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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
v3
0
-v3/2
1/2

2. Deriv of sec^(-1)x
1/(|x| v(x^2-1))
v3/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
1/v(1-x^2 )

3. sin p/4
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
-1
v2/2

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

5. Deriv of cot^(-1)x
-v2/2
-1/(1+x^2 )
1/2
-csc^2x

6. Deriv of tan^(-1)x
1/(u ln a ) du/dx
1/(1+x^2 )
slope of the tangent line
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

7. tan 11p/6
-1/2
-v3/3
0
1/(|x| v(x^2-1))

8. What is the product rule?

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9. Deriv of cos^(-1)x
-cscxcotx
-1/v(1-x^2 )
-v3/2
-v3

10. Deriv of log_au=
1/(u ln a ) du/dx
1/2
slope of the tangent line
v3

11. cos 2p
1
-csc^2x
v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

12. Deriv of f(x)=tanx is?
0
sec^2x
1/2
v2/2

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

14. Implicit differentiation
0
v3/3
-v3/3
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

15. cos 7p/4
v3/2
-v3/2
v2/2
-1/2

16. tan 7p/4
-1
-v3/2
1/2
-v3

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

18. When do derivatives not exist?
1/2
1/u du/dx
1/(u ln a ) du/dx
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

19. cos p
1
-v2/2
-v3
-1

20. Deriv of ln u
v2/2
1/u du/dx
-1/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

21. Guidelines for implicit differentiation
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/(1+x^2 )
1
-1

22. Deriv of e^x
slope of the tangent line
e^x
1/(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

23. sin p/2
1
-sinx
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

24. tan 2p/3
1
e^x
-v3/2
-v3

25. Deriv of f(x)=sinx is?
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
1/2
cosx
v3

26. sin p/6
tanxsecx
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
-1/2

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

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

29. What is the quotient rule?

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30. tan 5p/3
undefined
-v3/3
-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

31. cos 11p/6
0
-v3/3
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

32. tan p/6
1/(u ln a ) du/dx
-v3/2
v3/3
1

33. tan p/4
-1/(1+x^2 )
1/v(1-x^2 )
v3
1

34. Deriv of f(x)=cosx is?
-sinx
-1
0
-1/2

35. cos 5p/6
-1/2
-1
-v3/2
v3

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

37. cos 3p/4
-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
-v2/2
-v3/2

38. cos p/4
0
1/2
v2/2
-1/2

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

40. sin 5p/6
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3
1/2
-v3/3

41. tan p/2
v2/2
-1/2
undefined
v3/2

42. Explicit differentiation
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
v3/3
0

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

44. tan 5p/4
-v2/2
1
-v3/3
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

45. tan 3p/4
1/2
undefined
-v3/2
-1

46. sin 3p/4
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2
1
tanxsecx

47. cos p/3
-sinx
1/2
cosx
-1/2

48. cos p/6
-csc^2x
v3/2
1/2
-1/2

49. cos 7p/6
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
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

50. Deriv of f(x)=csc is?
-cscxcotx
0
-v3/3
0