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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. sin 4p/3
-v2/2
-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

2. tan 4p/3
0
-1/2
v3/3
v3

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

4. cos p/2
-1/(1+x^2 )
-1
0
v3

5. Deriv of cos^(-1)x
-v2/2
-1/v(1-x^2 )
-cscxcotx
-v2/2

6. tan p/2
-1/2
tanxsecx
1
undefined

7. sin p
0
undefined
-v2/2
-v3

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

9. What is the Chain Rule? When can it be used?
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
e^x
-v3
1

10. Deriv of f(x)=secx is?
1/2
tanxsecx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
1/2

11. Deriv of ln u
1/u du/dx
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/(|x| v(x^2-1))
v2/2

12. Deriv of sec^(-1)x
1/(|x| v(x^2-1))
sec^2x
tanxsecx
-v3/3

13. sin 2p
-v3/2
v3/2
-v3/2
0

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

15. tan 7p/6
v3/3
-v3/2
0
-v3/2

16. Deriv of sin^(-1)x
undefined
-1/(1+x^2 )
1/v(1-x^2 )
-v2/2

17. Deriv of a^u
cosx
v3/2
v3/3
a^u lna du/dx

18. sin p/3
1/2
v3/2
cosx
1

19. sin p/4
v3/3
-v3/2
v2/2
-1/v(1-x^2 )

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

21. tan 2p/3
-v3/3
0
-v3
-v3/2

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

23. cos p
-1
-v3
undefined
1/(|x| v(x^2-1))

24. sin 11p/6
1/(|x| v(x^2-1))
-1/2
-v2/2
-v3/2

25. cos p/4
v2/2
1
-1/2
-1/(|x| v(x^2-1))

26. tan 5p/3
-1/(|x| v(x^2-1))
-v3
-1/2
-v3/2

27. Guidelines for implicit differentiation
v3
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

28. tan 11p/6
-v3/3
1/2
-1/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

29. tan p/6
1/u du/dx
1/(u ln a ) du/dx
-csc^2x
v3/3

30. sin 7p/4
1/v(1-x^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
undefined
-v2/2

31. Deriv of f(x)=tanx is?
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
a^u lna du/dx
sec^2x
v2/2

32. cos 11p/6
v3/2
undefined
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v2/2

33. tan p/4
1
-1/2
-1/(1+x^2 )
0

34. cos 5p/3
1/2
v3/3
-1/2
1/u du/dx

35. cos 3p/2
1/v(1-x^2 )
0
v2/2
-1/2

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

37. Deriv of cot^(-1)x
1/v(1-x^2 )
1/(u ln a ) du/dx
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 )

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

39. What is the quotient rule?

40. sin 2p/3
-1
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

41. Deriv of csc^(-1)x
0
0
cosx
-1/(|x| v(x^2-1))

42. sin 5p/6
-1
-1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1/2

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

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

45. tan 5p/4
1/2
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

46. When do derivatives not exist?
-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
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v3/3

47. sin 3p/4
1/v(1-x^2 )
v3/2
v2/2
1/(|x| v(x^2-1))

48. tan p
-v3/2
0
cosx
-v3

49. tan 2p
-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
cosx
0

50. cos 2p
-v2/2
-v3
1
cosx