American Mathematics Competitions
2003 AMC 10 A Results for Michigan
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 1569
Number of unofficial participants: 20
Average score of participants: 74.4
Average score for female students is: 70.6 ( 688 Students)
Average score for male students is: 77.6 ( 815 Students)
Average score for unspecified gender is 74.1 ( 66 Students)
Average score for grade 10 is: 76.4 ( 847 Students)
Average score for grade 9 is: 70.4 ( 611 Students)
Average score for grade 8 and below is: 85.1 ( 81 Students)
Average score with unknown grade: 70.3 ( 30 Students)
AIME qualifying score = 119.0 or better
Number of AIME qualifers 26
Number of schools returning results 62
Average school winning score 106.17
American Mathematics Competitions
2003 AMC 12 A Results for Michigan
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 2040
Number of unofficial participants: 0
Average score of participants: 78.5
Average score for female students is: 73.6 ( 802 Students)
Average score for male students is: 81.8 ( 1193 Students)
Average score for unspecified gender is 79.8 ( 45 Students)
Average score for grade 13 is: 69.5 ( 2 Students)
Average score for grade 12 is: 81.1 ( 890 Students)
Average score for grade 11 is: 75.8 ( 972 Students)
Average score for grade 10 is: 78.1 ( 113 Students)
Average score for grade 9 is: 88.7 ( 40 Students)
Average score for grade 8 and below is: 95.8 ( 6 Students)
Average score with unknown grade: 72.9 ( 17 Students)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 282
Number of schools returning results 73
Average school winning score 108.60
Average school team score 304.57
American Mathematics Competitions
2003 AMC 10 B Results for Michigan
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 387
Number of unofficial participants: 0
Average score of participants: 76.0
Average score for female students is: 72.0 ( 171 Students)
Average score for male students is: 79.4 ( 203 Students)
Average score for unspecified gender is 75.7 ( 13 Students)
Average score for grade 10 is: 78.9 ( 159 Students)
Average score for grade 9 is: 75.6 ( 153 Students)
Average score for grade 8 and below is: 71.4 ( 69 Students)
Average score with unknown grade: 63.0 ( 6 Students)
AIME qualifying score = 121.0 or better
Number of AIME qualifers 8
Number of schools returning results 18
Average school winning score 106.14
American Mathematics Competitions
2003 AMC 12 B Results for Michigan
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 492
Number of unofficial participants: 0
Average score of participants: 73.5
Average score for female students is: 68.8 ( 200 Students)
Average score for male students is: 76.9 ( 283 Students)
Average score for unspecified gender is 66.8 ( 9 Students)
Average score for grade 12 is: 77.2 ( 193 Students)
Average score for grade 11 is: 71.0 ( 234 Students)
Average score for grade 10 is: 65.5 ( 39 Students)
Average score for grade 9 is: 95.8 ( 2 Students)
Average score for grade 8 and below is: 81.3 ( 20 Students)
Average score with unknown grade: 63.8 ( 4 Students)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 41
Number of schools returning results 23
Average school winning score 103.35
Average school team score 282.22
2003 AMC Contest Score Distributions
-----------------------------------------------
score 12 A 12 B 10 A 10 B
-----------------------------------------------
150.0 1 0 0 0
149.5 0 0 0 0
149.0 0 0 0 0
148.5 0 0 0 0
148.0 0 0 0 0
147.5 0 0 0 0
147.0 0 0 0 0
146.5 0 0 0 0
146.0 0 0 0 0
145.5 0 0 0 0
145.0 0 0 0 0
144.5 0 0 0 0
144.0 0 0 0 0
143.5 0 0 0 0
143.0 1 0 0 1
142.5 0 0 0 0
142.0 0 0 0 0
141.5 0 0 0 0
141.0 0 0 0 0
140.5 1 1 0 0
140.0 0 0 0 0
139.5 0 0 0 0
139.0 0 0 0 0
138.5 0 0 0 0
138.0 0 0 0 2
137.5 0 0 0 0
137.0 0 0 1 1
136.5 0 0 0 0
136.0 2 0 0 0
135.5 0 0 0 0
135.0 0 0 0 0
134.5 0 0 1 0
134.0 0 0 0 0
133.5 0 0 0 0
133.0 0 0 0 0
132.5 1 0 1 0
132.0 0 0 1 0
131.5 0 0 0 0
131.0 0 0 0 0
130.5 0 0 0 0
130.0 0 1 1 0
129.5 0 0 0 0
129.0 2 0 0 1
128.5 0 0 1 0
128.0 0 0 0 0
127.5 3 0 1 0
127.0 0 0 0 0
126.5 0 0 2 1
126.0 1 0 0 0
125.5 1 0 0 0
125.0 0 0 2 1
124.5 0 0 0 0
124.0 5 1 0 1
123.5 0 0 0 0
123.0 5 0 1 0
122.5 1 0 2 0
122.0 3 0 0 0
121.5 0 0 2 0
121.0 0 0 0 0
120.5 3 0 4 0
120.0 0 0 2 0
119.5 2 0 1 0
119.0 0 0 3 0
118.5 3 0 0 0
118.0 1 0 3 1
117.5 0 0 0 0
117.0 7 1 0 1
116.5 0 0 1 0
116.0 11 2 3 2
115.5 0 0 1 1
115.0 4 0 0 1
114.5 4 0 1 0
114.0 1 0 1 0
113.5 8 1 1 0
113.0 1 0 1 0
112.5 15 0 2 1
112.0 4 2 5 0
111.5 6 0 0 0
111.0 3 0 5 2
110.5 0 0 0 0
110.0 12 1 6 1
109.5 1 1 4 1
109.0 12 2 3 0
108.5 1 1 5 3
108.0 13 2 4 1
107.5 9 1 9 0
107.0 0 0 0 0
106.5 14 2 5 1
106.0 3 0 1 0
105.5 18 2 4 3
105.0 5 0 7 1
104.5 9 2 0 0
104.0 12 2 5 3
103.5 0 0 0 0
103.0 20 2 7 2
102.5 3 0 8 0
102.0 14 5 4 3
101.5 9 1 6 1
101.0 9 2 1 0
100.5 14 6 18 4
100.0 1 0 3 0
99.5 21 2 11 5
99.0 8 0 4 1
98.5 16 2 7 1
98.0 11 3 16 2
97.5 1 0 3 3
97.0 22 4 19 4
96.5 2 0 5 2
96.0 31 2 9 3
95.5 5 0 9 2
95.0 23 6 6 1
94.5 23 1 19 7
94.0 3 0 5 0
93.5 31 3 9 5
93.0 4 1 5 4
92.5 17 5 3 3
92.0 14 3 16 2
91.5 12 2 2 1
91.0 24 2 15 6
90.5 9 2 2 2
90.0 33 6 17 8
89.5 10 2 15 1
89.0 31 5 8 5
88.5 10 1 20 4
88.0 10 2 3 1
87.5 16 3 18 3
87.0 9 2 6 1
86.5 28 4 18 3
86.0 18 0 17 2
85.5 17 4 7 7
85.0 17 3 13 4
84.5 14 3 9 2
84.0 35 7 16 2
83.5 11 0 11 4
83.0 34 9 11 7
82.5 13 2 20 3
82.0 14 5 9 5
81.5 22 7 19 3
81.0 13 5 8 3
80.5 23 8 14 5
80.0 10 2 21 4
79.5 10 3 8 5
79.0 17 5 20 2
78.5 17 7 10 2
78.0 28 7 15 13
77.5 16 3 9 3
77.0 34 13 21 8
76.5 28 0 15 2
76.0 27 6 14 6
75.5 23 8 11 2
75.0 18 10 11 1
74.5 30 6 15 5
74.0 7 3 14 1
73.5 19 6 17 3
73.0 19 6 18 6
72.5 18 4 17 2
72.0 26 6 19 5
71.5 12 7 8 4
71.0 37 7 16 6
70.5 16 4 16 6
70.0 12 6 18 5
69.5 20 6 19 2
69.0 19 10 19 2
68.5 28 6 19 3
68.0 10 3 14 2
67.5 19 1 17 3
67.0 21 6 16 4
66.5 19 10 19 4
66.0 21 11 27 3
65.5 15 8 17 2
65.0 16 4 12 2
64.5 16 3 18 3
64.0 12 4 21 1
63.5 17 1 24 0
63.0 17 5 12 2
62.5 23 6 15 1
62.0 10 8 10 3
61.5 14 3 18 3
61.0 14 4 15 0
60.5 15 4 12 2
60.0 29 6 27 5
59.5 8 2 7 2
59.0 17 10 18 2
58.5 9 2 8 1
58.0 19 4 12 1
57.5 5 5 15 2
57.0 14 3 15 1
56.5 21 9 16 5
56.0 10 4 6 3
55.5 4 2 11 1
55.0 10 2 4 0
54.5 10 2 8 2
54.0 13 6 13 6
53.5 10 3 8 2
53.0 11 0 12 0
52.5 6 3 7 2
52.0 6 4 6 1
51.5 3 6 6 0
51.0 11 3 6 0
50.5 3 3 9 3
50.0 10 2 7 1
49.5 6 0 8 2
49.0 4 2 7 1
48.5 5 5 4 0
48.0 14 2 10 5
47.5 7 2 5 0
47.0 4 0 6 0
46.5 4 1 4 0
46.0 3 1 4 1
45.5 6 1 7 0
45.0 4 2 1 0
44.5 1 0 2 0
44.0 4 2 2 1
43.5 3 0 1 2
43.0 0 2 4 1
42.5 4 1 6 0
42.0 7 0 4 8
41.5 1 2 4 1
41.0 3 1 2 0
40.5 5 0 5 0
40.0 3 3 2 2
39.5 1 0 1 0
39.0 1 0 3 0
38.5 1 2 4 1
38.0 4 0 4 0
37.5 2 1 1 1
37.0 0 0 1 1
36.5 2 1 2 0
36.0 5 0 4 2
35.5 0 1 2 0
35.0 4 0 0 0
34.5 1 0 1 0
34.0 1 0 0 0
33.5 0 0 1 0
33.0 3 0 0 1
32.5 1 0 1 0
32.0 1 0 1 0
31.5 1 0 3 2
31.0 0 0 1 0
30.5 0 0 2 0
30.0 2 0 8 4
29.5 1 0 0 0
29.0 0 0 0 0
28.5 1 0 0 0
28.0 0 0 0 0
27.5 0 0 0 0
27.0 0 0 1 0
26.5 1 0 0 0
26.0 0 0 0 0
25.5 0 0 0 0
25.0 0 0 1 0
24.5 0 0 1 0
24.0 3 0 0 4
23.5 0 0 0 0
23.0 0 0 1 0
22.5 0 0 0 0
22.0 0 0 0 1
21.5 0 0 0 0
21.0 0 0 0 0
20.5 0 0 0 1
20.0 0 0 0 0
19.5 0 0 0 0
19.0 0 0 0 0
18.5 0 0 0 0
18.0 3 0 1 4
17.5 0 0 0 0
17.0 0 0 0 0
16.5 0 0 0 0
16.0 0 0 0 0
15.5 0 0 0 0
15.0 0 0 0 0
14.5 0 0 0 0
14.0 0 0 0 0
13.5 0 0 2 0
13.0 0 0 0 0
12.5 0 0 0 0
12.0 0 0 2 0
11.5 0 0 0 0
11.0 0 0 0 0
10.5 0 0 0 0
10.0 0 0 0 0
9.5 0 0 0 0
9.0 0 0 0 0
8.5 0 0 0 0
8.0 0 0 0 0
7.5 0 0 0 0
7.0 0 0 0 0
6.5 0 0 0 0
6.0 0 0 0 0
5.5 0 0 0 0
5.0 0 0 0 0
4.5 0 0 0 0
4.0 0 0 0 0
3.5 0 0 0 0
3.0 0 0 0 0
2.5 0 0 0 0
2.0 0 0 0 0
1.5 0 0 0 0
1.0 0 0 0 0
0.5 0 0 0 0
0 0 0 0
American Mathematics Competitions
2003 AMC 10 A Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 0 0 125.0 2 0 100.0 1 1
149.5 0 0 124.5 0 0 99.5 8 3
149.0 0 0 124.0 0 0 99.0 2 1
148.5 0 0 123.5 0 0 98.5 4 2
148.0 0 0 123.0 0 1 98.0 9 7
147.5 0 0 122.5 2 0 97.5 0 3
147.0 0 0 122.0 0 0 97.0 13 5
146.5 0 0 121.5 2 0 96.5 4 1
146.0 0 0 121.0 0 0 96.0 8 1
145.5 0 0 120.5 4 0 95.5 7 2
145.0 0 0 120.0 2 0 95.0 2 4
144.5 0 0 119.5 1 0 94.5 13 4
144.0 0 0 119.0 2 1 94.0 3 2
143.5 0 0 118.5 0 0 93.5 4 5
143.0 0 0 118.0 2 1 93.0 4 1
142.5 0 0 117.5 0 0 92.5 3 0
142.0 0 0 117.0 0 0 92.0 11 4
141.5 0 0 116.5 1 0 91.5 1 0
141.0 0 0 116.0 2 1 91.0 9 6
140.5 0 0 115.5 0 1 90.5 2 0
140.0 0 0 115.0 0 0 90.0 10 7
139.5 0 0 114.5 1 0 89.5 9 6
139.0 0 0 114.0 1 0 89.0 3 5
138.5 0 0 113.5 1 0 88.5 12 8
138.0 0 0 113.0 0 1 88.0 3 0
137.5 0 0 112.5 2 0 87.5 8 8
137.0 1 0 112.0 4 1 87.0 4 2
136.5 0 0 111.5 0 0 86.5 7 9
136.0 0 0 111.0 4 1 86.0 10 6
135.5 0 0 110.5 0 0 85.5 5 2
135.0 0 0 110.0 5 1 85.0 4 5
134.5 1 0 109.5 3 1 84.5 5 4
134.0 0 0 109.0 2 1 84.0 11 5
133.5 0 0 108.5 4 1 83.5 5 6
133.0 0 0 108.0 2 2 83.0 4 7
132.5 1 0 107.5 5 3 82.5 11 9
132.0 1 0 107.0 0 0 82.0 6 3
131.5 0 0 106.5 3 1 81.5 12 7
131.0 0 0 106.0 0 1 81.0 2 4
130.5 0 0 105.5 2 2 80.5 10 4
130.0 0 1 105.0 6 1 80.0 11 10
129.5 0 0 104.5 0 0 79.5 3 5
129.0 0 0 104.0 4 0 79.0 10 9
128.5 1 0 103.5 0 0 78.5 5 3
128.0 0 0 103.0 3 4 78.0 7 8
127.5 1 0 102.5 7 0 77.5 6 3
127.0 0 0 102.0 4 0 77.0 12 8
126.5 1 1 101.5 2 4 76.5 10 5
126.0 0 0 101.0 1 0 76.0 6 8
125.5 0 0 100.5 12 6 75.5 5 6
American Mathematics Competitions
2003 AMC 10 A Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 7 4 50.0 4 3 25.0 0 1
74.5 7 7 49.5 1 6 24.5 1 0
74.0 9 5 49.0 2 4 24.0 0 0
73.5 4 11 48.5 1 3 23.5 0 0
73.0 7 9 48.0 5 5 23.0 0 1
72.5 8 8 47.5 1 4 22.5 0 0
72.0 12 7 47.0 4 2 22.0 0 0
71.5 2 6 46.5 1 3 21.5 0 0
71.0 8 7 46.0 1 3 21.0 0 0
70.5 9 7 45.5 3 3 20.5 0 0
70.0 9 7 45.0 0 1 20.0 0 0
69.5 12 7 44.5 0 2 19.5 0 0
69.0 7 11 44.0 0 2 19.0 0 0
68.5 8 11 43.5 1 0 18.5 0 0
68.0 6 7 43.0 3 1 18.0 1 0
67.5 8 8 42.5 2 4 17.5 0 0
67.0 6 10 42.0 2 2 17.0 0 0
66.5 13 6 41.5 0 4 16.5 0 0
66.0 12 12 41.0 1 1 16.0 0 0
65.5 10 6 40.5 3 2 15.5 0 0
65.0 7 5 40.0 2 0 15.0 0 0
64.5 7 11 39.5 0 1 14.5 0 0
64.0 5 14 39.0 1 2 14.0 0 0
63.5 13 10 38.5 1 3 13.5 1 1
63.0 6 6 38.0 3 1 13.0 0 0
62.5 6 8 37.5 1 0 12.5 0 0
62.0 5 4 37.0 0 1 12.0 1 1
61.5 9 8 36.5 1 1 11.5 0 0
61.0 7 6 36.0 2 2 11.0 0 0
60.5 5 7 35.5 0 2 10.5 0 0
60.0 10 14 35.0 0 0 10.0 0 0
59.5 3 3 34.5 1 0 9.5 0 0
59.0 10 7 34.0 0 0 9.0 0 0
58.5 3 5 33.5 0 1 8.5 0 0
58.0 5 7 33.0 0 0 8.0 0 0
57.5 6 8 32.5 0 1 7.5 0 0
57.0 6 8 32.0 0 1 7.0 0 0
56.5 6 8 31.5 1 2 6.5 0 0
56.0 2 3 31.0 0 1 6.0 0 0
55.5 5 5 30.5 0 2 5.5 0 0
55.0 3 1 30.0 3 5 5.0 0 0
54.5 3 5 29.5 0 0 4.5 0 0
54.0 9 4 29.0 0 0 4.0 0 0
53.5 4 3 28.5 0 0 3.5 0 0
53.0 7 5 28.0 0 0 3.0 0 0
52.5 2 5 27.5 0 0 2.5 0 0
52.0 1 5 27.0 0 1 2.0 0 0
51.5 3 3 26.5 0 0 1.5 0 0
51.0 3 3 26.0 0 0 1.0 0 0
50.5 6 3 25.5 0 0 0.5 0 0
0.0 0 0
American Mathematics Competitions
2003 AMC 10 A Results for Michigan
SCORE DISTRIBUTION
score -----------grade-----------
5 6 7 8 9 10 unknown
---------------------------
150.0 0 0 0 0 0 0 0
149.5 0 0 0 0 0 0 0
149.0 0 0 0 0 0 0 0
148.5 0 0 0 0 0 0 0
148.0 0 0 0 0 0 0 0
147.5 0 0 0 0 0 0 0
147.0 0 0 0 0 0 0 0
146.5 0 0 0 0 0 0 0
146.0 0 0 0 0 0 0 0
145.5 0 0 0 0 0 0 0
145.0 0 0 0 0 0 0 0
144.5 0 0 0 0 0 0 0
144.0 0 0 0 0 0 0 0
143.5 0 0 0 0 0 0 0
143.0 0 0 0 0 0 0 0
142.5 0 0 0 0 0 0 0
142.0 0 0 0 0 0 0 0
141.5 0 0 0 0 0 0 0
141.0 0 0 0 0 0 0 0
140.5 0 0 0 0 0 0 0
140.0 0 0 0 0 0 0 0
139.5 0 0 0 0 0 0 0
139.0 0 0 0 0 0 0 0
138.5 0 0 0 0 0 0 0
138.0 0 0 0 0 0 0 0
137.5 0 0 0 0 0 0 0
137.0 0 0 0 0 0 1 0
136.5 0 0 0 0 0 0 0
136.0 0 0 0 0 0 0 0
135.5 0 0 0 0 0 0 0
135.0 0 0 0 0 0 0 0
134.5 0 0 0 0 0 1 0
134.0 0 0 0 0 0 0 0
133.5 0 0 0 0 0 0 0
133.0 0 0 0 0 0 0 0
132.5 0 0 0 0 1 0 0
132.0 0 0 0 0 1 0 0
131.5 0 0 0 0 0 0 0
131.0 0 0 0 0 0 0 0
130.5 0 0 0 0 0 0 0
130.0 0 0 0 0 1 0 0
129.5 0 0 0 0 0 0 0
129.0 0 0 0 0 0 0 0
128.5 0 0 0 0 1 0 0
128.0 0 0 0 0 0 0 0
127.5 0 0 0 0 0 1 0
127.0 0 0 0 0 0 0 0
126.5 0 0 0 0 1 1 0
126.0 0 0 0 0 0 0 0
125.5 0 0 0 0 0 0 0
125.0 0 0 1 0 1 0 0
124.5 0 0 0 0 0 0 0
124.0 0 0 0 0 0 0 0
123.5 0 0 0 0 0 0 0
123.0 0 0 0 1 0 0 0
122.5 0 0 0 1 0 1 0
122.0 0 0 0 0 0 0 0
121.5 0 0 0 0 0 2 0
121.0 0 0 0 0 0 0 0
120.5 0 1 0 1 1 1 0
120.0 0 0 0 0 1 1 0
119.5 0 0 0 0 0 1 0
119.0 0 0 1 1 0 1 0
118.5 0 0 0 0 0 0 0
118.0 0 0 1 0 0 2 0
117.5 0 0 0 0 0 0 0
117.0 0 0 0 0 0 0 0
116.5 0 0 0 0 0 1 0
116.0 0 0 0 1 1 1 0
115.5 0 0 0 0 1 0 0
115.0 0 0 0 0 0 0 0
114.5 0 0 0 0 0 1 0
114.0 0 0 0 0 0 1 0
113.5 0 0 0 0 0 1 0
113.0 0 0 0 0 0 1 0
112.5 0 0 0 0 0 2 0
112.0 0 0 0 0 1 4 0
111.5 0 0 0 0 0 0 0
111.0 0 0 0 0 0 5 0
110.5 0 0 0 0 0 0 0
110.0 0 0 0 0 2 4 0
109.5 0 0 0 0 0 4 0
109.0 0 0 0 0 1 2 0
108.5 0 0 0 1 1 3 0
108.0 0 0 0 0 2 2 0
107.5 0 0 1 1 1 5 1
107.0 0 0 0 0 0 0 0
106.5 0 0 0 0 2 3 0
106.0 0 0 0 0 1 0 0
105.5 0 0 0 0 0 4 0
105.0 0 0 0 0 0 7 0
104.5 0 0 0 0 0 0 0
104.0 0 0 0 1 3 1 0
103.5 0 0 0 0 0 0 0
103.0 0 0 0 1 0 6 0
102.5 0 0 1 0 2 5 0
102.0 0 0 0 0 1 3 0
101.5 0 0 0 2 1 3 0
101.0 0 0 0 0 0 1 0
100.5 0 0 0 1 7 10 0
100.0 0 0 0 0 1 2 0
99.5 0 0 0 0 5 6 0
99.0 0 0 0 1 1 2 0
98.5 0 0 0 1 1 4 1
98.0 0 1 1 1 3 10 0
97.5 0 0 0 0 1 2 0
97.0 0 1 0 0 3 15 0
96.5 0 0 0 1 1 3 0
96.0 0 0 0 0 2 7 0
95.5 0 0 0 0 6 3 0
95.0 0 0 0 0 2 4 0
94.5 0 1 0 1 3 14 0
94.0 0 1 0 0 0 4 0
93.5 0 0 0 0 2 7 0
93.0 0 0 0 0 1 3 1
92.5 0 0 0 0 0 3 0
92.0 0 0 1 3 3 8 1
91.5 0 0 0 0 2 0 0
91.0 0 0 1 0 6 7 1
90.5 0 0 0 1 0 1 0
90.0 0 0 0 1 5 11 0
89.5 0 0 0 2 5 8 0
89.0 0 0 0 0 2 6 0
88.5 0 0 1 0 6 13 0
88.0 0 0 0 1 1 1 0
87.5 0 0 1 0 8 9 0
87.0 0 1 0 0 2 3 0
86.5 0 0 0 0 2 15 1
86.0 0 0 0 0 5 12 0
85.5 0 0 0 0 2 5 0
85.0 0 0 2 0 3 7 1
84.5 0 0 1 1 5 2 0
84.0 0 0 0 0 7 9 0
83.5 0 0 1 0 3 7 0
83.0 0 0 0 1 2 8 0
82.5 0 0 0 0 9 11 0
82.0 0 0 0 0 6 3 0
81.5 0 0 0 0 7 12 0
81.0 0 0 0 0 1 7 0
80.5 0 0 0 0 7 7 0
80.0 0 0 0 2 6 13 0
79.5 0 0 0 0 3 5 0
79.0 0 0 1 0 4 15 0
78.5 0 0 1 0 4 5 0
78.0 0 0 0 0 8 7 0
77.5 0 0 1 0 0 7 1
77.0 0 0 0 0 11 10 0
76.5 0 0 0 1 5 8 1
76.0 0 0 0 0 9 5 0
75.5 0 0 0 0 5 6 0
75.0 0 0 0 0 2 9 0
74.5 0 1 0 0 6 8 0
74.0 0 0 0 3 3 8 0
73.5 0 1 1 0 5 10 0
73.0 0 0 0 0 6 12 0
72.5 0 0 0 1 9 5 2
72.0 0 0 0 0 6 12 1
71.5 0 0 0 0 4 4 0
71.0 0 0 0 1 6 8 1
70.5 0 1 0 0 5 10 0
70.0 0 0 0 1 11 4 2
69.5 0 0 0 0 6 13 0
69.0 0 0 0 0 12 6 1
68.5 0 0 0 0 10 9 0
68.0 0 0 1 0 5 7 1
67.5 0 0 0 0 8 8 1
67.0 0 0 0 0 7 9 0
66.5 0 0 0 1 8 10 0
66.0 0 0 0 0 9 16 2
65.5 0 0 0 1 12 3 1
65.0 0 0 0 0 3 9 0
64.5 0 0 0 0 6 12 0
64.0 0 0 0 0 13 8 0
63.5 0 0 0 1 13 9 1
63.0 0 0 0 0 10 2 0
62.5 0 0 0 1 5 9 0
62.0 0 0 0 0 3 6 1
61.5 0 0 0 0 11 7 0
61.0 0 0 0 0 6 8 1
60.5 0 0 0 0 7 5 0
60.0 0 1 0 0 15 10 1
59.5 0 0 0 1 4 2 0
59.0 0 0 0 0 9 9 0
58.5 0 0 1 0 3 3 1
58.0 0 0 0 0 3 9 0
57.5 0 0 0 0 10 5 0
57.0 0 0 0 2 6 7 0
56.5 0 0 1 0 8 6 1
56.0 0 0 0 0 3 3 0
55.5 0 0 0 1 5 5 0
55.0 0 0 0 0 1 3 0
54.5 0 0 0 0 3 5 0
54.0 0 0 0 1 6 6 0
53.5 0 0 0 1 3 4 0
53.0 0 0 0 0 8 4 0
52.5 0 0 0 0 4 3 0
52.0 0 0 0 0 3 3 0
51.5 0 0 0 0 4 2 0
51.0 0 1 0 1 3 1 0
50.5 0 0 0 0 2 7 0
50.0 0 0 0 0 2 5 0
49.5 0 0 0 0 4 3 1
49.0 0 0 0 0 6 1 0
48.5 0 0 0 0 0 4 0
48.0 0 1 0 0 7 2 0
47.5 0 0 0 0 1 4 0
47.0 0 0 0 0 4 2 0
46.5 0 0 0 0 4 0 0
46.0 0 0 0 0 1 3 0
45.5 0 0 0 0 4 3 0
45.0 0 0 0 0 1 0 0
44.5 0 0 0 0 1 1 0
44.0 0 0 0 0 1 1 0
43.5 0 0 0 0 0 1 0
43.0 0 0 0 0 1 3 0
42.5 0 0 0 1 2 3 0
42.0 0 0 0 0 3 1 0
41.5 0 0 0 0 4 0 0
41.0 0 0 0 0 2 0 0
40.5 0 0 0 0 2 3 0
40.0 0 0 0 0 1 1 0
39.5 0 0 0 0 0 1 0
39.0 0 0 0 0 1 2 0
38.5 0 0 0 0 1 3 0
38.0 0 0 0 0 2 2 0
37.5 0 0 0 0 0 1 0
37.0 0 0 0 0 1 0 0
36.5 0 0 0 0 2 0 0
36.0 0 0 0 0 1 3 0
35.5 0 0 0 0 0 2 0
35.0 0 0 0 0 0 0 0
34.5 0 0 0 0 0 1 0
34.0 0 0 0 0 0 0 0
33.5 0 0 0 0 0 1 0
33.0 0 0 0 0 0 0 0
32.5 0 0 0 0 0 1 0
32.0 0 0 0 0 1 0 0
31.5 0 0 0 0 2 1 0
31.0 0 0 0 0 0 1 0
30.5 0 0 0 0 1 0 1
30.0 0 0 0 0 5 2 1
29.5 0 0 0 0 0 0 0
29.0 0 0 0 0 0 0 0
28.5 0 0 0 0 0 0 0
28.0 0 0 0 0 0 0 0
27.5 0 0 0 0 0 0 0
27.0 0 0 0 0 1 0 0
26.5 0 0 0 0 0 0 0
26.0 0 0 0 0 0 0 0
25.5 0 0 0 0 0 0 0
25.0 0 0 0 0 0 1 0
24.5 0 0 0 0 0 1 0
24.0 0 0 0 0 0 0 0
23.5 0 0 0 0 0 0 0
23.0 0 0 0 0 0 1 0
22.5 0 0 0 0 0 0 0
22.0 0 0 0 0 0 0 0
21.5 0 0 0 0 0 0 0
21.0 0 0 0 0 0 0 0
20.5 0 0 0 0 0 0 0
20.0 0 0 0 0 0 0 0
19.5 0 0 0 0 0 0 0
19.0 0 0 0 0 0 0 0
18.5 0 0 0 0 0 0 0
18.0 0 0 0 0 0 1 0
17.5 0 0 0 0 0 0 0
17.0 0 0 0 0 0 0 0
16.5 0 0 0 0 0 0 0
16.0 0 0 0 0 0 0 0
15.5 0 0 0 0 0 0 0
15.0 0 0 0 0 0 0 0
14.5 0 0 0 0 0 0 0
14.0 0 0 0 0 0 0 0
13.5 0 0 0 0 0 2 0
13.0 0 0 0 0 0 0 0
12.5 0 0 0 0 0 0 0
12.0 0 0 0 0 1 1 0
11.5 0 0 0 0 0 0 0
11.0 0 0 0 0 0 0 0
10.5 0 0 0 0 0 0 0
10.0 0 0 0 0 0 0 0
9.5 0 0 0 0 0 0 0
9.0 0 0 0 0 0 0 0
8.5 0 0 0 0 0 0 0
8.0 0 0 0 0 0 0 0
7.5 0 0 0 0 0 0 0
7.0 0 0 0 0 0 0 0
6.5 0 0 0 0 0 0 0
6.0 0 0 0 0 0 0 0
5.5 0 0 0 0 0 0 0
5.0 0 0 0 0 0 0 0
4.5 0 0 0 0 0 0 0
4.0 0 0 0 0 0 0 0
3.5 0 0 0 0 0 0 0
3.0 0 0 0 0 0 0 0
2.5 0 0 0 0 0 0 0
2.0 0 0 0 0 0 0 0
1.5 0 0 0 0 0 0 0
1.0 0 0 0 0 0 0 0
0.5 0 0 0 0 0 0 0
0 0 0 0 0 0 0
American Mathematics Competitions
2003 AMC 10 A Results for Michigan
Analysis
Table of Item Difficulty for the 2003
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.55 2.17 0.73 4.50* 0.47 1.59 0.00
2 0.08 8.31* 0.13 1.16 0.04 0.27 0.00
3 0.51 2.39 0.41 4.15* 0.31 2.23 0.00
4 4.79* 0.18 0.33 3.31 0.07 1.31 0.00
5 0.81 5.78* 0.24 0.06 0.09 3.02 0.00
6 1.65 1.93 2.89* 0.65 0.74 2.14 0.00
7 1.49 2.12* 1.16 1.93 0.45 2.86 0.00
8 1.19 0.57 0.28 0.23 6.64* 1.08 0.01
9 2.45* 0.46 1.59 1.80 0.07 3.61 0.01
10 0.64 0.48 0.69 1.43 4.10* 2.66 0.01
11 0.31 0.17 0.18 0.22 6.56* 2.57 0.00
12 2.88* 2.92 0.22 0.89 0.98 2.10 0.01
13 6.07* 0.37 0.30 0.18 0.07 3.01 0.00
14 1.74* 1.20 0.50 0.83 1.10 4.63 0.00
15 0.88 1.89 4.07* 0.48 0.75 1.94 0.00
16 0.73 0.83 2.72* 0.18 0.68 4.86 0.00
17 0.57 0.91* 0.22 0.26 0.36 7.69 0.00
18 0.58 0.61* 0.26 0.71 0.80 7.05 0.00
19 0.33 0.31 0.54* 0.18 0.21 8.43 0.00
20 0.50 0.29 0.44 0.36 0.54* 7.86 0.00
21 0.63 0.45 1.16 2.06* 2.48 3.22 0.00
22 0.75 2.32* 0.66 0.21 0.12 5.93 0.00
23 0.40 0.26 0.87* 0.62 0.72 7.13 0.01
24 0.27 0.39 0.61 0.62 4.34* 3.77 0.00
25 0.25 0.52* 0.29 0.20 0.15 8.59 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
2003 AMC 12 A Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 1 0 125.0 0 0 100.0 1 0
149.5 0 0 124.5 0 0 99.5 10 10
149.0 0 0 124.0 5 0 99.0 8 0
148.5 0 0 123.5 0 0 98.5 12 2
148.0 0 0 123.0 5 0 98.0 7 4
147.5 0 0 122.5 1 0 97.5 1 0
147.0 0 0 122.0 2 1 97.0 12 10
146.5 0 0 121.5 0 0 96.5 1 0
146.0 0 0 121.0 0 0 96.0 24 7
145.5 0 0 120.5 2 1 95.5 3 2
145.0 0 0 120.0 0 0 95.0 15 8
144.5 0 0 119.5 2 0 94.5 15 7
144.0 0 0 119.0 0 0 94.0 3 0
143.5 0 0 118.5 2 1 93.5 21 9
143.0 1 0 118.0 1 0 93.0 4 0
142.5 0 0 117.5 0 0 92.5 14 3
142.0 0 0 117.0 2 4 92.0 11 3
141.5 0 0 116.5 0 0 91.5 8 4
141.0 0 0 116.0 9 2 91.0 17 7
140.5 1 0 115.5 0 0 90.5 8 1
140.0 0 0 115.0 4 0 90.0 25 7
139.5 0 0 114.5 3 1 89.5 7 3
139.0 0 0 114.0 1 0 89.0 18 13
138.5 0 0 113.5 7 1 88.5 8 2
138.0 0 0 113.0 1 0 88.0 7 2
137.5 0 0 112.5 12 3 87.5 11 5
137.0 0 0 112.0 4 0 87.0 5 4
136.5 0 0 111.5 4 2 86.5 16 10
136.0 2 0 111.0 2 1 86.0 11 7
135.5 0 0 110.5 0 0 85.5 5 11
135.0 0 0 110.0 7 4 85.0 10 7
134.5 0 0 109.5 0 1 84.5 10 4
134.0 0 0 109.0 8 4 84.0 27 7
133.5 0 0 108.5 1 0 83.5 7 4
133.0 0 0 108.0 7 6 83.0 24 10
132.5 1 0 107.5 6 3 82.5 7 6
132.0 0 0 107.0 0 0 82.0 9 4
131.5 0 0 106.5 12 2 81.5 12 10
131.0 0 0 106.0 3 0 81.0 5 8
130.5 0 0 105.5 12 5 80.5 18 5
130.0 0 0 105.0 3 2 80.0 6 4
129.5 0 0 104.5 5 3 79.5 7 3
129.0 2 0 104.0 7 5 79.0 9 8
128.5 0 0 103.5 0 0 78.5 8 8
128.0 0 0 103.0 15 4 78.0 15 13
127.5 3 0 102.5 3 0 77.5 10 5
127.0 0 0 102.0 11 3 77.0 19 15
126.5 0 0 101.5 9 0 76.5 13 14
126.0 1 0 101.0 7 2 76.0 18 9
125.5 0 1 100.5 9 3 75.5 11 10
American Mathematics Competitions
2003 AMC 12 A Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 10 7 50.0 7 3 25.0 0 0
74.5 14 16 49.5 2 4 24.5 0 0
74.0 3 4 49.0 1 3 24.0 3 0
73.5 8 10 48.5 1 4 23.5 0 0
73.0 10 9 48.0 5 9 23.0 0 0
72.5 13 5 47.5 4 3 22.5 0 0
72.0 15 10 47.0 2 2 22.0 0 0
71.5 6 6 46.5 0 4 21.5 0 0
71.0 19 16 46.0 1 1 21.0 0 0
70.5 9 6 45.5 4 1 20.5 0 0
70.0 7 5 45.0 0 4 20.0 0 0
69.5 11 9 44.5 0 1 19.5 0 0
69.0 7 12 44.0 1 3 19.0 0 0
68.5 15 13 43.5 1 2 18.5 0 0
68.0 4 6 43.0 0 0 18.0 1 2
67.5 9 9 42.5 2 2 17.5 0 0
67.0 9 12 42.0 4 3 17.0 0 0
66.5 7 11 41.5 0 1 16.5 0 0
66.0 9 11 41.0 1 2 16.0 0 0
65.5 6 8 40.5 3 2 15.5 0 0
65.0 7 9 40.0 1 2 15.0 0 0
64.5 5 9 39.5 0 1 14.5 0 0
64.0 6 6 39.0 0 1 14.0 0 0
63.5 9 8 38.5 0 1 13.5 0 0
63.0 11 5 38.0 3 1 13.0 0 0
62.5 10 12 37.5 1 1 12.5 0 0
62.0 4 6 37.0 0 0 12.0 0 0
61.5 6 8 36.5 1 1 11.5 0 0
61.0 6 6 36.0 3 2 11.0 0 0
60.5 6 9 35.5 0 0 10.5 0 0
60.0 18 10 35.0 0 4 10.0 0 0
59.5 4 4 34.5 0 1 9.5 0 0
59.0 9 8 34.0 0 1 9.0 0 0
58.5 6 3 33.5 0 0 8.5 0 0
58.0 8 10 33.0 2 1 8.0 0 0
57.5 2 3 32.5 0 1 7.5 0 0
57.0 9 5 32.0 0 1 7.0 0 0
56.5 10 11 31.5 0 1 6.5 0 0
56.0 7 3 31.0 0 0 6.0 0 0
55.5 2 2 30.5 0 0 5.5 0 0
55.0 6 4 30.0 1 1 5.0 0 0
54.5 4 6 29.5 0 1 4.5 0 0
54.0 6 7 29.0 0 0 4.0 0 0
53.5 4 6 28.5 0 1 3.5 0 0
53.0 6 5 28.0 0 0 3.0 0 0
52.5 4 2 27.5 0 0 2.5 0 0
52.0 3 3 27.0 0 0 2.0 0 0
51.5 2 1 26.5 0 1 1.5 0 0
51.0 6 5 26.0 0 0 1.0 0 0
50.5 2 1 25.5 0 0 0.5 0 0
0.0 0 0
American Mathematics Competitions
2003 AMC 12 A Results for Michigan
SCORE DISTRIBUTION
score -----------grade-----------
5 6 7 8 9 10 11 12 13 unknown
---------------------------
150.0 0 0 0 0 0 0 0 1 0 0
149.5 0 0 0 0 0 0 0 0 0 0
149.0 0 0 0 0 0 0 0 0 0 0
148.5 0 0 0 0 0 0 0 0 0 0
148.0 0 0 0 0 0 0 0 0 0 0
147.5 0 0 0 0 0 0 0 0 0 0
147.0 0 0 0 0 0 0 0 0 0 0
146.5 0 0 0 0 0 0 0 0 0 0
146.0 0 0 0 0 0 0 0 0 0 0
145.5 0 0 0 0 0 0 0 0 0 0
145.0 0 0 0 0 0 0 0 0 0 0
144.5 0 0 0 0 0 0 0 0 0 0
144.0 0 0 0 0 0 0 0 0 0 0
143.5 0 0 0 0 0 0 0 0 0 0
143.0 0 0 0 0 0 0 0 1 0 0
142.5 0 0 0 0 0 0 0 0 0 0
142.0 0 0 0 0 0 0 0 0 0 0
141.5 0 0 0 0 0 0 0 0 0 0
141.0 0 0 0 0 0 0 0 0 0 0
140.5 0 0 0 0 0 0 1 0 0 0
140.0 0 0 0 0 0 0 0 0 0 0
139.5 0 0 0 0 0 0 0 0 0 0
139.0 0 0 0 0 0 0 0 0 0 0
138.5 0 0 0 0 0 0 0 0 0 0
138.0 0 0 0 0 0 0 0 0 0 0
137.5 0 0 0 0 0 0 0 0 0 0
137.0 0 0 0 0 0 0 0 0 0 0
136.5 0 0 0 0 0 0 0 0 0 0
136.0 0 0 0 0 1 0 1 0 0 0
135.5 0 0 0 0 0 0 0 0 0 0
135.0 0 0 0 0 0 0 0 0 0 0
134.5 0 0 0 0 0 0 0 0 0 0
134.0 0 0 0 0 0 0 0 0 0 0
133.5 0 0 0 0 0 0 0 0 0 0
133.0 0 0 0 0 0 0 0 0 0 0
132.5 0 0 0 0 0 0 0 1 0 0
132.0 0 0 0 0 0 0 0 0 0 0
131.5 0 0 0 0 0 0 0 0 0 0
131.0 0 0 0 0 0 0 0 0 0 0
130.5 0 0 0 0 0 0 0 0 0 0
130.0 0 0 0 0 0 0 0 0 0 0
129.5 0 0 0 0 0 0 0 0 0 0
129.0 0 0 0 0 0 1 1 0 0 0
128.5 0 0 0 0 0 0 0 0 0 0
128.0 0 0 0 0 0 0 0 0 0 0
127.5 0 0 0 0 0 0 1 2 0 0
127.0 0 0 0 0 0 0 0 0 0 0
126.5 0 0 0 0 0 0 0 0 0 0
126.0 0 0 0 0 0 0 0 1 0 0
125.5 0 0 0 0 0 1 0 0 0 0
125.0 0 0 0 0 0 0 0 0 0 0
124.5 0 0 0 0 0 0 0 0 0 0
124.0 0 0 0 0 0 0 3 2 0 0
123.5 0 0 0 0 0 0 0 0 0 0
123.0 0 0 0 0 0 0 1 4 0 0
122.5 0 0 0 0 0 0 1 0 0 0
122.0 0 0 0 0 0 0 2 1 0 0
121.5 0 0 0 0 0 0 0 0 0 0
121.0 0 0 0 0 0 0 0 0 0 0
120.5 0 0 0 0 0 0 0 3 0 0
120.0 0 0 0 0 0 0 0 0 0 0
119.5 0 0 0 0 0 0 0 2 0 0
119.0 0 0 0 0 0 0 0 0 0 0
118.5 0 0 0 0 1 0 2 0 0 0
118.0 0 0 0 0 0 0 0 1 0 0
117.5 0 0 0 0 0 0 0 0 0 0
117.0 0 0 0 0 0 0 2 5 0 0
116.5 0 0 0 0 0 0 0 0 0 0
116.0 0 0 0 0 0 0 4 7 0 0
115.5 0 0 0 0 0 0 0 0 0 0
115.0 0 0 0 0 1 0 3 0 0 0
114.5 0 0 0 0 1 1 2 0 0 0
114.0 0 0 0 0 0 0 0 1 0 0
113.5 0 0 0 0 0 1 4 3 0 0
113.0 0 0 0 0 0 0 1 0 0 0
112.5 0 0 0 0 0 1 4 10 0 0
112.0 0 0 0 0 1 0 2 1 0 0
111.5 0 0 0 0 0 0 3 3 0 0
111.0 0 0 0 0 0 0 0 3 0 0
110.5 0 0 0 0 0 0 0 0 0 0
110.0 0 0 0 0 0 3 4 5 0 0
109.5 0 0 0 0 0 0 0 1 0 0
109.0 0 0 0 0 1 1 2 8 0 0
108.5 0 0 0 0 0 1 0 0 0 0
108.0 0 0 0 0 0 1 5 7 0 0
107.5 0 0 0 0 0 0 3 6 0 0
107.0 0 0 0 0 0 0 0 0 0 0
106.5 0 0 0 0 1 0 6 7 0 0
106.0 0 1 0 0 1 1 0 0 0 0
105.5 0 0 0 0 2 1 8 7 0 0
105.0 0 0 0 0 1 0 2 2 0 0
104.5 0 0 0 0 2 1 1 5 0 0
104.0 0 0 0 0 2 0 5 5 0 0
103.5 0 0 0 0 0 0 0 0 0 0
103.0 0 0 0 0 0 1 6 13 0 0
102.5 0 0 0 0 1 0 1 1 0 0
102.0 0 0 0 0 0 1 4 9 0 0
101.5 0 0 0 0 0 0 4 5 0 0
101.0 0 0 0 1 0 0 3 5 0 0
100.5 0 0 0 0 0 1 3 10 0 0
100.0 0 0 0 0 0 0 0 1 0 0
99.5 0 0 0 0 1 1 7 11 0 1
99.0 0 0 0 0 0 0 4 4 0 0
98.5 0 0 1 0 0 2 8 4 0 1
98.0 0 0 0 0 1 0 5 5 0 0
97.5 0 0 0 0 0 0 0 1 0 0
97.0 0 0 0 0 0 2 9 11 0 0
96.5 0 0 0 0 0 1 0 1 0 0
96.0 0 0 0 0 0 2 12 17 0 0
95.5 0 0 0 0 0 0 1 4 0 0
95.0 0 0 0 1 0 0 10 12 0 0
94.5 0 0 0 0 0 0 10 12 0 1
94.0 0 0 0 0 0 0 1 2 0 0
93.5 0 0 0 0 1 2 12 16 0 0
93.0 0 0 0 0 0 0 0 4 0 0
92.5 0 0 0 0 0 1 7 9 0 0
92.0 0 0 0 0 1 2 4 7 0 0
91.5 0 0 0 0 0 0 9 3 0 0
91.0 0 0 0 0 0 2 12 10 0 0
90.5 0 0 1 0 1 0 2 5 0 0
90.0 0 0 0 0 1 1 12 18 0 1
89.5 0 0 0 0 1 0 1 8 0 0
89.0 0 0 0 0 1 3 15 12 0 0
88.5 0 0 0 0 0 0 5 5 0 0
88.0 0 0 0 0 0 1 5 4 0 0
87.5 0 0 0 0 0 1 6 9 0 0
87.0 0 0 0 0 0 1 5 3 0 0
86.5 0 0 0 0 0 0 18 8 0 2
86.0 0 0 0 0 1 0 8 9 0 0
85.5 0 0 0 0 0 0 6 11 0 0
85.0 0 0 0 0 0 2 5 10 0 0
84.5 0 0 0 0 0 0 7 7 0 0
84.0 0 0 0 0 1 3 17 14 0 0
83.5 0 0 0 1 0 1 7 2 0 0
83.0 0 0 0 0 0 2 16 15 0 1
82.5 0 0 0 0 0 0 9 4 0 0
82.0 0 0 0 0 0 2 7 5 0 0
81.5 0 0 0 0 0 1 12 9 0 0
81.0 0 0 0 0 0 0 6 7 0 0
80.5 0 0 0 0 0 0 14 9 0 0
80.0 0 0 0 0 0 0 5 5 0 0
79.5 0 0 0 0 0 0 6 4 0 0
79.0 0 0 0 0 0 1 11 5 0 0
78.5 0 0 0 0 0 2 8 7 0 0
78.0 0 0 0 0 0 0 13 15 0 0
77.5 0 0 0 0 0 2 7 6 0 1
77.0 0 0 0 0 0 1 13 20 0 0
76.5 0 0 0 0 0 0 18 8 1 1
76.0 0 0 0 0 0 2 13 12 0 0
75.5 0 0 0 0 0 3 11 9 0 0
75.0 0 0 0 0 1 2 8 7 0 0
74.5 0 0 0 0 0 0 13 17 0 0
74.0 0 0 0 0 0 0 5 2 0 0
73.5 0 0 0 0 1 1 11 6 0 0
73.0 0 0 0 0 0 0 13 6 0 0
72.5 0 0 0 0 0 2 10 6 0 0
72.0 0 0 0 0 1 0 16 9 0 0
71.5 0 0 0 0 0 1 5 6 0 0
71.0 0 0 0 0 1 1 21 13 0 1
70.5 0 0 0 0 0 0 11 5 0 0
70.0 0 0 0 0 0 0 4 8 0 0
69.5 0 0 0 0 0 2 8 10 0 0
69.0 0 0 0 0 2 0 10 7 0 0
68.5 0 0 0 0 0 2 14 12 0 0
68.0 0 0 0 0 0 0 4 6 0 0
67.5 0 0 0 0 2 1 8 8 0 0
67.0 0 0 0 0 1 1 8 11 0 0
66.5 0 0 0 0 1 0 12 6 0 0
66.0 0 0 0 0 0 4 11 6 0 0
65.5 0 0 0 0 0 1 3 11 0 0
65.0 0 0 0 0 0 1 9 6 0 0
64.5 0 0 0 0 0 2 7 6 0 1
64.0 0 0 0 0 0 1 8 3 0 0
63.5 0 0 0 0 0 1 8 8 0 0
63.0 0 0 0 0 0 1 12 4 0 0
62.5 0 0 0 0 0 2 10 9 1 1
62.0 0 0 0 0 0 1 6 3 0 0
61.5 0 0 0 0 0 1 5 8 0 0
61.0 0 0 0 0 0 1 8 3 0 2
60.5 0 0 0 0 0 0 11 4 0 0
60.0 0 0 0 0 0 1 16 12 0 0
59.5 0 0 0 0 0 1 4 3 0 0
59.0 0 0 0 0 0 2 7 8 0 0
58.5 0 0 0 0 0 2 4 3 0 0
58.0 0 0 0 0 0 2 10 7 0 0
57.5 0 0 0 0 0 0 1 4 0 0
57.0 0 0 0 0 0 0 7 7 0 0
56.5 0 0 0 0 0 1 12 8 0 0
56.0 0 0 0 0 0 0 5 5 0 0
55.5 0 0 0 0 0 0 1 3 0 0
55.0 0 0 0 0 0 0 7 3 0 0
54.5 0 0 0 0 1 1 6 2 0 0
54.0 0 0 0 0 0 1 9 3 0 0
53.5 0 0 0 0 0 2 5 3 0 0
53.0 0 0 0 0 0 0 8 3 0 0
52.5 0 0 0 0 0 1 3 2 0 0
52.0 0 0 0 0 0 0 2 4 0 0
51.5 0 0 0 0 0 0 1 2 0 0
51.0 0 0 0 0 0 3 8 0 0 0
50.5 0 0 0 0 0 1 2 0 0 0
50.0 0 0 0 0 0 1 5 4 0 0
49.5 0 0 0 0 0 1 4 1 0 0
49.0 0 0 0 0 0 0 3 1 0 0
48.5 0 0 0 0 0 0 2 3 0 0
48.0 0 0 0 0 1 1 6 6 0 0
47.5 0 0 0 0 1 0 3 3 0 0
47.0 0 0 0 0 0 0 2 2 0 0
46.5 0 0 0 0 0 0 4 0 0 0
46.0 0 0 0 0 0 0 3 0 0 0
45.5 0 0 0 0 0 0 4 1 0 1
45.0 0 0 0 0 0 0 3 1 0 0
44.5 0 0 0 0 0 0 1 0 0 0
44.0 0 0 0 0 0 0 4 0 0 0
43.5 0 0 0 0 0 0 2 1 0 0
43.0 0 0 0 0 0 0 0 0 0 0
42.5 0 0 0 0 0 0 2 2 0 0
42.0 0 0 0 0 0 0 4 3 0 0
41.5 0 0 0 0 0 0 1 0 0 0
41.0 0 0 0 0 0 0 2 1 0 0
40.5 0 0 0 0 0 0 1 3 0 1
40.0 0 0 0 0 0 0 0 2 0 1
39.5 0 0 0 0 0 0 1 0 0 0
39.0 0 0 0 0 0 0 0 1 0 0
38.5 0 0 0 0 0 0 0 1 0 0
38.0 0 0 0 0 0 0 2 2 0 0
37.5 0 0 0 0 0 0 1 1 0 0
37.0 0 0 0 0 0 0 0 0 0 0
36.5 0 0 0 0 0 1 0 1 0 0
36.0 0 0 0 0 0 0 5 0 0 0
35.5 0 0 0 0 0 0 0 0 0 0
35.0 0 0 0 0 0 0 4 0 0 0
34.5 0 0 0 0 0 0 0 1 0 0
34.0 0 0 0 0 1 0 0 0 0 0
33.5 0 0 0 0 0 0 0 0 0 0
33.0 0 0 0 0 0 0 2 1 0 0
32.5 0 0 0 0 0 0 1 0 0 0
32.0 0 0 0 0 0 0 1 0 0 0
31.5 0 0 0 0 0 0 1 0 0 0
31.0 0 0 0 0 0 0 0 0 0 0
30.5 0 0 0 0 0 0 0 0 0 0
30.0 0 0 0 0 0 0 1 1 0 0
29.5 0 0 0 0 0 0 1 0 0 0
29.0 0 0 0 0 0 0 0 0 0 0
28.5 0 0 0 0 0 0 0 1 0 0
28.0 0 0 0 0 0 0 0 0 0 0
27.5 0 0 0 0 0 0 0 0 0 0
27.0 0 0 0 0 0 0 0 0 0 0
26.5 0 0 0 0 0 0 1 0 0 0
26.0 0 0 0 0 0 0 0 0 0 0
25.5 0 0 0 0 0 0 0 0 0 0
25.0 0 0 0 0 0 0 0 0 0 0
24.5 0 0 0 0 0 0 0 0 0 0
24.0 0 0 0 0 0 0 2 1 0 0
23.5 0 0 0 0 0 0 0 0 0 0
23.0 0 0 0 0 0 0 0 0 0 0
22.5 0 0 0 0 0 0 0 0 0 0
22.0 0 0 0 0 0 0 0 0 0 0
21.5 0 0 0 0 0 0 0 0 0 0
21.0 0 0 0 0 0 0 0 0 0 0
20.5 0 0 0 0 0 0 0 0 0 0
20.0 0 0 0 0 0 0 0 0 0 0
19.5 0 0 0 0 0 0 0 0 0 0
19.0 0 0 0 0 0 0 0 0 0 0
18.5 0 0 0 0 0 0 0 0 0 0
18.0 0 0 0 0 0 1 2 0 0 0
17.5 0 0 0 0 0 0 0 0 0 0
17.0 0 0 0 0 0 0 0 0 0 0
16.5 0 0 0 0 0 0 0 0 0 0
16.0 0 0 0 0 0 0 0 0 0 0
15.5 0 0 0 0 0 0 0 0 0 0
15.0 0 0 0 0 0 0 0 0 0 0
14.5 0 0 0 0 0 0 0 0 0 0
14.0 0 0 0 0 0 0 0 0 0 0
13.5 0 0 0 0 0 0 0 0 0 0
13.0 0 0 0 0 0 0 0 0 0 0
12.5 0 0 0 0 0 0 0 0 0 0
12.0 0 0 0 0 0 0 0 0 0 0
11.5 0 0 0 0 0 0 0 0 0 0
11.0 0 0 0 0 0 0 0 0 0 0
10.5 0 0 0 0 0 0 0 0 0 0
10.0 0 0 0 0 0 0 0 0 0 0
9.5 0 0 0 0 0 0 0 0 0 0
9.0 0 0 0 0 0 0 0 0 0 0
8.5 0 0 0 0 0 0 0 0 0 0
8.0 0 0 0 0 0 0 0 0 0 0
7.5 0 0 0 0 0 0 0 0 0 0
7.0 0 0 0 0 0 0 0 0 0 0
6.5 0 0 0 0 0 0 0 0 0 0
6.0 0 0 0 0 0 0 0 0 0 0
5.5 0 0 0 0 0 0 0 0 0 0
5.0 0 0 0 0 0 0 0 0 0 0
4.5 0 0 0 0 0 0 0 0 0 0
4.0 0 0 0 0 0 0 0 0 0 0
3.5 0 0 0 0 0 0 0 0 0 0
3.0 0 0 0 0 0 0 0 0 0 0
2.5 0 0 0 0 0 0 0 0 0 0
2.0 0 0 0 0 0 0 0 0 0 0
1.5 0 0 0 0 0 0 0 0 0 0
1.0 0 0 0 0 0 0 0 0 0 0
0.5 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
American Mathematics Competitions
2003 AMC 12 A Results for Michigan
Analysis
Table of Item Difficulty for the 2003
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.36 1.24 0.57 6.15* 0.43 1.26 0.00
2 0.04 9.01* 0.13 0.60 0.01 0.20 0.00
3 0.31 2.83 0.29 5.08* 0.19 1.30 0.00
4 6.00* 0.11 0.16 2.91 0.07 0.75 0.00
5 0.23 0.08 0.11 0.17 7.56* 1.84 0.00
6 0.93 1.95 4.22* 0.43 0.58 1.90 0.00
7 1.49 2.56* 0.88 1.65 0.28 3.13 0.00
8 1.00 0.37 0.17 0.13 7.50* 0.84 0.00
9 0.42 0.68 1.37 3.42* 0.18 3.94 0.00
10 0.51 0.89 0.44 3.57* 0.15 4.44 0.00
11 0.58 0.61 1.74* 0.39 0.73 5.95 0.00
12 0.12 0.25 0.52 0.37 6.54* 2.19 0.00
13 0.39 0.43 0.62 1.11 4.98* 2.47 0.00
14 0.71 0.38 0.41 5.14* 1.03 2.32 0.00
15 0.33 0.26 0.92* 0.16 0.42 7.90 0.00
16 0.50 0.36 3.98* 0.42 0.99 3.76 0.00
17 0.68 1.16* 0.29 0.59 0.26 7.01 0.00
18 0.11 0.55* 0.20 0.14 0.19 8.81 0.00
19 0.70 0.57 1.04 1.56* 0.61 5.51 0.00
20 0.52* 0.27 0.79 1.34 0.23 6.85 0.00
21 1.09 0.37 0.25 0.75* 1.33 6.21 0.00
22 0.52 0.57 0.40* 0.57 0.19 7.74 0.01
23 0.22 0.39* 0.29 0.22 0.19 8.69 0.00
24 0.17 1.88* 0.99 0.26 0.23 6.48 0.00
25 0.62 0.48 0.21* 0.11 1.78 6.79 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
2003 AMC 10 B Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 0 0 125.0 1 0 100.0 0 0
149.5 0 0 124.5 0 0 99.5 2 3
149.0 0 0 124.0 1 0 99.0 1 0
148.5 0 0 123.5 0 0 98.5 0 0
148.0 0 0 123.0 0 0 98.0 1 1
147.5 0 0 122.5 0 0 97.5 1 1
147.0 0 0 122.0 0 0 97.0 3 1
146.5 0 0 121.5 0 0 96.5 2 0
146.0 0 0 121.0 0 0 96.0 3 0
145.5 0 0 120.5 0 0 95.5 0 1
145.0 0 0 120.0 0 0 95.0 0 1
144.5 0 0 119.5 0 0 94.5 5 1
144.0 0 0 119.0 0 0 94.0 0 0
143.5 0 0 118.5 0 0 93.5 3 2
143.0 1 0 118.0 1 0 93.0 3 1
142.5 0 0 117.5 0 0 92.5 3 0
142.0 0 0 117.0 1 0 92.0 2 0
141.5 0 0 116.5 0 0 91.5 1 0
141.0 0 0 116.0 0 2 91.0 4 2
140.5 0 0 115.5 1 0 90.5 2 0
140.0 0 0 115.0 1 0 90.0 5 3
139.5 0 0 114.5 0 0 89.5 1 0
139.0 0 0 114.0 0 0 89.0 2 3
138.5 0 0 113.5 0 0 88.5 2 2
138.0 1 1 113.0 0 0 88.0 1 0
137.5 0 0 112.5 1 0 87.5 2 1
137.0 1 0 112.0 0 0 87.0 1 0
136.5 0 0 111.5 0 0 86.5 0 2
136.0 0 0 111.0 0 2 86.0 2 0
135.5 0 0 110.5 0 0 85.5 5 2
135.0 0 0 110.0 1 0 85.0 1 3
134.5 0 0 109.5 1 0 84.5 2 0
134.0 0 0 109.0 0 0 84.0 1 1
133.5 0 0 108.5 2 1 83.5 3 0
133.0 0 0 108.0 1 0 83.0 3 4
132.5 0 0 107.5 0 0 82.5 1 2
132.0 0 0 107.0 0 0 82.0 0 5
131.5 0 0 106.5 1 0 81.5 1 2
131.0 0 0 106.0 0 0 81.0 3 0
130.5 0 0 105.5 1 2 80.5 3 2
130.0 0 0 105.0 1 0 80.0 3 0
129.5 0 0 104.5 0 0 79.5 3 2
129.0 1 0 104.0 3 0 79.0 1 1
128.5 0 0 103.5 0 0 78.5 0 2
128.0 0 0 103.0 1 1 78.0 7 6
127.5 0 0 102.5 0 0 77.5 1 2
127.0 0 0 102.0 2 1 77.0 4 4
126.5 1 0 101.5 1 0 76.5 1 1
126.0 0 0 101.0 0 0 76.0 2 4
125.5 0 0 100.5 1 3 75.5 0 2
American Mathematics Competitions
2003 AMC 10 B Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 0 1 50.0 0 1 25.0 0 0
74.5 1 3 49.5 1 1 24.5 0 0
74.0 1 0 49.0 0 1 24.0 2 2
73.5 1 2 48.5 0 0 23.5 0 0
73.0 1 5 48.0 2 3 23.0 0 0
72.5 2 0 47.5 0 0 22.5 0 0
72.0 4 1 47.0 0 0 22.0 1 0
71.5 2 1 46.5 0 0 21.5 0 0
71.0 2 4 46.0 0 1 21.0 0 0
70.5 4 2 45.5 0 0 20.5 0 0
70.0 2 3 45.0 0 0 20.0 0 0
69.5 2 0 44.5 0 0 19.5 0 0
69.0 1 1 44.0 0 1 19.0 0 0
68.5 3 0 43.5 2 0 18.5 0 0
68.0 2 0 43.0 0 1 18.0 2 2
67.5 2 1 42.5 0 0 17.5 0 0
67.0 2 2 42.0 4 4 17.0 0 0
66.5 0 4 41.5 1 0 16.5 0 0
66.0 1 1 41.0 0 0 16.0 0 0
65.5 0 2 40.5 0 0 15.5 0 0
65.0 0 1 40.0 1 1 15.0 0 0
64.5 3 0 39.5 0 0 14.5 0 0
64.0 0 1 39.0 0 0 14.0 0 0
63.5 0 0 38.5 0 1 13.5 0 0
63.0 1 1 38.0 0 0 13.0 0 0
62.5 1 0 37.5 0 1 12.5 0 0
62.0 1 2 37.0 0 1 12.0 0 0
61.5 1 2 36.5 0 0 11.5 0 0
61.0 0 0 36.0 1 1 11.0 0 0
60.5 0 2 35.5 0 0 10.5 0 0
60.0 2 3 35.0 0 0 10.0 0 0
59.5 2 0 34.5 0 0 9.5 0 0
59.0 1 1 34.0 0 0 9.0 0 0
58.5 1 0 33.5 0 0 8.5 0 0
58.0 0 1 33.0 1 0 8.0 0 0
57.5 2 0 32.5 0 0 7.5 0 0
57.0 1 0 32.0 0 0 7.0 0 0
56.5 1 4 31.5 0 2 6.5 0 0
56.0 0 3 31.0 0 0 6.0 0 0
55.5 0 1 30.5 0 0 5.5 0 0
55.0 0 0 30.0 2 2 5.0 0 0
54.5 0 2 29.5 0 0 4.5 0 0
54.0 4 2 29.0 0 0 4.0 0 0
53.5 1 1 28.5 0 0 3.5 0 0
53.0 0 0 28.0 0 0 3.0 0 0
52.5 2 0 27.5 0 0 2.5 0 0
52.0 0 1 27.0 0 0 2.0 0 0
51.5 0 0 26.5 0 0 1.5 0 0
51.0 0 0 26.0 0 0 1.0 0 0
50.5 1 1 25.5 0 0 0.5 0 0
0.0 0 0
American Mathematics Competitions
2003 AMC 10 B Results for Michigan
SCORE DISTRIBUTION
score -----------grade-----------
5 6 7 8 9 10 unknown
---------------------------
150.0 0 0 0 0 0 0 0
149.5 0 0 0 0 0 0 0
149.0 0 0 0 0 0 0 0
148.5 0 0 0 0 0 0 0
148.0 0 0 0 0 0 0 0
147.5 0 0 0 0 0 0 0
147.0 0 0 0 0 0 0 0
146.5 0 0 0 0 0 0 0
146.0 0 0 0 0 0 0 0
145.5 0 0 0 0 0 0 0
145.0 0 0 0 0 0 0 0
144.5 0 0 0 0 0 0 0
144.0 0 0 0 0 0 0 0
143.5 0 0 0 0 0 0 0
143.0 0 1 0 0 0 0 0
142.5 0 0 0 0 0 0 0
142.0 0 0 0 0 0 0 0
141.5 0 0 0 0 0 0 0
141.0 0 0 0 0 0 0 0
140.5 0 0 0 0 0 0 0
140.0 0 0 0 0 0 0 0
139.5 0 0 0 0 0 0 0
139.0 0 0 0 0 0 0 0
138.5 0 0 0 0 0 0 0
138.0 0 0 0 0 2 0 0
137.5 0 0 0 0 0 0 0
137.0 0 0 0 0 0 1 0
136.5 0 0 0 0 0 0 0
136.0 0 0 0 0 0 0 0
135.5 0 0 0 0 0 0 0
135.0 0 0 0 0 0 0 0
134.5 0 0 0 0 0 0 0
134.0 0 0 0 0 0 0 0
133.5 0 0 0 0 0 0 0
133.0 0 0 0 0 0 0 0
132.5 0 0 0 0 0 0 0
132.0 0 0 0 0 0 0 0
131.5 0 0 0 0 0 0 0
131.0 0 0 0 0 0 0 0
130.5 0 0 0 0 0 0 0
130.0 0 0 0 0 0 0 0
129.5 0 0 0 0 0 0 0
129.0 0 0 0 0 1 0 0
128.5 0 0 0 0 0 0 0
128.0 0 0 0 0 0 0 0
127.5 0 0 0 0 0 0 0
127.0 0 0 0 0 0 0 0
126.5 0 0 0 1 0 0 0
126.0 0 0 0 0 0 0 0
125.5 0 0 0 0 0 0 0
125.0 0 0 0 0 0 1 0
124.5 0 0 0 0 0 0 0
124.0 0 0 1 0 0 0 0
123.5 0 0 0 0 0 0 0
123.0 0 0 0 0 0 0 0
122.5 0 0 0 0 0 0 0
122.0 0 0 0 0 0 0 0
121.5 0 0 0 0 0 0 0
121.0 0 0 0 0 0 0 0
120.5 0 0 0 0 0 0 0
120.0 0 0 0 0 0 0 0
119.5 0 0 0 0 0 0 0
119.0 0 0 0 0 0 0 0
118.5 0 0 0 0 0 0 0
118.0 0 0 0 0 0 1 0
117.5 0 0 0 0 0 0 0
117.0 0 0 1 0 0 0 0
116.5 0 0 0 0 0 0 0
116.0 0 0 1 0 0 1 0
115.5 0 0 0 0 0 1 0
115.0 0 0 0 0 0 1 0
114.5 0 0 0 0 0 0 0
114.0 0 0 0 0 0 0 0
113.5 0 0 0 0 0 0 0
113.0 0 0 0 0 0 0 0
112.5 0 0 1 0 0 0 0
112.0 0 0 0 0 0 0 0
111.5 0 0 0 0 0 0 0
111.0 0 0 0 0 2 0 0
110.5 0 0 0 0 0 0 0
110.0 0 0 0 0 1 0 0
109.5 0 0 0 0 1 0 0
109.0 0 0 0 0 0 0 0
108.5 0 0 1 2 0 0 0
108.0 0 0 0 0 0 1 0
107.5 0 0 0 0 0 0 0
107.0 0 0 0 0 0 0 0
106.5 0 0 1 0 0 0 0
106.0 0 0 0 0 0 0 0
105.5 0 0 0 0 2 1 0
105.0 0 0 0 1 0 0 0
104.5 0 0 0 0 0 0 0
104.0 0 0 1 0 1 1 0
103.5 0 0 0 0 0 0 0
103.0 0 0 0 0 0 2 0
102.5 0 0 0 0 0 0 0
102.0 0 0 0 0 0 3 0
101.5 0 0 0 0 1 0 0
101.0 0 0 0 0 0 0 0
100.5 0 0 2 0 1 1 0
100.0 0 0 0 0 0 0 0
99.5 0 1 0 0 1 3 0
99.0 0 0 0 0 1 0 0
98.5 0 0 1 0 0 0 0
98.0 0 0 0 0 0 2 0
97.5 0 0 0 0 3 0 0
97.0 0 0 1 1 0 2 0
96.5 0 0 0 1 0 1 0
96.0 0 0 0 0 1 2 0
95.5 0 0 1 1 0 0 0
95.0 0 0 0 0 0 1 0
94.5 0 0 1 0 3 2 1
94.0 0 0 0 0 0 0 0
93.5 0 0 0 0 3 2 0
93.0 0 0 1 0 1 2 0
92.5 0 0 0 0 2 1 0
92.0 0 1 0 0 0 1 0
91.5 0 0 0 0 0 1 0
91.0 0 0 0 0 3 3 0
90.5 0 0 0 0 0 2 0
90.0 0 0 1 1 3 3 0
89.5 0 0 0 0 1 0 0
89.0 0 0 0 1 2 2 0
88.5 0 0 0 1 0 3 0
88.0 0 0 0 0 0 1 0
87.5 0 0 0 0 2 1 0
87.0 0 0 0 0 1 0 0
86.5 0 0 0 0 2 1 0
86.0 0 0 0 0 2 0 0
85.5 0 0 1 0 4 2 0
85.0 0 0 0 0 1 3 0
84.5 0 1 0 0 1 0 0
84.0 0 0 0 0 0 2 0
83.5 0 0 1 0 1 2 0
83.0 0 0 0 1 1 5 0
82.5 0 0 0 0 1 2 0
82.0 0 0 0 0 5 0 0
81.5 0 0 0 0 2 1 0
81.0 0 0 0 0 0 3 0
80.5 0 0 0 0 0 5 0
80.0 0 0 0 1 2 1 0
79.5 0 0 0 0 3 2 0
79.0 0 0 0 0 1 1 0
78.5 0 0 0 1 1 0 0
78.0 0 0 0 1 5 7 0
77.5 0 0 0 0 0 3 0
77.0 0 0 0 0 7 1 0
76.5 0 0 0 0 1 1 0
76.0 0 0 0 0 2 3 1
75.5 0 0 0 0 0 2 0
75.0 0 0 0 0 1 0 0
74.5 0 0 0 0 2 3 0
74.0 0 0 0 0 0 0 1
73.5 0 0 0 1 1 1 0
73.0 0 0 0 0 2 4 0
72.5 0 0 0 0 2 0 0
72.0 0 0 0 0 2 3 0
71.5 0 0 0 1 1 2 0
71.0 0 0 0 1 3 2 0
70.5 0 1 0 0 1 4 0
70.0 0 0 0 0 4 1 0
69.5 0 0 1 0 1 0 0
69.0 0 0 0 0 1 1 0
68.5 0 0 1 0 0 2 0
68.0 0 0 0 0 2 0 0
67.5 0 0 0 0 1 2 0
67.0 0 0 0 0 1 3 0
66.5 0 0 0 1 3 0 0
66.0 0 0 0 0 1 2 0
65.5 0 0 0 0 1 1 0
65.0 0 0 0 0 1 0 1
64.5 0 0 0 0 2 1 0
64.0 0 0 0 0 1 0 0
63.5 0 0 0 0 0 0 0
63.0 0 0 0 0 1 1 0
62.5 0 0 0 0 1 0 0
62.0 0 0 1 0 2 0 0
61.5 0 0 0 0 0 3 0
61.0 0 0 0 0 0 0 0
60.5 0 0 0 0 2 0 0
60.0 0 0 0 0 2 3 0
59.5 0 0 0 0 1 1 0
59.0 0 0 0 0 1 1 0
58.5 0 0 0 0 0 1 0
58.0 0 0 0 0 1 0 0
57.5 0 0 0 0 2 0 0
57.0 0 0 0 0 1 0 0
56.5 0 0 0 0 0 5 0
56.0 0 1 0 0 2 0 0
55.5 0 0 0 0 1 0 0
55.0 0 0 0 0 0 0 0
54.5 0 0 0 0 0 2 0
54.0 0 0 0 2 0 4 0
53.5 0 0 0 0 1 1 0
53.0 0 0 0 0 0 0 0
52.5 0 0 0 0 2 0 0
52.0 0 0 0 0 1 0 0
51.5 0 0 0 0 0 0 0
51.0 0 0 0 0 0 0 0
50.5 0 0 0 1 0 1 1
50.0 0 0 0 0 1 0 0
49.5 0 0 0 0 2 0 0
49.0 0 0 0 0 1 0 0
48.5 0 0 0 0 0 0 0
48.0 0 0 0 0 2 3 0
47.5 0 0 0 0 0 0 0
47.0 0 0 0 0 0 0 0
46.5 0 0 0 0 0 0 0
46.0 0 0 0 0 1 0 0
45.5 0 0 0 0 0 0 0
45.0 0 0 0 0 0 0 0
44.5 0 0 0 0 0 0 0
44.0 0 0 0 0 1 0 0
43.5 0 0 0 0 2 0 0
43.0 0 0 0 0 1 0 0
42.5 0 0 0 0 0 0 0
42.0 0 4 1 1 1 1 0
41.5 0 0 0 0 0 1 0
41.0 0 0 0 0 0 0 0
40.5 0 0 0 0 0 0 0
40.0 0 0 1 0 1 0 0
39.5 0 0 0 0 0 0 0
39.0 0 0 0 0 0 0 0
38.5 0 0 0 1 0 0 0
38.0 0 0 0 0 0 0 0
37.5 0 0 0 0 1 0 0
37.0 0 0 0 0 1 0 0
36.5 0 0 0 0 0 0 0
36.0 0 0 0 1 1 0 0
35.5 0 0 0 0 0 0 0
35.0 0 0 0 0 0 0 0
34.5 0 0 0 0 0 0 0
34.0 0 0 0 0 0 0 0
33.5 0 0 0 0 0 0 0
33.0 0 0 0 0 0 1 0
32.5 0 0 0 0 0 0 0
32.0 0 0 0 0 0 0 0
31.5 0 1 0 0 0 1 0
31.0 0 0 0 0 0 0 0
30.5 0 0 0 0 0 0 0
30.0 0 2 0 2 0 0 0
29.5 0 0 0 0 0 0 0
29.0 0 0 0 0 0 0 0
28.5 0 0 0 0 0 0 0
28.0 0 0 0 0 0 0 0
27.5 0 0 0 0 0 0 0
27.0 0 0 0 0 0 0 0
26.5 0 0 0 0 0 0 0
26.0 0 0 0 0 0 0 0
25.5 0 0 0 0 0 0 0
25.0 0 0 0 0 0 0 0
24.5 0 0 0 0 0 0 0
24.0 0 0 2 2 0 0 0
23.5 0 0 0 0 0 0 0
23.0 0 0 0 0 0 0 0
22.5 0 0 0 0 0 0 0
22.0 0 0 0 0 1 0 0
21.5 0 0 0 0 0 0 0
21.0 0 0 0 0 0 0 0
20.5 0 1 0 0 0 0 0
20.0 0 0 0 0 0 0 0
19.5 0 0 0 0 0 0 0
19.0 0 0 0 0 0 0 0
18.5 0 0 0 0 0 0 0
18.0 0 1 2 0 0 0 1
17.5 0 0 0 0 0 0 0
17.0 0 0 0 0 0 0 0
16.5 0 0 0 0 0 0 0
16.0 0 0 0 0 0 0 0
15.5 0 0 0 0 0 0 0
15.0 0 0 0 0 0 0 0
14.5 0 0 0 0 0 0 0
14.0 0 0 0 0 0 0 0
13.5 0 0 0 0 0 0 0
13.0 0 0 0 0 0 0 0
12.5 0 0 0 0 0 0 0
12.0 0 0 0 0 0 0 0
11.5 0 0 0 0 0 0 0
11.0 0 0 0 0 0 0 0
10.5 0 0 0 0 0 0 0
10.0 0 0 0 0 0 0 0
9.5 0 0 0 0 0 0 0
9.0 0 0 0 0 0 0 0
8.5 0 0 0 0 0 0 0
8.0 0 0 0 0 0 0 0
7.5 0 0 0 0 0 0 0
7.0 0 0 0 0 0 0 0
6.5 0 0 0 0 0 0 0
6.0 0 0 0 0 0 0 0
5.5 0 0 0 0 0 0 0
5.0 0 0 0 0 0 0 0
4.5 0 0 0 0 0 0 0
4.0 0 0 0 0 0 0 0
3.5 0 0 0 0 0 0 0
3.0 0 0 0 0 0 0 0
2.5 0 0 0 0 0 0 0
2.0 0 0 0 0 0 0 0
1.5 0 0 0 0 0 0 0
1.0 0 0 0 0 0 0 0
0.5 0 0 0 0 0 0 0
0 0 0 0 0 0 0
American Mathematics Competitions
2003 AMC 10 B Results for Michigan
Analysis
Table of Item Difficulty for the 2003
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.05 0.23 9.28* 0.08 0.28 0.08 0.00
2 0.03 0.18 0.98 7.78* 0.62 0.41 0.00
3 0.70 6.43* 0.93 0.54 0.16 1.24 0.00
4 8.45* 0.44 0.26 0.08 0.26 0.52 0.00
5 0.28 0.49 4.19* 0.98 1.42 2.64 0.00
6 0.98 1.83 0.54 3.20* 0.83 2.61 0.00
7 0.88 5.71* 0.41 0.88 0.18 1.94 0.00
8 0.23 1.86* 0.34 0.75 0.44 6.38 0.00
9 0.47 3.02* 0.72 0.39 0.59 4.81 0.00
10 0.36 0.65 3.98* 1.14 0.54 3.33 0.00
11 4.60* 0.72 0.41 0.44 1.27 2.56 0.00
12 0.75 0.78 5.94* 0.26 0.34 1.94 0.00
13 2.97 0.54 0.34 1.01 1.21* 3.93 0.00
14 1.29 0.65 0.59 3.23* 0.13 4.11 0.00
15 2.14 2.45 0.28 1.06 2.48* 1.58 0.00
16 0.47 0.26 0.62 0.80 4.99* 2.87 0.00
17 0.18 1.65* 1.32 0.44 0.41 5.99 0.00
18 0.39 1.37 0.54 2.33* 1.73 3.64 0.00
19 0.18 0.39 0.75 0.70 0.80* 7.18 0.00
20 0.49 0.54 0.83 1.83* 1.58 4.73 0.00
21 2.14 0.57 0.90* 1.55 0.59 4.24 0.00
22 1.34 2.89* 2.30 0.80 0.44 2.22 0.00
23 0.34 0.59 0.39 1.27* 1.01 6.41 0.00
24 0.28 0.31 2.14 0.36 0.18* 6.72 0.00
25 1.32 2.66* 1.40 0.41 0.31 3.90 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
2003 AMC 12 B Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 0 0 125.0 0 0 100.0 0 0
149.5 0 0 124.5 0 0 99.5 2 0
149.0 0 0 124.0 1 0 99.0 0 0
148.5 0 0 123.5 0 0 98.5 1 1
148.0 0 0 123.0 0 0 98.0 3 0
147.5 0 0 122.5 0 0 97.5 0 0
147.0 0 0 122.0 0 0 97.0 1 3
146.5 0 0 121.5 0 0 96.5 0 0
146.0 0 0 121.0 0 0 96.0 1 1
145.5 0 0 120.5 0 0 95.5 0 0
145.0 0 0 120.0 0 0 95.0 3 3
144.5 0 0 119.5 0 0 94.5 1 0
144.0 0 0 119.0 0 0 94.0 0 0
143.5 0 0 118.5 0 0 93.5 3 0
143.0 0 0 118.0 0 0 93.0 1 0
142.5 0 0 117.5 0 0 92.5 4 1
142.0 0 0 117.0 0 0 92.0 1 2
141.5 0 0 116.5 0 0 91.5 0 2
141.0 0 0 116.0 2 0 91.0 2 0
140.5 1 0 115.5 0 0 90.5 1 1
140.0 0 0 115.0 0 0 90.0 1 4
139.5 0 0 114.5 0 0 89.5 2 0
139.0 0 0 114.0 0 0 89.0 3 2
138.5 0 0 113.5 1 0 88.5 1 0
138.0 0 0 113.0 0 0 88.0 2 0
137.5 0 0 112.5 0 0 87.5 2 1
137.0 0 0 112.0 1 1 87.0 2 0
136.5 0 0 111.5 0 0 86.5 2 2
136.0 0 0 111.0 0 0 86.0 0 0
135.5 0 0 110.5 0 0 85.5 2 1
135.0 0 0 110.0 1 0 85.0 2 1
134.5 0 0 109.5 1 0 84.5 2 1
134.0 0 0 109.0 2 0 84.0 6 1
133.5 0 0 108.5 1 0 83.5 0 0
133.0 0 0 108.0 2 0 83.0 8 1
132.5 0 0 107.5 1 0 82.5 2 0
132.0 0 0 107.0 0 0 82.0 3 2
131.5 0 0 106.5 1 1 81.5 6 1
131.0 0 0 106.0 0 0 81.0 4 1
130.5 0 0 105.5 2 0 80.5 6 2
130.0 1 0 105.0 0 0 80.0 1 1
129.5 0 0 104.5 2 0 79.5 1 2
129.0 0 0 104.0 2 0 79.0 4 1
128.5 0 0 103.5 0 0 78.5 5 2
128.0 0 0 103.0 1 1 78.0 4 3
127.5 0 0 102.5 0 0 77.5 2 1
127.0 0 0 102.0 4 1 77.0 8 5
126.5 0 0 101.5 1 0 76.5 0 0
126.0 0 0 101.0 2 0 76.0 6 0
125.5 0 0 100.5 5 1 75.5 2 6
American Mathematics Competitions
2003 AMC 12 B Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 2 8 50.0 2 0 25.0 0 0
74.5 5 1 49.5 0 0 24.5 0 0
74.0 1 2 49.0 2 0 24.0 0 0
73.5 5 1 48.5 1 4 23.5 0 0
73.0 5 1 48.0 0 1 23.0 0 0
72.5 2 2 47.5 1 1 22.5 0 0
72.0 6 0 47.0 0 0 22.0 0 0
71.5 3 3 46.5 0 1 21.5 0 0
71.0 3 4 46.0 1 0 21.0 0 0
70.5 1 3 45.5 0 1 20.5 0 0
70.0 4 2 45.0 1 0 20.0 0 0
69.5 5 1 44.5 0 0 19.5 0 0
69.0 6 4 44.0 0 2 19.0 0 0
68.5 4 2 43.5 0 0 18.5 0 0
68.0 1 2 43.0 0 2 18.0 0 0
67.5 1 0 42.5 0 0 17.5 0 0
67.0 2 4 42.0 0 0 17.0 0 0
66.5 3 7 41.5 0 2 16.5 0 0
66.0 5 6 41.0 1 0 16.0 0 0
65.5 3 5 40.5 0 0 15.5 0 0
65.0 3 1 40.0 2 1 15.0 0 0
64.5 2 1 39.5 0 0 14.5 0 0
64.0 1 3 39.0 0 0 14.0 0 0
63.5 1 0 38.5 2 0 13.5 0 0
63.0 2 3 38.0 0 0 13.0 0 0
62.5 3 3 37.5 1 0 12.5 0 0
62.0 3 5 37.0 0 0 12.0 0 0
61.5 1 2 36.5 1 0 11.5 0 0
61.0 1 3 36.0 0 0 11.0 0 0
60.5 2 2 35.5 0 1 10.5 0 0
60.0 3 3 35.0 0 0 10.0 0 0
59.5 0 2 34.5 0 0 9.5 0 0
59.0 6 4 34.0 0 0 9.0 0 0
58.5 1 1 33.5 0 0 8.5 0 0
58.0 2 2 33.0 0 0 8.0 0 0
57.5 2 3 32.5 0 0 7.5 0 0
57.0 2 1 32.0 0 0 7.0 0 0
56.5 1 8 31.5 0 0 6.5 0 0
56.0 1 3 31.0 0 0 6.0 0 0
55.5 1 1 30.5 0 0 5.5 0 0
55.0 2 0 30.0 0 0 5.0 0 0
54.5 1 1 29.5 0 0 4.5 0 0
54.0 5 1 29.0 0 0 4.0 0 0
53.5 0 3 28.5 0 0 3.5 0 0
53.0 0 0 28.0 0 0 3.0 0 0
52.5 0 3 27.5 0 0 2.5 0 0
52.0 2 2 27.0 0 0 2.0 0 0
51.5 2 3 26.5 0 0 1.5 0 0
51.0 2 1 26.0 0 0 1.0 0 0
50.5 1 1 25.5 0 0 0.5 0 0
0.0 0 0
American Mathematics Competitions
2003 AMC 12 B Results for Michigan
SCORE DISTRIBUTION
score -----------grade-----------
5 6 7 8 9 10 11 12 13 unknown
---------------------------
150.0 0 0 0 0 0 0 0 0 0 0
149.5 0 0 0 0 0 0 0 0 0 0
149.0 0 0 0 0 0 0 0 0 0 0
148.5 0 0 0 0 0 0 0 0 0 0
148.0 0 0 0 0 0 0 0 0 0 0
147.5 0 0 0 0 0 0 0 0 0 0
147.0 0 0 0 0 0 0 0 0 0 0
146.5 0 0 0 0 0 0 0 0 0 0
146.0 0 0 0 0 0 0 0 0 0 0
145.5 0 0 0 0 0 0 0 0 0 0
145.0 0 0 0 0 0 0 0 0 0 0
144.5 0 0 0 0 0 0 0 0 0 0
144.0 0 0 0 0 0 0 0 0 0 0
143.5 0 0 0 0 0 0 0 0 0 0
143.0 0 0 0 0 0 0 0 0 0 0
142.5 0 0 0 0 0 0 0 0 0 0
142.0 0 0 0 0 0 0 0 0 0 0
141.5 0 0 0 0 0 0 0 0 0 0
141.0 0 0 0 0 0 0 0 0 0 0
140.5 0 0 0 0 0 0 1 0 0 0
140.0 0 0 0 0 0 0 0 0 0 0
139.5 0 0 0 0 0 0 0 0 0 0
139.0 0 0 0 0 0 0 0 0 0 0
138.5 0 0 0 0 0 0 0 0 0 0
138.0 0 0 0 0 0 0 0 0 0 0
137.5 0 0 0 0 0 0 0 0 0 0
137.0 0 0 0 0 0 0 0 0 0 0
136.5 0 0 0 0 0 0 0 0 0 0
136.0 0 0 0 0 0 0 0 0 0 0
135.5 0 0 0 0 0 0 0 0 0 0
135.0 0 0 0 0 0 0 0 0 0 0
134.5 0 0 0 0 0 0 0 0 0 0
134.0 0 0 0 0 0 0 0 0 0 0
133.5 0 0 0 0 0 0 0 0 0 0
133.0 0 0 0 0 0 0 0 0 0 0
132.5 0 0 0 0 0 0 0 0 0 0
132.0 0 0 0 0 0 0 0 0 0 0
131.5 0 0 0 0 0 0 0 0 0 0
131.0 0 0 0 0 0 0 0 0 0 0
130.5 0 0 0 0 0 0 0 0 0 0
130.0 0 0 0 0 0 0 0 1 0 0
129.5 0 0 0 0 0 0 0 0 0 0
129.0 0 0 0 0 0 0 0 0 0 0
128.5 0 0 0 0 0 0 0 0 0 0
128.0 0 0 0 0 0 0 0 0 0 0
127.5 0 0 0 0 0 0 0 0 0 0
127.0 0 0 0 0 0 0 0 0 0 0
126.5 0 0 0 0 0 0 0 0 0 0
126.0 0 0 0 0 0 0 0 0 0 0
125.5 0 0 0 0 0 0 0 0 0 0
125.0 0 0 0 0 0 0 0 0 0 0
124.5 0 0 0 0 0 0 0 0 0 0
124.0 0 0 0 0 0 0 0 1 0 0
123.5 0 0 0 0 0 0 0 0 0 0
123.0 0 0 0 0 0 0 0 0 0 0
122.5 0 0 0 0 0 0 0 0 0 0
122.0 0 0 0 0 0 0 0 0 0 0
121.5 0 0 0 0 0 0 0 0 0 0
121.0 0 0 0 0 0 0 0 0 0 0
120.5 0 0 0 0 0 0 0 0 0 0
120.0 0 0 0 0 0 0 0 0 0 0
119.5 0 0 0 0 0 0 0 0 0 0
119.0 0 0 0 0 0 0 0 0 0 0
118.5 0 0 0 0 0 0 0 0 0 0
118.0 0 0 0 0 0 0 0 0 0 0
117.5 0 0 0 0 0 0 0 0 0 0
117.0 0 0 0 0 0 0 0 1 0 0
116.5 0 0 0 0 0 0 0 0 0 0
116.0 0 0 0 0 0 0 0 2 0 0
115.5 0 0 0 0 0 0 0 0 0 0
115.0 0 0 0 0 0 0 0 0 0 0
114.5 0 0 0 0 0 0 0 0 0 0
114.0 0 0 0 0 0 0 0 0 0 0
113.5 0 0 0 0 0 0 1 0 0 0
113.0 0 0 0 0 0 0 0 0 0 0
112.5 0 0 0 0 0 0 0 0 0 0
112.0 0 0 0 0 0 0 0 2 0 0
111.5 0 0 0 0 0 0 0 0 0 0
111.0 0 0 0 0 0 0 0 0 0 0
110.5 0 0 0 0 0 0 0 0 0 0
110.0 0 0 0 0 0 0 0 1 0 0
109.5 0 0 0 0 0 0 1 0 0 0
109.0 0 0 0 0 0 0 0 2 0 0
108.5 0 0 0 0 1 0 0 0 0 0
108.0 0 0 0 0 0 0 0 2 0 0
107.5 0 0 0 0 0 0 0 1 0 0
107.0 0 0 0 0 0 0 0 0 0 0
106.5 0 0 0 0 0 0 2 0 0 0
106.0 0 0 0 0 0 0 0 0 0 0
105.5 0 0 0 1 0 0 1 0 0 0
105.0 0 0 0 0 0 0 0 0 0 0
104.5 0 0 0 0 0 0 1 1 0 0
104.0 0 0 0 0 0 0 1 1 0 0
103.5 0 0 0 0 0 0 0 0 0 0
103.0 0 0 0 0 0 0 1 1 0 0
102.5 0 0 0 0 0 0 0 0 0 0
102.0 0 0 0 0 0 1 2 2 0 0
101.5 0 0 0 1 0 0 0 0 0 0
101.0 0 0 0 0 0 0 1 1 0 0
100.5 0 0 0 1 0 1 1 3 0 0
100.0 0 0 0 0 0 0 0 0 0 0
99.5 0 0 0 0 0 0 0 2 0 0
99.0 0 0 0 0 0 0 0 0