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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/2
-v3
undefined
v3/2
-v2/2

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

3. sin 5p/4
-v3
-1/2
-v2/2
e^x

4. Deriv of e^x
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
e^x
1/(1+x^2 )
-v3/2

5. Explicit differentiation
-v3/3
-v2/2
v2/2
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

6. cos p
1/u du/dx
-1/2
-1/2
-1

7. sin 7p/4
-v2/2
-v3/2
v3/2
undefined

8. What is the Chain Rule? When can it be used?
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v2/2
0
-v2/2

9. tan p/4
undefined
-v3/3
e^x
1

10. Deriv of ln u
1/u du/dx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v2/2
-1/2

11. sin 4p/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
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3

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

13. sin p
-1
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-csc^2x
0

14. tan 7p/6
v3/3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v2/2

15. tan 7p/4
v2/2
v3/2
-1
-1/(1+x^2 )

16. Deriv of cot^(-1)x
-1/(1+x^2 )
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
1
1/(u ln a ) du/dx

17. Deriv of f(x)=secx is?
-1
1/2
tanxsecx
-v2/2

18. cos p/2
-v2/2
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
0
-1/2

19. tan 4p/3
v3
1/u du/dx
-v3
-v2/2

20. When do derivatives not exist?
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
-v2/2
v3

21. Deriv of tan^(-1)x
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
sec^2x
1/2
1/(1+x^2 )

22. cos 2p
1
-v2/2
-sinx
1/2

23. cos p/4
v3/2
0
-v3/2
v2/2

24. derivative
v3/2
-v2/2
slope of the tangent line
v2/2

25. tan 5p/6
-v3/2
-v3/3
-sinx
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

26. sin 7p/6
-1/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-1

27. cos 5p/4
undefined
0
-v2/2
-v3

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

29. sin p/2
-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

30. sin p/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
-cscxcotx
undefined
v2/2

31. What is the quotient rule?

32. What is the product rule?

33. tan 2p/3
-v3
-1/(1+x^2 )
1/2
1/v(1-x^2 )

34. cos 5p/6
-v3/2
1/u du/dx
-1/v(1-x^2 )
cosx

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

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

37. tan 3p/4
-1
-sinx
0
1/2

38. 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
v3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1/(|x| v(x^2-1))

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

40. cos 7p/4
-1
-1
v3
v2/2

41. tan p
a^u lna du/dx
-1/(|x| v(x^2-1))
0
undefined

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

43. sin 2p/3
1/(1+x^2 )
v3/2
-v2/2
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

44. Deriv of log_au=
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
1/(u ln a ) du/dx
1/2

45. Deriv of a^u
1/(|x| v(x^2-1))
a^u lna du/dx
undefined
slope of the tangent line

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

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

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

49. Guidelines for implicit differentiation
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
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-1

50. tan 5p/4
-v2/2
1
0
cosx