American Mathematics Competitions
                   2005 AMC 10 A Results for Michigan                   
                          GRAND STATISTICS  

      TOTAL NUMBER of official students taking exam:   1387

      Number of unofficial participants:          1

      Average score of participants:           73.9

      Average score for female students  is:   70.7  (   623 Students)
      Average score for male students is:      76.8  (   725 Students)
      Average score for unspecified gender is  70.6  (    39 Students)
      Average score for grade 10 is:           75.1  (   694 Students)
      Average score for grade 9 is:            70.3  (   599 Students)
      Average score for grade 8 and below is:  91.5  (    83 Students)
      Average score with unknown grade:        57.2  (    11 Students)

        AIME qualifying score =  120.0 or better
        Number of AIME qualifers                 32

        Number of schools returning results      52
        Average school winning score          105.44


                   American Mathematics Competitions
                   2005 AMC 12 A Results for Michigan                   
                          GRAND STATISTICS  

      TOTAL NUMBER of official students taking exam:   1465

      Number of unofficial participants:          0

      Average score of participants:           79.0

      Average score for female students  is:   74.8  (   642 Students)
      Average score for male students is:      82.5  (   785 Students)
      Average score for unspecified gender is  80.1  (    38 Students)
      Average score for grade 13 is:           91.5  (     1 Student) 
      Average score for grade 12 is:           80.3  (   636 Students)
      Average score for grade 11 is:           76.4  (   713 Students)
      Average score for grade 10 is:           83.4  (    73 Students)
      Average score for grade 9 is:           100.7  (    25 Students)
      Average score for grade 8 and below is:  92.9  (    12 Students)
      Average score with unknown grade:        83.0  (     5 Students)

        AIME qualifying score =  100.0 or better
        Number of AIME qualifers                187

        Number of schools returning results      61
        Average school winning score          107.98
        Average school team score             298.46
 


                   American Mathematics Competitions
                   2005 AMC 10 B Results for Michigan                   
                          GRAND STATISTICS  

      TOTAL NUMBER of official students taking exam:    481

      Number of unofficial participants:          0

      Average score of participants:           81.1

      Average score for female students  is:   78.8  (   186 Students)
      Average score for male students is:      82.8  (   276 Students)
      Average score for unspecified gender is  78.4  (    19 Students)
      Average score for grade 10 is:           82.3  (   200 Students)
      Average score for grade 9 is:            82.1  (   217 Students)
      Average score for grade 8 and below is:  75.0  (    49 Students)
      Average score with unknown grade:        70.3  (    15 Students)

        AIME qualifying score =  120.0 or better
        Number of AIME qualifers                 15

        Number of schools returning results      15
        Average school winning score          110.17


                   American Mathematics Competitions
                   2005 AMC 12 B Results for Michigan                   
                          GRAND STATISTICS  

      TOTAL NUMBER of official students taking exam:    553

      Number of unofficial participants:          0

      Average score of participants:           86.4

      Average score for female students  is:   83.7  (   183 Students)
      Average score for male students is:      88.5  (   343 Students)
      Average score for unspecified gender is  78.6  (    27 Students)
      Average score for grade 12 is:           87.1  (   206 Students)
      Average score for grade 11 is:           84.5  (   273 Students)
      Average score for grade 10 is:           87.4  (    42 Students)
      Average score for grade 9 is:           105.6  (     8 Students)
      Average score for grade 8 and below is:  98.1  (    19 Students)
      Average score with unknown grade:        78.6  (     5 Students)

        AIME qualifying score =  100.0 or better
        Number of AIME qualifers                 98

        Number of schools returning results      21
        Average school winning score          110.76
        Average school team score             317.43
 
 


    2005 State AMC 12  TEAM Score Distribution
    -----------------------------------------------
    score         A         B       Rank
    -----------------------------------------------
    389.0         1                   1
    379.5         1                   2
    375.5         1         1         3
    372.5         1                   5
    367.0                   1         6
    360.0         1                   7
    359.5         1                   8
    357.5         1                   9
    352.5                   1        10
    352.0         1                  11
    350.5         1                  12
    348.0                   1        13
    347.0         1                  14
    346.0         1                  15
    344.5         1                  16
    341.0         2                  17
    338.5                   1        19
    336.5                   1        20
    335.5         1                  21
    334.5                   1        22
    332.5         1                  23
    328.0         1         1        24
    327.0         1                  26
    325.5         1                  27
    323.0         1                  28
    320.5                   1        29
    318.5         1                  30
    317.5         2                  31
    316.5                   1        33
    315.0         1                  34
    314.0         1         1        35
    313.0         1                  37
    310.5         2                  38
    308.5         1                  40
    308.0                   1        41
    306.0                   1        42
    301.5                   1        43
    300.0         1         1        44
    299.0         1                  46
    298.0         1                  47
    297.5         1                  48
    295.0         1                  49
    294.5                   1        50
    294.0                   1        51
    293.0         1                  52
    292.0                   1        53
    291.5         2                  54
    289.5         2                  56
    288.5                   1        58
    286.0         1                  59
    284.0         1                  60
    283.0         1                  61
    282.0         1                  62
    280.0         1                  63
    279.0                   1        64
    274.0         1                  65
    271.5         1                  66
    271.0                   1        67
    270.5         1                  68
    265.0         1                  69
    262.0         1                  70
    261.5         1                  71
    260.0         1                  72
    259.0         1                  73
    257.5         1                  74
    248.0         1                  75
    239.5         1                  76
    239.0         1                  77
    237.5         1                  78
    233.0         1                  79
    220.5         1                  80
    130.5         1                  81
    105.5         1                  82


         2005 AMC Contest Score Distributions
    -----------------------------------------------
    score      12 A      12 B      10 A      10 B
    -----------------------------------------------
    150.0                                       1
    144.0                             1
    143.0                   1
    140.5         1
    139.5                             1
    138.0                             4         1
    137.0         1                   1
    134.5         1                   1
    133.5         1         1         2
    132.5         2         1
    132.0                             1         1
    131.0                             1         1
    130.0                   1         2
    129.0         1         1
    127.5                             2         1
    126.5         2                             1
    125.5         1         1
    125.0         1                   2
    124.0         1         1
    123.0         6                   2         3
    122.5                                       1
    122.0         3                   2
    121.5         1                   3         2
    120.5         1         1         6         2
    120.0                             1         1
    119.5         3         1         1         1
    119.0                             1
    118.5         6                             1
    118.0         2         2         2
    117.0         3         1         4         1
    116.5                                       1
    116.0         7         7         1         2
    115.5         2                             1
    115.0         4         1
    114.5                             2         2
    114.0                             1
    113.5         4         2         3
    112.5         5         5
    112.0                   1         3         1
    111.5         1         2         2         2
    111.0         3         1         4         2
    110.5                   1
    110.0         6         2         1         6
    109.5         1
    109.0         7         4         4         4
    108.5         2         1         7         1
    108.0         8         3         2
    107.5         3         3         3         7
    106.5         6         7         6         4
    106.0                             1
    105.5        17         8         4         2
    105.0         1         2         6         2
    104.5         9         7         1         2
    104.0         1         3         9         4
    103.5                             3         1
    103.0        14         6         4         4
    102.5         5         2         3         1
    102.0        20         6         5         4
    101.5         4         1         8         2
    101.0        15         5         2         1
    100.5         5         5         9         1
    100.0                   1         1         1
     99.5        20         7         2         5
     99.0                             6         2
     98.5        21        11         4         3
     98.0         3                   8         6
     97.5         9         3         1         1
     97.0         8         9         5         5
     96.5                             2         2
     96.0        18        17        13         6
     95.5         2         2         3         4
     95.0        32        17         7         4
     94.5         5         2         9         5
     94.0         7         7         5
     93.5        15         6         8         4
     93.0                   1         6         5
     92.5        27        14        20         5
     92.0         6         4        11         6
     91.5        10         9         7         3
     91.0        12         4         7         7
     90.5         8         3         5         4
     90.0        17        13        11         6
     89.5         2         2         3         3
     89.0        37        18        16         8
     88.5         5         5         4         8
     88.0        14        14         5         2
     87.5        12         7         5         3
     87.0         7         3         4         1
     86.5        26        10        11         9
     86.0         3         2         8         5
     85.5        12         8        13         7
     85.0         7         5        12         6
     84.5        23         4        20         3
     84.0        17        16         9        10
     83.5         6         1         6         7
     83.0        50         9        18         6
     82.5         5         5         3         4
     82.0        19         4        15         2
     81.5        12        11        11         5
     81.0        12         4        15         2
     80.5        24        16        16         6
     80.0        13         6        12         2
     79.5        16        13        16         8
     79.0         9         5         3         8
     78.5        24         5        21         3
     78.0        17         4        16         8
     77.5        10         2        15         6
     77.0        21         8        17        10
     76.5         8         1        11         5
     76.0        16         8        19         4
     75.5        13         6         7         5
     75.0        22         5        23         1
     74.5        22        13        23         5
     74.0        13         1        21         1
     73.5        11         2        18         6
     73.0        11         3         8         4
     72.5        27         5        24         5
     72.0        24         9        15         5
     71.5        18                  23         4
     71.0        15         2        21         3
     70.5        12         4         9         1
     70.0        18         5        21         5
     69.5         6         3         5         7
     69.0        14         5        21         3
     68.5        13         5        22         6
     68.0         8         3        20         5
     67.5        10         3        12
     67.0         8                   9         3
     66.5        15         2        15         4
     66.0        13         6        16         3
     65.5        13         2        20         1
     65.0        17         6        19         2
     64.5         8         1         9         4
     64.0        16         1        12         2
     63.5         7         2         9         1
     63.0        15         1        15         1
     62.5         7         3        10         8
     62.0        11         1        16         3
     61.5         6         1        18         2
     61.0        12                   4         1
     60.5         7         2        11         1
     60.0        11         2        18         4
     59.5         7         1        14         1
     59.0        15         1         9         4
     58.5         8         1         3         3
     58.0         7         2         6
     57.5         9                   9         3
     57.0         7         2         6         2
     56.5         7         3         8         1
     56.0         4         1         7         1
     55.5         5         1        10         2
     55.0         3         1         5
     54.5         1                   4         2
     54.0        10         4        19         2
     53.5         1                   9         1
     53.0         8                   3         1
     52.5         8                   5
     52.0         5                   7         2
     51.5         2                   5
     51.0         3         1         3
     50.5         9                  13         3
     50.0         2                   4         1
     49.5         6         1         4         2
     49.0                             6         1
     48.5         1         2         4
     48.0         5         3         9         2
     47.5         2                   1         2
     47.0         7                   4
     46.5         2                   7
     46.0         1                   3
     45.5         4                   4         1
     45.0         3                   3
     44.5         3                   4
     44.0                   1         7
     43.5         1                   7         3
     43.0         3                   2         1
     42.5                             5         1
     42.0        10                  10         2
     41.5         2                   8
     41.0         1                   2         1
     40.5         2                   4
     40.0         2                   2         2
     39.5                             2         1
     39.0                             2         1
     38.5         1                   1
     38.0         4                   1         1
     37.5                             1         1
     37.0         2                   3
     36.5         1                   1
     36.0         3                   8         2
     35.5         3                   1
     35.0         1                   1
     34.5         1                   1         1
     34.0         1         1         1
     33.0                             1
     32.5         2                   1
     32.0                                       1
     31.5                             2
     30.5                                       1
     30.0         2                   5         5
     29.5                             1
     29.0                                       1
     28.5         1
     28.0         1
     27.0                             1
     26.5         1                   3         1
     25.5         1                   1
     24.0         5                   4
     23.0                             1
     22.5                             1
     21.0         1
     20.5                             2
     18.0                                       1
     17.0         1
     12.0                             1         1
      8.5                             1
      6.0                             1



                   American Mathematics Competitions
                   2005 AMC 10 A Results for Michigan                   
                         SCORE DISTRIBUTION 

                               GENDER       

    Score    # Students        Score    # Students        Score    # Students
            male  female               male  female               male  female
    150.0                      125.0      2               100.0      1
    149.5                      124.5                       99.5      1     1
    149.0                      124.0                       99.0      3     3
    148.5                      123.5                       98.5      4
    148.0                      123.0      1     1          98.0      6     2
    147.5                      122.5                       97.5      1
    147.0                      122.0      1     1          97.0      3     2
    146.5                      121.5      3                96.5            2
    146.0                      121.0                       96.0      9     4
    145.5                      120.5      3     3          95.5      1     2
    145.0                      120.0      1                95.0      7
    144.5                      119.5      1                94.5      9
    144.0      1               119.0      1                94.0      3     2
    143.5                      118.5                       93.5      2     6
    143.0                      118.0      1     1          93.0      2     4
    142.5                      117.5                       92.5     14     6
    142.0                      117.0      3                92.0      8     1
    141.5                      116.5                       91.5      3     4
    141.0                      116.0            1          91.0      4     3
    140.5                      115.5                       90.5            5
    140.0                      115.0                       90.0      6     4
    139.5      1               114.5      2                89.5      2     1
    139.0                      114.0      1                89.0      9     6
    138.5                      113.5      1     2          88.5      1     3
    138.0      4               113.0                       88.0      5
    137.5                      112.5                       87.5      3     1
    137.0      1               112.0      3                87.0      1     3
    136.5                      111.5      2                86.5      4     7
    136.0                      111.0      1     3          86.0      6     2
    135.5                      110.5                       85.5      7     6
    135.0                      110.0      1                85.0      5     7
    134.5      1               109.5                       84.5     13     7
    134.0                      109.0      2     2          84.0      5     4
    133.5      2               108.5      4     3          83.5      3     3
    133.0                      108.0      2                83.0      8    10
    132.5                      107.5      3                82.5      3
    132.0                      107.0                       82.0      5     9
    131.5                      106.5      4     2          81.5      7     4
    131.0            1         106.0            1          81.0      8     7
    130.5                      105.5      4                80.5      5     9
    130.0      1     1         105.0      4     2          80.0      6     6
    129.5                      104.5      1                79.5      7     8
    129.0                      104.0      9                79.0      3
    128.5                      103.5      3                78.5      4    16
    128.0                      103.0      2     2          78.0      9     7
    127.5      2               102.5      2     1          77.5      6     9
    127.0                      102.0      2     3          77.0     12     5
    126.5                      101.5      7     1          76.5      8     3
    126.0                      101.0      1     1          76.0      8    11
    125.5                      100.5      7     2          75.5      3     4



                   American Mathematics Competitions
                   2005 AMC 10 A Results for Michigan                   
                         SCORE DISTRIBUTION 

                               GENDER       

    Score    # Students        Score    # Students        Score    # Students
            male  female               male  female               male  female
     75.0     10    11          50.0      2     2          25.0
     74.5     15     7          49.5      2     2          24.5
     74.0     13     8          49.0      3     3          24.0      1     3
     73.5      9     9          48.5      1     2          23.5
     73.0      3     5          48.0      4     4          23.0      1
     72.5     10    13          47.5      1                22.5      1
     72.0      7     8          47.0      1     3          22.0
     71.5     16     7          46.5      4     2          21.5
     71.0     14     7          46.0      2                21.0
     70.5      3     6          45.5      2     2          20.5            2
     70.0      7    11          45.0      1     2          20.0
     69.5      2     3          44.5      2     2          19.5
     69.0      8    12          44.0      4     3          19.0
     68.5     11    10          43.5      3     3          18.5
     68.0     11     9          43.0      1     1          18.0
     67.5      6     6          42.5      3     1          17.5
     67.0      2     7          42.0      6     4          17.0
     66.5      5     9          41.5      5     3          16.5
     66.0      8     8          41.0      2                16.0
     65.5     10    10          40.5      1     3          15.5
     65.0     12     7          40.0            2          15.0
     64.5      5     3          39.5      2                14.5
     64.0      8     3          39.0            2          14.0
     63.5      5     3          38.5      1                13.5
     63.0      8     6          38.0      1                13.0
     62.5      5     4          37.5            1          12.5
     62.0      8     8          37.0      2     1          12.0            1
     61.5     12     6          36.5      1                11.5
     61.0      3     1          36.0      3     5          11.0
     60.5      2     7          35.5            1          10.5
     60.0     10     7          35.0            1          10.0
     59.5      8     6          34.5            1           9.5
     59.0      4     4          34.0            1           9.0
     58.5      1     2          33.5                        8.5      1
     58.0            6          33.0            1           8.0
     57.5      3     6          32.5      1                 7.5
     57.0      4     2          32.0                        7.0
     56.5      2     5          31.5            2           6.5
     56.0      4     3          31.0                        6.0            1
     55.5      5     5          30.5                        5.5
     55.0      1     4          30.0      2     3           5.0
     54.5      1     3          29.5            1           4.5
     54.0      8    11          29.0                        4.0
     53.5      3     6          28.5                        3.5
     53.0            3          28.0                        3.0
     52.5      4     1          27.5                        2.5
     52.0      2     5          27.0      1                 2.0
     51.5      1     4          26.5      1     2           1.5
     51.0      2                26.0                        1.0
     50.5      4     9          25.5            1            .5
                                                            0.0      0     0



                   American Mathematics Competitions
                   2005 AMC 10 A Results for Michigan                   
                         SCORE DISTRIBUTION 

    score          -----------grade-----------
             6      7      8      9     10    unknown
                   ---------------------------
   144.0                           1
   139.5                                  1
   138.0                    1      1      2
   137.0                                  1
   134.5                                  1
   133.5                    2
   132.0                    1
   131.0                           1
   130.0             1                    1
   127.5             1                    1
   125.0                    1             1
   123.0                           1      1
   122.0                           1      1
   121.5                           1      2
   120.5                    1      2      3
   120.0                    1
   119.5                                  1
   119.0      1
   118.0                                  2
   117.0                    1             3
   116.0                           1
   114.5                                  2
   114.0             1
   113.5                    1      2
   112.0             1             1      1
   111.5                           1      1
   111.0                           2      2
   110.0                           1
   109.0                           2      2
   108.5                    2      1      4
   108.0                           1      1
   107.5                    1      2
   106.5                    1      3      2
   106.0                    1
   105.5                           2      2
   105.0                           4      2
   104.5                                  1
   104.0                           4      5
   103.5                    1      1      1
   103.0                           3      1
   102.5      1                    1      1
   102.0             1             1      3
   101.5             1      1      1      5
   101.0                                  2
   100.5      1      1             1      6
   100.0                                  1
    99.5                    1      1
    99.0             1                    5
    98.5                           2      2
    98.0                           3      5
    97.5                           1
    97.0             2                    3
    96.5                           1      1
    96.0             1             8      4
    95.5                    1             2
    95.0             1             2      4
    94.5             1      1      3      4
    94.0                    1      2      2
    93.5                           4      4
    93.0                    1             5
    92.5      1             1     10      8
    92.0                    1      3      7
    91.5                    1      2      4
    91.0                    1      3      3
    90.5                           3      2
    90.0             1             5      5
    89.5                           2      1
    89.0      1                    8      7
    88.5                           2      2
    88.0                    1             4
    87.5                    1      2      1      1
    87.0                           4
    86.5                    1      5      5
    86.0                    1      1      6
    85.5                           5      8
    85.0      1                    3      8
    84.5      1      1            10      8
    84.0                    2      3      4
    83.5             1             2      3
    83.0                    1      6     11
    82.5             1             1      1
    82.0                          10      5
    81.5                           2      9
    81.0             1      2      5      7
    80.5             1             6      9
    80.0                           6      6
    79.5                           9      7
    79.0                           1      2
    78.5             1             7     13
    78.0                    1      6      9
    77.5      1                    7      7
    77.0      1      1      1      5      9
    76.5                    1      7      3
    76.0                           9      9      1
    75.5      1                    1      5
    75.0                          12     11
    74.5      1                    8     14
    74.0                    1      7     13
    73.5      1                    7     10
    73.0                    1      4      3
    72.5                           8     16
    72.0                           8      7
    71.5                    1      9     13
    71.0                           6     15
    70.5             1             6      2
    70.0                           6     14      1
    69.5                           3      2
    69.0                           7     13      1
    68.5                          10     12
    68.0                          12      8
    67.5                           4      8
    67.0                                  9
    66.5                    1      7      7
    66.0                    1      3     12
    65.5                          10     10
    65.0                           7     12
    64.5                    1      3      5
    64.0                           3      9
    63.5                           3      6
    63.0                          11      4
    62.5                           5      5
    62.0                           5     11
    61.5                          10      8
    61.0                    1      1      2
    60.5                           7      4
    60.0                          10      7      1
    59.5                           8      5      1
    59.0                           5      4
    58.5      1                    1      1
    58.0                                  6
    57.5                           4      5
    57.0                           4      2
    56.5                           6      2
    56.0                    1      3      3
    55.5                           4      6
    55.0                           4      1
    54.5                           3      1
    54.0                    1      9      9
    53.5                    1      3      4      1
    53.0                           2      1
    52.5                           4      1
    52.0                           4      3
    51.5                           1      4
    51.0                           3
    50.5                           7      6
    50.0                           1      3
    49.5                           4
    49.0                           3      3
    48.5                           2      2
    48.0                           6      3
    47.5                                  1
    47.0                           1      3
    46.5                           3      4
    46.0                           2      1
    45.5                           1      3
    45.0                           3
    44.5                           2      1      1
    44.0                           4      3
    43.5                           6      1
    43.0                           1      1
    42.5                           2      1      2
    42.0                    1      4      5
    41.5                           7      1
    41.0                           1      1
    40.5                           2      2
    40.0                           2
    39.5                           1      1
    39.0                           1      1
    38.5                           1
    38.0                           1
    37.5                           1
    37.0                           1      2
    36.5                           1
    36.0                           3      5
    35.5                                  1
    35.0                           1
    34.5                           1
    34.0                           1
    33.0                           1
    32.5                           1
    31.5                           1      1
    30.0                           4      1
    29.5                           1
    27.0                           1
    26.5                           3
    25.5                           1
    24.0                           2      1      1
    23.0                           1
    22.5                           1
    20.5                           1      1
    12.0                           1
     8.5                           1
     6.0                           1



                   American Mathematics Competitions
                   2005 AMC 10 A Results for Michigan                   
                              Analysis      


                   Table of Item Difficulty for the 2005
              American High School Mathematics Examination
           Tabulation of responses for all Participants
                             Percent of Responses


    ITEM    A         B         C         D         E       OMITS       ?
    ____  _____     _____     _____     _____     _____     _____     _____

      1    0.17      0.12      0.25      8.73*     0.43      0.29      0.00
      2    0.26      0.14      5.90*     0.09      1.46      2.16      0.01
      3    0.06      8.86*     0.38      0.32      0.12      0.25      0.00
      4    0.46      2.11*     1.93      0.49      0.35      4.66      0.01
      5    6.00*     0.43      3.28      0.09      0.04      0.15      0.00
      6    0.28      5.07*     2.93      0.21      0.05      1.46      0.00
      7    0.62      3.63*     0.40      0.45      0.63      4.27      0.00
      8    1.02      0.35      4.06*     0.19      0.14      4.23      0.00
      9    1.18      5.54*     0.98      0.20      0.29      1.80      0.00
     10    2.18*     0.52      1.09      0.40      0.13      5.68      0.00
     11    0.48      2.46*     0.29      1.00      0.14      5.64      0.00
     12    0.42      1.37*     0.54      0.30      0.61      6.76      0.00
     13    1.54      0.55      0.37      0.38      1.23*     5.93      0.00
     14    0.76      0.54      0.49      0.53      2.18*     5.50      0.01
     15    0.48      0.90      0.87      1.23      1.23*     5.28      0.00
     16    0.56      0.42      0.81      2.44*     0.13      5.65      0.00
     17    0.41      0.39      0.54      1.93*     0.42      6.31      0.00
     18    1.36*     1.89      1.31      3.26      0.22      1.97      0.00
     19    0.39      0.77      0.71      2.93*     0.67      4.53      0.00
     20    0.71*     0.46      0.53      0.40      0.37      7.51      0.00
     21    1.73      0.92*     0.25      0.33      0.67      6.10      0.00
     22    0.66      0.63      0.32      2.40*     0.45      5.54      0.00
     23    0.27      0.43      1.14*     1.07      0.64      6.45      0.00
     24    1.13      1.14*     0.43      0.22      0.15      6.93      0.00
     25    0.42      0.66      0.74      0.85*     0.12      7.21      0.00


   (*)  Correct Response

   (?)  Response the computer was unable to read due to incomplete
        erasures or two answers marked in the same column




                   American Mathematics Competitions
                   2005 AMC 12 A Results for Michigan                   
                         SCORE DISTRIBUTION 

                               GENDER       

    Score    # Students        Score    # Students        Score    # Students
            male  female               male  female               male  female
    150.0                      125.0      1               100.0
    149.5                      124.5                       99.5     14     6
    149.0                      124.0      1                99.0
    148.5                      123.5                       98.5     14     7
    148.0                      123.0      6                98.0      3
    147.5                      122.5                       97.5      4     4
    147.0                      122.0      2     1          97.0      5     3
    146.5                      121.5      1                96.5
    146.0                      121.0                       96.0      9     8
    145.5                      120.5      1                95.5      2
    145.0                      120.0                       95.0     17    13
    144.5                      119.5      3                94.5      4     1
    144.0                      119.0                       94.0      3     4
    143.5                      118.5      3     1          93.5      9     5
    143.0                      118.0      2                93.0
    142.5                      117.5                       92.5     16    10
    142.0                      117.0      2     1          92.0      4     2
    141.5                      116.5                       91.5      4     5
    141.0                      116.0      5     2          91.0     10     2
    140.5      1               115.5      1                90.5      3     5
    140.0                      115.0      4                90.0      8     9
    139.5                      114.5                       89.5            2
    139.0                      114.0                       89.0     23    12
    138.5                      113.5      4                88.5      3     1
    138.0                      113.0                       88.0      8     6
    137.5                      112.5      5                87.5      6     6
    137.0      1               112.0                       87.0      5     2
    136.5                      111.5      1                86.5     13    11
    136.0                      111.0      3                86.0      1     2
    135.5                      110.5                       85.5      4     8
    135.0                      110.0      4     1          85.0      5     2
    134.5      1               109.5      1                84.5     14     8
    134.0                      109.0      7                84.0     11     5
    133.5      1               108.5      1     1          83.5      4     2
    133.0                      108.0      6     2          83.0     28    22
    132.5      2               107.5      3                82.5      4     1
    132.0                      107.0                       82.0      7    11
    131.5                      106.5      5     1          81.5      6     6
    131.0                      106.0                       81.0      5     7
    130.5                      105.5     13     4          80.5     12    11
    130.0                      105.0      1                80.0      6     7
    129.5                      104.5      8     1          79.5      9     6
    129.0      1               104.0            1          79.0      5     4
    128.5                      103.5                       78.5     10    14
    128.0                      103.0     10     4          78.0      8     8
    127.5                      102.5      4     1          77.5      2     7
    127.0                      102.0     16     4          77.0     10    11
    126.5      2               101.5      2     2          76.5      2     6
    126.0                      101.0      8     7          76.0      9     7
    125.5      1               100.5      4     1          75.5      8     5



                   American Mathematics Competitions
                   2005 AMC 12 A Results for Michigan                   
                         SCORE DISTRIBUTION 

                               GENDER       

    Score    # Students        Score    # Students        Score    # Students
            male  female               male  female               male  female
     75.0      6    15          50.0      2                25.0
     74.5     13     9          49.5      4     2          24.5
     74.0      6     7          49.0                       24.0      2     3
     73.5      4     7          48.5      1                23.5
     73.0      7     4          48.0      5                23.0
     72.5     10    16          47.5            2          22.5
     72.0     10    13          47.0      3     3          22.0
     71.5      9     9          46.5      1     1          21.5
     71.0      8     7          46.0      1                21.0            1
     70.5      6     6          45.5      1     3          20.5
     70.0      9     9          45.0      1     1          20.0
     69.5      5     1          44.5      3                19.5
     69.0      7     7          44.0                       19.0
     68.5      7     6          43.5      1                18.5
     68.0      3     5          43.0      1     2          18.0
     67.5      5     4          42.5                       17.5
     67.0      4     4          42.0      4     6          17.0            1
     66.5      5     9          41.5      2                16.5
     66.0      6     7          41.0            1          16.0
     65.5      6     7          40.5      1     1          15.5
     65.0      9     8          40.0      2                15.0
     64.5      5     3          39.5                       14.5
     64.0      6     9          39.0                       14.0
     63.5      2     5          38.5            1          13.5
     63.0      7     8          38.0      2     2          13.0
     62.5      5     2          37.5                       12.5
     62.0      3     8          37.0            2          12.0
     61.5      3     3          36.5      1                11.5
     61.0      5     6          36.0      2     1          11.0
     60.5      1     6          35.5      1     2          10.5
     60.0      4     6          35.0      1                10.0
     59.5      3     3          34.5      1                 9.5
     59.0      6     7          34.0            1           9.0
     58.5      2     6          33.5                        8.5
     58.0      3     3          33.0                        8.0
     57.5      6     3          32.5      2                 7.5
     57.0      4     3          32.0                        7.0
     56.5      3     4          31.5                        6.5
     56.0      2     2          31.0                        6.0
     55.5      1     4          30.5                        5.5
     55.0            3          30.0      1     1           5.0
     54.5            1          29.5                        4.5
     54.0      4     6          29.0                        4.0
     53.5            1          28.5      1                 3.5
     53.0      4     4          28.0            1           3.0
     52.5      2     6          27.5                        2.5
     52.0      2     3          27.0                        2.0
     51.5            2          26.5            1           1.5
     51.0            3          26.0                        1.0
     50.5      5     3          25.5            1            .5
                                                            0.0      0     0



                   American Mathematics Competitions
                   2005 AMC 12 A Results for Michigan                   
                         SCORE DISTRIBUTION 

    score                  -----------grade-----------
             6      7      8      9     10     11     12     13  unknown
                           ---------------------------
   140.5                                         1
   137.0                                  1
   134.5                                                1
   133.5                                         1
   132.5                    1                    1
   129.0                                                1
   126.5                                         2
   125.5                                                1
   125.0                                         1
   124.0                                                1
   123.0             1             1             1      3
   122.0                                  1      2
   121.5                                         1
   120.5                                                1
   119.5                                                3
   118.5                           1      2      1      2
   118.0                                  1      1
   117.0                                         2      1
   116.0                           2      1      2      2
   115.5                                         2
   115.0                           1             1      2
   113.5                                         2      2
   112.5                           2      1      1      1
   111.5                                         1
   111.0                                         2      1
   110.0             1                           1      4
   109.5                           1
   109.0                                         4      3
   108.5                                                2
   108.0                           2      2      3      1
   107.5                                                3
   106.5                                  1             5
   105.5                           2      1      8      6
   105.0                                                1
   104.5                                         2      7
   104.0                                         1
   103.0      1                    1             3      9
   102.5                    1      1             1      2
   102.0                                  1      6     13
   101.5                                         3      1
   101.0                                  1      6      8
   100.5                                  1      2      2
    99.5                           1      1      7     11
    98.5                                  3      9      9
    98.0                                                3
    97.5                                  1      3      5
    97.0                                         4      4
    96.0                           1      1      7      9
    95.5                                                2
    95.0                           1      2     15     13             1
    94.5                                  1      1      3
    94.0                                         2      5
    93.5                           1      1      5      8
    92.5                                        11     16
    92.0                           1             4      1
    91.5                                         5      4      1
    91.0                                  1      4      7
    90.5                                         5      3
    90.0                                  1      6     10
    89.5                                         2
    89.0                           1      3     15     17             1
    88.5                                  1      1      3
    88.0             1                           8      5
    87.5                                         6      6
    87.0                                         7
    86.5             1                    2      5     18
    86.0                                         1      2
    85.5                                        10      2
    85.0                                         2      5
    84.5                                        14      9
    84.0                                         9      8
    83.5                                         3      3
    83.0                    2             1     24     23
    82.5                                  1      1      3
    82.0                                  3      6     10
    81.5                                  1      4      7
    81.0                           1      1      6      4
    80.5                                  4     11      9
    80.0                           1             6      6
    79.5                                         8      8
    79.0                                         8      1
    78.5                           2      1      9     11             1
    78.0                           1            11      5
    77.5                                         3      6             1
    77.0                                  1     12      8
    76.5                                         4      4
    76.0                                         8      8
    75.5                                         7      6
    75.0      1                           1     11      8             1
    74.5                                  3      9     10
    74.0                                  1      7      5
    73.5                                  2      6      3
    73.0                                         7      4
    72.5                                        14     13
    72.0                                  2     10     12
    71.5                                        12      6
    71.0                                         8      7
    70.5                                  1      6      5
    70.0                                  1     10      7
    69.5                                  1      3      2
    69.0                                         9      5
    68.5                                  2      6      5
    68.0                                         6      2
    67.5                                  1      8      1
    67.0                    1                    5      2
    66.5                                         9      6
    66.0                                         7      6
    65.5                                  1     12
    65.0                                  1     14      2
    64.5                                         4      4
    64.0                                  2      7      7
    63.5                                         3      4
    63.0                                         7      8
    62.5                                         6      1
    62.0                                         6      5
    61.5                                  1      3      2
    61.0      1                                  5      6
    60.5                                         5      2
    60.0                                         6      5
    59.5                                         6      1
    59.0                                  1     10      4
    58.5                                         5      3
    58.0                                  1      5      1
    57.5                                         6      3
    57.0                                         3      4
    56.5                                         5      2
    56.0                                         3      1
    55.5                                         4      1
    55.0                                         3
    54.5                                  1
    54.0                                         4      6
    53.5                                         1
    53.0                                         7      1
    52.5                                  1      4      3
    52.0                                         2      3
    51.5                                         2
    51.0                                                3
    50.5                                  1      4      4
    50.0                                         1      1
    49.5                                         2      4
    48.5                                         1
    48.0                                         2      3
    47.5                                                2
    47.0                                  2      3      2
    46.5                                         1      1
    46.0                                         1
    45.5                                         2      2
    45.0                                         2      1
    44.5                                         2      1
    43.5                                         1
    43.0                                         1      2
    42.0                                         7      3
    41.5                                         1      1
    41.0                                                1
    40.5                                         2
    40.0                                         1      1
    38.5                                                1
    38.0                                         1      3
    37.0                                         2
    36.5                                         1
    36.0                                                3
    35.5                                         2      1
    35.0                                         1
    34.5                                                1
    34.0                                         1
    32.5                                         1      1
    30.0                                                2
    28.5                                         1
    28.0                                                1
    26.5                                                1
    25.5                                                1
    24.0                                         3      2
    21.0                                  1
    17.0                                         1



                   American Mathematics Competitions
                   2005 AMC 12 A Results for Michigan                   
                              Analysis      


                   Table of Item Difficulty for the 2005
              American High School Mathematics Examination
           Tabulation of responses for all Participants
                             Percent of Responses


    ITEM    A         B         C         D         E       OMITS       ?
    ____  _____     _____     _____     _____     _____     _____     _____

      1    0.02      0.08      0.11      9.40*     0.14      0.26      0.00
      2    0.01      9.45*     0.17      0.23      0.03      0.10      0.00
      3    0.46      4.42*     1.24      0.39      0.51      2.98      0.00
      4    7.13*     0.33      2.33      0.08      0.02      0.12      0.00
      5    0.18      6.89*     1.90      0.07      0.08      0.87      0.00
      6    0.59      5.34*     0.31      0.31      0.66      2.79      0.01
      7    0.60      0.25      6.76*     0.10      0.09      2.20      0.00
      8    0.34      0.42      0.42      2.22*     0.24      6.37      0.00
      9    3.60*     0.45      1.02      0.38      0.11      4.44      0.01
     10    0.37      3.34*     0.20      0.60      0.13      5.37      0.00
     11    1.00      0.38      0.38      0.65      3.17*     4.41      0.01
     12    0.97      0.27      0.28      3.84*     1.23      3.42      0.00
     13    0.16      0.27      0.46      2.99*     0.33      5.78      0.01
     14    0.35      0.36      3.33      1.24*     0.44      4.27      0.00
     15    0.31      0.43      1.51*     0.67      0.73      6.35      0.00
     16    0.27      0.38      0.66      0.67*     0.35      7.68      0.00
     17    1.79*     0.94      1.22      0.33      0.37      5.35      0.00
     18    0.48*     0.46      0.36      0.29      0.15      8.25      0.00
     19    0.95      2.48*     0.99      0.53      0.81      4.25      0.00
     20    0.34      0.23      0.18      0.16      0.30*     8.79      0.01
     21    0.47      0.48      0.49*     0.22      0.06      8.27      0.01
     22    0.31      0.66*     0.28      0.39      0.16      8.20      0.00
     23    0.58      0.74*     0.35      0.25      0.55      7.54      0.00
     24    0.14      0.16*     0.25      0.23      0.08      9.14      0.00
     25    0.33      0.29      0.14*     0.19      0.14      8.90      0.00


   (*)  Correct Response

   (?)  Response the computer was unable to read due to incomplete
        erasures or two answers marked in the same column




                   American Mathematics Competitions
                   2005 AMC 10 B Results for Michigan                   
                         SCORE DISTRIBUTION 

                               GENDER       

    Score    # Students        Score    # Students        Score    # Students
            male  female               male  female               male  female
    150.0      1               125.0                      100.0            1
    149.5                      124.5                       99.5      1     3
    149.0                      124.0                       99.0      2
    148.5                      123.5                       98.5      1     2
    148.0                      123.0      3                98.0      2     4
    147.5                      122.5            1          97.5      1
    147.0                      122.0                       97.0      4     1
    146.5                      121.5      1     1          96.5      1     1
    146.0                      121.0                       96.0      4     2
    145.5                      120.5      2                95.5      3     1
    145.0                      120.0      1                95.0      2     2
    144.5                      119.5      1                94.5      2     3
    144.0                      119.0                       94.0
    143.5                      118.5      1                93.5      2     2
    143.0                      118.0                       93.0      3     2
    142.5                      117.5                       92.5      2     3
    142.0                      117.0      1                92.0      5     1
    141.5                      116.5      1                91.5      3
    141.0                      116.0      1     1          91.0      4     3
    140.5                      115.5      1                90.5      3
    140.0                      115.0                       90.0      1     4
    139.5                      114.5      2                89.5      1     2
    139.0                      114.0                       89.0      3     4
    138.5                      113.5                       88.5      6     2
    138.0      1               113.0                       88.0            2
    137.5                      112.5                       87.5      2
    137.0                      112.0      1                87.0      1
    136.5                      111.5      1     1          86.5      7     2
    136.0                      111.0      2                86.0      2     3
    135.5                      110.5                       85.5      3     4
    135.0                      110.0      3     3          85.0      2     3
    134.5                      109.5                       84.5      1     2
    134.0                      109.0            4          84.0      9     1
    133.5                      108.5      1                83.5      2     4
    133.0                      108.0                       83.0      2     3
    132.5                      107.5      6     1          82.5      1     2
    132.0      1               107.0                       82.0            2
    131.5                      106.5      4                81.5      3     2
    131.0      1               106.0                       81.0      2
    130.5                      105.5      1                80.5      3     3
    130.0                      105.0      2                80.0      2
    129.5                      104.5      1     1          79.5      4     3
    129.0                      104.0      2     2          79.0      7     1
    128.5                      103.5      1                78.5      2     1
    128.0                      103.0      3     1          78.0      6     2
    127.5      1               102.5      1                77.5      5     1
    127.0                      102.0      1     3          77.0      5     5
    126.5            1         101.5      1                76.5      2     2
    126.0                      101.0            1          76.0      4
    125.5                      100.5      1                75.5      5



                   American Mathematics Competitions
                   2005 AMC 10 B Results for Michigan                   
                         SCORE DISTRIBUTION 

                               GENDER       

    Score    # Students        Score    # Students        Score    # Students
            male  female               male  female               male  female
     75.0            1          50.0      1                25.0
     74.5      2     3          49.5            2          24.5
     74.0      1                49.0            1          24.0
     73.5      4     2          48.5                       23.5
     73.0      1     3          48.0      1     1          23.0
     72.5      1     4          47.5            2          22.5
     72.0      1     4          47.0                       22.0
     71.5      3     1          46.5                       21.5
     71.0      2     1          46.0                       21.0
     70.5            1          45.5      1                20.5
     70.0      4     1          45.0                       20.0
     69.5      4     3          44.5                       19.5
     69.0            3          44.0                       19.0
     68.5      1     4          43.5      2     1          18.5
     68.0      4     1          43.0      1                18.0      1
     67.5                       42.5            1          17.5
     67.0      3                42.0      1     1          17.0
     66.5      3     1          41.5                       16.5
     66.0      1     1          41.0      1                16.0
     65.5            1          40.5                       15.5
     65.0      1     1          40.0            2          15.0
     64.5      3     1          39.5            1          14.5
     64.0      1     1          39.0      1                14.0
     63.5      1                38.5                       13.5
     63.0      1                38.0            1          13.0
     62.5      3     4          37.5      1                12.5
     62.0      3                37.0                       12.0            1
     61.5      1     1          36.5                       11.5
     61.0      1                36.0      1     1          11.0
     60.5      1                35.5                       10.5
     60.0      2     2          35.0                       10.0
     59.5      1                34.5            1           9.5
     59.0      2     2          34.0                        9.0
     58.5      3                33.5                        8.5
     58.0                       33.0                        8.0
     57.5      2     1          32.5                        7.5
     57.0      1     1          32.0      1                 7.0
     56.5      1                31.5                        6.5
     56.0                       31.0                        6.0
     55.5      1     1          30.5            1           5.5
     55.0                       30.0      3     1           5.0
     54.5      2                29.5                        4.5
     54.0      1     1          29.0      1                 4.0
     53.5      1                28.5                        3.5
     53.0                       28.0                        3.0
     52.5                       27.5                        2.5
     52.0      1     1          27.0                        2.0
     51.5                       26.5            1           1.5
     51.0                       26.0                        1.0
     50.5            3          25.5                         .5
                                                            0.0      0     0



                   American Mathematics Competitions
                   2005 AMC 10 B Results for Michigan                   
                         SCORE DISTRIBUTION 

    score          -----------grade-----------
             6      7      8      9     10    unknown
                   ---------------------------
   150.0                                  1
   138.0                                  1
   132.0                    1
   131.0                           1
   127.5                           1
   126.5                           1
   123.0                    1      1      1
   122.5                           1
   121.5                           1      1
   120.5                           2
   120.0                           1
   119.5                           1
   118.5                                  1
   117.0                                  1
   116.5             1
   116.0                                  2
   115.5                                  1
   114.5                           1      1
   112.0                                  1
   111.5                           1      1
   111.0             1                    1
   110.0             1             1      3      1
   109.0             1             2      1
   108.5                           1
   107.5                           4      3
   106.5                           2      2
   105.5                                  2
   105.0                           1      1
   104.5                           1      1
   104.0                                  4
   103.5                           1
   103.0      1                    3
   102.5             1
   102.0             1      1      1      1
   101.5                                  2
   101.0                                  1
   100.5                    1
   100.0                                  1
    99.5                           4             1
    99.0                           1      1
    98.5                           2      1
    98.0                           2      4
    97.5                    1
    97.0                           1      4
    96.5                    1             1
    96.0                           2      4
    95.5      1                    1      2
    95.0      1                    2      1
    94.5      1                    1      2      1
    93.5                           2      2
    93.0                           5
    92.5             1             4
    92.0             1             2      3
    91.5                           2      1
    91.0                           3      4
    90.5                           1      3
    90.0                           6
    89.5                           2      1
    89.0      1                    4      3
    88.5                    2      1      5
    88.0                    1      1
    87.5                           1      2
    87.0      1
    86.5      1                    5      3
    86.0                           2      3
    85.5                           4      3
    85.0                           1      5
    84.5                           1      2
    84.0      1                    5      4
    83.5                    1      3      3
    83.0                           4      1      1
    82.5                           1      3
    82.0                           2
    81.5                           4      1
    81.0                           1      1
    80.5             1             2      3
    80.0                           1      1
    79.5                           5      3
    79.0                           5      2      1
    78.5                           3
    78.0                           2      6
    77.5                           4      2
    77.0                           9      1
    76.5             1             2      2
    76.0                           4
    75.5                           3      2
    75.0                                  1
    74.5                           3      2
    74.0                           1
    73.5                           2      4
    73.0                           1      3
    72.5                           1      4
    72.0                           2      3
    71.5                           2      2
    71.0                    1      2
    70.5                           1
    70.0                    1      1      2      1
    69.5                           4      3
    69.0                           2      1
    68.5      1                    2      1      2
    68.0                           2      3
    67.0                           2             1
    66.5                                  4
    66.0                           2             1
    65.5                           1
    65.0                           1      1
    64.5                           2      1      1
    64.0                    1      1
    63.5                           1
    63.0                                  1
    62.5             1             2      4      1
    62.0                           1      2
    61.5                           2
    61.0                    1
    60.5                           1
    60.0                           1      3
    59.5                           1
    59.0                           2      2
    58.5                    1      1      1
    57.5                           1      2
    57.0                                  2
    56.5                           1
    56.0                                  1
    55.5                    1      1
    54.5                           1      1
    54.0                           1      1
    53.5                    1
    53.0                                  1
    52.0                    1      1
    50.5                           1      2
    50.0                           1
    49.5                           2
    49.0                                  1
    48.0             1             1
    47.5                                  1      1
    45.5                           1
    43.5                                  2      1
    43.0                                  1
    42.5                           1
    42.0                                  2
    41.0                                  1
    40.0                           1      1
    39.5                                  1
    39.0                    1
    38.0                           1
    37.5                           1
    36.0             1                    1
    34.5                           1
    32.0                    1
    30.5                    1
    30.0                    2      1      1      1
    29.0                    1
    26.5             1
    18.0                    1
    12.0                    1



                   American Mathematics Competitions
                   2005 AMC 10 B Results for Michigan                   
                              Analysis      


                   Table of Item Difficulty for the 2005
              American High School Mathematics Examination
           Tabulation of responses for all Participants
                             Percent of Responses


    ITEM    A         B         C         D         E       OMITS       ?
    ____  _____     _____     _____     _____     _____     _____     _____

      1    8.63*     0.48      0.23      0.17      0.37      0.12      0.00
      2    0.08      0.12      0.06      8.92*     0.21      0.60      0.00
      3    0.02      0.79      1.73      6.01*     1.23      0.23      0.00
      4    0.62      0.12      0.48      5.41*     0.27      3.10      0.00
      5    0.12      0.12      8.92*     0.08      0.44      0.31      0.00
      6    0.21      8.54*     0.29      0.25      0.23      0.48      0.00
      7    0.89      1.91*     0.27      1.08      0.77      5.05      0.02
      8    6.59*     0.15      0.73      0.08      0.10      2.35      0.00
      9    0.62      0.73      1.83      5.16*     0.48      1.19      0.00
     10    2.02*     1.29      0.67      0.25      0.29      5.49      0.00
     11    0.27      0.67      0.29      1.81      2.52*     4.45      0.00
     12    0.60      1.00      0.58      0.29      0.58*     6.94      0.00
     13    0.54      0.56      2.35*     1.89      0.37      4.28      0.00
     14    0.44      0.29      3.06*     1.33      0.50      4.39      0.00
     15    1.27      0.69      0.91      4.18*     0.50      2.43      0.02
     16    0.31      0.77      0.87      0.73*     0.06      7.26      0.00
     17    0.69      3.10*     0.91      0.31      0.25      4.74      0.00
     18    0.37      4.12      1.23      2.60*     0.62      1.06      0.00
     19    0.69      5.84*     0.44      0.58      0.54      1.91      0.00
     20    0.29      0.52      1.39*     0.35      0.37      7.07      0.00
     21    0.50*     0.48      0.44      0.27      0.23      8.09      0.00
     22    0.52      1.31      0.71*     0.44      0.40      6.63      0.00
     23    2.97      0.96      0.46*     0.25      0.23      5.14      0.00
     24    0.35      0.31      0.37      0.35      1.39*     7.21      0.00
     25    0.35      0.37      3.89*     0.37      0.17      4.84      0.00


   (*)  Correct Response

   (?)  Response the computer was unable to read due to incomplete
        erasures or two answers marked in the same column




                   American Mathematics Competitions
                   2005 AMC 12 B Results for Michigan                   
                         SCORE DISTRIBUTION 

                               GENDER       

    Score    # Students        Score    # Students        Score    # Students
            male  female               male  female               male  female
    150.0                      125.0                      100.0      1
    149.5                      124.5                       99.5      6     1
    149.0                      124.0      1                99.0
    148.5                      123.5                       98.5      6     5
    148.0                      123.0                       98.0
    147.5                      122.5                       97.5      3
    147.0                      122.0                       97.0      6     3
    146.5                      121.5                       96.5
    146.0                      121.0                       96.0      9     8
    145.5                      120.5      1                95.5      2
    145.0                      120.0                       95.0     11     6
    144.5                      119.5      1                94.5      1
    144.0                      119.0                       94.0      5     2
    143.5                      118.5                       93.5      4     2
    143.0      1               118.0      2                93.0      1
    142.5                      117.5                       92.5      9     4
    142.0                      117.0      1                92.0      2     1
    141.5                      116.5                       91.5      4     5
    141.0                      116.0      7                91.0      4
    140.5                      115.5                       90.5      2     1
    140.0                      115.0      1                90.0      7     3
    139.5                      114.5                       89.5      2
    139.0                      114.0                       89.0     14     3
    138.5                      113.5      1     1          88.5      3     2
    138.0                      113.0                       88.0      6     8
    137.5                      112.5      5                87.5      6     1
    137.0                      112.0      1                87.0            3
    136.5                      111.5      2                86.5      4     6
    136.0                      111.0      1                86.0      2
    135.5                      110.5                       85.5      4     4
    135.0                      110.0      1     1          85.0      4
    134.5                      109.5                       84.5      3     1
    134.0                      109.0      3     1          84.0     10     5
    133.5      1               108.5      1                83.5            1
    133.0                      108.0      3                83.0      5     3
    132.5      1               107.5      2     1          82.5      4     1
    132.0                      107.0                       82.0      1     2
    131.5                      106.5      6     1          81.5      4     6
    131.0                      106.0                       81.0      1     3
    130.5                      105.5      6     2          80.5      8     7
    130.0      1               105.0      2                80.0      3     3
    129.5                      104.5      5     2          79.5      7     6
    129.0      1               104.0      2     1          79.0      5
    128.5                      103.5                       78.5      2     3
    128.0                      103.0      4     2          78.0      2     1
    127.5                      102.5            2          77.5      1     1
    127.0                      102.0      5     1          77.0      4     4
    126.5                      101.5      1                76.5      1
    126.0                      101.0      2     3          76.0      3     4
    125.5      1               100.5      5                75.5      3     3



                   American Mathematics Competitions
                   2005 AMC 12 B Results for Michigan                   
                         SCORE DISTRIBUTION 

                               GENDER       

    Score    # Students        Score    # Students        Score    # Students
            male  female               male  female               male  female
     75.0      2     3          50.0                       25.0
     74.5      5     6          49.5      1                24.5
     74.0            1          49.0                       24.0
     73.5            1          48.5      1     1          23.5
     73.0      3                48.0      2     1          23.0
     72.5      2     3          47.5                       22.5
     72.0      5     3          47.0                       22.0
     71.5                       46.5                       21.5
     71.0      2                46.0                       21.0
     70.5      3     1          45.5                       20.5
     70.0      4                45.0                       20.0
     69.5      1     2          44.5                       19.5
     69.0      5                44.0                       19.0
     68.5      2     2          43.5                       18.5
     68.0      1     2          43.0                       18.0
     67.5      1     2          42.5                       17.5
     67.0                       42.0                       17.0
     66.5      1     1          41.5                       16.5
     66.0      2     3          41.0                       16.0
     65.5      2                40.5                       15.5
     65.0      3     2          40.0                       15.0
     64.5      1                39.5                       14.5
     64.0      1                39.0                       14.0
     63.5      2                38.5                       13.5
     63.0      1                38.0                       13.0
     62.5      2     1          37.5                       12.5
     62.0      1                37.0                       12.0
     61.5            1          36.5                       11.5
     61.0                       36.0                       11.0
     60.5      1     1          35.5                       10.5
     60.0      2                35.0                       10.0
     59.5                       34.5                        9.5
     59.0            1          34.0      1                 9.0
     58.5            1          33.5                        8.5
     58.0      2                33.0                        8.0
     57.5                       32.5                        7.5
     57.0      2                32.0                        7.0
     56.5      3                31.5                        6.5
     56.0      1                31.0                        6.0
     55.5                       30.5                        5.5
     55.0            1          30.0                        5.0
     54.5                       29.5                        4.5
     54.0      2     2          29.0                        4.0
     53.5                       28.5                        3.5
     53.0                       28.0                        3.0
     52.5                       27.5                        2.5
     52.0                       27.0                        2.0
     51.5                       26.5                        1.5
     51.0            1          26.0                        1.0
     50.5                       25.5                         .5
                                                            0.0      0     0



                   American Mathematics Competitions
                   2005 AMC 12 B Results for Michigan                   
                         SCORE DISTRIBUTION 

    score                  -----------grade-----------
             6      7      8      9     10     11     12     13  unknown
                           ---------------------------
   143.0                           1
   133.5                                         1
   132.5                                         1
   130.0                                         1
   129.0                                  1
   125.5                                  1
   124.0                                         1
   120.5                                                1
   119.5                                         1
   118.0                                         1      1
   117.0                                                1
   116.0             2      1                    3      1
   115.0                                                1
   113.5                                         1      1
   112.5                           1             3      1
   112.0                                         1
   111.5             1                                  1
   111.0                                                1
   110.5                                         1
   110.0                    1      1
   109.0                                  1      3
   108.5                                         1
   108.0             1                           1      1
   107.5                                  1      1      1
   106.5                                  1      2      4
   105.5                                  1      3      3             1
   105.0                           1      1
   104.5                                         3      4
   104.0                                                3
   103.0                    1             1             4
   102.5                           1      1
   102.0                                  1      1      4
   101.5                                         1
   101.0                           1                    4
   100.5                    1                    2      2
   100.0                                                1
    99.5      1             1             1      1      3
    98.5                                         4      7
    97.5                                         2      1
    97.0                                         4      5
    96.0                                  1     13      3
    95.5                                         1      1
    95.0             1                           8      8
    94.5                                         2
    94.0                                         4      3
    93.5                                         3      3
    93.0                                         1
    92.5                    1                    7      6
    92.0                                  1      1      2
    91.5      1                           2      4      2
    91.0                                         1      3
    90.5                                         1      2
    90.0                           1             4      8
    89.5                                         1      1
    89.0                                  1     11      6
    88.5                                  1      2      2
    88.0      1                           1      4      8
    87.5                                         6      1
    87.0                                         2      1
    86.5                                  2      4      4
    86.0                                  1      1
    85.5                    1             1             5             1
    85.0                                  1      3      1
    84.5             1                           2      1
    84.0             1                    2      8      5
    83.5                                         1
    83.0                    1             2      3      3
    82.5                                         5
    82.0                                         3      1
    81.5                                  1      8      2
    81.0                                         2      2
    80.5                    1      1      1      7      6
    80.0                                  1      3      2
    79.5                                  2      6      5
    79.0                                  1      3      1
    78.5                                         3      2
    78.0                                         2      2
    77.5                                  1      1
    77.0                                         6      2
    76.5                                         1
    76.0                                         5      3
    75.5                                         4      2
    75.0                                         3      2
    74.5                                  1      9      2             1
    74.0                                         1
    73.5                                         1      1
    73.0                                                3
    72.5                                         4      1
    72.0                                         5      4
    71.0                                                2
    70.5                                  1      2      1
    70.0                                  1      4
    69.5                                         3
    69.0                                  1      4
    68.5                                         1      4
    68.0                                         2      1
    67.5                                         2      1
    66.5                                         2
    66.0                                  1      4      1
    65.5                                         2
    65.0                                  1      3      1             1
    64.5                                                1
    64.0                                                1
    63.5                                         1      1
    63.0                                                1
    62.5                                         2                    1
    62.0                                         1
    61.5                                         1
    60.5                                         1      1
    60.0                                         2
    59.5                                         1
    59.0                                                1
    58.5                                         1
    58.0                                         1      1
    57.0                                         1      1
    56.5                                  1             2
    56.0                                                1
    55.5                                         1
    55.0                                         1
    54.0                                         2      2
    51.0                                         1
    49.5                                                1
    48.5                                  1             1
    48.0                                         1      2
    44.0                                         1
    34.0                                         1



                   American Mathematics Competitions
                   2005 AMC 12 B Results for Michigan                   
                              Analysis      


                   Table of Item Difficulty for the 2005
              American High School Mathematics Examination
           Tabulation of responses for all Participants
                             Percent of Responses


    ITEM    A         B         C         D         E       OMITS       ?
    ____  _____     _____     _____     _____     _____     _____     _____

      1    9.35*     0.22      0.16      0.05      0.18      0.04      0.00
      2    0.00      0.07      0.05      9.58*     0.14      0.14      0.00
      3    0.05      0.02      9.42*     0.16      0.18      0.16      0.00
      4    0.04      9.37*     0.09      0.11      0.18      0.22      0.00
      5    8.41*     0.07      0.40      0.02      0.00      1.10      0.00
      6    4.00*     0.80      0.56      0.34      0.14      4.16      0.00
      7    1.43      1.37      0.18      2.73*     0.63      3.65      0.00
      8    0.98      1.25      5.24*     0.05      0.85      1.63      0.00
      9    0.31      8.19*     0.18      0.27      0.27      0.78      0.00
     10    0.18      0.42      0.25      1.77      4.01*     3.36      0.00
     11    1.14      0.92      0.74      4.85*     0.25      2.10      0.00
     12    0.24      0.71      0.83      1.21*     0.09      6.93      0.00
     13    0.60      0.20      0.29      2.30*     0.20      6.42      0.00
     14    0.81      1.37      0.65      0.27      1.12*     5.77      0.00
     15    0.33      0.27      0.33      5.03*     0.60      3.45      0.00
     16    0.16      0.22      1.16      1.01*     0.18      7.27      0.00
     17    0.34      0.92*     0.24      0.24      0.56      7.70      0.00
     18    1.56      0.54      0.42*     0.29      0.31      6.89      0.00
     19    0.25      0.14      0.18      0.29      2.80*     6.33      0.00
     20    0.07      0.29      5.28*     0.65      1.56      2.15      0.00
     21    0.18      0.27      0.90*     0.29      0.31      8.05      0.00
     22    0.36      0.65      0.33      0.18      0.04*     8.44      0.00
     23    0.14      0.33*     0.24      0.09      0.09      9.11      0.00
     24    0.24*     0.16      0.38      0.42      0.24      8.57      0.00
     25    0.24*     0.36      0.18      0.29      0.47      8.46      0.00


   (*)  Correct Response

   (?)  Response the computer was unable to read due to incomplete
        erasures or two answers marked in the same column