American Mathematics Competitions
                   2009 AMC 10 A Results for Michigan                   
                          GRAND STATISTICS  

      TOTAL NUMBER of official students taking exam:   1376

      Number of unofficial participants:          0

      Average score of participants:           69.0

      Average score for female students  is:   61.8  (   528 Students)
      Average score for male students is:      75.1  (   643 Students)
      Average score for unspecified gender is  68.4  (   205 Students)
      Average score for grade 10 is:           68.8  (   682 Students)
      Average score for grade 9 is:            66.4  (   508 Students)
      Average score for grade 8 and below is:  85.4  (   119 Students)
      Average score with unknown grade:        61.4  (    67 Students)

        AIME qualifying score =  120.0 or better
        Number of AIME qualifers                 41

        Number of schools returning results      48
        Average school winning score          105.81


                   American Mathematics Competitions
                   2009 AMC 12 A Results for Michigan                   
                          GRAND STATISTICS  

      TOTAL NUMBER of official students taking exam:   1547

      Number of unofficial participants:          0

      Average score of participants:           66.0

      Average score for female students  is:   61.0  (   569 Students)
      Average score for male students is:      70.0  (   820 Students)
      Average score for unspecified gender is  63.3  (   158 Students)
      Average score for grade 13 is:           67.5  (     1 Student) 
      Average score for grade 12 is:           66.5  (   612 Students)
      Average score for grade 11 is:           64.3  (   786 Students)
      Average score for grade 10 is:           75.8  (    81 Students)
      Average score for grade 9 is:            81.3  (    21 Students)
      Average score for grade 8 and below is:  81.7  (     9 Students)
      Average score with unknown grade:        60.5  (    37 Students)

        AIME qualifying score =   97.5 or better
        Number of AIME qualifers                 82

        Number of schools returning results      56
        Average school winning score           99.13
        Average school team score             272.30
 


                   American Mathematics Competitions
                   2009 AMC 10 B Results for Michigan                   
                          GRAND STATISTICS  

      TOTAL NUMBER of official students taking exam:    298

      Number of unofficial participants:          0

      Average score of participants:           71.0

      Average score for female students  is:   60.4  (    82 Students)
      Average score for male students is:      76.2  (   181 Students)
      Average score for unspecified gender is  69.4  (    35 Students)
      Average score for grade 10 is:           65.3  (   136 Students)
      Average score for grade 9 is:            66.5  (    93 Students)
      Average score for grade 8 and below is:  90.3  (    57 Students)
      Average score with unknown grade:        80.0  (    12 Students)

        AIME qualifying score =  120.0 or better
        Number of AIME qualifers                 17

        Number of schools returning results      19
        Average school winning score           97.42


                   American Mathematics Competitions
                   2009 AMC 12 B Results for Michigan                   
                          GRAND STATISTICS  

      TOTAL NUMBER of official students taking exam:    373

      Number of unofficial participants:          0

      Average score of participants:           66.5

      Average score for female students  is:   57.4  (   130 Students)
      Average score for male students is:      71.8  (   198 Students)
      Average score for unspecified gender is  69.9  (    45 Students)
      Average score for grade 12 is:           63.2  (   149 Students)
      Average score for grade 11 is:           63.8  (   171 Students)
      Average score for grade 10 is:           81.0  (    26 Students)
      Average score for grade 9 is:            94.3  (     7 Students)
      Average score for grade 8 and below is:  99.5  (    11 Students)
      Average score with unknown grade:        69.2  (     9 Students)

        AIME qualifying score =  100.0 or better
        Number of AIME qualifers                 36

        Number of schools returning results      22
        Average school winning score           98.93
        Average school team score             251.66
 


    2009 State AMC 12  TEAM Score Distribution
    -----------------------------------------------
    score         A         B       Rank
    -----------------------------------------------
    415.5         1                   1
    399.0                   1         2
    394.5                   1         3
    369.0         1                   4
    355.5         1                   5
    342.0         1                   6
    340.5                   1         7
    330.0         1                   8
    325.5         1                   9
    324.0                   1        10
    322.5         1                  11
    321.0         2                  12
    319.5         1                  14
    316.5         1                  15
    310.5         1                  16
    309.0         2                  17
    307.5         1         1        19
    301.5                   1        21
    297.0         1                  22
    294.0         1         1        23
    292.5         2                  25
    291.0         2                  27
    288.0         1                  29
    286.5         1                  30
    285.0         1                  31
    277.5         1                  32
    276.0                   1        33
    273.0         1                  34
    267.0         1                  35
    265.5         2                  36
    264.0         1                  38
    262.5                   1        39
    256.5         3                  40
    255.0         1                  43
    253.5                   1        44
    252.0         1         1        45
    249.0         2                  47
    246.0         1                  49
    243.0         2                  50
    240.0         1                  52
    238.5         1         1        53
    237.0         2                  55
    235.5         1                  57
    231.0                   1        58
    226.5         1                  59
    225.0         1         2        60
    223.5         1                  63
    220.5         1                  64
    219.0         2                  65
    216.0         1                  67
    213.0         1                  68
    210.0         1         1        69
    208.5                   1        71
    201.0         1                  72
    193.5                   1        73
    187.5                   1        74
    177.0         1                  75
    166.5                   1        76
    147.0                   1        77
     99.0                   1        78
 


         2009 AMC Contest Score Distributions
    -----------------------------------------------
    score      12 A      12 B      10 A      10 B
    -----------------------------------------------
    150.0                                       4
    144.0         1         1         2         2
    141.0                   1
    138.0                   1         6         1
    136.5         2                   1
    135.0         3                   2         1
    133.5         1
    132.0         2                   4         1
    130.5         1                   2
    129.0         1         2         3
    127.5                             1
    126.0         1                   5         2
    124.5                             2         1
    123.0         1                   1
    121.5         3         2         4
    120.0         2         1         8         5
    118.5         4                   2
    117.0                   1         5         1
    115.5         1         1         8         4
    114.0         1         1        10         3
    112.5         4                   5         1
    111.0         1                   4         2
    109.5         4         4         6         3
    108.0         2         6         9         5
    106.5         3         1         6         4
    105.0         1         2         8         3
    103.5         4         5         3
    102.0         5         3        13         3
    100.5        15         4        10         1
     99.0         8         6        11         5
     97.5        11         5        13         1
     96.0        16         3        14         3
     94.5        16         7        10         2
     93.0        10         8        11         3
     91.5        11         6        18         4
     90.0        11         5        22         6
     88.5        16         5        17         6
     87.0        23         4        17         5
     85.5        21         2        25         5
     84.0        38         3        29         3
     82.5        35         3        28         3
     81.0        30         4        38         1
     79.5        28         7        26         6
     78.0        48         6        35         4
     76.5        40         4        35         4
     75.0        35         7        27         9
     73.5        37         9        27         5
     72.0        60         9        37         7
     70.5        48         5        29         5
     69.0        54         7        31         4
     67.5        50         9        43         6
     66.0        72        15        47        12
     64.5        54         8        37         6
     63.0        50        12        29        12
     61.5        59         2        52         4
     60.0        62        12        44        10
     58.5        59        11        36         8
     57.0        32         8        38         1
     55.5        23        13        42         7
     54.0        50        14        41        10
     52.5        40         8        36         6
     51.0        37         7        19         5
     49.5        31         7        28         6
     48.0        35        14        36         7
     46.5        35         8        25        10
     45.0        23         6        22         6
     43.5        23         9        31         2
     42.0        36         9        27         3
     40.5        14        11        19         4
     39.0         5         8        18         5
     37.5        17         4        15         6
     36.0        17         5        17        10
     34.5        12         6        11         4
     33.0         7         4         5         1
     31.5        13         2         7
     30.0         8         3         4
     28.5         8         3         6         2
     27.0         2                   3         1
     25.5         3                             3
     24.0         4         1         4         1
     22.5         3                             1
     21.0         1         1                   1
     19.5                             1
     18.0         3         1         3
     16.5                   1



                   American Mathematics Competitions
                   2009 AMC 10 A Results for Michigan                   
                         SCORE DISTRIBUTION 

    score ----gender-----------   -----------grade-----------------
            male   female    ?    <=6      7      8      9     10      ?
    ----------------------------------------------------------------------------------------
    144.0      2                                  1             1
    138.0      3      3                           1      1      4
    136.5      1                                         1
    135.0      1      1                           1             1
    132.0      4                                  1      1      2
    130.5      1      1                           1             1
    129.0      2                                  1      1      1
    127.5      1                                         1
    126.0      4                                  1      1      3
    124.5      2                                         1      1
    123.0             1                                         1
    121.5      4                    1             1      1      1
    120.0      7      1                    1             5      2
    118.5      2                                  1             1
    117.0      3      1                    1             2      2
    115.5      6      2                           1      1      5      1
    114.0      7                           1      2      1      5      1
    112.5      3      2             1                    1      3
    111.0      3                    1      1             1      1
    109.5      4      1                    1      2             3
    108.0      6      1                           1      4      4
    106.5      5                           1             3      2
    105.0      4      3                    1      2      1      3      1
    103.5             1                                  2      1
    102.0      6      3             1      1      2      4      5
    100.5      5      4             1                    1      8
     99.0      5      3                           2      4      4      1
     97.5      6      2                                  4      9
     96.0     10      3                    1      1      1     11
     94.5      7                           1             2      7
     93.0      5      2             1             3      2      4      1
     91.5     11      5                           2      7      9
     90.0     16      2             1      2      3      8      7      1
     88.5     11      4             1      2      1      3      9      1
     87.0      9      5                    2      1      7      6      1
     85.5     20      4                    1      1     11     12
     84.0     17      8                    6      1      5     17
     82.5     16      7                           1     10     15      2
     81.0     22     11             1             1     17     16      3
     79.5     15      7             1      2             7     16
     78.0     22      8                    4      3     10     17      1
     76.5     16     15             1                   15     19
     75.0     15     11                    2      1      9     15
     73.5      9     10                    1      1      8     16      1
     72.0     22     12             1      1      4     11     20
     70.5     15     12             2                   13     11      3
     69.0     18     11                                 16     13      2
     67.5     20     17                    1            18     22      2
     66.0     20     17             1      3            22     18      3
     64.5     17     14                           1     16     16      4
     63.0     10     13             1      1            11     15      1
     61.5     19     25                    1            22     25      4
     60.0     21     23                    1            19     24
     58.5     16     15                           1     15     18      2
     57.0     20     13                    2      2     19     14      1
     55.5     18     19                    2            17     21      2
     54.0     17     17                                 13     26      2
     52.5     15     16                                 17     17      2
     51.0      7      8                    1             5     11      2
     49.5      7     18                                 14     11      3
     48.0     13     17                           1     15     18      2
     46.5      6     14                    1      1      6     15      2
     45.0      3     12                           1      5     12      4
     43.5      7     19                           1     16     13      1
     42.0      6     16                                 14     10      3
     40.5      6     11                    1      2      2     14
     39.0      1     13                                  7     10      1
     37.5      6      7                                  9      5      1
     36.0      5     11                                  8      8      1
     34.5      2      8                                  2      8      1
     33.0             4                                  2      3
     31.5      2      3                                  2      5
     30.0      1      3                                  1      2      1
     28.5      3      3                           1      3      2
     27.0      1                                         1      1      1
     24.0             3                                         3      1
     19.5                                                1
     18.0      1      2                                  2      1



                   American Mathematics Competitions
                   2009 AMC 10 A Results for Michigan                   
                              Analysis      


                   Table of Item Difficulty for the 2009
              American Mathematics Competitions 10/12
           Tabulation of responses for all Participants
                             Percent of Responses


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

      1    0.29      0.29      0.44      7.49     90.99*     0.51      0.00
      2   92.88*     1.60      0.94      0.73      1.60      2.25      0.00
      3    2.69      6.90     75.00*     6.10      3.20      6.10      0.00
      4   34.16*     6.54      6.83      5.96     14.90     31.61      0.00
      5   10.03      5.16      4.22      4.29     53.27*    23.04      0.00
      6   61.85*     2.47      7.56      3.27      1.45     23.40      0.00
      7    6.69      3.20     33.79*     3.49     29.22     23.62      0.00
      8    9.52     79.65*     2.76      1.45      1.31      5.23      0.07
      9    8.07     27.62*     7.41      5.81      1.38     49.64      0.07
     10    4.43     24.06*     5.38     10.54      1.89     53.71      0.00
     11    2.11      2.54      3.42     59.59*     1.02     31.32      0.00
     12    3.56      6.83     28.56*     7.99      7.34     45.71      0.00
     13   20.20      5.52      4.43     13.37     19.26*    37.21      0.00
     14   42.66*     1.96      6.40      3.85     12.14     32.99      0.00
     15    2.25      4.51      4.51      6.47     50.22*    32.05      0.00
     16   23.18      5.74      3.13     14.32*     6.69     46.95      0.00
     17    4.07     12.28      8.79*     3.49      3.05     68.31      0.00
     18   17.95     14.24      6.90     18.02*     8.07     34.81      0.00
     19    5.09     13.66*     9.74      7.27      2.62     61.63      0.00
     20    8.58      8.58     11.12     35.97*     1.45     34.30      0.00
     21    3.78      3.71     14.17*     3.20      2.76     72.38      0.00
     22    6.25      6.47     31.32      8.36*     3.85     43.68      0.07
     23    4.22      3.34      5.38      4.00      9.16*    73.84      0.07
     24    7.34     16.64      7.63*     5.45      6.54     56.25      0.15
     25    8.72      5.74*     6.32      3.49      4.87     70.86      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
                   2009 AMC 12 A Results for Michigan                   
                         SCORE DISTRIBUTION 

    score ----gender-----------   -----------grade-----------------
            male   female    ?    <=6      7      8      9     10     11     12     13      ?
    ----------------------------------------------------------------------------------------
    144.0      1                                                       1
    136.5      2                                                1             1
    135.0      3                                         1                    1             1
    133.5      1                                                              1
    132.0      2                                                       1      1
    130.5      1                                                       1
    129.0      1                                                1
    126.0      1                                                       1
    123.0             1                                         1
    121.5      3                                                       2      1
    120.0      2                                                       1      1
    118.5      2      2                                         1             3
    115.5      1                                                              1
    114.0      1                                                              1
    112.5      4                                         1             1      2
    111.0      1                                                       1
    109.5      2                                                       2      2
    108.0      1      1                                         1             1
    106.5      2                                                       2                    1
    105.0      1                                                       1
    103.5      3      1                                  1             1      2
    102.0      5                                                3      1      1
    100.5     10      4                                  1      1      7      6
     99.0      7      1                                  1             5      2
     97.5     10      1                           1      1             6      3
     96.0     11      2                                         3      6      7
     94.5     13      3                                         2      6      8
     93.0      7      2                                         1      3      6
     91.5      3      6                                         1      5      5
     90.0     11                                  1             2      4      4
     88.5     12      2                                         3      6      7
     87.0     16      4                           1      1            13      8
     85.5     12      7                                         2     15      4
     84.0     26      7                    1                    4     18     15
     82.5     20     10                           1      1      1     20     12
     81.0     16     10                           1             4     11     13             1
     79.5     16      7                                  2            18      7             1
     78.0     31     13                                         4     20     23             1
     76.5     29      8                           1      1      3     17     18
     75.0     22     11                           1             2     16     16
     73.5     22     13                                         3     16     18
     72.0     31     25                                         3     28     28             1
     70.5     19     22                                  4      5     21     16             2
     69.0     31     19                                  1      2     22     28             1
     67.5     26     23                                         2     28     18      1      1
     66.0     42     22                                  1      7     39     22             3
     64.5     24     27                                  1      1     28     24
     63.0     33     14                                               24     23             3
     61.5     30     20                           1                   31     24             3
     60.0     33     23                                         1     31     30
     58.5     34     18                                  2      3     32     21             1
     57.0     11     19                                         1     20     11
     55.5      8     11                                  1            14      7             1
     54.0     20     27                                         1     29     18             2
     52.5     17     21                                         2     24     14
     51.0     12     19                                               18     17             2
     49.5     14     13                                         1     15     15
     48.0     18     14                                         1     21     11             2
     46.5     13     19                                         1     22      9             3
     45.0      7     12                                         1     12      9             1
     43.5      5     11                                         1      9     12             1
     42.0     16     12                                         1     23     10             2
     40.5      3      9                                                9      4             1
     39.0      2      3                                                3      2
     37.5      2     13                                         1      7      9
     36.0      9      6                                                9      8
     34.5      3      7                                               10      1             1
     33.0      3      4                                         1      3      3
     31.5      5      6                                                6      6             1
     30.0      6      1                                                6      2
     28.5      2      4                                                3      5
     27.0             2                                                1      1
     25.5      1      2                                                2      1
     24.0      3      1                                         1      1      2
     22.5      2      1                                                3
     21.0             1                                                1
     18.0      1      2                                                3



                   American Mathematics Competitions
                   2009 AMC 12 A Results for Michigan                   
                              Analysis      


                   Table of Item Difficulty for the 2009
              American Mathematics Competitions 10/12
           Tabulation of responses for all Participants
                             Percent of Responses


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

      1   85.65*     7.37      1.16      1.10      1.94      2.78      0.00
      2    1.23      5.43     85.65*     4.40      1.94      1.36      0.00
      3    5.88     77.70*     3.81      5.75      2.78      4.01      0.06
      4   94.05*     0.97      0.45      1.23      1.49      1.75      0.06
      5    1.29      2.91      2.71     77.70*     1.62     13.77      0.00
      6   20.30      5.56      4.40     13.51     36.59*    19.52      0.13
      7    2.91     27.28*     9.18      4.72      2.52     53.39      0.00
      8   59.34*     1.94      6.46      4.98      9.70     17.39      0.19
      9    2.26      5.37      6.33     37.23*     6.01     42.66      0.13
     10    3.36      7.76     39.50*    10.54      6.40     32.39      0.06
     11    1.75      3.43      4.33      5.69     68.52*    16.22      0.06
     12   12.22     28.51*     7.11     10.28      4.33     37.43      0.13
     13   10.41     12.09     16.35     20.17*     6.59     34.32      0.06
     14    4.07      8.14*    11.31     12.41      7.11     56.88      0.06
     15    8.02      6.66     10.21     25.34*     4.85     44.73      0.19
     16   14.87      8.99      9.50      8.14*     3.23     55.20      0.06
     17    4.85      5.30     12.15*     6.46     10.54     60.57      0.13
     18   14.67      8.14*     7.89      4.33      3.62     61.28      0.06
     19    7.24      9.76     10.41*     9.18     10.60     52.75      0.06
     20    4.27      4.07      9.44      6.27      9.31*    66.58      0.06
     21    6.14      6.08      8.02*     4.20      5.11     70.27      0.19
     22    3.10      6.79      6.08      5.37      3.36*    75.24      0.06
     23    3.10      3.62      5.49      4.46*     1.23     82.03      0.06
     24   10.67      7.82      5.49      4.33      1.55*    70.14      0.00
     25    3.30*     7.05      7.11      7.24      8.34     66.97      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
                   2009 AMC 10 B Results for Michigan                   
                         SCORE DISTRIBUTION 

    score ----gender-----------   -----------grade-----------------
            male   female    ?    <=6      7      8      9     10      ?
    ----------------------------------------------------------------------------------------
    150.0      4                                         1      2      1
    144.0      2                                         1      1
    138.0             1                                         1
    135.0             1                           1
    132.0                                                1
    126.0      2                           1      1
    124.5      1                                  1
    120.0      4                    1             2             2
    117.0      1                                         1
    115.5      2      2                           2      1      1
    114.0      2      1                    1      1      1
    112.5      1                                  1
    111.0      2                                  1      1
    109.5      2                           1      1      1
    108.0      4                    1             2      1             1
    106.5      4                    1                    2      1
    105.0      2      1                           1      1      1
    102.0      3                                  1      1      1
    100.5             1                           1
     99.0      4      1                           1      2      2
     97.5      1                                                       1
     96.0      2      1                    1             2
     94.5      2                    1                    1
     93.0      2      1             1                    1      1
     91.5      3      1             1      1                    2
     90.0      5      1                    1      1      2      2
     88.5      5                    2             1      2      1
     87.0      4      1                           1             4
     85.5      2      2                           1             3      1
     84.0      2                                         2      1
     82.5      2      1             1                    2
     81.0      1                    1
     79.5      4      1             1      1                    4
     78.0      2      1                                         3      1
     76.5      3                                  1             3
     75.0      6      1                    1      2             5      1
     73.5      4                    1             1             2      1
     72.0      7                                         2      5
     70.5      3      1                    1                    3      1
     69.0             2                                  2      2
     67.5      3                    1      1             2      1      1
     66.0      5      4                           1      4      6      1
     64.5      5      1             1                    2      3
     63.0      9      3                                  3      9
     61.5      4                                         1      3
     60.0      7      2             1      1             3      5
     58.5      3      4                           1      2      5
     57.0      1                                         1
     55.5      5      1                                  3      4
     54.0      4      4                                  7      3
     52.5      2      2                                  3      3
     51.0      3      2                                  4      1
     49.5             4             1                    1      3      1
     48.0      4      3             1                    3      3
     46.5      5      4                                  5      5
     45.0      1      5             1                    2      3
     43.5             2                                  1      1
     42.0      1      2                                  2      1
     40.5      3      1                                  1      3
     39.0      1      3                                         4      1
     37.5      1      5                                  2      4
     36.0      6      3                                  3      7
     34.5      2      2                                  2      2
     33.0      1                                                1
     28.5             1                                  2
     27.0      1                                         1
     25.5      1      2                                  2      1
     24.0      1                    1
     22.5      1                                                1
     21.0      1                                                1



                   American Mathematics Competitions
                   2009 AMC 10 B Results for Michigan                   
                              Analysis      


                   Table of Item Difficulty for the 2009
              American Mathematics Competitions 10/12
           Tabulation of responses for all Participants
                             Percent of Responses


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

      1    1.01     64.77*    11.74     18.79      3.69      0.00      0.00
      2    3.02      2.01     89.26*     0.00      0.67      5.03      0.00
      3    2.01      5.70     74.16*    11.07      2.01      5.03      0.00
      4    1.68      4.03     68.12*    12.42      4.03      9.73      0.00
      5    7.05      4.36     16.44     61.41*     1.34      9.40      0.00
      6    1.01      2.01      6.38     74.50*     4.36     11.74      0.00
      7   12.75     16.11     50.67*    11.74      6.04      2.68      0.00
      8    2.35     43.29*     9.06     29.19      4.36     11.74      0.00
      9   39.93*     5.70      4.36      9.06      5.70     35.23      0.00
     10   15.77      2.01      6.71      7.38     39.26*    28.86      0.00
     11   61.41*    10.07      7.05      2.01      2.35     17.11      0.00
     12   33.56*    12.75      7.05     16.78      8.05     21.81      0.00
     13    2.68     10.07     41.95*    11.74     10.74     22.82      0.00
     14    6.71     24.16     21.81     19.46*    10.07     17.79      0.00
     15    7.38      7.72      6.38      6.04     49.66*    22.48      0.34
     16    3.02     19.46*     8.05      3.02      6.04     60.40      0.00
     17   17.45     12.75     28.19*     4.36      2.35     34.90      0.00
     18    3.02      6.04     10.40     17.11*     5.37     58.05      0.00
     19   28.19*    20.13     13.76      8.72      5.03     24.16      0.00
     20    7.05     20.13*     7.72      2.35      3.36     59.40      0.00
     21    7.72     15.10      6.04     17.79*     4.36     48.99      0.00
     22    3.02      9.06*     6.38      6.71      1.34     73.49      0.00
     23    8.39      9.73     14.43*     9.40      7.05     51.01      0.00
     24   18.46*     3.36      7.05      5.37      4.70     61.07      0.00
     25   22.82     17.45*     8.72      6.38      8.05     36.58      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
                   2009 AMC 12 B Results for Michigan                   
                         SCORE DISTRIBUTION 

    score ----gender-----------   -----------grade-----------------
            male   female    ?    <=6      7      8      9     10     11     12     13      ?
    ----------------------------------------------------------------------------------------
    144.0      1                                                       1
    141.0      1                                                              1
    138.0      1                                                       1
    129.0      2                                                       2
    121.5      1                                  1                                         1
    120.0      1                                                       1
    117.0                                                                     1
    115.5                                                                     1
    114.0      1                                                              1
    109.5      4                           1      1                    2
    108.0      3      3                           2                    1      3
    106.5      1                                                1
    105.0      1      1                                         1             1
    103.5      4      1                                  1             2      2
    102.0      3                                                       1      2
    100.5      3                           1      1             1      1
     99.0      4      1                                         2      2      2
     97.5      4      1                           1      2      1      1
     96.0      3                                                1      2
     94.5      3      2                                  1      2      3                    1
     93.0      5      2                                         1      3      4
     91.5      3                                  1             1      3      1
     90.0      4                                         2             1      2
     88.5      4      1                                         2      3
     87.0      2      1                                  1             1      1             1
     85.5      1      1                                         2
     84.0      2      1                                                1      2
     82.5      1      1                                                1      2
     81.0      3                                                       2      2
     79.5      4      2                                                2      5
     78.0      5      1                                                4      2
     76.5      3      1                                                2      2
     75.0      3      2                           1             1      4      1
     73.5      6      2                           1             1      3      4
     72.0      3      4                                                5      3             1
     70.5      3      2                                         1      2      2
     69.0      5      2                                                4      3
     67.5      7      2                                                6      3
     66.0      6      6                                         1      6      8
     64.5      3      4                                         1      2      4             1
     63.0      6      4                                         1      5      6
     61.5      1                                                       1      1
     60.0      8      4                                                7      5
     58.5      5      6                                         1      4      6
     57.0      5      3                                                5      3
     55.5      7      4                                         2      5      5             1
     54.0      7      5                                                9      4             1
     52.5      4      3                                                2      6
     51.0      3      4                                         1      2      4
     49.5      3      3                                                6      1
     48.0      5      6                                         1      8      5
     46.5      3      3                                                3      5
     45.0      2      3                                                3      3
     43.5      3      6                                                3      6
     42.0      2      6                                                7      2
     40.5      7      3                                                7      4
     39.0      3      3                                                3      4             1
     37.5      1      3                                                2      2
     36.0      2      3                                                4      1
     34.5      2      3                                                1      4             1
     33.0      1      3                                                3      1
     31.5             2                                                       2
     30.0      1      2                                                2      1
     28.5      1      2                                                1      2
     24.0      1                                                       1
     21.0      1                                                       1
     18.0             1                                                       1
     16.5             1                                                1



                   American Mathematics Competitions
                   2009 AMC 12 B Results for Michigan                   
                              Analysis      


                   Table of Item Difficulty for the 2009
              American Mathematics Competitions 10/12
           Tabulation of responses for all Participants
                             Percent of Responses


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

      1    1.07     78.02*     6.97     11.53      1.61      0.80      0.00
      2    1.61      4.29     79.62*    10.72      1.07      2.68      0.00
      3    8.85      2.95     16.89     58.71*     2.41     10.19      0.00
      4    3.75      3.49     76.41*     6.43      4.02      5.63      0.27
      5    0.27      1.07      6.70     74.80*     4.83     12.06      0.27
      6   12.33     12.06     62.73*     7.77      2.95      2.14      0.00
      7    4.29     43.16*     6.43     32.44      3.75      9.92      0.00
      8    9.12     10.19      3.22      5.36     58.18*    13.94      0.00
      9   46.11*     5.63      2.68      6.70      2.68     36.19      0.00
     10   34.58*    28.95      9.12      7.24      3.49     16.62      0.00
     11    3.75     24.13     19.84     26.54*     8.58     17.16      0.00
     12    3.22      3.22      5.63      3.22     32.71*    52.01      0.00
     13    2.95      5.09      6.17     22.79*     5.90     57.10      0.00
     14   15.82     17.69     34.32*     1.61      1.07     29.49      0.00
     15    0.80     48.26*    12.33      5.63      3.75     28.95      0.27
     16    5.63      5.90*     6.43      3.22      2.14     76.68      0.00
     17   23.06     18.50*     8.31      6.97      5.36     37.80      0.00
     18    5.90      9.38     19.84*     6.97      5.09     52.82      0.00
     19    2.14      5.90      4.29      3.75      4.29*    79.62      0.00
     20    3.49      4.02      4.29*     4.29      2.41     81.50      0.00
     21    9.38*     5.09      7.77     14.48     18.23     45.04      0.00
     22    2.41      5.36      6.70*     3.22      2.68     79.62      0.00
     23    1.88      5.09      3.49      6.43*     2.14     80.70      0.27
     24    5.63      8.31*     3.49      3.49      2.14     76.94      0.00
     25   12.33      5.90      4.83      4.29      5.09*    67.56      0.00


   (*)  Correct Response

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