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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 7p/6
-1/2
undefined
1/(u ln a ) du/dx
v2/2

2. tan 4p/3
1/2
-v3/3
v3
0

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

4. cos 5p/3
-cscxcotx
1/2
v3/2
-v3/3

5. cos 7p/6
v3/2
-v3/2
undefined
1

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

7. tan p/2
0
undefined
-1/2
0

8. Deriv of sin^(-1)x
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/(1+x^2 )
1/v(1-x^2 )
-v2/2

9. sin 3p/4
-v3/3
0
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v2/2

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

11. What is the quotient rule?

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12. Deriv of f(x)=cosx is?
1/(|x| v(x^2-1))
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
cosx
-sinx

13. When do derivatives not exist?
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
-v3/3
1

14. sin 5p/3
1/u du/dx
-v3
-v3/2
-1

15. sin 4p/3
tanxsecx
sec^2x
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

16. sin 11p/6
-v3
-sinx
-1/2
-v3/2

17. Deriv of sec^(-1)x
-1
a^u lna du/dx
1/(|x| v(x^2-1))
sec^2x

18. tan p/6
-v3
0
-sinx
v3/3

19. cos 4p/3
cosx
sec^2x
1
-1/2

20. Deriv of f(x)=cotx is?
v3/2
v2/2
-csc^2x
v3

21. tan 7p/4
undefined
-1
v2/2
a^u lna du/dx

22. Deriv of cos^(-1)x
-1/(|x| v(x^2-1))
-v2/2
-1/v(1-x^2 )
sec^2x

23. sin 5p/4
-v3
-v2/2
tanxsecx
1/(u ln a ) du/dx

24. Deriv of f(x)=secx is?
tanxsecx
1/(1+x^2 )
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
v2/2

25. sin 5p/6
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
-1/2
0

26. cos p/6
-1
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
v3/2

27. sin 7p/4
e^x
-1/2
-v3/3
-v2/2

28. What is the Chain Rule? When can it be used?
slope of the tangent line
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v2/2
e^x

29. tan 5p/6
-v3/3
v2/2
-csc^2x
-1/v(1-x^2 )

30. Deriv of cot^(-1)x
-1/(1+x^2 )
-1
v2/2
0

31. sin 3p/2
cosx
v3/2
-1
1/2

32. Deriv of e^x
e^x
v3
1/2
1/(|x| v(x^2-1))

33. tan 5p/3
1/u du/dx
v3/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3

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

35. sin p/2
1/v(1-x^2 )
-1/2
1
tanxsecx

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

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37. tan 5p/4
-1/2
0
1
v3/3

38. cos 5p/6
-1/(1+x^2 )
1/(1+x^2 )
0
-v3/2

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

40. tan 7p/6
v3/2
cosx
-1/(1+x^2 )
v3/3

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

42. Guidelines for implicit differentiation
-1/2
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
1

43. sin p
1/v(1-x^2 )
undefined
0
v3

44. tan p/3
v3/2
1/(u ln a ) du/dx
v3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

45. cos p
undefined
-1
v2/2
sec^2x

46. tan p
v2/2
-v3
-1/v(1-x^2 )
0

47. cos 7p/4
v2/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/3
1

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

49. derivative
slope of the tangent line
-v3/2
-v3/2
v3

50. Deriv of f(x)=csc is?
-cscxcotx
-csc^2x
v3
undefined