# AP Calc study cards

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1. Area of a Triangle
2. Area of a triangle (SAS Formula)
3. Area of a trapeziod
4. Area of a circle
A=πr2
5. Curcumference of a circle
• C = 2πr
• C = πd
6. Lateral surface area of a cylinder
S = 2πrh
7. Total surface area of a cylinder
S = 2πrh + 2πr2
8. Surface of a sphere
S = 4πr2
9. Volume of a prism
• V = bh
• B = Area of base
10. Volume of a pyramid
• B = Area of Base
11. Volume of a cylinder
V = πr2h
12. Volume of a cone
πr2h
13. Volume of a sphere
V = 4/3πr2
14. Double angle identity for cos2x
1/2 (1+cos2x)
15. Double angle identity for sin2x
1/2 (1-cos2x)
16. sin(π/2 -x)
cosx
17. tan(
18. tan (π/2 - x)
cotx
19. sec (π/2 - x)
cscx
20. cos2x + sin2x
1
21. 1 + cot2x
csc2x
22. 1 + tan2x
sec2x
23. 1/ sinX
cscX
24. 1 / cosX
secX
25. 1 / tanX
cotX
26. sinx / cosx
tanx
27. cosx / sinx
cotx
28. sin2x
2sinXcosX
29. cos2x (in terms of cosX and sinX)
cos2x - sin2x
30. cos2X (in terms of cosX)
2cos2X-1
31. cos2X (in terms of sinX)
1 - 2sin2X
32. sin(-x)
-sinx
33. cos(-x)
cosx
34. tan(-x)
-tanx
35. law of sines
a / sinA = b / sinB = c / sinC
36. Law of cosines
a= b2 + c2 -2bccosA
37. logab = c
ac = b
38. log ( AB )
log A + log B
39. log ( A / B )
log A - log B
40. log Ax
x log A
41. ln e
1
42. ln 1
0
43. eln x
x
44. Pythagorean Theorem
a2 + b2 = c2
45. Distance between points ( x1, y) and ( x2, y2 )
46. Slope of the line between points ( x1, y) and ( x2, y2 )
47. Point-Slope equation of a line
y - y1 = m( x -x1 )
48. slope intercept equation of a line
y = mx + b
49. standard form of the equation of a line
Ax + Bx = C
50. Circle with center at point (h, k) and raduis r
( x - h )2 + ( y - k )2 = r2
51. ellipse
Ax2 + By2 = C
52. Hyperbola
Ax2 - By2 = C
53. Hyperbola with axes as asymptotes
xy = k
54. Parabola (vertical axis of symmetry)
y = ax2 + bx + c
55. Parabola (horizontal axis of symmetry)
x = ay2 + by + c
56. Domain of a function
the set of all possible values of x for a functions
57. Range of a function
the set of all possible values of y for a function
58. function symmetric across the y-axis
f(-x) = f(x)
59. Even functions
f(-x) = -f(x)
60. function symmetric through the origin
f(-x) = -f(x)
61. Odd Function
f(-x) = -f(x)
62. Quadratic formula (roots of y = ax2 +bx +c)
63. Inverse of a function
( f o f--1)(x) =  x
64. To graph the inverse of a function...
reflect the graph of the function across the line y = x
65. To find the equation of the inverse of a function
interchange x and y, then solve the equation for y
66. If point ( a,b ) lies on the inverse function f-1 then...
point ( b,a ) lies on function f
67. Inverse of y = ex
y = ln x
68. Inverse of y = lnx
y = ex
69. Line parallel to y = mx + b through point ( x1,y1 )
• y - y1 = m ( x-x1 )
• or
• y = mx + b1, where b1 = (y1-mx1)
70. Line perpendicular to y = mx + b through point ( x1,y1 )
or where
 Author: Anonymous ID: 165940 Card Set: AP Calc study cards Updated: 2012-08-14 01:01:55 Tags: Calculus Folders: Description: calculus Show Answers: