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. cos 5p/3
1/2
-1
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime

2. cos 7p/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
-1/2
v2/2

3. cos 3p/2
tanxsecx
-1/(|x| v(x^2-1))
0
1/2

4. cos 11p/6
v3/3
-1/(1+x^2 )
v3/2
v2/2

5. sin 5p/6
-1
-1
1/2
-csc^2x

6. What is the quotient rule?

7. sin p/3
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
slope of the tangent line
v3/2
0

8. Deriv of f(x)=csc is?
-cscxcotx
cosx
v2/2
0

9. What is the product rule?

10. tan 11p/6
-1/(1+x^2 )
-v2/2
-v3/3
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

11. cos 2p
0
v3/2
0
1

12. tan 2p/3
-v3
-1
-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

13. sin p/4
0
v2/2
-v2/2
1/2

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

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

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

17. Explicit differentiation
-1/2
1/(u ln a ) du/dx
0
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

18. tan 5p/4
undefined
v3/2
1
-sinx

19. Deriv of tan^(-1)x
-v2/2
-1/2
0
1/(1+x^2 )

20. tan 5p/6
1/2
-1/(1+x^2 )
-v3/3
sec^2x

21. tan 7p/4
-1/2
-1/2
-1
-v3

22. sin 3p/2
-csc^2x
1/2
-1
v2/2

23. sin 5p/4
-v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1/2
-1/(1+x^2 )

24. Deriv of a^u
-1/v(1-x^2 )
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v3/2
a^u lna du/dx

25. sin p/6
1/(1+x^2 )
-v3/2
1/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

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

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

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

29. tan 3p/2
a^u lna du/dx
undefined
-sinx
-v2/2

30. sin p
-v3/3
tanxsecx
1/v(1-x^2 )
0

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

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

33. sin 3p/4
tanxsecx
undefined
-v3
v2/2

34. cos p/2
sec^2x
-v3/2
0
-v2/2

35. sin 11p/6
-v2/2
tanxsecx
v2/2
-1/2

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

37. cos p/6
1/2
-1
v3/2
-1

38. Deriv of log_au=
1/(u ln a ) du/dx
-v3/2
-v3/3
-v2/2

39. sin 4p/3
1/2
-v3/2
1/(1+x^2 )
sec^2x

40. sin 2p
1/(u ln a ) du/dx
1/2
0
tanxsecx

41. Deriv of cot^(-1)x
-1/(1+x^2 )
tanxsecx
-1/2
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

42. sin p/2
-v3/2
1
slope of the tangent line
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)

43. cos 5p/4
-v3/2
-v2/2
-v3
-csc^2x

44. Deriv of f(x)=cosx is?
1
-v3
-sinx
0

45. tan p/2
slope of the tangent line
v2/2
-v2/2
undefined

46. tan 5p/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
1
-v3
v2/2

47. cos p/4
v2/2
-v2/2
0
0

48. tan 4p/3
0
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3
-v2/2

49. tan p
-v3/3
v2/2
0
-1

50. tan p/3
1/2
-v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v3