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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 3p/4
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
-1
0

2. cos 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
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
0

3. What is the quotient rule?

4. Deriv of tan^(-1)x
1
-1/2
1/(1+x^2 )
1/u du/dx

5. Deriv of f(x)=tanx is?
1/(|x| v(x^2-1))
sec^2x
-1/2
-v3/3

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

7. cos 2p
-1/2
1
-csc^2x
-1

8. sin 7p/6
-v3
1/u du/dx
-1/2
v3/2

9. cos 3p/4
-csc^2x
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
-1
-v2/2

10. cos 11p/6
v3/2
slope of the tangent line
0
-1/(1+x^2 )

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

12. What is the Chain Rule? When can it be used?
-v2/2
1/2
v3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

13. sin p/4
-v3/2
-cscxcotx
v2/2
1

14. cos 5p/6
-cscxcotx
-v3
v3/2
-v3/2

15. sin 2p/3
-1/v(1-x^2 )
v3/2
-v3/3
1/v(1-x^2 )

16. Deriv of sec^(-1)x
1/(|x| v(x^2-1))
-v3
undefined
1/u du/dx

17. tan p/4
1/u du/dx
1
-sinx
-1/2

18. Explicit differentiation
-1
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
1

19. cos p/4
-1/v(1-x^2 )
v2/2
e^x
1/u du/dx

20. tan 7p/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
sec^2x
tanxsecx
-1

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
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

22. sin 5p/6
v2/2
1/2
0
v3/2

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

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

25. derivative
-1
0
slope of the tangent line
-1/(|x| v(x^2-1))

26. sin p/6
1/v(1-x^2 )
-v3
-v3/2
1/2

27. Deriv of cos^(-1)x
-1/v(1-x^2 )
sec^2x
-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

28. tan 2p/3
1
1/u du/dx
v2/2
-v3

29. Deriv of e^x
e^x
1
-csc^2x
0

30. cos 4p/3
v3/3
undefined
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-1/2

31. cos p/6
-1/2
-1/(|x| v(x^2-1))
cosx
v3/2

32. tan 2p
1
1/2
-1/2
0

33. cos 5p/4
-v2/2
-v3/2
-v3
-v3/2

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

35. cos 3p/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
a^u lna du/dx
0

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

37. tan 4p/3
v3
1/2
-v2/2
v3/2

38. sin p/2
0
1
v3/2
v3

39. sin 4p/3
-v3/2
0
1/(|x| v(x^2-1))
-1

40. sin 5p/4
1/v(1-x^2 )
-v2/2
1/(1+x^2 )
v3/2

41. Deriv of sin^(-1)x
0
1/2
1/v(1-x^2 )
v3

42. cos 7p/6
v3/2
-v3/2
1/(1+x^2 )
-v2/2

43. tan p/3
v3
v3/2
v3/3
0

44. Deriv of a^u
a^u lna du/dx
v2/2
-v3/2
v3/2

45. tan p
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
undefined

46. When do derivatives not exist?
v3/3
1/(1+x^2 )
-1/(|x| v(x^2-1))
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

47. What is the product rule?

48. Deriv of log_au=
-v3/3
1/(u ln a ) du/dx
0
1/2

49. sin p/3
-1
1
v3/2
0

50. cos 5p/3
1
1/2
0
v3/2