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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 3p/4
v2/2
-v3
-1/2
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

2. sin 7p/4
-v3/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v2/2
e^x

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

4. tan 7p/4
1
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v3/2
-1

5. sin 4p/3
e^x
v3/2
-v3/2
1

6. Deriv of log_au=
v3/2
1/(u ln a ) du/dx
undefined
1/u du/dx

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

8. Deriv of f(x)=cotx is?
-csc^2x
0
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

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

10. Deriv of f(x)=tanx is?
v3/2
1/2
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
sec^2x

11. sin 5p/3
-v3/2
-1
-v3
v2/2

12. cos 7p/4
-1/2
1
v2/2
cosx

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

14. Guidelines for implicit differentiation
v2/2
-1/2
-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

15. tan 2p
-1/2
-sinx
0
-1/(|x| v(x^2-1))

16. What is the quotient rule?

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

18. tan 7p/6
v3
-v3
v3/3
v2/2

19. Deriv of f(x)=cosx is?
v2/2
-v3/2
-sinx
-1/2

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

21. Deriv of f(x)=csc is?
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
-cscxcotx
-v3/3
v2/2

22. tan 5p/6
-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

23. cos p/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
v3

24. What is the product rule?

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

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

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

28. Deriv of f(x)=sinx is?
-v2/2
cosx
1/(u ln a ) du/dx
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

29. cos 5p/6
sec^2x
-v3/2
-1
-1

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

31. cos 2p
1/(1+x^2 )
-1/v(1-x^2 )
1/v(1-x^2 )
1

32. sin 2p
v2/2
0
-1/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

33. Deriv of cos^(-1)x
-v3/2
slope of the tangent line
v3/2
-1/v(1-x^2 )

34. sin 11p/6
-1/v(1-x^2 )
0
-1/2
-v2/2

35. sin 7p/6
-v3/2
v2/2
-1/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

36. cos 3p/2
v3/3
v2/2
0
-1/2

37. tan 5p/4
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
e^x
1
-v3/2

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

39. sin p/3
v3/2
-v3/2
-v3
-1/2

40. Deriv of ln u
-v3/2
1/u du/dx
a^u lna du/dx
e^x

41. Implicit differentiation
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
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
1

42. tan 5p/3
undefined
1
-1/2
-v3

43. tan 11p/6
-v3/3
slope of the tangent line
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3/2

44. tan 4p/3
0
v3
v3/2
0

45. cos p/6
sec^2x
v3/2
-1
1

46. derivative
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
slope of the tangent line
-1

47. Deriv of e^x
1/(1+x^2 )
e^x
-1
-v3/2

48. sin p/4
-v2/2
-1/2
e^x
v2/2

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

50. sin p
0
-v2/2
v3/2
v3/2