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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. 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?
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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?
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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?
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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