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

2. What is the quotient rule?

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3. Deriv of cos^(-1)x
sec^2x
-1/v(1-x^2 )
-v3/3
1/v(1-x^2 )

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

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5. Deriv of sec^(-1)x
e^x
-cscxcotx
1/(|x| v(x^2-1))
1

6. tan p/6
v3/3
0
-1/2
-v3/2

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

8. cos 4p/3
0
-1/2
v2/2
-v2/2

9. Explicit differentiation
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
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

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

11. Deriv of f(x)=cotx is?
-csc^2x
-v3/3
-1/v(1-x^2 )
1/(u ln a ) du/dx

12. What is the Chain Rule? When can it be used?
1/(1+x^2 )
-v3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

13. tan 7p/6
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/u du/dx
v3/3

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

15. derivative
slope of the tangent line
-1
undefined
-v3/2

16. sin p/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
0
1

17. sin 4p/3
1
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
0
-v3/2

18. sin 3p/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
-1
-1/(|x| v(x^2-1))

19. sin 3p/4
v2/2
-v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-1/v(1-x^2 )

20. cos 7p/4
v2/2
v3/2
-v3
1/(1+x^2 )

21. cos 3p/4
1/(u ln a ) du/dx
-v2/2
1/(|x| v(x^2-1))
v2/2

22. tan 5p/4
undefined
-v3
1/2
1

23. When do derivatives not exist?
-v3/3
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
v2/2
-1

24. tan p/4
v2/2
-1/2
v3/2
1

25. tan 3p/2
1/(|x| v(x^2-1))
0
undefined
0

26. cos p/4
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1
v2/2
-v2/2

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

28. sin 11p/6
-1/2
-1
a^u lna du/dx
1

29. cos p/6
v3/2
e^x
-v2/2
-1

30. Deriv of sin^(-1)x
-v3/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
1/v(1-x^2 )
slope of the tangent line

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

32. What is the product rule?

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33. tan p/2
v2/2
undefined
0
1/(u ln a ) du/dx

34. tan p/3
-1/(|x| v(x^2-1))
0
v3
1

35. sin p/4
1/u du/dx
v2/2
-v3/2
-sinx

36. Deriv of f(x)=secx is?
tanxsecx
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
-1/2
1/2

37. sin p
v2/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2
0

38. sin 5p/6
0
f(x) = (u)(v) AND f'(x) = u'v + v'u
1/2
1/v(1-x^2 )

39. cos 5p/3
1/2
-v3
-v3/2
0

40. sin 5p/4
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
-1
-v2/2

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

42. cos 2p
1
-v2/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-1

43. tan p
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
v2/2
0
v3/3

44. cos p/3
-1
1/2
-v3/3
0

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

46. sin 2p
1
slope of the tangent line
0
-1/2

47. Deriv of cot^(-1)x
1/2
0
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1/(1+x^2 )

48. cos 3p/2
undefined
0
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

49. Implicit differentiation
1
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=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
-v3/2

50. cos 11p/6
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
v2/2
v3/2