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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/6
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
1/u du/dx
a^u lna du/dx
-v3/2

2. cos 5p/3
f(x) = (u)(v) AND f'(x) = u'v + v'u
1/2
v3
0

3. tan 5p/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
0
1/(1+x^2 )
1

4. cos p/6
0
v3/2
undefined
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

5. Deriv of f(x)=cotx is?
-1
-1
undefined
-csc^2x

6. When do derivatives not exist?
f(x) = (u)(v) AND f'(x) = u'v + v'u
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

7. tan 5p/6
-v3/2
-1
-v2/2
-v3/3

8. sin 7p/6
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v2/2
-1/v(1-x^2 )
-1/2

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

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10. cos p/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1
0
-sinx

11. cos 2p
1
-1/2
-cscxcotx
cosx

12. Deriv of csc^(-1)x
-1/(|x| v(x^2-1))
v3
undefined
0

13. tan p/2
-v2/2
undefined
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

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

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

16. tan 2p/3
-cscxcotx
-1/v(1-x^2 )
-v3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

17. cos 7p/4
v2/2
-v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1

18. Deriv of e^x
0
1
e^x
v3/2

19. sin 7p/4
-v2/2
1/(1+x^2 )
v3/2
-v3

20. Deriv of a^u
a^u lna du/dx
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
v3/3
-v2/2

21. tan 7p/4
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-1
-1/2
1/(u ln a ) du/dx

22. sin p/6
v2/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-cscxcotx
1/2

23. sin 5p/3
1/2
undefined
-1
-v3/2

24. Deriv of f(x)=csc is?
v2/2
-sinx
-v3
-cscxcotx

25. Deriv of cot^(-1)x
tanxsecx
sec^2x
1/(|x| v(x^2-1))
-1/(1+x^2 )

26. sin 5p/6
0
1/2
1/(|x| v(x^2-1))
1/v(1-x^2 )

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

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

29. cos 3p/4
sec^2x
v2/2
-v2/2
-1/2

30. derivative
0
sec^2x
-1/2
slope of the tangent line

31. sin p/2
1
v3/3
v3
-csc^2x

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

33. cos 7p/6
-v3
-v3/2
cosx
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

34. sin 11p/6
-1/2
v3/3
-1
-1

35. tan p/4
v2/2
1
1/u du/dx
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

36. What is the product rule?

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37. Deriv of f(x)=cosx is?
-sinx
1/u du/dx
-1/2
-v3

38. tan 7p/6
v3/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v2/2
v3/2

39. Deriv of tan^(-1)x
e^x
-csc^2x
0
1/(1+x^2 )

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

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41. tan 2p
-v3/2
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
1/2

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

43. cos 4p/3
1/2
-v3/2
-1/2
-v3/3

44. tan p
sec^2x
0
undefined
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

45. sin p/4
-sinx
v2/2
-v3/2
v3

46. cos 5p/4
-v2/2
0
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

47. Deriv of sec^(-1)x
v3
0
-1/(1+x^2 )
1/(|x| v(x^2-1))

48. cos 11p/6
v3/2
-v3/2
1/2
cosx

49. cos 3p/2
0
-v3/2
-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

50. Deriv of f(x)=secx is?
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
1/u du/dx
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