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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/3
-1/2
-v3
-sinx
0

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

3. Deriv of log_au=
-v3/3
1/u du/dx
1/(u ln a ) du/dx
0

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

5. Deriv of sin^(-1)x
-1/2
1/v(1-x^2 )
-sinx
v2/2

6. sin 3p/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
0
-1
v2/2

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

8. cos 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
-1/2
-v3
v2/2

9. tan p/2
-v3
undefined
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

10. cos 11p/6
-v2/2
v3/2
-v3/2
v2/2

11. Deriv of e^x
0
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
e^x
-1/2

12. sin 7p/6
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
1/(u ln a ) du/dx
-1

13. Deriv of cos^(-1)x
0
1/(|x| v(x^2-1))
1
-1/v(1-x^2 )

14. sin p/6
-1/(1+x^2 )
cosx
1/2
1/v(1-x^2 )

15. sin 5p/6
v3
v3
1/2
-v3/3

16. tan 5p/4
1
v3/2
-cscxcotx
0

17. cos p/3
1/2
v2/2
-1
-1

18. sin p/3
v3/3
0
-1/(|x| v(x^2-1))
v3/2

19. sin 5p/4
-1
-1/(|x| v(x^2-1))
-v2/2
undefined

20. cos 5p/4
slope of the tangent line
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
-v2/2

21. Deriv of f(x)=cotx is?
-1/2
-1/(|x| v(x^2-1))
-v3/3
-csc^2x

22. cos 7p/4
-1/(|x| v(x^2-1))
a^u lna du/dx
v2/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

23. What is the quotient rule?

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24. sin 5p/3
1
-v3/2
0
0

25. What is the product rule?

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26. tan 5p/6
-v3/2
slope of the tangent line
-v3/3
-csc^2x

27. Deriv of f(x)=csc is?
1
-1
tanxsecx
-cscxcotx

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

29. sin p
v3/3
v3/2
0
-v3

30. tan p/6
-v3
v3/3
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

31. tan 7p/6
-v3/2
-v2/2
v3/3
-1

32. sin 11p/6
-v2/2
v3/2
-1/2
-v3

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

34. cos p
cosx
0
-1
1/2

35. sin 7p/4
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
0
-1/2
-v2/2

36. tan 5p/3
1
-v2/2
-v2/2
-v3

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

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

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

40. tan 4p/3
v3
e^x
-v3/2
1

41. sin p/2
0
v3
-1/2
1

42. Deriv of a^u
0
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
-v2/2
a^u lna du/dx

43. cos 3p/2
1/(u ln a ) du/dx
v3/3
0
-1/2

44. cos 3p/4
v3/2
-v2/2
v3/2
0

45. cos p/2
-cscxcotx
0
e^x
-1

46. Deriv of tan^(-1)x
0
1/(1+x^2 )
-1/2
-1

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

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48. Deriv of cot^(-1)x
0
v2/2
-1/(1+x^2 )
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

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

50. Explicit differentiation
-sinx
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
-v2/2
0