undefined
-v3/2

27. Deriv of f(x)=secx is?
v3
-csc^2x
-1/(1+x^2 )
tanxsecx

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

29. Deriv of f(x)=cotx is?
-1/(1+x^2 )
-v3/3
-csc^2x
-v2/2

30. tan 7p/4
-1/2
-1
-v2/2
1/(|x| v(x^2-1))

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

32. tan 3p/2
v3/2
undefined
-v3/2
-v3

33. tan 4p/3
v3/2
v3
1/(1+x^2 )
1/2

34. cos 5p/3
0
v2/2
-v3
1/2

35. cos 2p/3
-1/v(1-x^2 )
1
-1/2
v3

36. sin 3p/4
v2/2
v3/3
-v3/3
v3/3

37. What is the product rule?

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

39. sin p/2
v2/2
1
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

40. sin 2p/3
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
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
v3/2

41. cos 3p/4
-1/2
-v2/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1/2

42. cos 7p/4
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v3/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2

43. cos p/4
v3/2
v2/2
-v3
-1/(1+x^2 )

44. Deriv of f(x)=tanx is?
sec^2x
v2/2
-v3/3
1/(|x| v(x^2-1))

45. sin 4p/3
-1/2
-1
-v3/2
1/v(1-x^2 )

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

47. cos p/3
1/2
-1/2
e^x
v3/3

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

49. Deriv of cot^(-1)x
undefined
1/2
v2/2
-1/(1+x^2 )

50. Deriv of f(x)=sinx is?
-v2/2
v3
undefined
cosx