AP Calc study cards

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AP Calc study cards
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2012-08-13 21:01:55
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Calculus
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calculus
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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 

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