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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 reenforces your understanding as you take the test each time.
1. tan p/3
v2/2
v3
sinx
v3/2
2. what is the the limit definition of a derivative and what does it find?
3. Deriv of f(x)=secx is?
1
1
tanxsecx
1/u du/dx
4. sin 2p
0
v2/2
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2
5. tan 4p/3
csc^2x
1
v3
0
6. derivative
v3/2
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^25
slope of the tangent line
7. tan 11p/6
v3/3
v3/3
1/(x v(x^21))
a^u lna du/dx
8. tan 5p/6
sinx
v3/3
v2/2
tanxsecx
9. sin 5p/4
1/2
1/(x v(x^21))
v2/2
v3/3
10. cos 3p/4
1/2
v2/2
v3
1
11. sin p/3
Deriv of Outside(Inside)*Deriv of Inside  It can be used anytime
v3/3
v3/2
v2/2
12. Explicit differentiation
1/2
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^25
v3
13. When do derivatives not exist?
v3/2
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
1
14. Deriv of log_au=
0
1/(u ln a ) du/dx
1/2
v2/2
15. What is the Chain Rule? When can it be used?
1/(u ln a ) du/dx
e^x
0
Deriv of Outside(Inside)*Deriv of Inside  It can be used anytime
16. Deriv of ln u
v3
1/u du/dx
sinx
Deriv of Outside(Inside)*Deriv of Inside  It can be used anytime
17. sin 2p/3
Deriv of Outside(Inside)*Deriv of Inside  It can be used anytime
1/2
v3/2
v3
18. tan 5p/3
not clear; when you can solve for y as a function of x  EX) y^3+y^25yx^2=4
1/(x v(x^21))
v3/2
v3
19. Implicit differentiation
1/2
v2/2
v3/3
not clear; when you can solve for y as a function of x  EX) y^3+y^25yx^2=4
20. tan p/4
v3/2
Deriv of Outside(Inside)*Deriv of Inside  It can be used anytime
1
undefined
21. Deriv of f(x)=sinx is?
1/(x v(x^21))
v3/3
1/(1+x^2 )
cosx
22. Deriv of a^u
a^u lna du/dx
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^25
f^' (a)=lim(x?a)??(f(x)f(a))/(xa)?  It is finding the slope of the tangent line at a particular xvalue
1/2
23. Deriv of f(x)=cotx is?
cosx
1/2
csc^2x
v3/3
24. sin p/6
1/(u ln a ) du/dx
1/(x v(x^21))
sec^2x
1/2
25. cos 7p/6
1
v2/2
v3/2
1/2
26. cos 2p
f(x) = (u)(v) AND f'(x) = u'v + v'u
1
v3/3
v3/2
27. cos 2p/3
0
cosx
1/2
1/(1+x^2 )
28. Deriv of e^x
0
1/2
f^' (a)=lim(x?a)??(f(x)f(a))/(xa)?  It is finding the slope of the tangent line at a particular xvalue
e^x
29. tan 5p/4
csc^2x
1/u du/dx
v3/2
1
30. tan 2p/3
1/(x v(x^21))
v3
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^25
v3
31. tan p/6
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
v3/3
v3/2
32. Deriv of sec^(1)x
1/(x v(x^21))
v3
1/2
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
33. What is the quotient rule?
34. cos 3p/2
v3/3
sinx
0
1
35. Deriv of cos^(1)x
1/v(1x^2 )
1
1/2
v2/2
36. cos p/6
e^x
f^' (a)=lim(x?a)??(f(x)f(a))/(xa)?  It is finding the slope of the tangent line at a particular xvalue
v3/2
v3/2
37. sin 3p/2
v2/2
1
f^' (a)=lim(x?a)??(f(x)f(a))/(xa)?  It is finding the slope of the tangent line at a particular xvalue
f(x) = u/v AND f'(x) = vu'uv'/v^2 (lo de hi minus hi de lo/ lo squared)
38. cos 5p/6
v2/2
1/(1+x^2 )
v3/2
tanxsecx
39. Deriv of cot^(1)x
0
v3/2
e^x
1/(1+x^2 )
40. sin p
1/2
e^x
v2/2
0
41. Deriv of sin^(1)x
0
1
v3/2
1/v(1x^2 )
42. cos p/3
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
e^x
43. tan p/2
sinx
1/v(1x^2 )
undefined
1/(x v(x^21))
44. tan 3p/2
undefined
0
sinx
cscxcotx
45. Deriv of tan^(1)x
v2/2
1/(1+x^2 )
1/(x v(x^21))
v3/3
46. sin 7p/4
v2/2
cscxcotx
v3/2
v3
47. What is the product rule?
48. sin 3p/4
v3/3
sinx
1
v2/2
49. cos 5p/3
undefined
v2/2
v2/2
1/2
50. cos p
v2/2
1
v3
f(x) = (u)(v) AND f'(x) = u'v + v'u