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

2. cos 11p/6
-v2/2
v3/2
1/2
undefined

3. sin 3p/4
-1/2
-cscxcotx
-v3
v2/2

4. tan p/6
0
-v3/2
1
v3/3

5. tan 11p/6
0
-v3
-cscxcotx
-v3/3

6. tan 7p/4
tanxsecx
0
-v2/2
-1

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

8. sin 2p/3
a^u lna du/dx
f(x) = (u)(v) AND f'(x) = u'v + v'u
-1/v(1-x^2 )
v3/2

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

10. cos 7p/4
-1/(|x| v(x^2-1))
v3/2
v2/2
0

11. sin 3p/2
0
-v3/2
-1
v2/2

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

13. tan p/4
v2/2
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
1

14. sin p/3
undefined
-1/(|x| v(x^2-1))
v3/2
1

15. Deriv of sin^(-1)x
-1
1/v(1-x^2 )
1
-v3/2

16. sin 11p/6
-1/2
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-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

17. cos 5p/4
-sinx
v3/2
-v2/2
v3/2

18. cos p/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
0
cosx

19. sin 7p/4
-1/2
1
v3
-v2/2

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

21. Explicit differentiation
-cscxcotx
v2/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
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

22. sin p/2
1/(u ln a ) 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
1
-v3/2

23. Deriv of csc^(-1)x
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/(1+x^2 )
-v3
-1/(|x| v(x^2-1))

24. tan 4p/3
v3
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
e^x
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

25. sin p
-1/2
-1/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
0

26. Deriv of ln u
v2/2
1/u du/dx
-csc^2x
-v3/3

27. derivative
slope of the tangent line
v3/3
v3
-v2/2

28. Guidelines for implicit differentiation
1/u du/dx
-v3/3
-1/(|x| v(x^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

29. tan 5p/3
0
-v3
v2/2
cosx

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

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

32. sin 7p/6
-1/2
e^x
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
0

33. cos 5p/3
1
0
-v3
1/2

34. Implicit differentiation
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
v3/3
-v2/2
0

35. Deriv of sec^(-1)x
cosx
undefined
-v2/2
1/(|x| v(x^2-1))

36. tan 5p/6
v3/2
0
-v3/3
-v3/2

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

38. cos p/4
-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
-v3/2

39. Deriv of f(x)=sinx is?
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
cosx

40. cos 3p/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
-v2/2
-1
v2/2

41. Deriv of f(x)=tanx is?
1
sec^2x
-v2/2
1/2

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

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

44. sin 2p
0
1/(1+x^2 )
v3/2
-1/(|x| v(x^2-1))

45. sin 4p/3
-v2/2
-v3/2
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
-v3

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

47. cos p/3
-csc^2x
1/2
a^u lna du/dx
-v3/3

48. Deriv of f(x)=csc is?
-cscxcotx
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
1/(u ln a ) du/dx

49. tan 2p/3
-v3
-csc^2x
-v2/2
v2/2

50. tan 7p/6
-1/2
v3/3
1/2
-1/(1+x^2 )