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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 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 )