AP Calculus 2

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. When do derivatives not exist?
v3/2
0
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


2. sin p/6
1/2
-1/(|x| v(x^2-1))
-v2/2
-v3/3


3. Deriv of f(x)=secx is?
1/(u ln a ) du/dx
v2/2
tanxsecx
v2/2


4. sin p/3
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/2
1
-v2/2


5. Deriv of f(x)=cotx is?
-v3/2
-csc^2x
1/2
v3/2


6. Implicit differentiation
0
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
tanxsecx
-v2/2


7. cos 7p/6
-v3/2
-1
0
1/(|x| v(x^2-1))


8. Deriv of cos^(-1)x
-1/v(1-x^2 )
-1/2
1/u du/dx
0


9. tan 7p/4
-v3
v2/2
v3
-1


10. tan p/6
1
v3/2
1
v3/3


11. tan 3p/2
v2/2
undefined
-1/2
-v3/3


12. tan 7p/6
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
slope of the tangent line
v3/3


13. Deriv of a^u
a^u lna du/dx
1/(|x| v(x^2-1))
-1/2
-v3


14. Explicit 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
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
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


15. sin p/4
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
v2/2
v3/2
-1


16. cos p/6
-v2/2
1/2
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v3/2


17. What is the Chain Rule? When can it be used?
tanxsecx
1
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
v2/2


18. cos 7p/4
v3/2
-v2/2
v2/2
undefined


19. tan p/4
0
1
0
v2/2


20. sin 5p/3
-1
-v3/2
v3/2
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?


21. Deriv of cot^(-1)x
v3
tanxsecx
1/(u ln a ) du/dx
-1/(1+x^2 )


22. tan p
0
-cscxcotx
v3/2
-v3


23. sin 5p/6
1/2
sec^2x
v2/2
-v2/2


24. What is the Alternate definition of a derivative and what does it find?


25. sin 7p/6
f(x) = u/v AND f'(x) = vu'-uv'/v^2 (lo de hi minus hi de lo/ lo squared)
-v3/2
-1/2
-1


26. sin 7p/4
-v2/2
0
sec^2x
0


27. Deriv of sin^(-1)x
-1/2
1/v(1-x^2 )
1/(u ln a ) du/dx
v2/2


28. Deriv of f(x)=tanx is?
-v2/2
-1/(1+x^2 )
-1/v(1-x^2 )
sec^2x


29. What is the quotient rule?


30. Deriv of e^x
-v3/2
v3/2
cosx
e^x


31. cos 5p/4
1/2
-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
-v2/2


32. derivative
slope of the tangent line
f^' (x)=lim-(h?0)??(f(x+h)-f(x))/h?
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
-v2/2


33. tan 2p/3
-v3
-cscxcotx
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
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


34. cos 2p
-sinx
1/v(1-x^2 )
1
sec^2x


35. Deriv of f(x)=csc is?
-v3/2
-cscxcotx
0
0


36. cos p/4
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
f(x) = (u)(v) AND f'(x) = u'v + v'u
v2/2


37. What is the product rule?


38. tan 2p
-1/2
0
1/2
1/u du/dx


39. cos 3p/2
0
-v3/2
e^x
-1/(|x| v(x^2-1))


40. cos 5p/3
0
v3/2
1/2
1/(|x| v(x^2-1))


41. cos 2p/3
0
1/(u ln a ) du/dx
-1/2
-csc^2x


42. tan 4p/3
v3
1/2
v2/2
f(x) = (u)(v) AND f'(x) = u'v + v'u


43. Deriv of log_au=
-1
f(x) = (u)(v) AND f'(x) = u'v + v'u
1/(u ln a ) du/dx
1/2


44. tan 11p/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
-v3/2
-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


45. cos p/3
-v2/2
v2/2
-v3/3
1/2


46. Deriv of f(x)=sinx is?
-v3/2
cosx
1
1


47. tan 3p/4
-1
Deriv of Outside(Inside)*Deriv of Inside - It can be used anytime
not clear; when you can solve for y as a function of x - EX) y^3+y^2-5y-x^2=4
-1/(|x| v(x^2-1))


48. Deriv of tan^(-1)x
1/(1+x^2 )
1
1
v3/2


49. tan 5p/4
1
-v3/2
-1
-1/v(1-x^2 )


50. cos p/2
-v3/2
0
1/(|x| v(x^2-1))
v3/2