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