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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 p/4
v2/2
-1
1/(1+x^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

2. sin 2p
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v3/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
0

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

4. tan p/6
undefined
-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
v3/3

5. cos 5p/6
-v3/2
-1/(1+x^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

6. tan 7p/4
0
-1/(1+x^2 )
-1/2
-1

7. sin p/2
-1/2
-1
1
a^u lna du/dx

8. sin 7p/6
1
a^u lna du/dx
-1/2
-v2/2

9. Deriv of f(x)=tanx is?
slope of the tangent line
0
sec^2x
1/2

10. cos p/6
v3/2
1/u du/dx
-1
0

11. cos 3p/4
1/2
-v2/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
e^x

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

13. cos p/2
-sinx
tanxsecx
-v2/2
0

14. Deriv of a^u
a^u lna du/dx
1
v2/2
1/v(1-x^2 )

15. tan 5p/4
0
1
v3/2
-sinx

16. tan 7p/6
v3/3
v2/2
slope of the tangent line
1/u du/dx

17. When do derivatives not exist?
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
v3/2
1/v(1-x^2 )

18. Deriv of f(x)=secx is?
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-sinx
tanxsecx
f(x) = (u)(v) AND f'(x) = u'v + v'u

19. sin 5p/3
-1/(|x| v(x^2-1))
-v3/2
1
v2/2

20. Deriv of log_au=
1/(u ln a ) du/dx
v3/3
-v3/2
-1

21. What is the product rule?

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

23. sin 2p/3
v3/2
1/(u ln a ) du/dx
-v3/2
-1/(1+x^2 )

24. Explicit differentiation
-1
1/2
-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

25. cos 7p/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
0
-1

26. sin p/6
v3/3
cosx
1/2
undefined

27. What is the Chain Rule? When can it be used?
0
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-csc^2x
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

28. Deriv of cot^(-1)x
v3/2
-1/(1+x^2 )
-1
v2/2

29. cos 4p/3
0
v2/2
-1/2
-v3

30. Deriv of cos^(-1)x
1/(u ln a ) du/dx
-1/v(1-x^2 )
v2/2
-v3

31. tan p/4
1
v3/2
-1
v2/2

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

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

34. What is the quotient rule?

35. tan p/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
-v3/2
cosx
undefined

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

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

38. tan 4p/3
slope of the tangent line
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

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

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

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

42. sin p
-1/2
cosx
0
v2/2

43. tan 5p/3
1
-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
slope of the tangent line

44. cos 11p/6
-v2/2
0
v3/2
-v3/2

45. sin 4p/3
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
-v3/2
1

46. cos 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
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1
-v3/3

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

48. Deriv of ln u
0
1
-v3/2
1/u du/dx

49. Deriv of f(x)=cosx is?
-sinx
-v3/2
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

50. cos 2p/3
a^u lna du/dx
-1/2
1
1/(|x| v(x^2-1))