American Mathematics Competitions
2005 AMC 10 A Results for Massachusetts
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 1798
Number of unofficial participants: 97
Average score of participants: 80.1
Average score for female students is: 76.7 ( 772 Students)
Average score for male students is: 83.6 ( 928 Students)
Average score for unspecified gender is 74.1 ( 98 Students)
Average score for grade 10 is: 81.2 ( 991 Students)
Average score for grade 9 is: 78.1 ( 708 Students)
Average score for grade 8 and below is: 87.1 ( 76 Students)
Average score with unknown grade: 74.2 ( 23 Students)
AIME qualifying score = 120.0 or better
Number of AIME qualifers 51
Number of schools returning results 68
Average school winning score 109.91
American Mathematics Competitions
2005 AMC 12 A Results for Massachusetts
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 1857
Number of unofficial participants: 114
Average score of participants: 84.2
Average score for female students is: 79.5 ( 726 Students)
Average score for male students is: 87.5 ( 1071 Students)
Average score for unspecified gender is 81.4 ( 60 Students)
Average score for grade 13 is: 128.0 ( 2 Students)
Average score for grade 12 is: 85.9 ( 794 Students)
Average score for grade 11 is: 81.9 ( 967 Students)
Average score for grade 10 is: 95.0 ( 54 Students)
Average score for grade 9 is: 92.0 ( 18 Students)
Average score for grade 8 and below is: 100.2 ( 5 Students)
Average score with unknown grade: 79.2 ( 17 Students)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 336
Number of schools returning results 75
Average school winning score 112.65
Average school team score 312.04
American Mathematics Competitions
2005 AMC 10 B Results for Massachusetts
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 962
Number of unofficial participants: 0
Average score of participants: 82.5
Average score for female students is: 78.1 ( 397 Students)
Average score for male students is: 86.3 ( 510 Students)
Average score for unspecified gender is 79.5 ( 55 Students)
Average score for grade 10 is: 82.8 ( 487 Students)
Average score for grade 9 is: 81.4 ( 428 Students)
Average score for grade 8 and below is: 96.1 ( 34 Students)
Average score with unknown grade: 70.2 ( 13 Students)
AIME qualifying score = 120.0 or better
Number of AIME qualifers 35
Number of schools returning results 38
Average school winning score 114.57
American Mathematics Competitions
2005 AMC 12 B Results for Massachusetts
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 766
Number of unofficial participants: 0
Average score of participants: 87.6
Average score for female students is: 83.7 ( 315 Students)
Average score for male students is: 90.4 ( 418 Students)
Average score for unspecified gender is 90.8 ( 33 Students)
Average score for grade 13 is: 90.7 ( 3 Students)
Average score for grade 12 is: 88.3 ( 315 Students)
Average score for grade 11 is: 85.4 ( 378 Students)
Average score for grade 10 is: 100.2 ( 46 Students)
Average score for grade 9 is: 91.0 ( 12 Students)
Average score for grade 8 and below is: 93.5 ( 2 Students)
Average score with unknown grade: 85.5 ( 10 Students)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 143
Number of schools returning results 42
Average school winning score 112.56
Average school team score 307.00
2005 State AMC 12 TEAM Score Distribution
-----------------------------------------------
score A B Rank
-----------------------------------------------
409.0 1 1
393.0 1 2
388.5 1 3
385.5 1 4
381.5 2 5
381.0 1 7
377.0 1 8
375.5 1 9
373.0 1 10
370.0 1 11
367.5 1 12
366.5 1 13
366.0 1 14
365.5 1 15
365.0 1 16
362.5 1 17
358.5 1 1 18
357.5 2 20
356.0 1 22
355.5 1 23
354.5 2 24
354.0 1 1 26
350.0 1 28
349.0 1 29
347.0 1 3 30
339.5 1 1 34
338.5 1 36
338.0 1 37
336.0 1 1 38
335.5 1 40
335.0 1 41
331.5 1 42
331.0 1 43
329.5 1 44
329.0 1 45
328.5 1 1 46
327.0 1 48
326.0 1 49
325.5 1 50
325.0 2 1 51
323.5 1 54
322.5 1 55
322.0 1 56
320.5 1 57
319.0 1 58
317.0 1 59
316.5 1 1 60
316.0 1 62
315.5 1 63
314.0 1 64
313.0 1 65
310.5 1 1 66
310.0 1 68
308.5 1 69
308.0 1 70
307.5 1 71
306.5 1 72
305.5 1 73
304.5 1 74
303.5 1 75
302.5 1 76
302.0 1 77
301.0 2 78
300.0 1 80
299.0 1 81
298.0 1 82
295.5 1 83
293.5 1 1 84
293.0 1 1 86
289.5 1 88
288.5 1 89
288.0 1 90
285.0 1 91
283.5 1 92
282.0 1 93
281.5 1 94
280.5 1 95
279.5 1 96
273.5 2 97
273.0 1 99
272.5 1 100
268.5 1 101
268.0 1 102
264.0 1 103
256.0 1 104
254.5 1 105
253.5 1 106
250.0 1 107
245.0 1 108
244.0 1 109
233.0 1 110
225.0 1 111
194.5 1 112
179.0 1 113
100.5 1 114
97.0 1 115
95.0 1 116
70.5 1 117
2005 AMC Contest Score Distributions
-----------------------------------------------
score 12 A 12 B 10 A 10 B
-----------------------------------------------
150.0 1 1
144.0 1 1 3
140.5 1
139.5 2
138.0 2 5 2
137.0 2
136.0 1 1
134.5 2 1 2
133.5 1 4 2 1
132.5 1 1
132.0 1 3 1
131.0 1 3
130.0 1 1 3
129.0 3 1 1
128.5 3 2
127.5 5 3 4 2
126.5 4 1 2 2
126.0 3 2
125.5 5 2
125.0 3 1 3 1
124.0 5 2 1
123.0 3 1 2 3
122.5 4 2
122.0 3 1 1
121.5 1 1 5 1
120.5 4 6 3 2
120.0 1 2
119.5 2 3 3 3
119.0 1 1
118.5 6 1 2 2
118.0 2 1 4 2
117.0 2 2 5 5
116.5 1
116.0 10 5 4 5
115.5 2 3 4
115.0 6 5 1 5
114.5 2 8 2
114.0 3 1
113.5 7 3 7 9
113.0 1
112.5 12 8 1 4
112.0 1 1 5 2
111.5 13 4 2 1
111.0 4 2 11 1
110.5 1 1
110.0 5 6 12 9
109.5 1 1
109.0 25 3 6 4
108.5 4 1 3 2
108.0 14 5 8 5
107.5 3 2 8 4
107.0 1 2 1
106.5 11 1 5 12
106.0 1 6 4
105.5 29 12 7 1
105.0 4 2 2 3
104.5 22 4 6 4
104.0 8 1 14 14
103.5 5 2
103.0 19 6 13 10
102.5 2 7 5
102.0 36 9 8 8
101.5 4 1 8 4
101.0 24 15 4
100.5 12 5 16 11
100.0 3
99.5 21 8 11 6
99.0 1 5 4 3
98.5 24 15 14 8
98.0 7 4 9 10
97.5 10 5 4 1
97.0 16 11 19 8
96.5 1 3 1
96.0 32 14 30 16
95.5 6 5 9 7
95.0 50 24 14 3
94.5 7 8 17 9
94.0 13 2 10 2
93.5 22 18 15 17
93.0 1 1 6 1
92.5 47 24 28 10
92.0 7 1 10 10
91.5 26 6 12 7
91.0 11 9 18 11
90.5 11 2 9 3
90.0 30 16 18 21
89.5 7 9 5
89.0 68 37 23 16
88.5 10 7 12 15
88.0 26 10 19 3
87.5 15 13 24 10
87.0 12 4 7 4
86.5 24 12 24 11
86.0 4 3 17 10
85.5 30 15 25 11
85.0 13 9 12 13
84.5 20 7 14 6
84.0 19 16 33 10
83.5 13 2 8 2
83.0 35 20 28 9
82.5 13 9 18 11
82.0 26 6 28 12
81.5 21 10 17 11
81.0 21 7 19 6
80.5 32 14 24 14
80.0 5 5 9 7
79.5 30 17 34 11
79.0 8 5 17 12
78.5 17 8 18 10
78.0 20 13 18 24
77.5 18 3 17 3
77.0 34 21 26 9
76.5 19 5 10 7
76.0 25 11 19 11
75.5 14 7 10 9
75.0 31 3 23 4
74.5 25 11 29 24
74.0 13 1 14 12
73.5 27 10 20 11
73.0 12 5 14 7
72.5 26 6 23 7
72.0 19 11 25 12
71.5 12 8 9 6
71.0 25 5 33 10
70.5 12 4 14 2
70.0 13 6 28 6
69.5 5 6 19 5
69.0 19 2 14 3
68.5 15 4 24 6
68.0 14 1 12 3
67.5 10 3 23 13
67.0 9 2 10 4
66.5 21 5 13 5
66.0 14 7 16 10
65.5 12 11 5
65.0 15 21 8
64.5 14 2 9 2
64.0 14 1 21 4
63.5 6 2 11 12
63.0 23 5 6
62.5 5 4 11 3
62.0 8 2 15 5
61.5 11 4 14 6
61.0 2 1 8 4
60.5 13 1 8 4
60.0 11 5 23 13
59.5 6 3 3
59.0 8 1 11 4
58.5 7 3 8 2
58.0 6 11 1
57.5 7 7 4
57.0 3 1 2 3
56.5 5 1 9 12
56.0 5 1 5 4
55.5 6 2 4 2
55.0 2 9 5
54.5 5 1 7 3
54.0 3 14 7
53.5 5 1 8 2
53.0 2 1 3 3
52.5 1 1 6 4
52.0 1 1 6 3
51.5 3 3
51.0 2 5 3
50.5 5 2 5 2
50.0 1 7 2
49.5 1 1 3 4
49.0 1 2 3
48.5 1 3 4
48.0 3 2 10 6
47.5 4 2
47.0 2 1
46.5 4 2 1
46.0 1 1 1
45.5 1 1 1
45.0 2 1
44.5 2 1
44.0 5 2 1
43.5 1 1 1
43.0 2 2 1
42.5 1 1
42.0 4 1 8 4
41.5 3 2 1
41.0 3
40.5 3
40.0 1 2 1
39.0 1
38.5 3 2 2
38.0 1 1
37.5 2
37.0 1
36.5 1
36.0 1 6 3
35.5 1
35.0 1
34.5 2
34.0 3 1
33.5 2
32.5 1
32.0 2
31.5 1 1
31.0 1
30.5 2 1 1
30.0 2 1 5 2
29.5 1
29.0 1
27.0 1 2 1
24.0 1
23.0 1
18.0 1 1 1
17.0 1
14.5 1
12.0 2
American Mathematics Competitions
2005 AMC 10 A Results for Massachusetts
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 1 125.0 1 2 100.0
149.5 124.5 99.5 6 5
149.0 124.0 1 1 99.0 3 1
148.5 123.5 98.5 10 4
148.0 123.0 1 1 98.0 6 2
147.5 122.5 2 2 97.5 2 2
147.0 122.0 97.0 12 5
146.5 121.5 3 2 96.5 2 1
146.0 121.0 96.0 13 15
145.5 120.5 2 95.5 7 2
145.0 120.0 1 1 95.0 6 6
144.5 119.5 2 1 94.5 11 5
144.0 1 119.0 1 94.0 6 4
143.5 118.5 2 93.5 8 5
143.0 118.0 4 93.0 5 1
142.5 117.5 92.5 15 8
142.0 117.0 4 1 92.0 7 3
141.5 116.5 1 91.5 6 6
141.0 116.0 4 91.0 8 10
140.5 115.5 4 90.5 7 2
140.0 115.0 1 90.0 12 4
139.5 114.5 7 1 89.5 7 2
139.0 114.0 2 1 89.0 12 11
138.5 113.5 3 3 88.5 7 4
138.0 4 1 113.0 1 88.0 7 12
137.5 112.5 1 87.5 9 15
137.0 112.0 3 2 87.0 1 6
136.5 111.5 1 1 86.5 10 12
136.0 111.0 7 2 86.0 12 5
135.5 110.5 1 85.5 11 13
135.0 110.0 9 3 85.0 8 4
134.5 2 109.5 1 84.5 9 5
134.0 109.0 3 3 84.0 19 13
133.5 2 108.5 1 2 83.5 2 6
133.0 108.0 3 5 83.0 12 15
132.5 107.5 6 1 82.5 10 8
132.0 3 107.0 1 1 82.0 14 13
131.5 106.5 4 1 81.5 8 9
131.0 3 106.0 4 2 81.0 7 10
130.5 105.5 3 3 80.5 12 12
130.0 1 105.0 2 80.0 4 5
129.5 104.5 3 3 79.5 17 13
129.0 104.0 14 79.0 10 7
128.5 3 103.5 4 1 78.5 9 9
128.0 103.0 10 3 78.0 10 7
127.5 3 1 102.5 5 1 77.5 10 7
127.0 102.0 7 1 77.0 13 12
126.5 2 101.5 5 2 76.5 8 2
126.0 3 101.0 3 1 76.0 12 6
125.5 100.5 10 6 75.5 6 3
American Mathematics Competitions
2005 AMC 10 A Results for Massachusetts
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 5 16 50.0 1 4 25.0
74.5 16 10 49.5 2 1 24.5
74.0 5 8 49.0 1 1 24.0
73.5 13 6 48.5 1 2 23.5
73.0 5 9 48.0 5 3 23.0 1
72.5 11 9 47.5 1 1 22.5
72.0 11 14 47.0 1 22.0
71.5 5 3 46.5 1 21.5
71.0 17 14 46.0 1 21.0
70.5 4 8 45.5 1 20.5
70.0 13 13 45.0 1 1 20.0
69.5 9 9 44.5 1 19.5
69.0 5 8 44.0 1 1 19.0
68.5 10 14 43.5 18.5
68.0 6 5 43.0 2 18.0 1
67.5 10 12 42.5 1 17.5
67.0 4 5 42.0 3 5 17.0
66.5 4 9 41.5 1 1 16.5
66.0 8 8 41.0 3 16.0
65.5 3 8 40.5 3 15.5
65.0 11 8 40.0 2 15.0
64.5 5 4 39.5 14.5 1
64.0 10 10 39.0 14.0
63.5 6 5 38.5 1 13.5
63.0 3 2 38.0 1 13.0
62.5 5 6 37.5 1 1 12.5
62.0 4 10 37.0 1 12.0 2
61.5 10 4 36.5 1 11.5
61.0 6 1 36.0 3 3 11.0
60.5 5 1 35.5 10.5
60.0 6 14 35.0 1 10.0
59.5 1 2 34.5 2 9.5
59.0 2 8 34.0 3 9.0
58.5 2 4 33.5 2 8.5
58.0 6 5 33.0 8.0
57.5 3 4 32.5 7.5
57.0 2 32.0 7.0
56.5 4 4 31.5 1 6.5
56.0 4 31.0 6.0
55.5 2 2 30.5 5.5
55.0 2 6 30.0 3 2 5.0
54.5 3 1 29.5 4.5
54.0 4 7 29.0 1 4.0
53.5 2 6 28.5 3.5
53.0 1 2 28.0 3.0
52.5 3 3 27.5 2.5
52.0 3 3 27.0 1 1 2.0
51.5 2 26.5 1.5
51.0 2 3 26.0 1.0
50.5 4 25.5 .5
0.0 0 0
American Mathematics Competitions
2005 AMC 10 A Results for Massachusetts
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 unknown
---------------------------
150.0 1
144.0 1
138.0 2 1 2
134.5 2
133.5 1 1
132.0 1 2
131.0 2 1
130.0 1
128.5 2 1
127.5 1 3
126.5 2
126.0 1 2
125.0 1 2
124.0 2
123.0 2
122.5 1 3
121.5 2 3
120.5 3
120.0 1 1
119.5 1 2
119.0 1
118.5 2
118.0 4
117.0 1 1 1 2
116.5 1
116.0 1 3
115.5 1 3
115.0 1
114.5 3 5
114.0 3
113.5 2 5
113.0 1
112.5 1
112.0 1 4
111.5 1 1
111.0 1 4 6
110.5 1
110.0 1 5 6
109.5 1
109.0 1 5
108.5 1 2
108.0 1 1 6
107.5 5 3
107.0 2
106.5 1 4
106.0 1 5
105.5 1 6
105.0 1 1
104.5 3 3
104.0 7 7
103.5 5
103.0 1 8 4
102.5 2 4 1
102.0 1 2 5
101.5 4 4
101.0 1 3
100.5 3 13
99.5 5 6
99.0 1 3
98.5 7 6 1
98.0 1 3 5
97.5 1 1 2
97.0 5 13 1
96.5 2 1
96.0 1 12 17
95.5 1 3 5
95.0 1 7 6
94.5 8 8 1
94.0 5 5
93.5 2 5 8
93.0 3 3
92.5 1 10 17
92.0 1 3 6
91.5 1 2 9
91.0 6 12
90.5 7 2
90.0 2 8 8
89.5 1 7 1
89.0 8 15
88.5 3 9
88.0 13 6
87.5 1 8 15
87.0 3 4
86.5 11 13
86.0 1 6 10
85.5 12 12 1
85.0 1 5 5 1
84.5 2 7 5
84.0 1 8 24
83.5 5 3
83.0 2 10 15 1
82.5 7 11
82.0 1 10 17
81.5 1 6 10
81.0 1 1 3 14
80.5 1 9 14
80.0 1 2 6
79.5 15 19
79.0 9 8
78.5 10 8
78.0 1 5 12
77.5 6 11
77.0 1 1 11 13
76.5 4 6
76.0 12 7
75.5 4 5 1
75.0 9 14
74.5 15 11 3
74.0 5 9
73.5 1 10 9
73.0 7 7
72.5 1 1 13 7 1
72.0 12 13
71.5 5 3 1
71.0 2 15 16
70.5 4 10
70.0 1 12 14 1
69.5 1 8 10
69.0 3 11
68.5 12 12
68.0 1 4 6 1
67.5 1 10 12
67.0 3 6 1
66.5 1 4 8
66.0 2 8 6
65.5 6 5
65.0 10 11
64.5 4 5
64.0 1 1 11 8
63.5 8 3
63.0 3 2
62.5 6 5
62.0 5 9 1
61.5 1 4 9
61.0 1 4 3
60.5 5 3
60.0 2 11 9 1
59.5 1 1 1
59.0 8 3
58.5 3 5
58.0 8 3
57.5 4 3
57.0 2
56.5 1 4 4
56.0 3 2
55.5 2 2
55.0 3 5 1
54.5 3 4
54.0 1 1 6 5 1
53.5 4 4
53.0 1 2
52.5 1 5
52.0 1 5
51.5 1 2
51.0 1 4
50.5 3 1 1
50.0 2 5
49.5 1 2
49.0 1 1
48.5 3
48.0 3 7
47.5 3 1
47.0 1
46.5 2
46.0 1
45.5 1
45.0 2
44.5 1
44.0 2
43.5 1
43.0 2
42.5 1
42.0 1 6 1
41.5 1 1
41.0 3
40.5 3
40.0 1 1
38.5 1 1
38.0 1
37.5 1 1
37.0 1
36.5 1
36.0 2 4
35.0 1
34.5 2
34.0 1 2
33.5 1 1
31.5 1
30.5 1
30.0 4 1
29.0 1
27.0 1 1
23.0 1
18.0 1
14.5 1
12.0 2
American Mathematics Competitions
2005 AMC 10 A Results for Massachusetts
Analysis
Table of Item Difficulty for the 2005
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.15 0.12 0.28 9.09* 0.27 0.09 0.00
2 0.06 0.09 7.16* 0.07 1.17 1.45 0.01
3 0.04 9.10* 0.24 0.34 0.07 0.20 0.01
4 0.39 2.81* 1.55 0.49 0.49 4.25 0.01
5 6.80* 0.37 2.63 0.03 0.06 0.12 0.00
6 0.26 6.50* 2.20 0.16 0.08 0.81 0.00
7 0.46 4.51* 0.32 0.24 0.80 3.67 0.01
8 0.79 0.29 5.24* 0.11 0.12 3.45 0.00
9 1.17 6.30* 0.92 0.19 0.14 1.28 0.00
10 2.59* 0.38 1.00 0.26 0.14 5.63 0.00
11 0.38 2.60* 0.17 0.71 0.11 6.02 0.01
12 0.26 1.89* 0.52 0.13 0.55 6.66 0.01
13 1.51 0.49 0.31 0.34 1.36* 5.98 0.01
14 1.04 0.39 0.26 0.39 3.41* 4.49 0.00
15 0.46 0.77 0.91 1.19 1.13* 5.53 0.00
16 0.37 0.30 0.83 3.06* 0.17 5.26 0.01
17 0.25 0.27 0.42 2.25* 0.38 6.43 0.00
18 1.16* 2.65 0.87 3.30 0.14 1.88 0.00
19 0.34 0.65 0.66 3.93* 0.62 3.80 0.00
20 0.97* 0.34 0.49 0.34 0.31 7.55 0.00
21 1.49 0.88* 0.18 0.24 0.63 6.56 0.01
22 0.92 0.54 0.28 2.96* 0.50 4.80 0.00
23 0.29 0.39 1.25* 0.87 0.70 6.50 0.01
24 1.12 0.98* 0.26 0.12 0.07 7.46 0.00
25 0.33 0.49 0.67 0.76* 0.08 7.66 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
American Mathematics Competitions
2005 AMC 12 A Results for Massachusetts
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 125.0 3 100.0
149.5 124.5 99.5 15 6
149.0 124.0 99.0 1
148.5 123.5 98.5 16 7
148.0 123.0 3 98.0 6 1
147.5 122.5 97.5 4 5
147.0 122.0 3 97.0 13 3
146.5 121.5 96.5 1
146.0 121.0 96.0 21 8
145.5 120.5 4 95.5 6
145.0 120.0 1 95.0 28 22
144.5 119.5 2 94.5 3 4
144.0 1 119.0 1 94.0 7 6
143.5 118.5 5 1 93.5 16 6
143.0 118.0 2 93.0 1
142.5 117.5 92.5 25 21
142.0 117.0 2 92.0 4 3
141.5 116.5 91.5 14 12
141.0 116.0 8 2 91.0 7 2
140.5 115.5 2 90.5 3 7
140.0 115.0 6 90.0 15 13
139.5 2 114.5 2 89.5 6 1
139.0 114.0 89.0 42 25
138.5 113.5 6 1 88.5 6 4
138.0 2 113.0 88.0 13 11
137.5 112.5 10 2 87.5 10 5
137.0 1 1 112.0 1 87.0 8 4
136.5 111.5 9 4 86.5 6 18
136.0 1 111.0 4 86.0 1 3
135.5 110.5 85.5 11 17
135.0 110.0 4 85.0 7 6
134.5 2 109.5 1 84.5 10 10
134.0 109.0 22 3 84.0 13 5
133.5 1 108.5 4 83.5 9 4
133.0 108.0 12 2 83.0 20 13
132.5 107.5 2 1 82.5 9 4
132.0 107.0 82.0 13 12
131.5 106.5 9 2 81.5 10 11
131.0 106.0 81.0 12 9
130.5 105.5 23 6 80.5 19 12
130.0 105.0 2 2 80.0 4 1
129.5 104.5 17 5 79.5 17 12
129.0 3 104.0 7 1 79.0 6 2
128.5 103.5 78.5 8 9
128.0 103.0 13 4 78.0 10 9
127.5 4 102.5 1 1 77.5 6 12
127.0 102.0 26 9 77.0 17 17
126.5 3 1 101.5 3 76.5 10 9
126.0 101.0 16 6 76.0 18 7
125.5 5 100.5 10 1 75.5 8 6
American Mathematics Competitions
2005 AMC 12 A Results for Massachusetts
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 17 12 50.0 1 25.0
74.5 15 7 49.5 1 24.5
74.0 6 7 49.0 1 24.0 1
73.5 14 13 48.5 1 23.5
73.0 3 9 48.0 2 1 23.0
72.5 12 13 47.5 22.5
72.0 9 9 47.0 22.0
71.5 6 5 46.5 1 3 21.5
71.0 9 12 46.0 1 21.0
70.5 5 7 45.5 20.5
70.0 5 8 45.0 20.0
69.5 2 2 44.5 2 19.5
69.0 10 8 44.0 3 2 19.0
68.5 6 8 43.5 1 18.5
68.0 5 9 43.0 2 18.0
67.5 3 7 42.5 17.5
67.0 6 3 42.0 3 1 17.0
66.5 8 12 41.5 2 1 16.5
66.0 7 5 41.0 16.0
65.5 7 5 40.5 15.5
65.0 9 6 40.0 1 15.0
64.5 7 7 39.5 14.5
64.0 6 8 39.0 14.0
63.5 4 2 38.5 2 13.5
63.0 13 10 38.0 13.0
62.5 1 4 37.5 12.5
62.0 2 5 37.0 12.0
61.5 2 8 36.5 11.5
61.0 1 1 36.0 11.0
60.5 5 8 35.5 10.5
60.0 7 4 35.0 10.0
59.5 1 5 34.5 9.5
59.0 4 3 34.0 9.0
58.5 2 4 33.5 8.5
58.0 3 3 33.0 8.0
57.5 4 3 32.5 7.5
57.0 1 2 32.0 7.0
56.5 1 3 31.5 6.5
56.0 1 3 31.0 1 6.0
55.5 1 5 30.5 1 1 5.5
55.0 2 30.0 1 1 5.0
54.5 2 3 29.5 1 4.5
54.0 1 1 29.0 4.0
53.5 4 1 28.5 3.5
53.0 1 1 28.0 3.0
52.5 1 27.5 2.5
52.0 27.0 1 2.0
51.5 2 1 26.5 1.5
51.0 1 1 26.0 1.0
50.5 2 3 25.5 .5
0.0 0 0
American Mathematics Competitions
2005 AMC 12 A Results for Massachusetts
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 11 12 13 unknown
---------------------------
144.0 1
139.5 1 1
138.0 2
137.0 1 1
136.0 1
134.5 1 1
133.5 1
129.0 1 1 1
127.5 3 1 1
126.5 3 1
125.5 1 4
125.0 1 2
123.0 1 2
122.0 2 1
121.5 1
120.5 4
120.0 1
119.5 1 1
119.0 1
118.5 4 2
118.0 1 1
117.0 2
116.0 1 4 5
115.5 1 1
115.0 1 2 3
114.5 1 1
113.5 1 5 1
112.5 1 2 9
112.0 1
111.5 1 1 7 4
111.0 1 3
110.0 2 3
109.5 1
109.0 3 12 10
108.5 1 2 1
108.0 2 5 7
107.5 3
106.5 1 5 5
105.5 2 3 12 12
105.0 1 3
104.5 8 13 1
104.0 4 4
103.0 1 1 4 13
102.5 2
102.0 1 18 17
101.5 1 3
101.0 1 1 8 13 1
100.5 4 7 1
99.5 1 8 12
99.0 1
98.5 1 13 10
98.0 3 4
97.5 1 4 5
97.0 1 6 9
96.5 1
96.0 17 15
95.5 2 4
95.0 1 1 26 22
94.5 5 2
94.0 5 8
93.5 1 15 6
93.0 1
92.5 1 27 19
92.0 5 2
91.5 15 10 1
91.0 1 1 3 6
90.5 5 5 1
90.0 1 9 20
89.5 3 4
89.0 2 32 32 2
88.5 1 5 4
88.0 2 15 9
87.5 1 7 7
87.0 3 9
86.5 11 12 1
86.0 2 2
85.5 1 16 12 1
85.0 7 6
84.5 1 13 6
84.0 9 10
83.5 1 9 3
83.0 1 16 18
82.5 1 7 5
82.0 15 11
81.5 7 14
81.0 1 10 10
80.5 2 20 8 2
80.0 4 1
79.5 20 10
79.0 6 2
78.5 1 11 5
78.0 11 8 1
77.5 13 5
77.0 1 17 16
76.5 8 11
76.0 17 8
75.5 8 6
75.0 20 11
74.5 1 18 5 1
74.0 1 9 3
73.5 1 15 11
73.0 1 1 6 4
72.5 13 13
72.0 13 6
71.5 7 5
71.0 1 1 13 10
70.5 8 4
70.0 6 7
69.5 5
69.0 1 11 7
68.5 12 3
68.0 1 9 4
67.5 6 4
67.0 2 3 4
66.5 14 7
66.0 1 8 5
65.5 7 5
65.0 8 7
64.5 1 1 9 3
64.0 9 5
63.5 2 4
63.0 1 1 9 12
62.5 3 2
62.0 7 1
61.5 7 4
61.0 1 1
60.5 11 2
60.0 8 3
59.5 5 1
59.0 1 6 1
58.5 5 2
58.0 4 2
57.5 1 3 3
57.0 1 2
56.5 3 2
56.0 5
55.5 3 3
55.0 2
54.5 4 1
54.0 2 1
53.5 2 3
53.0 2
52.5 1
52.0 1
51.5 1 2
51.0 2
50.5 3 2
50.0 1
49.5 1
49.0 1
48.5 1
48.0 1 2
46.5 1 3
46.0 1
44.5 1 1
44.0 2 3
43.5 1
43.0 1 1
42.0 4
41.5 3
40.0 1
38.5 2 1
31.0 1
30.5 1 1
30.0 1 1
29.5 1
27.0 1
24.0 1
American Mathematics Competitions
2005 AMC 12 A Results for Massachusetts
Analysis
Table of Item Difficulty for the 2005
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.03 0.05 0.12 9.61* 0.05 0.13 0.01
2 0.01 9.42* 0.12 0.36 0.01 0.08 0.00
3 0.26 5.32* 0.89 0.30 0.51 2.71 0.00
4 7.74* 0.25 1.83 0.04 0.02 0.12 0.01
5 0.10 8.05* 1.17 0.09 0.03 0.56 0.00
6 0.49 5.69* 0.23 0.18 0.77 2.64 0.00
7 0.39 0.16 7.57* 0.11 0.08 1.69 0.00
8 0.29 0.38 0.27 2.88* 0.17 6.01 0.00
9 4.61* 0.27 0.97 0.20 0.13 3.81 0.01
10 0.30 3.68* 0.16 0.46 0.08 5.32 0.00
11 1.03 0.30 0.37 0.41 4.16* 3.72 0.00
12 0.97 0.20 0.10 4.23* 1.13 3.37 0.00
13 0.11 0.19 0.30 3.47* 0.32 5.61 0.00
14 0.26 0.33 3.14 1.55* 0.31 4.40 0.00
15 0.30 0.31 1.62* 0.79 0.66 6.32 0.00
16 0.22 0.20 0.84 0.67* 0.25 7.81 0.01
17 2.07* 0.52 1.11 0.23 0.34 5.73 0.00
18 0.43* 0.34 0.22 0.23 0.20 8.57 0.00
19 0.87 2.42* 0.68 0.43 0.65 4.95 0.00
20 0.23 0.08 0.11 0.09 0.29* 9.21 0.00
21 0.38 0.46 0.39* 0.13 0.08 8.56 0.00
22 0.31 0.51* 0.20 0.18 0.13 8.67 0.00
23 0.37 0.79* 0.17 0.17 0.45 8.04 0.00
24 0.06 0.08* 0.15 0.15 0.02 9.55 0.01
25 0.22 0.10 0.12* 0.12 0.08 9.36 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
American Mathematics Competitions
2005 AMC 10 B Results for Massachusetts
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 1 125.0 1 100.0 1 2
149.5 124.5 99.5 2 4
149.0 124.0 1 99.0 3
148.5 123.5 98.5 3 4
148.0 123.0 3 98.0 8 1
147.5 122.5 2 97.5 1
147.0 122.0 1 97.0 4 4
146.5 121.5 1 96.5 1
146.0 121.0 96.0 7 8
145.5 120.5 2 95.5 5 2
145.0 120.0 95.0 3
144.5 119.5 2 1 94.5 3 4
144.0 2 1 119.0 94.0 1
143.5 118.5 2 93.5 11 6
143.0 118.0 2 93.0 1
142.5 117.5 92.5 4 5
142.0 117.0 3 1 92.0 5 5
141.5 116.5 91.5 4 3
141.0 116.0 4 1 91.0 6 5
140.5 1 115.5 90.5 1 2
140.0 115.0 3 2 90.0 11 10
139.5 114.5 1 1 89.5 4 1
139.0 114.0 1 89.0 8 7
138.5 113.5 6 1 88.5 8 7
138.0 2 113.0 88.0 1 2
137.5 112.5 2 2 87.5 7 3
137.0 112.0 1 87.0 3 1
136.5 111.5 1 86.5 4 7
136.0 111.0 86.0 5 4
135.5 110.5 1 85.5 7 3
135.0 110.0 7 2 85.0 7 6
134.5 109.5 84.5 5 1
134.0 109.0 4 84.0 2 5
133.5 1 108.5 1 1 83.5 1 1
133.0 108.0 4 83.0 6 3
132.5 1 107.5 3 1 82.5 8 3
132.0 1 107.0 1 82.0 8 4
131.5 106.5 5 7 81.5 5 5
131.0 106.0 1 2 81.0 4 2
130.5 105.5 1 80.5 8 4
130.0 3 105.0 3 80.0 2 5
129.5 104.5 3 1 79.5 5 6
129.0 1 104.0 10 3 79.0 8 3
128.5 2 103.5 1 1 78.5 4 6
128.0 103.0 6 2 78.0 15 8
127.5 2 102.5 5 77.5 2 1
127.0 102.0 5 3 77.0 3 5
126.5 2 101.5 3 76.5 2 5
126.0 2 101.0 76.0 6 3
125.5 2 100.5 5 6 75.5 5 4
American Mathematics Competitions
2005 AMC 10 B Results for Massachusetts
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 2 2 50.0 2 25.0
74.5 10 11 49.5 4 24.5
74.0 7 5 49.0 2 1 24.0
73.5 7 4 48.5 3 1 23.5
73.0 3 4 48.0 5 23.0
72.5 4 2 47.5 2 22.5
72.0 7 5 47.0 22.0
71.5 2 4 46.5 1 21.5
71.0 4 6 46.0 1 21.0
70.5 1 1 45.5 1 20.5
70.0 3 3 45.0 1 20.0
69.5 2 3 44.5 19.5
69.0 2 44.0 1 19.0
68.5 6 43.5 1 18.5
68.0 1 2 43.0 1 18.0 1
67.5 4 8 42.5 1 17.5
67.0 3 1 42.0 1 2 17.0 1
66.5 4 41.5 1 16.5
66.0 8 2 41.0 16.0
65.5 1 2 40.5 15.5
65.0 2 6 40.0 1 15.0
64.5 1 39.5 14.5
64.0 4 39.0 14.0
63.5 4 7 38.5 2 13.5
63.0 1 4 38.0 1 13.0
62.5 1 2 37.5 12.5
62.0 2 1 37.0 12.0
61.5 4 2 36.5 11.5
61.0 4 36.0 1 2 11.0
60.5 2 2 35.5 1 10.5
60.0 6 7 35.0 10.0
59.5 3 34.5 9.5
59.0 3 34.0 1 9.0
58.5 1 1 33.5 8.5
58.0 1 33.0 8.0
57.5 2 2 32.5 1 7.5
57.0 2 1 32.0 2 7.0
56.5 7 4 31.5 1 6.5
56.0 2 2 31.0 6.0
55.5 1 30.5 1 5.5
55.0 4 30.0 1 5.0
54.5 1 2 29.5 4.5
54.0 4 3 29.0 4.0
53.5 1 1 28.5 3.5
53.0 2 1 28.0 3.0
52.5 3 27.5 2.5
52.0 1 2 27.0 2.0
51.5 26.5 1.5
51.0 1 2 26.0 1.0
50.5 2 25.5 .5
0.0 0 0
American Mathematics Competitions
2005 AMC 10 B Results for Massachusetts
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 unknown
---------------------------
150.0 1
144.0 2 1
140.5 1
138.0 2
133.5 1
132.5 1
132.0 1
130.0 1 2
129.0 1
128.5 1 1
127.5 1 1
126.5 2
126.0 1 1
125.5 1 1
125.0 1
124.0 1
123.0 3
122.5 1 1
122.0 1
121.5 1
120.5 2
119.5 3
118.5 2
118.0 2
117.0 2 3
116.0 3 2
115.0 2 3
114.5 1 1
114.0 1
113.5 5 4
112.5 1 3
112.0 1 1
111.5 1
111.0 1
110.5 1
110.0 1 4 4
109.0 2 2
108.5 2
108.0 2 3
107.5 1 3
107.0 1
106.5 1 2 9
106.0 1 3
105.5 1
105.0 1 2
104.5 3 1
104.0 1 8 5
103.5 1 1
103.0 1 2 7
102.5 1 1 3
102.0 2 5 1
101.5 1 3
100.5 4 7
100.0 3
99.5 4 2
99.0 2 1
98.5 3 5
98.0 5 5
97.5 1
97.0 3 5
96.5 1
96.0 1 8 7
95.5 1 2 4
95.0 2 1
94.5 4 5
94.0 1 1
93.5 7 10
93.0 1
92.5 7 3
92.0 3 7
91.5 5 2
91.0 4 7
90.5 2 1
90.0 10 10 1
89.5 3 2
89.0 5 11
88.5 5 10
88.0 1 2
87.5 1 4 5
87.0 1 3
86.5 4 7
86.0 5 5
85.5 1 3 7
85.0 5 8
84.5 1 4 1
84.0 2 7 1
83.5 1 1
83.0 5 4
82.5 1 1 4 5
82.0 8 4
81.5 5 6
81.0 5 1
80.5 8 6
80.0 5 2
79.5 5 6
79.0 1 5 6
78.5 1 4 5
78.0 2 9 12 1
77.5 2 1
77.0 3 6
76.5 3 4
76.0 1 5 4 1
75.5 3 6
75.0 1 3
74.5 8 16
74.0 8 4
73.5 8 3
73.0 5 1 1
72.5 4 2 1
72.0 6 5 1
71.5 5 1
71.0 6 4
70.5 1 1
70.0 3 3
69.5 4 1
69.0 1 2
68.5 3 3
68.0 1 2
67.5 4 8 1
67.0 1 3
66.5 5
66.0 4 6
65.5 4 1
65.0 4 4
64.5 2
64.0 3 1
63.5 5 7
63.0 4 2
62.5 2 1
62.0 2 3
61.5 1 1 4
61.0 4
60.5 2 2
60.0 1 7 5
59.5 3
59.0 1 3
58.5 2
58.0 1
57.5 1 3
57.0 1 2
56.5 10 2
56.0 1 3
55.5 2
55.0 4 1
54.5 1 1 1
54.0 3 4
53.5 1 1
53.0 1 2
52.5 3 1
52.0 2 1
51.0 2 1
50.5 1 1
50.0 2
49.5 3 1
49.0 2 1
48.5 3 1
48.0 3 3
47.5 2
46.5 1
46.0 1
45.5 1
45.0 1
44.0 1
43.5 1
43.0 1
42.5 1
42.0 1 2 1
41.5 1
40.0 1
38.5 1 1
38.0 1
36.0 3
35.5 1
34.0 1
32.5 1
32.0 1 1
31.5 1
30.5 1
30.0 2
27.0 1
18.0 1
17.0 1
American Mathematics Competitions
2005 AMC 10 B Results for Massachusetts
Analysis
Table of Item Difficulty for the 2005
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 8.66* 0.33 0.45 0.11 0.38 0.06 0.00
2 0.08 0.24 0.18 8.78* 0.22 0.50 0.00
3 0.02 0.80 1.56 6.26* 1.01 0.35 0.00
4 0.88 0.06 0.54 5.15* 0.32 3.05 0.00
5 0.11 0.02 8.99* 0.16 0.27 0.45 0.00
6 0.14 8.43* 0.21 0.27 0.17 0.79 0.00
7 0.90 1.96* 0.40 1.05 0.64 5.04 0.00
8 6.32* 0.11 0.89 0.04 0.11 2.52 0.00
9 0.36 0.59 1.42 6.23* 0.48 0.91 0.00
10 2.05* 0.58 0.54 0.34 0.28 6.21 0.00
11 0.30 0.60 0.24 1.95 2.32* 4.56 0.02
12 0.36 1.30 0.51 0.44 0.46* 6.91 0.02
13 0.47 0.50 2.45* 1.76 0.48 4.33 0.01
14 0.45 0.22 2.55* 1.76 0.46 4.56 0.01
15 1.12 0.44 0.85 4.89* 0.48 2.21 0.01
16 0.29 0.68 0.54 0.56* 0.07 7.85 0.01
17 0.49 3.18* 1.10 0.25 0.17 4.81 0.00
18 0.30 4.76 1.00 2.35* 0.50 1.08 0.01
19 0.35 6.48* 0.30 0.46 0.41 2.00 0.01
20 0.67 0.26 1.08* 0.25 0.23 7.52 0.00
21 0.27* 0.28 0.37 0.22 0.12 8.72 0.01
22 0.70 0.99 0.60* 0.23 0.23 7.26 0.00
23 2.47 0.48 0.85* 0.20 0.24 5.75 0.01
24 0.19 0.23 0.23 0.37 1.24* 7.74 0.00
25 0.26 0.23 3.33* 0.22 0.18 5.79 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
2005 AMC 12 B Results for Massachusetts
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 125.0 100.0
149.5 124.5 99.5 5 3
149.0 124.0 5 99.0 5
148.5 123.5 98.5 6 9
148.0 123.0 1 98.0 1 3
147.5 122.5 97.5 3 2
147.0 122.0 1 97.0 5 5
146.5 121.5 1 96.5
146.0 121.0 96.0 9 5
145.5 120.5 3 2 95.5 4 1
145.0 120.0 95.0 14 7
144.5 119.5 3 94.5 5 2
144.0 119.0 94.0 2
143.5 118.5 1 93.5 13 4
143.0 118.0 1 93.0 1
142.5 117.5 92.5 13 9
142.0 117.0 1 1 92.0 1
141.5 116.5 91.5 1 5
141.0 116.0 3 2 91.0 6 1
140.5 115.5 3 90.5 2
140.0 115.0 3 2 90.0 7 8
139.5 114.5 89.5
139.0 114.0 89.0 19 14
138.5 113.5 2 1 88.5 6 1
138.0 113.0 88.0 5 5
137.5 112.5 5 3 87.5 8 5
137.0 112.0 1 87.0 2 2
136.5 111.5 4 86.5 5 6
136.0 1 111.0 2 86.0 1 2
135.5 110.5 85.5 8 5
135.0 110.0 3 3 85.0 5 4
134.5 1 109.5 84.5 4 3
134.0 109.0 3 84.0 9 7
133.5 3 108.5 1 83.5 1 1
133.0 108.0 4 1 83.0 10 10
132.5 1 107.5 1 1 82.5 7 2
132.0 1 107.0 1 82.0 1 5
131.5 106.5 1 81.5 6 4
131.0 1 106.0 1 81.0 3 4
130.5 105.5 9 1 80.5 6 8
130.0 1 105.0 1 1 80.0 1 4
129.5 104.5 1 2 79.5 10 6
129.0 1 104.0 1 79.0 2 3
128.5 103.5 78.5 5 3
128.0 103.0 4 2 78.0 4 7
127.5 3 102.5 77.5 2 1
127.0 102.0 6 3 77.0 7 13
126.5 1 101.5 1 76.5 3 2
126.0 101.0 10 5 76.0 6 4
125.5 100.5 4 1 75.5 5 2
American Mathematics Competitions
2005 AMC 12 B Results for Massachusetts
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 2 1 50.0 25.0
74.5 6 3 49.5 1 24.5
74.0 1 49.0 24.0
73.5 1 9 48.5 23.5
73.0 2 3 48.0 2 23.0
72.5 5 47.5 22.5
72.0 5 6 47.0 2 22.0
71.5 3 5 46.5 21.5
71.0 1 4 46.0 21.0
70.5 3 1 45.5 1 20.5
70.0 4 2 45.0 20.0
69.5 4 2 44.5 19.5
69.0 2 44.0 19.0
68.5 1 3 43.5 18.5
68.0 1 43.0 18.0 1
67.5 3 42.5 17.5
67.0 2 42.0 1 17.0
66.5 1 4 41.5 16.5
66.0 3 4 41.0 16.0
65.5 40.5 15.5
65.0 40.0 15.0
64.5 1 1 39.5 14.5
64.0 1 39.0 1 14.0
63.5 2 38.5 13.5
63.0 38.0 13.0
62.5 2 2 37.5 12.5
62.0 2 37.0 12.0
61.5 3 1 36.5 11.5
61.0 1 36.0 1 11.0
60.5 1 35.5 10.5
60.0 1 4 35.0 10.0
59.5 34.5 9.5
59.0 1 34.0 9.0
58.5 1 2 33.5 8.5
58.0 33.0 8.0
57.5 32.5 7.5
57.0 1 32.0 7.0
56.5 1 31.5 6.5
56.0 1 31.0 6.0
55.5 2 30.5 5.5
55.0 30.0 1 5.0
54.5 1 29.5 4.5
54.0 29.0 4.0
53.5 1 28.5 3.5
53.0 1 28.0 3.0
52.5 1 27.5 2.5
52.0 1 27.0 2.0
51.5 26.5 1.5
51.0 26.0 1.0
50.5 1 25.5 .5
0.0 0 0
American Mathematics Competitions
2005 AMC 12 B Results for Massachusetts
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 11 12 13 unknown
---------------------------
136.0 1
134.5 1
133.5 1 2 1
132.5 1
132.0 1
131.0 1
130.0 1
129.0 1
127.5 1 1 1
126.5 1
125.0 1
124.0 2 3
123.0 1
122.0 1
121.5 1
120.5 2 2 2
119.5 1 1 1
118.5 1
118.0 1
117.0 2
116.0 4 1
115.5 3
115.0 1 1 1 2
113.5 3
112.5 1 2 5
112.0 1
111.5 1 2 1
111.0 1 1
110.0 1 2 3
109.0 1 1 1
108.5 1
108.0 1 4
107.5 1 1
107.0 1
106.5 1
106.0 1
105.5 1 4 7
105.0 1 1
104.5 2 2
104.0 1
103.0 1 2 3
102.0 1 3 5
101.5 1
101.0 1 6 8
100.5 1 4
99.5 1 2 4 1
99.0 2 3
98.5 1 2 5 7
98.0 1 3
97.5 3 2
97.0 1 5 5
96.0 1 6 6 1
95.5 5
95.0 1 1 17 5
94.5 1 6 1
94.0 2
93.5 1 8 9
93.0 1
92.5 1 2 11 9 1
92.0 1
91.5 5 1
91.0 4 5
90.5 1 1
90.0 10 6
89.0 5 18 12 2
88.5 1 3 3
88.0 4 6
87.5 8 5
87.0 1 3
86.5 7 5
86.0 2 1
85.5 6 9
85.0 4 5
84.5 1 3 3
84.0 9 7
83.5 1 1
83.0 2 1 11 6
82.5 3 4 2
82.0 2 4
81.5 5 5
81.0 3 4
80.5 1 8 5
80.0 5
79.5 1 11 5
79.0 2 3
78.5 3 5
78.0 1 5 7
77.5 2 1
77.0 2 12 7
76.5 4 1
76.0 5 5 1
75.5 2 5
75.0 1 2
74.5 4 6 1
74.0 1
73.5 1 6 3
73.0 3 2
72.5 3 2 1
72.0 7 4
71.5 4 3 1
71.0 1 2 2
70.5 1 2 1
70.0 3 3
69.5 2 4
69.0 2
68.5 1 3
68.0 1
67.5 2 1
67.0 2
66.5 3 2
66.0 4 3
64.5 2
64.0 1
63.5 2
62.5 3 1
62.0 1 1
61.5 2 2
61.0 1
60.5 1
60.0 4 1
59.0 1
58.5 2 1
57.0 1
56.5 1
56.0 1
55.5 2
54.5 1
53.5 1
53.0 1
52.5 1
52.0 1
50.5 2
49.5 1
48.0 2
47.0 1 1
45.5 1
42.0 1
39.0 1
36.0 1
30.0 1
18.0 1
American Mathematics Competitions
2005 AMC 12 B Results for Massachusetts
Analysis
Table of Item Difficulty for the 2005
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 9.45* 0.07 0.22 0.08 0.16 0.03 0.00
2 0.08 0.13 0.05 9.60* 0.04 0.10 0.00
3 0.01 0.03 9.45* 0.07 0.20 0.25 0.00
4 0.07 9.23* 0.07 0.16 0.17 0.31 0.00
5 8.66* 0.05 0.38 0.07 0.03 0.82 0.00
6 3.79* 0.78 0.57 0.22 0.17 4.46 0.00
7 1.11 1.42 0.10 3.28* 0.59 3.50 0.00
8 0.90 1.78 4.99* 0.01 0.85 1.48 0.00
9 0.25 8.39* 0.17 0.31 0.23 0.64 0.00
10 0.08 0.43 0.08 1.87 4.58* 2.96 0.00
11 0.90 1.10 0.56 4.62* 0.35 2.47 0.00
12 0.30 0.56 0.78 1.49* 0.09 6.78 0.00
13 0.29 0.20 0.22 2.45* 0.14 6.70 0.00
14 0.65 1.04 0.52 0.20 1.37* 6.21 0.00
15 0.40 0.20 0.29 5.30* 0.43 3.38 0.00
16 0.31 0.17 1.01 0.86* 0.21 7.44 0.00
17 0.42 0.93* 0.20 0.09 0.59 7.78 0.00
18 1.38 0.42 0.56* 0.48 0.33 6.83 0.00
19 0.13 0.16 0.13 0.17 2.65* 6.76 0.00
20 0.04 0.25 4.52* 0.93 1.68 2.58 0.00
21 0.18 0.21 0.64* 0.38 0.17 8.42 0.00
22 0.26 0.64 0.13 0.14 0.10* 8.72 0.00
23 0.08 0.29* 0.10 0.05 0.07 9.41 0.00
24 0.17* 0.17 0.14 0.14 0.14 9.23 0.00
25 0.18* 0.27 0.08 0.14 0.20 9.13 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column