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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 p/3
-v3/2
v3
v3/2
0

2. cos 5p/3
1/v(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
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
1/2

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

4. sin 2p
1/2
e^x
0
-v3/3

5. cos 7p/6
-v3/3
-v3/2
1
v3

6. cos p/2
-1/2
0
-v3/2
-v3

7. What is the product rule?

8. tan 5p/3
-1
-v3
a^u lna du/dx
1/u du/dx

9. sin 3p/4
v3/2
1/u du/dx
v2/2
0

10. sin 5p/4
-v2/2
1
-1/2
cosx

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

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

13. tan 2p
0
-1
1
1/(u ln a ) du/dx

14. derivative
slope of the tangent line
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
-1/(1+x^2 )

15. Deriv of f(x)=cotx is?
-sinx
-csc^2x
-v3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

16. cos 2p/3
v3
-csc^2x
1/u du/dx
-1/2

17. tan 5p/4
-sinx
1
-1/2
-v2/2

18. tan p/4
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
1/v(1-x^2 )
1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

19. Deriv of f(x)=secx is?
-1
v3/2
tanxsecx
-1/(|x| v(x^2-1))

20. tan p/2
-v3/3
undefined
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
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

21. tan 5p/6
1/u du/dx
-1/2
-v3/2
-v3/3

22. sin 5p/3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
v3/2
1/(|x| v(x^2-1))
-v3/2

23. Deriv of tan^(-1)x
0
1/(1+x^2 )
v3
1/2

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

25. cos 5p/6
0
-v3/2
-1/2
-v3/3

26. cos p/6
undefined
v3/2
v2/2
-v2/2

27. Deriv of sin^(-1)x
-v2/2
1/v(1-x^2 )
1/(|x| v(x^2-1))
-1/2

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

29. Guidelines for implicit differentiation
-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
v3/2
-1/v(1-x^2 )

30. sin 7p/6
-1/2
1/v(1-x^2 )
-v3/2
-v3/3

31. Deriv of f(x)=csc is?
-1/2
-v2/2
-cscxcotx
-1/(|x| v(x^2-1))

32. Deriv of ln u
1/u du/dx
1
slope of the tangent line
1/2

33. Deriv of sec^(-1)x
1/(|x| v(x^2-1))
sec^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
undefined

34. tan p/6
1/v(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
1
v3/3

35. What is the quotient rule?

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

37. Deriv of cot^(-1)x
-1/(1+x^2 )
-csc^2x
1
-v3/3

38. tan 3p/4
1
-1
1
-sinx

39. Deriv of a^u
-v3/2
1
a^u lna du/dx
-v3/2

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

41. sin 3p/2
1/(u ln a ) du/dx
1
-1
f(x) = (u)(v) AND f'(x) = u'v + v'u

42. Deriv of f(x)=cosx is?
0
-sinx
v3/2
-1

43. Explicit differentiation
1/2
undefined
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

44. sin p/6
0
v2/2
-cscxcotx
1/2

45. sin 4p/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3/2
-1/2
1/2

46. cos p/4
v2/2
-csc^2x
v3/2
-1/2

47. sin 5p/6
1/2
0
-v3/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

48. cos 4p/3
1
-1/2
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

49. cos 7p/4
v3/2
v2/2
-v3/2
f(x) = (u)(v) AND f'(x) = u'v + v'u

50. cos 5p/4
-v2/2
-cscxcotx
1/2
undefined