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AP Calculus 2

Instructions:

Answer 50 questions in 15 minutes.
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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 7p/4
f(x) = (u)(v) AND f'(x) = u'v + v'u
-cscxcotx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v2/2

2. sin 3p/4
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/(|x| v(x^2-1))
v2/2
0

3. Deriv of csc^(-1)x
-1/(|x| v(x^2-1))
1/2
v3/2
1/2

4. Deriv of f(x)=secx is?
1
e^x
undefined
tanxsecx

5. Deriv of sin^(-1)x
v3/2
v2/2
1/v(1-x^2 )
-v3/3

6. cos 5p/4
v2/2
-1
v2/2
-v2/2

7. cos p/3
-csc^2x
-1/(|x| v(x^2-1))
1/2
v3/3

8. Deriv of tan^(-1)x
-1/v(1-x^2 )
-v3/3
1/(1+x^2 )
1

9. cos 3p/4
-v2/2
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
1/2
-1/2

10. Deriv of f(x)=csc is?
f(x) = (u)(v) AND f'(x) = u'v + v'u
-cscxcotx
1/(1+x^2 )
tanxsecx

11. Deriv of cot^(-1)x
1/2
-1/(1+x^2 )
-v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

12. cos 4p/3
1
-1/2
0
-csc^2x

13. tan 5p/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3
-cscxcotx
f(x) = (u)(v) AND f'(x) = u'v + v'u

14. sin p
-1
-v3
0
tanxsecx

15. tan 5p/6
-v3/3
e^x
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

16. sin 7p/6
sec^2x
undefined
-1/2
v2/2

17. Deriv of f(x)=tanx is?
slope of the tangent line
v3/2
-1/2
sec^2x

18. Deriv of e^x
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v2/2
e^x
v2/2

19. cos 5p/6
-v3/2
tanxsecx
sec^2x
v3/3

20. tan 2p
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
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
0

21. cos 7p/4
-1/v(1-x^2 )
1/2
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
v2/2

22. What is the Chain Rule? When can it be used?
-1/2
-v3
1/u du/dx
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

23. sin 4p/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3/2
slope of the tangent line
v2/2

24. sin p/3
sec^2x
v3/2
v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

25. Deriv of f(x)=cosx is?
-sinx
-csc^2x
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

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

27. cos p/4
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
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
0

28. tan p/2
undefined
-v2/2
1/2
1/(|x| v(x^2-1))

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

30. tan 3p/4
1/(u ln a ) du/dx
slope of the tangent line
-1
-1/(|x| v(x^2-1))

31. sin 3p/2
-1
-v3/2
-v3/2
a^u lna du/dx

32. Deriv of f(x)=sinx is?
-1/v(1-x^2 )
0
cosx
sec^2x

33. tan p/6
1
-v3
v3/3
0

34. sin 5p/6
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1/2
-1
v2/2

35. cos 3p/2
-v3/3
-1/2
-1
0

36. Deriv of ln u
1/u du/dx
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
0

37. cos 2p/3
v3
-sinx
-1/2
-1

38. tan 11p/6
-v3
-v3/3
-1
-1/2

39. 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
-v3
undefined

40. Deriv of log_au=
a^u lna du/dx
sec^2x
-v3
1/(u ln a ) du/dx

41. cos 2p
-v3/2
1
-v2/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

42. cos 5p/3
1/2
-1
-1
v3/2

43. sin 5p/4
-v2/2
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
undefined

44. sin 2p/3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
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
0
v3/2

45. sin 2p
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
-csc^2x
0

46. Deriv of a^u
1
v2/2
a^u lna du/dx
-1

47. tan 2p/3
1/(1+x^2 )
-v3
-v3/3
v3/2

48. sin p/6
-v2/2
-v3/2
1/2
v3/2

49. sin p/4
v2/2
v3/2
-1/v(1-x^2 )
0

50. sin 11p/6
v3/2
-1/2
sec^2x
v3/2

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AP Calculus 2

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