Accelerated Integrated Algebra I by 3072Qn5

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									Accelerated Integrated Algebra I                                            Name _________________________
Final Exam Review – Fall 2010

Answer each problem completely on a separate sheet (or sheets) of paper in an organized way.

  1.   Determine the equation of the line through the                                      2
                                                                   25. Graph y                 3 . State the domain and
       points (4, 7) and (2, 10).                                                     x 1
  2.   Compare the rate of change of a linear function,                range.
       quadratic function and cubic function.                      26. Determine the asymptotes of the graph of
  3.   Graph y   x  5 .                                                    1
                                                                       y          7.
                                                                           2x  6
  4.   State the domain and range of y  x  8  3 .
                                                                                  x 2  26x  48 3x  12
  5.   State the domain and range of y  x 2  6x  5 .            27. Simplify:                           .
                                                                                   x 2  6x  8 x 2  4
  6.   State the domain and range of y = 3x + 2.                                  x 3  5x 2  6x   8x 3
  7.   Factor completely: 100x 2  25y 2 .                         28. Simplify:                        .
                                                                                       2x  4       x 3
  8.   Factor completely: 2x 2  26x  72 .                                      3      x 1
                                                                   29. Add:                  .
  9.   Factor completely: x 3  3x 2y  3xy 2  y 3 .                         x 2 x 2
  10. Find the zeros: f (x )  x 2  2x  15 .                                            6              x
                                                                   30. Subtract:                              .
  11. Find the zeros: f (x )  2x 2  11x  21 .                                   x 2  5x  50 x 2  9x  20
  12. Use the Quadratic Formula to solve                           31. Convert to vertex form: y  x 2  10x  3 .
      3x 2  9x  7  0 .                                          32. Find the axis of symmetry: y  x 2  11x  18 .
  13. Express as a complex number in standard form:                33. Find the x- and y-intercepts: y  3x 2  x  10 .
        81  2 .                                                  34. Determine the solution to f(x) = g(x).
  14. Express as a complex number in standard form:
      (2  7i )(5  4i ) .
  15. Express as a complex number in standard form:
       1  3i
              .
      8  7i
  16. Express as a complex number in standard form:
      (5  100)  (3  6i ) .
                    1
  17. Graph g (x )  x  4  2 . Explain the
                    3
      transformations represented by this function.
  18. Graph y  x 2  9 . Discuss the end behavior of
      the graph.                                                   35. Solve f(x) = g(x) if f(x) = 3x - 2 and g(x) = x2.
                                                                                           2
  19. Sketch the graph of a function with the                      36. Solve:   x    9   10  14 .
      following end behavior:                                      37. Solve: x 2  9x  22 .
      As x  ,f (x )  . As x  ,f (x )  .                             1
                                                                   38. Solve:     3x  1  2 .
  20. Determine whether the function is odd, even or                          4
      neither: y  x 3  1 .
                                                                                     3  5 
                                                                                                2
                                                                   39. Simplify:                    .
  21. Determine whether the function is odd, even or
                                                                                   3
      neither:                                                     40. Simplify:     .
                                                                                   8
                                                                                   4
                                                                   41. Simplify:       .
                                                                                 1 7
                                                                   42. The maximum walking speed S (in feet per
                                                                       second) of an animal is given by the function
                                                                       S  32L where L is the length of the animal’s
                                                                       legs (in feet). How fast can an animal whose legs
                                                                       are 18 inches long walk?
  22. Explain two ways to tell that a function is odd.             43. Write a rule for a radical function with domain
  23. Divide:  4x 2  8x  9   2x  1  .                           x  3 and range y  1 .
                                                                                        x 7
  24. Divide:   16x   2
                            49    4x  7  .                   44. Simplify:
                                                                                     x  16x  63
                                                                                       2
                                                                                                  .
45. Determine the asymptotes of the graph of              63. Find the equation of the line parallel to
        2x  9                                                y = 2x – 9 that passes through the point (1, 4).
    y 
         x 5                                             64. Joe’s cell phone plan costs $45 per month and
                                                              includes 750 free anytime minutes. There is a
46. Represent the area of the rectangle as a                  $0.49 per minute charge for every additional
    polynomial expression.                                    minute. Write an equation to represent Joe’s
                                                              monthly cell phone charges.
                                      2x - 1              65. Find f(4) for f(x) = 2x2 + 4x – 3.
                                                          66. f(x) = 9x – 11. Find x when f(x) = 12.
                   3x + 7                                 67. A roof shingle is dropped from 100 ft above the
47. Find the formula that generates the sequence:             ground. The height y (in ft) of the dropped
    3, 9, 15, 21, 27, . . .                                   shingle is given by the function     y = -16t2 +
48. Find the formula that generates the sequence:             100 where t is the time (in sec) since the shingle
    3, 12, 48, 192, 768, . . .                                is dropped. Estimate when the shingle is at a
49. What type of sequence is 12, 9, 6, 3, 0, -3, . . .?       height of 50 feet.
    Explain.                                              68. Compare the graph of g(x) = x2 + 4 to
50. Write a polynomial expression that repesents              f(x) = x2 – 3.
    only the shaded area:                                                              1
                                                          69. Find the vertex of y  x 2  4x  5 .
                                                                                       3
          10
                                                          70. Describe the graph of y  4(x  2)2  10 .
      x
                                                          71. Find the zeros of the function by graphing:
                                                              f (x )  3x 2  6x  24 .
                                                          72. Graph y  x 3  2 .
                                               19
                                                          73. Explain how to find the asymptotes of a rational
                            x + 23
                                                              function.
                                  4                       74. Explain how to find the excluded values of a
51. Expand: 2x  3 .
                                                              rational expression.
                              5
52. Expand:  x  2 .                                    75. Determine the function graphed below.
                                                    2
53. Find the product:                 3x    8 .
54. Find the product: (2x + 5)(x2 – 3).
55. Find the product: (4x + 11)(2x + 7).
56. Write a polynomial expression that represents
    the perimeter of the polygon:
                            x + 21


      5x - 8

                                        4x + 13



           x +1
               2                                          76. Determine the function graphed below.
57. Identify the degree and leading coefficient of
    5x 7  4x 3  2x  3x 10 .
58. Find the difference: (9x  11)  (7x 2  8) .
59. Find the product: (2x 3  7x 2  x  3)(5x 2  4) .
60. Identify the slope of the line with the equation
    2x + 5y = 15.
61. Identify the y-intercept of the line with the
    equation 3x – 7y = 11.
62. Determine the equation of the line.

								
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