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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 p/2
0
-cscxcotx
1
-v3/2

2. tan p/6
v3/3
-sinx
v3
-v2/2

3. tan 5p/4
v3/3
1
1/v(1-x^2 )
-v2/2

4. Implicit differentiation
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v2/2
0
-v3

5. tan 5p/6
-v3/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
-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

6. sin p
v3
-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
0

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

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

9. Deriv of log_au=
v3/2
0
-csc^2x
1/(u ln a ) du/dx

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

11. cos 11p/6
v3/3
v3/2
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
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?

12. tan 7p/4
0
-1
-v2/2
slope of the tangent line

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

14. Deriv of cot^(-1)x
-1/(1+x^2 )
1/u du/dx
1/2
-1/(|x| v(x^2-1))

15. What is the product rule?

16. 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
undefined
-1/(|x| v(x^2-1))
slope of the tangent line

17. sin 3p/2
undefined
-1
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
-v2/2

18. sin 7p/4
sec^2x
-v2/2
0
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

19. sin 2p
-1
0
-1
-v3/2

20. cos 3p/4
f(x) = (u)(v) AND f'(x) = u'v + v'u
-1/2
-1
-v2/2

21. cos p
1/2
-1
v3/2
1/2

22. Deriv of f(x)=sinx is?
0
0
cosx
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

23. Deriv of f(x)=tanx is?
-csc^2x
1/2
sec^2x
1/2

24. cos 7p/4
v2/2
0
undefined
cosx

25. cos 2p
1
-csc^2x
undefined
tanxsecx

26. tan 2p
v3/3
0
v3/2
-v2/2

27. sin 3p/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/u du/dx
v2/2
v3/3

28. tan 7p/6
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-sinx
v3/3
1/2

29. 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
1
-sinx
0

30. Deriv of cos^(-1)x
-1/v(1-x^2 )
-1
-v3/2
0

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

32. cos 4p/3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
v2/2
v2/2
-1/2

33. sin 5p/3
-v3/2
cosx
-csc^2x
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

34. When do derivatives not exist?
-1/(1+x^2 )
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
-cscxcotx

35. Explicit differentiation
-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
0

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

37. Deriv of f(x)=csc is?
-cscxcotx
-1
v3/2
-1/2

38. What is the quotient rule?

39. tan 2p/3
-1
v2/2
-v3
-1/(1+x^2 )

40. Deriv of ln u
1/2
1/u du/dx
1/2
undefined

41. tan p/2
0
-v3/2
v3/2
undefined

42. Deriv of a^u
1/(|x| v(x^2-1))
a^u lna du/dx
-cscxcotx
-v3/2

43. Deriv of tan^(-1)x
-sinx
1
1/(1+x^2 )
-1/2

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

45. cos p/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
v3/2
-v2/2
undefined

46. Deriv of sec^(-1)x
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
slope of the tangent line
1/(|x| v(x^2-1))
1/2

47. tan 11p/6
-v3/3
1
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
-cscxcotx

48. sin p/6
-1
1/2
-1
-v3

49. tan 5p/3
-v3
1/2
-sinx
v3/2

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