Test your basic knowledge |

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. Deriv of f(x)=tanx is?
1/2
v3
tanxsecx
sec^2x

2. Deriv of f(x)=cotx is?
v2/2
-v2/2
1/2
-csc^2x

3. derivative
0
tanxsecx
slope of the tangent line
v2/2

4. What is the quotient rule?

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

6. cos 2p/3
v3/2
1
slope of the tangent line
-1/2

7. tan p
-v3/2
-csc^2x
0
1

8. Implicit differentiation
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-1/2

9. What is the product rule?

10. Explicit differentiation
f(x) = (u)(v) AND f'(x) = u'v + v'u
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
sec^2x
v3/2

11. cos p
-v3/2
sec^2x
-1/2
-1

12. tan 11p/6
1/u du/dx
sec^2x
-cscxcotx
-v3/3

13. Deriv of sin^(-1)x
1/(|x| v(x^2-1))
1/v(1-x^2 )
v3
undefined

14. cos 4p/3
-1/2
-v3
-v2/2
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

15. cos p/4
v2/2
v3/2
v3/2
0

16. cos 11p/6
-1/2
-v3/2
1/(|x| v(x^2-1))
v3/2

17. Guidelines for implicit differentiation
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
v3/2
-1/2

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

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

20. tan 7p/4
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-1
undefined
-1/v(1-x^2 )

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

22. cos 5p/6
-1/2
slope of the tangent line
-v3/2
v2/2

23. sin 2p
0
-v2/2
1
1/v(1-x^2 )

24. cos 3p/4
-sinx
-v2/2
-v3/2
-1/2

25. Deriv of f(x)=cosx is?
-sinx
0
sec^2x
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

26. tan p/6
v3/3
-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

27. tan 3p/2
-sinx
undefined
v3
0

28. tan 7p/6
v3
sec^2x
v3/3
-1

29. sin 3p/2
0
-v2/2
-1
-1/2

30. tan 5p/4
0
1
1/2
-1

31. tan 5p/3
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v3
-1
slope of the tangent line

32. cos p/2
0
1/(1+x^2 )
v2/2
-sinx

33. Deriv of cos^(-1)x
-1/v(1-x^2 )
1/v(1-x^2 )
-v2/2
1

34. sin p/6
1/2
-1
-1/2
v2/2

35. sin 5p/3
v2/2
v2/2
-v3/2
0

36. Deriv of a^u
1/v(1-x^2 )
-v3
a^u lna du/dx
-sinx

37. tan p/3
v3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v2/2
-sinx

38. sin 4p/3
-1
-v3/2
v3/2
1/2

39. cos 7p/6
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-csc^2x
-v3/2
v2/2

40. sin 3p/4
-sinx
1/(1+x^2 )
undefined
v2/2

41. cos 7p/4
v2/2
v3/2
-1
0

42. Deriv of e^x
e^x
-1/(|x| v(x^2-1))
-1/2
0

43. When do derivatives not exist?
1/u 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
v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

44. Deriv of tan^(-1)x
-1/v(1-x^2 )
-1
1/(1+x^2 )
undefined

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

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

47. Deriv of ln u
-1/2
v3/2
1/(u ln a ) du/dx
1/u du/dx

48. sin 11p/6
-1/2
0
v3/3
slope of the tangent line

49. sin 5p/4
-1
-v2/2
v3/2
-1

50. sin 2p/3
1/(|x| v(x^2-1))
1/2
sec^2x
v3/2