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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 11p/6
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
0
-v2/2
-1/2

2. tan 7p/4
1
e^x
-1
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

3. derivative
v3/2
tanxsecx
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
slope of the tangent line

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

5. sin 7p/4
-v3/2
1/2
-v2/2
0

6. tan 5p/4
v3
-v3/2
1
v3

7. cos p/6
v3/2
-v3/3
-v2/2
-1/2

8. sin 3p/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
v3/2
-cscxcotx
v2/2

9. sin 2p/3
v3/2
1
-v3/2
v2/2

10. cos p/4
0
1/2
v2/2
undefined

11. cos 2p/3
a^u lna du/dx
v2/2
-1/2
tanxsecx

12. cos 7p/6
-v3/2
sec^2x
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-v2/2

13. Deriv of cot^(-1)x
-1/(1+x^2 )
-1
-v2/2
1/u du/dx

14. What is the quotient rule?

15. Deriv of e^x
-v2/2
v3/2
e^x
-v3

16. What is the product rule?

17. sin 5p/6
1/2
1/(u ln a ) du/dx
0
-v3/3

18. tan 2p/3
1/2
-v3
-v3/3
-v3/2

19. sin p/2
1
-1/2
sec^2x
-1/2

20. cos p
1/v(1-x^2 )
1/(|x| v(x^2-1))
-1/v(1-x^2 )
-1

21. sin 5p/4
v3/2
-v2/2
1/2
v3/2

22. sin 2p
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-1/2
0
-v2/2

23. cos 4p/3
1/2
-1/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3/2

24. sin 3p/2
-v3/2
-v2/2
1/(1+x^2 )
-1

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

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

27. Deriv of ln u
0
v3/3
-sinx
1/u du/dx

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

29. Deriv of log_au=
1/(|x| v(x^2-1))
1/(u ln a ) du/dx
-sinx
v2/2

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

31. Deriv of f(x)=secx is?
f(x) = (u)(v) AND f'(x) = u'v + v'u
1/(|x| v(x^2-1))
-1/(1+x^2 )
tanxsecx

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

33. cos p/2
v2/2
0
-v3/2
cosx

34. Deriv of a^u
-1/2
a^u lna du/dx
-1/2
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. tan p/4
1
0
-sinx
-1/2

36. cos 7p/4
v2/2
1
-v2/2
v3/3

37. When do derivatives not exist?
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
1
-1

38. sin 4p/3
-v3/2
a^u lna du/dx
v3/2
-v2/2

39. cos 5p/3
1/2
v3/2
0
-1/2

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

41. sin p/4
-1
1/(u ln a ) du/dx
-v2/2
v2/2

42. sin 5p/3
-v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
f(x) = (u)(v) AND f'(x) = u'v + v'u
cosx

43. sin p/3
v3/2
v2/2
-v3
-sinx

44. cos 2p
-v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1/u du/dx
1

45. tan 11p/6
1/(1+x^2 )
-v3/3
v3
1

46. sin 7p/6
v3/2
v3/2
-1/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

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

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

49. Deriv of f(x)=csc is?
tanxsecx
-cscxcotx
undefined
-v3/3

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