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Test your basic knowledge |
AP Calculus 2
Start Test
Study First
Subjects
:
math
,
ap
,
calculus
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 p/6
-1/2
-1/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v3/2
2. tan 5p/4
-v3/3
v3/2
1
v2/2
3. Deriv of ln u
1/u du/dx
1
slope of the tangent line
-1/v(1-x^2 )
4. tan p/3
v3/3
-v3/2
v3
-1
5. Deriv of csc^(-1)x
1/(1+x^2 )
-1/(1+x^2 )
-v2/2
-1/(|x| v(x^2-1))
6. tan 2p/3
1/2
-v2/2
v3
-v3
7. Deriv of f(x)=cosx is?
-1/(|x| v(x^2-1))
-v3/2
-sinx
1/v(1-x^2 )
8. Deriv of f(x)=tanx is?
1/v(1-x^2 )
v3/2
-sinx
sec^2x
9. cos p/3
1/(1+x^2 )
-v2/2
1/2
-1/2
10. cos p
-1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-1/2
-v3
11. When do derivatives not exist?
-v3/3
v3
e^x
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
12. tan 3p/4
-1
v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
-v2/2
13. cos 2p
1
-1
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
14. What is the Chain Rule? When can it be used?
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
1
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
undefined
15. tan p/2
v3/2
slope of the tangent line
-1/2
undefined
16. Explicit differentiation
v3/2
1/v(1-x^2 )
v3/3
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
17. Deriv of a^u
-v3/2
a^u lna du/dx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-1/2
18. cos p/4
1
v2/2
-1
-cscxcotx
19. sin 5p/3
1
-v3/2
0
e^x
20. Deriv of f(x)=cotx is?
-1/v(1-x^2 )
0
-csc^2x
1
21. Deriv of tan^(-1)x
v3/2
1/(1+x^2 )
tanxsecx
0
22. sin 2p/3
undefined
v3/2
0
1/2
23. sin 5p/6
1/2
-v3/2
1
-1/2
24. What is the product rule?
25. sin p/2
v2/2
1
-v3/2
-1
26. Deriv of sin^(-1)x
-1
-1/(1+x^2 )
1/v(1-x^2 )
v3/3
27. tan 5p/3
-v2/2
-v3
f(x) = (u)(v) AND f'(x) = u'v + v'u
0
28. tan p/4
v3
tanxsecx
1
-1
29. sin 3p/2
-v3/3
undefined
1/(|x| v(x^2-1))
-1
30. Deriv of sec^(-1)x
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
f(x) = (u)(v) AND f'(x) = u'v + v'u
-1/2
31. Deriv of log_au=
1/(1+x^2 )
cosx
-csc^2x
1/(u ln a ) du/dx
32. tan p
1
-v3
-1
0
33. sin 2p
v3/2
0
f(x) = (u)(v) AND f'(x) = u'v + v'u
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
34. Deriv of f(x)=sinx is?
v2/2
1/v(1-x^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
cosx
35. Deriv of f(x)=csc is?
-cscxcotx
-v2/2
-v3/2
-1
36. tan 3p/2
-v2/2
0
v3/3
undefined
37. sin p/6
-1/v(1-x^2 )
undefined
1/2
-v3
38. sin p/4
1/2
-csc^2x
0
v2/2
39. Deriv of cos^(-1)x
-v3/2
cosx
a^u lna du/dx
-1/v(1-x^2 )
40. cos 7p/4
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
0
undefined
v2/2
41. cos 5p/3
1/2
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
sec^2x
0
42. sin 7p/6
-1/2
-v3/2
cosx
a^u lna du/dx
43. cos 3p/2
1
-v3/2
0
e^x
44. cos 3p/4
1/v(1-x^2 )
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-v2/2
-1/2
45. Guidelines for implicit differentiation
0
v3/2
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
46. what is the the limit definition of a derivative and what does it find?
47. What is the Alternate definition of a derivative and what does it find?
48. sin 3p/4
v2/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
-v3/2
1/(u ln a ) du/dx
49. Implicit differentiation
-1
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-v3/2
v3/3
50. tan 5p/6
v3
1/2
-v3/3
-1/2