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. sin 7p/6
-1/v(1-x^2 )
-1/2
-sinx
-cscxcotx

2. Deriv of e^x
v2/2
1/v(1-x^2 )
e^x
0

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

4. cos 5p/6
undefined
-v3/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
1

5. Deriv of f(x)=sinx is?
-v2/2
0
cosx
1

6. Deriv of csc^(-1)x
-1/(|x| v(x^2-1))
-1
tanxsecx
0

7. cos 5p/3
1/u du/dx
1/2
0
v3/2

8. sin p/2
1/2
-csc^2x
sec^2x
1

9. sin 7p/4
-v2/2
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/(1+x^2 )
tanxsecx

10. Deriv of sin^(-1)x
1/v(1-x^2 )
-v3/2
0
1/(u ln a ) du/dx

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

12. Deriv of sec^(-1)x
1/(|x| v(x^2-1))
-v2/2
-v3/3
-sinx

13. tan 5p/3
-cscxcotx
-v3
-v2/2
-v3/2

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

15. What is the Chain Rule? When can it be used?
v3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
0
-csc^2x

16. Deriv of cos^(-1)x
-v2/2
-csc^2x
-v3
-1/v(1-x^2 )

17. tan 5p/6
-v3/3
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

18. cos 4p/3
1/(u ln a ) du/dx
-1/2
1/2
-v3/2

19. sin 11p/6
f(x) = (u)(v) AND f'(x) = u'v + v'u
0
-1/2
0

20. cos p/6
1
undefined
1
v3/2

21. Deriv of cot^(-1)x
-1
-v3
-1/(1+x^2 )
-v3

22. sin p
v3/2
1/u du/dx
0
-1/(1+x^2 )

23. Guidelines for implicit differentiation
-1/(1+x^2 )
v2/2
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

24. tan 3p/2
a^u lna du/dx
v3/3
undefined
sec^2x

25. Deriv of a^u
-v3/3
a^u lna 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
undefined

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

27. derivative
1/2
slope of the tangent line
-1
0

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

29. Deriv of ln u
1/u du/dx
-csc^2x
v2/2
-v3/2

30. cos 2p/3
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v2/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
-1/2

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

32. sin p/4
v3/2
-v3/2
v3
v2/2

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

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

35. When do derivatives not exist?
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
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

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

37. sin 5p/6
1/2
-1/(1+x^2 )
0
undefined

38. cos p/2
1/v(1-x^2 )
v2/2
-1/v(1-x^2 )
0

39. tan p/6
-v3/2
v3/3
tanxsecx
e^x

40. sin p/3
v3/2
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
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

41. tan 3p/4
1/2
slope of the tangent line
-v3/3
-1

42. sin 3p/2
v2/2
-1/2
-v3/3
-1

43. Explicit differentiation
tanxsecx
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
a^u lna du/dx

44. tan 4p/3
1/(|x| v(x^2-1))
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
v3

45. cos 7p/6
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
-v3/2
undefined
-1

46. What is the product rule?

47. cos 7p/4
v2/2
-1/2
-v2/2
0

48. tan p
-1/v(1-x^2 )
-v3/2
0
v3/2

49. tan p/2
1
1/2
-v2/2
undefined

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