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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 5p/3
1/2
-1
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
2. cos 7p/4
v3/2
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
-1/2
v2/2
3. cos 3p/2
tanxsecx
-1/(|x| v(x^2-1))
0
1/2
4. cos 11p/6
v3/3
-1/(1+x^2 )
v3/2
v2/2
5. sin 5p/6
-1
-1
1/2
-csc^2x
6. What is the quotient rule?
7. sin p/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
slope of the tangent line
v3/2
0
8. Deriv of f(x)=csc is?
-cscxcotx
cosx
v2/2
0
9. What is the product rule?
10. tan 11p/6
-1/(1+x^2 )
-v2/2
-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
11. cos 2p
0
v3/2
0
1
12. tan 2p/3
-v3
-1
-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
13. sin p/4
0
v2/2
-v2/2
1/2
14. Deriv of f(x)=tanx is?
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
sec^2x
1
-1/(1+x^2 )
15. cos 3p/4
-1
-v2/2
-1
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
16. Deriv of cos^(-1)x
-1/v(1-x^2 )
0
v3
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. Explicit differentiation
-1/2
1/(u ln a ) du/dx
0
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
18. tan 5p/4
undefined
v3/2
1
-sinx
19. Deriv of tan^(-1)x
-v2/2
-1/2
0
1/(1+x^2 )
20. tan 5p/6
1/2
-1/(1+x^2 )
-v3/3
sec^2x
21. tan 7p/4
-1/2
-1/2
-1
-v3
22. sin 3p/2
-csc^2x
1/2
-1
v2/2
23. sin 5p/4
-v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-1/2
-1/(1+x^2 )
24. Deriv of a^u
-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
a^u lna du/dx
25. sin p/6
1/(1+x^2 )
-v3/2
1/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
26. Deriv of sec^(-1)x
-cscxcotx
1/2
1
1/(|x| v(x^2-1))
27. cos 4p/3
-1/2
-v3/3
-1
v2/2
28. Deriv of csc^(-1)x
-1
1/(1+x^2 )
-1/(|x| v(x^2-1))
-1/2
29. tan 3p/2
a^u lna du/dx
undefined
-sinx
-v2/2
30. sin p
-v3/3
tanxsecx
1/v(1-x^2 )
0
31. When do derivatives not exist?
-v2/2
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)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
32. Deriv of f(x)=cotx is?
-1/(1+x^2 )
-csc^2x
-1
-1/2
33. sin 3p/4
tanxsecx
undefined
-v3
v2/2
34. cos p/2
sec^2x
-v3/2
0
-v2/2
35. sin 11p/6
-v2/2
tanxsecx
v2/2
-1/2
36. What is the Alternate definition of a derivative and what does it find?
37. cos p/6
1/2
-1
v3/2
-1
38. Deriv of log_au=
1/(u ln a ) du/dx
-v3/2
-v3/3
-v2/2
39. sin 4p/3
1/2
-v3/2
1/(1+x^2 )
sec^2x
40. sin 2p
1/(u ln a ) du/dx
1/2
0
tanxsecx
41. Deriv of cot^(-1)x
-1/(1+x^2 )
tanxsecx
-1/2
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
42. sin p/2
-v3/2
1
slope of the tangent line
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
43. cos 5p/4
-v3/2
-v2/2
-v3
-csc^2x
44. Deriv of f(x)=cosx is?
1
-v3
-sinx
0
45. tan p/2
slope of the tangent line
v2/2
-v2/2
undefined
46. tan 5p/3
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
-v3
v2/2
47. cos p/4
v2/2
-v2/2
0
0
48. tan 4p/3
0
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3
-v2/2
49. tan p
-v3/3
v2/2
0
-1
50. tan p/3
1/2
-v2/2
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
v3