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 cos^(-1)x
-1/v(1-x^2 )
-1
-1/2
-v3/2

2. sin 11p/6
v2/2
-1/2
1/2
0

3. Explicit differentiation
-v3
cosx
-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

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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

5. sin 5p/4
-v2/2
1/(|x| v(x^2-1))
-v3/3
-v3/2

6. sin p/6
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
1/u du/dx
1/2
-1/(1+x^2 )

7. tan 5p/3
1/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-v3
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

8. Deriv of f(x)=csc is?
-csc^2x
-cscxcotx
v3/2
-1/2

9. cos p/3
-v2/2
0
1/2
-1/2

10. Deriv of f(x)=sinx is?
v2/2
-1
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
cosx

11. cos p/2
v3/2
0
-1/(1+x^2 )
v2/2

12. Deriv of sin^(-1)x
v2/2
-v2/2
a^u lna du/dx
1/v(1-x^2 )

13. Deriv of f(x)=secx is?
-v2/2
-v3
tanxsecx
-v3/2

14. tan 5p/4
-1/2
-1
-1/(|x| v(x^2-1))
1

15. When do derivatives not exist?
slope of the tangent line
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
v2/2

16. cos 5p/4
-sinx
v2/2
-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

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

18. cos p/4
1
v2/2
1/2
-v2/2

19. Deriv of f(x)=cosx is?
cosx
v3/2
-sinx
a^u lna du/dx

20. cos 7p/6
undefined
-v3/2
v3
-v2/2

21. sin p/3
1
1/2
0
v3/2

22. Deriv of ln u
e^x
1/u du/dx
-v3/2
-1/2

23. cos 3p/2
0
undefined
-1/(1+x^2 )
cosx

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

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

26. tan 4p/3
v3/3
v3
-1/(|x| v(x^2-1))
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4

27. sin p/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
sec^2x
1
0

28. Guidelines for implicit differentiation
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
-v3
tanxsecx

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

30. Deriv of cot^(-1)x
-v3/3
tanxsecx
v2/2
-1/(1+x^2 )

31. tan 7p/4
0
-1
1
v2/2

32. tan 3p/4
-1
-1/2
1/(u ln a ) du/dx
v2/2

33. cos 5p/3
-1/2
1/(|x| v(x^2-1))
1/2
-v3/3

34. tan 2p/3
-v2/2
v3/3
-v3
slope of the tangent line

35. Deriv of f(x)=cotx is?
-csc^2x
0
v3/3
-v2/2

36. tan 7p/6
-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
v3/3
1/2

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

38. sin 7p/4
a^u lna du/dx
-v2/2
tanxsecx
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

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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

40. Deriv of log_au=
-v3/2
1/(u ln a ) du/dx
1/(1+x^2 )
v3/2

41. tan 2p
0
1/(1+x^2 )
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
-v3

42. tan 3p/2
-v3/2
-sinx
1/(1+x^2 )
undefined

43. What is the product rule?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

44. sin 4p/3
-v2/2
0
-v3/2
0

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

46. sin 2p
0
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v2/2
1/u du/dx

47. sin p
e^x
0
v3
-csc^2x

48. sin 3p/4
1
v3/3
a^u lna du/dx
v2/2

49. cos p/6
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
0

50. tan p/4
-1
1/v(1-x^2 )
1
-v2/2