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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/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
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
1/2

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

3. tan p
v2/2
0
v3/2
-1

4. Deriv of f(x)=tanx is?
1/(1+x^2 )
-v3/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
sec^2x

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

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

7. sin 4p/3
-v2/2
-1
-v3/2
-1/2

8. Deriv of ln u
-1
1/u du/dx
v2/2
-v2/2

9. cos 5p/3
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
v3/2
-v3/3

10. derivative
slope of the tangent line
1
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

11. sin 7p/4
0
-v2/2
1/(u ln a ) du/dx
-1/2

12. tan 3p/2
-1
-1
-1/2
undefined

13. cos p/6
-v2/2
v3/2
slope of the tangent line
tanxsecx

14. sin p
0
-v3/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3/2

15. Deriv of a^u
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
a^u lna du/dx
-1/v(1-x^2 )
-1/2

16. sin 3p/2
a^u lna du/dx
-1
-1/v(1-x^2 )
1

17. tan 11p/6
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3/3
-v2/2
0

18. Deriv of f(x)=cotx is?
-csc^2x
v2/2
slope of the tangent line
f(x) = (u)(v) AND f'(x) = u'v + v'u

19. Deriv of f(x)=secx is?
v3/2
1/2
0
tanxsecx

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

21. sin 5p/4
-v2/2
-v3/2
1/(|x| v(x^2-1))
undefined

22. sin p/6
v3/2
v2/2
1/2
tanxsecx

23. tan 5p/4
1
1/(|x| v(x^2-1))
-v2/2
v3/3

24. Deriv of e^x
e^x
-v3/3
0
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

25. tan p/2
a^u lna du/dx
undefined
0
-1

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

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

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

29. cos 5p/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
-v3/2
sec^2x

30. When do derivatives not exist?
1/(u ln a ) du/dx
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
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

31. tan 5p/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3
1/2
v3/2

32. What is the Chain Rule? When can it be used?
undefined
1/v(1-x^2 )
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1/(|x| v(x^2-1))

33. sin 7p/6
v3/2
undefined
-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

34. Deriv of tan^(-1)x
1/(1+x^2 )
-cscxcotx
0
-v3/3

35. sin 3p/4
slope of the tangent line
v2/2
0
-v3/3

36. tan 4p/3
-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
sec^2x
v3

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

38. cos 11p/6
v3/2
-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

39. Deriv of f(x)=cosx is?
v2/2
v3/3
-sinx
slope of the tangent line

40. cos p/4
v2/2
0
-sinx
v3/2

41. Deriv of sec^(-1)x
e^x
undefined
1/(|x| v(x^2-1))
-1/2

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

43. tan 5p/6
1/v(1-x^2 )
-v3/3
v3/2
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

44. What is the product rule?

45. 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
1/(|x| v(x^2-1))
-v3/2

46. sin 11p/6
-cscxcotx
1/u du/dx
v3/2
-1/2

47. cos 2p
a^u lna du/dx
-v2/2
1
-csc^2x

48. Deriv of f(x)=csc is?
-cscxcotx
v3/2
slope of the tangent line
1/(1+x^2 )

49. sin 5p/3
-v3/2
tanxsecx
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1

50. tan 7p/4
-1
1/2
-1/(1+x^2 )
v3