- About MAA
- Membership
- MAA Publications
- Periodicals
- Blogs
- MAA Book Series
- MAA Press (an imprint of the AMS)
- MAA Notes
- MAA Reviews
- Mathematical Communication
- Information for Libraries
- Author Resources
- Advertise with MAA
- Meetings
- Competitions
- Programs
- Communities
- MAA Sections
- SIGMAA
- MAA Connect
- Students
- MAA Awards
- Awards Booklets
- Writing Awards
- Teaching Awards
- Service Awards
- Research Awards
- Lecture Awards
- Putnam Competition Individual and Team Winners
- D. E. Shaw Group AMC 8 Awards & Certificates
- Maryam Mirzakhani AMC 10 A Awards & Certificates
- Two Sigma AMC 10 B Awards & Certificates
- Jane Street AMC 12 A Awards & Certificates
- Akamai AMC 12 B Awards & Certificates
- High School Teachers
- News
You are here
Missing Title
American Mathematics Competitions
2006 AMC 10 A Results for Michigan
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 1234
Number of unofficial participants: 0
Average score of participants: 80.6
Average score for female students is: 75.5 ( 535 Students)
Average score for male students is: 85.2 ( 639 Students)
Average score for unspecified gender is 76.9 ( 60 Students)
Average score for grade 10 is: 82.1 ( 611 Students)
Average score for grade 9 is: 76.7 ( 490 Students)
Average score for grade 8 and below is: 91.1 ( 111 Students)
Average score with unknown grade: 74.2 ( 22 Students)
AIME qualifying score = 120.0 or better
Number of AIME qualifers 46
Number of schools returning results 43
Average school winning score 113.10
American Mathematics Competitions
2006 AMC 12 A Results for Michigan
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 1462
Number of unofficial participants: 9
Average score of participants: 86.3
Average score for female students is: 81.7 ( 596 Students)
Average score for male students is: 89.7 ( 823 Students)
Average score for unspecified gender is 86.1 ( 43 Students)
Average score for grade 13 is: 113.5 ( 1 Student)
Average score for grade 12 is: 85.6 ( 601 Students)
Average score for grade 11 is: 85.3 ( 736 Students)
Average score for grade 10 is: 95.9 ( 76 Students)
Average score for grade 9 is: 93.3 ( 31 Students)
Average score for grade 8 and below is: 106.3 ( 9 Students)
Average score with unknown grade: 84.9 ( 8 Students)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 357
Number of schools returning results 54
Average school winning score 113.71
Average school team score 323.85
American Mathematics Competitions
2006 AMC 10 B Results for Michigan
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 640
Number of unofficial participants: 0
Average score of participants: 66.7
Average score for female students is: 58.7 ( 242 Students)
Average score for male students is: 72.0 ( 355 Students)
Average score for unspecified gender is 67.9 ( 43 Students)
Average score for grade 10 is: 66.0 ( 312 Students)
Average score for grade 9 is: 61.8 ( 240 Students)
Average score for grade 8 and below is: 89.5 ( 62 Students)
Average score with unknown grade: 66.0 ( 26 Students)
AIME qualifying score = 120.0 or better
Number of AIME qualifers 21
Number of schools returning results 24
Average school winning score 107.60
American Mathematics Competitions
2006 AMC 12 B Results for Michigan
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 778
Number of unofficial participants: 0
Average score of participants: 85.6
Average score for female students is: 81.6 ( 256 Students)
Average score for male students is: 87.5 ( 463 Students)
Average score for unspecified gender is 87.6 ( 59 Students)
Average score for grade 12 is: 84.7 ( 294 Students)
Average score for grade 11 is: 82.8 ( 325 Students)
Average score for grade 10 is: 98.0 ( 58 Students)
Average score for grade 9 is: 95.4 ( 24 Students)
Average score for grade 8 and below is: 98.4 ( 23 Students)
Average score with unknown grade: 84.2 ( 54 Students)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 180
Number of schools returning results 36
Average school winning score 112.33
Average school team score 300.22
2006 State AMC 12 TEAM Score Distribution
-----------------------------------------------
score A B Rank
-----------------------------------------------
401.5 1 1
391.0 1 2
390.0 1 3
386.5 1 4
382.0 1 5
371.5 1 6
370.0 1 1 7
369.0 1 9
363.5 1 10
362.5 1 11
361.0 1 12
360.5 1 13
360.0 3 14
358.5 1 17
356.5 1 18
355.5 1 19
355.0 1 20
354.0 1 21
353.0 1 22
352.5 1 23
352.0 1 24
351.5 1 25
350.5 1 26
349.5 1 27
349.0 1 28
348.0 1 29
347.0 1 30
345.5 1 31
344.5 1 32
343.5 1 33
343.0 1 34
338.5 2 35
337.5 1 37
337.0 1 38
333.0 1 39
331.5 1 40
329.5 1 41
327.0 1 42
326.5 1 43
324.5 1 44
323.5 1 45
321.0 1 46
319.5 1 47
319.0 1 48
317.5 1 49
316.5 1 50
314.0 1 51
313.5 1 52
311.5 1 53
309.5 1 54
307.5 1 55
306.0 1 56
305.0 1 57
303.5 1 58
302.0 1 59
301.0 1 60
300.5 2 61
298.0 1 63
294.5 1 64
292.5 1 65
290.5 1 66
286.0 1 67
284.0 1 68
282.5 1 69
281.5 1 70
280.5 1 71
279.0 1 72
278.0 2 73
277.0 1 75
275.0 2 76
271.0 1 78
270.0 1 79
268.5 1 80
264.5 1 81
261.0 1 82
260.0 1 83
251.0 1 84
212.5 1 85
200.5 1 86
191.0 1 87
187.0 1 88
115.0 1 89
109.0 1 90
2006 AMC Contest Score Distributions
-----------------------------------------------
score 12 A 12 B 10 A 10 B
-----------------------------------------------
150.0 1 1
146.5 1
144.0 1 3
140.5 1
138.0 1 3 1
137.0 1 1 2
136.0 1
134.5 1 1
133.5 1 2 1
132.5 1 1
132.0 1
131.0 1 1
130.0 3 1 1
129.0 3 4 1
128.5 2
127.5 1 2
126.5 4 5 3
126.0 3 1
125.5 2 3 1
125.0 1 1
124.0 3 3 2 2
123.0 5 2 5 2
122.5 1
122.0 5 2 1
121.5 1 3 3
120.5 2 5 4 1
120.0 3
119.5 7 4 1 1
119.0 1 2
118.5 30 5 1
118.0 2 5
117.0 5 4 2 2
116.0 10 3 7 2
115.5 1 2
115.0 6 4
114.5 1 2 6
114.0 1 1
113.5 9 2 1
113.0 3 1
112.5 35 5 2 1
112.0 2 9 1
111.5 2 10 1
111.0 3 4 12 3
110.0 20 2 7 3
109.5 1
109.0 20 7 3
108.5 1 2
108.0 6 9 4
107.5 5 1 8
107.0 3 1
106.5 23 6 2 1
106.0 2 1 1
105.5 16 16 5 1
105.0 2 1 8 1
104.5 6 10 1
104.0 19 2 17 1
103.5 1 4
103.0 27 8 6 1
102.5 2 1 6
102.0 20 13 3
101.5 8 4 5 3
101.0 7 17 1 1
100.5 33 6 10 3
100.0 1 2
99.5 17 8 6 1
99.0 8 2 9 3
98.5 8 12 3 1
98.0 17 6 10 5
97.5 2 2
97.0 25 6 8 4
96.5 5 1 6 1
96.0 32 15 9 2
95.5 7 1 18 2
95.0 18 25 9 4
94.5 22 6 12 3
94.0 3 4 8
93.5 24 15 11 6
93.0 2 1 7 2
92.5 14 15 8 2
92.0 18 1 18 1
91.5 4 5 13 3
91.0 25 11 12 1
90.5 4 1 6 3
90.0 28 14 12 4
89.5 8 1 14 4
89.0 24 33 11 1
88.5 22 3 11 2
88.0 6 17 7
87.5 26 13 14 3
87.0 3 5 16 3
86.5 20 14 11
86.0 12 2 18 7
85.5 9 5 10 1
85.0 24 4 8 3
84.5 9 6 4 2
84.0 17 10 20 3
83.5 6 3 15 5
83.0 26 15 15 4
82.5 16 4 11 2
82.0 8 10 10 2
81.5 25 8 9 3
81.0 7 8 5 1
80.5 26 7 15 4
80.0 11 2 23 4
79.5 11 5 12 3
79.0 17 4 12 7
78.5 15 4 14 3
78.0 15 8 16 5
77.5 7 4 19 2
77.0 23 8 14 5
76.5 13 5 7 3
76.0 4 11 8 4
75.5 23 3 8 1
75.0 7 6 12 4
74.5 17 10 12 11
74.0 9 4 11 8
73.5 8 5 17 4
73.0 21 7 8 2
72.5 7 5 5 6
72.0 17 8 14 4
71.5 10 9 10 3
71.0 16 7 9 9
70.5 16 4 11 3
70.0 6 6 8 11
69.5 11 10 10
69.0 4 6 7 5
68.5 10 6 15 11
68.0 6 3 16 6
67.5 5 3 11 5
67.0 13 5 11 2
66.5 9 5 9 10
66.0 18 6 9 9
65.5 11 6 12 2
65.0 15 7 9 4
64.5 7 5 7 6
64.0 7 4 10 5
63.5 7 3 9 8
63.0 2 4 11 6
62.5 4 4 10 6
62.0 3 1 9 3
61.5 3 5 6
61.0 2 3 7 5
60.5 2 3 5 7
60.0 15 5 15 8
59.5 1 2 9 5
59.0 9 3 6 8
58.5 4 2 9 3
58.0 3 3 4 2
57.5 5 1 5 4
57.0 2 5 4
56.5 5 2 8 14
56.0 5 2 6 8
55.5 2 2 4 3
55.0 2 1 7
54.5 2 3 5 5
54.0 6 8 10 11
53.5 6 6
53.0 4 4 3 6
52.5 2 1 4 7
52.0 1 3 8
51.5 1 2 4
51.0 3 1 3 5
50.5 2 3 4
50.0 1 4 6
49.5 1 2 5
49.0 4 2 3 6
48.5 1 2 2 6
48.0 4 3 9 8
47.5 1 3 2
47.0 1 1 2 5
46.5 1 1 5 5
46.0 3 1 2 3
45.5 1 2 6
45.0 1 3 3
44.5 1 3 2 1
44.0 1 1 2 5
43.5 1 1 1
43.0 2 1 2 3
42.5 1 2 3
42.0 3 6 6 6
41.5 1 4
41.0 2 1 1
40.5 1 3
40.0 1 2 2
39.0 1 1 1 3
38.5 2 2
38.0 1 4
37.5 1 1
37.0 4
36.5 1 2
36.0 4 2 5 6
35.5 4
35.0 1
34.5 1 1
34.0 2 2
33.5 1 1
33.0 1 1
32.5 1
32.0 1
31.5 1 1 1
31.0 1
30.5 1 1 2
30.0 5 2 6 5
29.5 1 3
29.0 1 1
28.5 1
28.0 1
27.0 1
26.5 1
25.5 1
25.0 1
24.0 3 1 4 7
23.5 1
20.5 1
18.5 1
18.0 1 1 3
14.5 1
11.0 1
8.5 1
7.5 1
American Mathematics Competitions
2006 AMC 10 A Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 1 125.0 1 100.0 1 1
149.5 124.5 99.5 2 3
149.0 124.0 2 99.0 4 5
148.5 123.5 98.5 3
148.0 123.0 4 98.0 8 2
147.5 122.5 1 97.5 2
147.0 122.0 2 97.0 7
146.5 121.5 2 1 96.5 5 1
146.0 121.0 96.0 4 5
145.5 120.5 4 95.5 11 6
145.0 120.0 3 95.0 4 4
144.5 119.5 1 94.5 8 4
144.0 3 119.0 2 94.0 5 3
143.5 118.5 1 93.5 6 5
143.0 118.0 4 1 93.0 5 1
142.5 117.5 92.5 5 2
142.0 117.0 2 92.0 9 9
141.5 116.5 91.5 6 7
141.0 116.0 5 2 91.0 4 7
140.5 115.5 1 90.5 4 2
140.0 115.0 90.0 8 4
139.5 114.5 4 1 89.5 7 6
139.0 114.0 89.0 4 7
138.5 113.5 1 1 88.5 8 3
138.0 3 113.0 2 1 88.0 4 3
137.5 112.5 2 87.5 6 8
137.0 1 112.0 7 2 87.0 11 4
136.5 111.5 1 86.5 7 3
136.0 111.0 10 2 86.0 9 8
135.5 110.5 85.5 8 2
135.0 110.0 4 2 85.0 4 4
134.5 1 109.5 1 84.5 3 1
134.0 109.0 3 84.0 13 7
133.5 2 108.5 1 83.5 7 8
133.0 108.0 1 3 83.0 7 7
132.5 107.5 4 3 82.5 5 5
132.0 107.0 2 1 82.0 6 3
131.5 106.5 1 1 81.5 4 5
131.0 1 106.0 1 81.0 2 3
130.5 105.5 4 80.5 5 9
130.0 1 105.0 5 2 80.0 9 14
129.5 104.5 1 79.5 7 4
129.0 1 104.0 12 4 79.0 9 3
128.5 2 103.5 3 1 78.5 9 5
128.0 103.0 2 4 78.0 6 10
127.5 2 102.5 6 77.5 10 7
127.0 102.0 2 1 77.0 10 4
126.5 3 101.5 3 1 76.5 3 4
126.0 2 1 101.0 1 76.0 5 2
125.5 1 100.5 6 2 75.5 4 4
American Mathematics Competitions
2006 AMC 10 A Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 6 5 50.0 4 25.0
74.5 4 7 49.5 1 24.5
74.0 5 6 49.0 3 24.0 1 2
73.5 8 8 48.5 2 23.5
73.0 5 3 48.0 6 3 23.0
72.5 4 1 47.5 2 1 22.5
72.0 4 7 47.0 2 22.0
71.5 7 3 46.5 2 3 21.5
71.0 2 7 46.0 2 21.0
70.5 8 3 45.5 2 20.5
70.0 6 2 45.0 2 1 20.0
69.5 3 6 44.5 1 19.5
69.0 1 5 44.0 1 1 19.0
68.5 7 8 43.5 1 18.5
68.0 8 6 43.0 1 1 18.0 1
67.5 5 6 42.5 1 17.5
67.0 2 8 42.0 1 4 17.0
66.5 5 3 41.5 1 16.5
66.0 3 6 41.0 1 16.0
65.5 4 7 40.5 15.5
65.0 6 3 40.0 1 1 15.0
64.5 1 6 39.5 14.5
64.0 2 8 39.0 1 14.0
63.5 2 6 38.5 13.5
63.0 4 7 38.0 13.0
62.5 4 3 37.5 1 12.5
62.0 4 5 37.0 12.0
61.5 1 4 36.5 11.5
61.0 1 5 36.0 1 3 11.0
60.5 3 2 35.5 10.5
60.0 3 11 35.0 1 10.0
59.5 2 7 34.5 9.5
59.0 1 3 34.0 2 9.0
58.5 2 7 33.5 8.5
58.0 3 1 33.0 1 8.0
57.5 1 4 32.5 7.5
57.0 1 4 32.0 7.0
56.5 3 4 31.5 1 6.5
56.0 3 3 31.0 6.0
55.5 3 1 30.5 1 5.5
55.0 1 30.0 2 3 5.0
54.5 3 2 29.5 1 4.5
54.0 3 6 29.0 4.0
53.5 3 3 28.5 3.5
53.0 2 1 28.0 3.0
52.5 2 2 27.5 2.5
52.0 1 2 27.0 2.0
51.5 1 1 26.5 1.5
51.0 1 2 26.0 1.0
50.5 1 2 25.5 .5
0.0 0 0
American Mathematics Competitions
2006 AMC 10 A Results for Michigan
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 unknown
---------------------------
150.0 1
144.0 2 1
138.0 1 2
137.0 1
134.5 1
133.5 2
131.0 1
130.0 1
129.0 1
128.5 1 1
127.5 2
126.5 1 2
126.0 1 2
125.5 1
125.0 1
124.0 1 1
123.0 1 1 3
122.5 1
122.0 1 1
121.5 1 2
120.5 3 1
120.0 1 1 1
119.5 1
119.0 1 1
118.5 1
118.0 1 1 1 2
117.0 2
116.0 1 3 1 2
115.5 1
114.5 1 3 2
113.5 2
113.0 1 1 1
112.5 1 1
112.0 1 2 6
111.5 1
111.0 2 2 8
110.0 1 5 1
109.5 1
109.0 1 2
108.5 2
108.0 1 1 2
107.5 1 1 2 4
107.0 1 2
106.5 1 1
106.0 1
105.5 2 2 1
105.0 1 1 6
104.5 1
104.0 1 3 12 1
103.5 2 2
103.0 1 2 3
102.5 1 2 3
102.0 1 2
101.5 1 1 3
101.0 1
100.5 2 6 2
100.0 1 1
99.5 1 2 3
99.0 4 5
98.5 1 1 1
98.0 2 8
97.5 1 1
97.0 2 2 2 2
96.5 1 5
96.0 1 4 4
95.5 5 13
95.0 1 5 3
94.5 1 2 9
94.0 1 1 1 5
93.5 2 2 7
93.0 1 1 3 2
92.5 1 4 3
92.0 1 1 6 10
91.5 1 6 6
91.0 5 7
90.5 1 5
90.0 1 4 7
89.5 2 8 4
89.0 6 5
88.5 3 8
88.0 2 5
87.5 5 9
87.0 1 4 11
86.5 8 2 1
86.0 8 10
85.5 1 4 5
85.0 1 3 4
84.5 2 2
84.0 1 2 1 3 13
83.5 6 9
83.0 2 7 6
82.5 1 2 1 7
82.0 1 5 3 1
81.5 3 5 1
81.0 2 3
80.5 1 1 7 6
80.0 1 1 11 10
79.5 7 5
79.0 1 1 4 6
78.5 2 12
78.0 7 9
77.5 9 10
77.0 1 7 6
76.5 4 3
76.0 1 3 4
75.5 1 3 4
75.0 6 6
74.5 5 7
74.0 1 1 8 1
73.5 8 9
73.0 3 5
72.5 2 3
72.0 1 5 7 1
71.5 6 4
71.0 3 5 1
70.5 1 1 6 3
70.0 1 1 3 3
69.5 1 6 3
69.0 1 2 4
68.5 1 4 9 1
68.0 11 3 2
67.5 1 1 3 6
67.0 9 2
66.5 1 6 2
66.0 1 5 3
65.5 2 5 5
65.0 6 3
64.5 1 3 3
64.0 1 4 5
63.5 1 4 4
63.0 5 6
62.5 3 5 2
62.0 1 6 2
61.5 2 3
61.0 2 5
60.5 2 3
60.0 1 1 1 7 5
59.5 5 4
59.0 3 3
58.5 6 3
58.0 1 3
57.5 2 3
57.0 2 3
56.5 1 3 4
56.0 2 3 1
55.5 4
55.0 1
54.5 1 1 3
54.0 6 2 2
53.5 1 3 2
53.0 1 2
52.5 2 2
52.0 1 2
51.5 2
51.0 2 1
50.5 1 2
50.0 3 1
49.5 1 1
49.0 1 2
48.5 1 1
48.0 7 1 1
47.5 3
47.0 2
46.5 1 1 3
46.0 1 1
45.5 1 1
45.0 1 2
44.5 2
44.0 2
43.5 1
43.0 2
42.5 1 1
42.0 5 1
41.5 1
41.0 1
40.0 1 1
39.0 1
37.5 1
36.0 3 2
35.0 1
34.0 1 1
33.0 1
31.5 1
30.5 1
30.0 5 1
29.5 1
24.0 3 1
18.0 1
American Mathematics Competitions
2006 AMC 10 A Results for Michigan
Analysis
Table of Item Difficulty for the 2006
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 9.88* 0.02 0.04 0.03 0.01 0.02 0.00
2 1.56 0.22 3.50* 0.12 1.43 3.16 0.00
3 0.10 8.26* 0.12 0.06 1.29 0.17 0.00
4 2.04 0.11 0.06 0.18 7.23* 0.39 0.00
5 0.27 1.02 1.26 6.86* 0.22 0.36 0.00
6 0.15 8.31* 0.39 0.13 0.07 0.95 0.00
7 7.38* 0.11 0.36 0.34 0.27 1.55 0.00
8 1.03 0.36 0.50 0.24 3.15* 4.72 0.00
9 1.47 1.39 5.86* 0.32 0.17 0.79 0.00
10 0.22 0.26 0.90 3.28 1.26* 4.07 0.01
11 1.73 1.44 2.16* 0.75 0.74 3.18 0.01
12 0.78 0.33 5.03* 1.13 0.30 2.43 0.00
13 0.34 1.16 0.30 5.38* 0.19 2.63 0.00
14 1.69 4.02* 0.32 1.09 0.67 2.21 0.00
15 0.75 0.43 0.57 1.79* 0.58 5.89 0.00
16 0.27 0.34 0.60 0.48* 0.70 7.62 0.00
17 2.49* 0.39 0.24 0.50 0.24 6.13 0.00
18 2.15 0.10 3.57* 0.30 0.19 3.69 0.00
19 0.47 1.47 1.32* 0.45 0.30 5.98 0.01
20 0.47 1.06 0.38 0.41 0.76* 6.91 0.01
21 0.73 0.77 0.42 0.74 1.24* 6.10 0.00
22 0.16 0.84 3.92* 2.93 0.73 1.42 0.00
23 0.54 1.72* 0.23 0.28 0.65 6.59 0.00
24 0.82 0.71* 0.58 0.22 0.48 7.20 0.00
25 2.14 0.83 0.62* 0.41 0.32 5.67 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
2006 AMC 12 A Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 125.0 1 100.0 1
149.5 124.5 99.5 8 9
149.0 124.0 3 99.0 4 2
148.5 123.5 98.5 7 1
148.0 123.0 5 98.0 12 4
147.5 122.5 97.5
147.0 122.0 5 97.0 14 11
146.5 121.5 1 96.5 4 1
146.0 121.0 96.0 18 13
145.5 120.5 2 95.5 7
145.0 120.0 95.0 12 6
144.5 119.5 7 94.5 11 11
144.0 1 119.0 94.0 3
143.5 118.5 23 7 93.5 10 13
143.0 118.0 2 93.0 1 1
142.5 117.5 92.5 8 6
142.0 117.0 4 1 92.0 10 7
141.5 116.5 91.5 4
141.0 116.0 7 2 91.0 14 9
140.5 115.5 90.5 2 2
140.0 115.0 3 3 90.0 18 10
139.5 114.5 1 89.5 4 4
139.0 114.0 89.0 13 9
138.5 113.5 8 1 88.5 12 10
138.0 113.0 88.0 3 2
137.5 112.5 24 10 87.5 11 14
137.0 1 112.0 87.0 3
136.5 111.5 2 86.5 10 10
136.0 111.0 1 2 86.0 5 6
135.5 110.5 85.5 3 6
135.0 110.0 18 1 85.0 15 8
134.5 109.5 84.5 5 4
134.0 109.0 13 6 84.0 9 8
133.5 108.5 83.5 3 3
133.0 108.0 5 1 83.0 11 12
132.5 107.5 5 82.5 9 5
132.0 107.0 82.0 2 5
131.5 106.5 17 4 81.5 16 9
131.0 106.0 2 81.0 5 2
130.5 105.5 9 5 80.5 13 12
130.0 105.0 2 80.0 6 5
129.5 104.5 3 3 79.5 8 2
129.0 2 1 104.0 14 4 79.0 8 8
128.5 103.5 1 78.5 4 11
128.0 103.0 20 7 78.0 7 7
127.5 1 102.5 2 77.5 4 3
127.0 102.0 9 11 77.0 12 9
126.5 4 101.5 6 2 76.5 6 7
126.0 101.0 4 3 76.0 2 1
125.5 2 100.5 22 11 75.5 10 13
American Mathematics Competitions
2006 AMC 12 A Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 3 4 50.0 1 25.0
74.5 7 10 49.5 24.5
74.0 8 1 49.0 1 3 24.0 2 1
73.5 2 6 48.5 1 23.5
73.0 12 9 48.0 4 23.0
72.5 2 5 47.5 1 22.5
72.0 9 8 47.0 1 22.0
71.5 7 3 46.5 1 21.5
71.0 12 4 46.0 3 21.0
70.5 11 5 45.5 1 20.5
70.0 3 3 45.0 20.0
69.5 4 6 44.5 1 19.5
69.0 2 2 44.0 1 19.0
68.5 5 5 43.5 18.5
68.0 2 4 43.0 2 18.0 1
67.5 2 3 42.5 17.5
67.0 9 4 42.0 2 1 17.0
66.5 3 6 41.5 16.5
66.0 10 7 41.0 1 1 16.0
65.5 6 5 40.5 15.5
65.0 8 7 40.0 15.0
64.5 3 4 39.5 14.5
64.0 3 3 39.0 1 14.0
63.5 1 6 38.5 13.5
63.0 1 1 38.0 1 13.0
62.5 2 2 37.5 12.5
62.0 1 2 37.0 12.0
61.5 1 2 36.5 1 11.5
61.0 1 1 36.0 1 2 11.0
60.5 1 1 35.5 10.5
60.0 8 7 35.0 10.0
59.5 1 34.5 9.5
59.0 4 5 34.0 9.0
58.5 1 3 33.5 8.5
58.0 1 2 33.0 8.0
57.5 2 3 32.5 1 7.5
57.0 1 1 32.0 7.0
56.5 4 1 31.5 6.5
56.0 1 3 31.0 6.0
55.5 1 30.5 5.5
55.0 2 30.0 1 4 5.0
54.5 1 29.5 4.5
54.0 3 3 29.0 1 4.0
53.5 28.5 3.5
53.0 4 28.0 3.0
52.5 2 27.5 2.5
52.0 27.0 1 2.0
51.5 1 26.5 1.5
51.0 3 26.0 1.0
50.5 2 25.5 .5
0.0 0 0
American Mathematics Competitions
2006 AMC 12 A Results for Michigan
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 11 12 13 unknown
---------------------------
144.0 1
137.0 1
129.0 1 2
127.5 1
126.5 1 1 1 1
125.5 1 1
125.0 1
124.0 1 2
123.0 2 3
122.0 1 2 2
121.5 1
120.5 2
119.5 1 2 3 1
118.5 1 1 18 10
118.0 2
117.0 2 3
116.0 1 1 4 4
115.0 1 3 2
114.5 1
113.5 4 4 1
112.5 1 2 2 22 8
111.5 1 1
111.0 1 2
110.0 4 9 7
109.0 1 1 1 1 10 6
108.0 2 4
107.5 1 2 2
106.5 1 12 10
106.0 2
105.5 1 3 4 7 1
105.0 1 1
104.5 1 3 2
104.0 1 10 8
103.5 1
103.0 1 2 11 13
102.5 2
102.0 1 10 9
101.5 4 4
101.0 2 2 3
100.5 7 9 17
100.0 1
99.5 2 2 5 8
99.0 3 5
98.5 1 5 2
98.0 1 8 7 1
97.0 1 1 15 8
96.5 4 1
96.0 2 5 11 14
95.5 1 4 2
95.0 1 1 8 8
94.5 2 3 9 8
94.0 1 2
93.5 4 12 8
93.0 1 1
92.5 1 6 7
92.0 11 7
91.5 1 3
91.0 1 13 11
90.5 2 2
90.0 1 17 10
89.5 1 4 3
89.0 1 1 1 9 12
88.5 1 2 13 6
88.0 4 2
87.5 1 15 10
87.0 2 1
86.5 10 9 1
86.0 4 8
85.5 1 4 4
85.0 1 1 11 10 1
84.5 6 3
84.0 11 6
83.5 3 3
83.0 1 13 11 1
82.5 11 5
82.0 1 2 5
81.5 1 16 7 1
81.0 3 4
80.5 12 14
80.0 1 6 4
79.5 1 6 4
79.0 1 9 7
78.5 9 6
78.0 1 1 4 9
77.5 5 2
77.0 10 13
76.5 8 5
76.0 2 2
75.5 2 11 10
75.0 4 3
74.5 11 6
74.0 1 5 3
73.5 5 2 1
73.0 2 14 5
72.5 4 3
72.0 14 3
71.5 6 4
71.0 7 9
70.5 1 11 4
70.0 4 2
69.5 6 5
69.0 1 3
68.5 1 6 3
68.0 6
67.5 2 3
67.0 2 1 7 3
66.5 4 5
66.0 12 5 1
65.5 1 1 3 6
65.0 7 8
64.5 1 6
64.0 1 3 3
63.5 3 4
63.0 1 1
62.5 3 1
62.0 2 1
61.5 2 1
61.0 2
60.5 2
60.0 1 9 5
59.5 1
59.0 3 6
58.5 2 2
58.0 2 1
57.5 3 2
57.0 2
56.5 3 2
56.0 4 1
55.5 2
55.0 1 1
54.5 2
54.0 1 1 4
53.0 3 1
52.5 1 1
51.5 1
51.0 2 1
50.5 1 1
50.0 1
49.0 2 2
48.5 1
48.0 1 3
47.5 1
47.0 1
46.5 1
46.0 2 1
45.5 1
44.5 1
44.0 1
43.0 2
42.0 1 2
41.0 1 1
39.0 1
38.0 1
36.5 1
36.0 1 3
32.5 1
30.0 1 4
29.0 1
27.0 1
24.0 3
18.0 1
American Mathematics Competitions
2006 AMC 12 A Results for Michigan
Analysis
Table of Item Difficulty for the 2006
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 9.95* 0.01 0.02 0.01 0.00 0.01 0.00
2 1.48 0.17 5.25* 0.09 0.70 2.31 0.00
3 0.05 8.66* 0.02 0.05 1.16 0.05 0.00
4 1.52 0.08 0.06 0.03 8.08* 0.23 0.00
5 0.16 0.63 0.87 7.98* 0.15 0.21 0.00
6 7.61* 0.12 0.28 0.27 0.16 1.56 0.00
7 0.69 5.62* 0.64 0.72 0.42 1.90 0.00
8 1.08 1.18 6.74* 0.29 0.09 0.61 0.01
9 8.17* 0.20 0.15 0.05 0.26 1.17 0.00
10 0.21 0.18 0.72 3.64 2.19* 3.06 0.00
11 1.50 1.06 3.14* 0.91 0.57 2.82 0.00
12 1.47 5.49* 0.15 0.70 0.36 1.83 0.00
13 0.40 0.15 0.23 0.08 6.11* 3.02 0.00
14 0.05 0.52 5.21* 2.37 0.29 1.56 0.00
15 3.90* 1.40 0.28 0.68 1.49 2.26 0.00
16 0.38 3.93* 0.16 0.23 0.62 4.69 0.00
17 0.33 0.60* 0.50 0.44 0.08 8.06 0.00
18 1.28 0.11 0.36 0.69 0.51* 7.06 0.00
19 0.21 0.16 0.21 0.21 0.35* 8.86 0.00
20 1.73 0.58 0.75* 0.28 0.19 6.47 0.00
21 0.06 0.21 0.38 0.18 0.21* 8.95 0.00
22 0.18 0.12 0.15 0.27* 0.05 9.22 0.00
23 0.10 0.21* 0.19 0.12 0.23 9.15 0.00
24 1.14 0.30 0.23 0.33* 0.13 7.87 0.00
25 0.18 0.27 0.18 0.17 0.15* 9.04 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
2006 AMC 10 B Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 1 125.0 100.0
149.5 124.5 99.5 1
149.0 124.0 2 99.0 2 1
148.5 123.5 98.5 1
148.0 123.0 2 98.0 4 1
147.5 122.5 97.5
147.0 122.0 1 97.0 3
146.5 1 121.5 3 96.5 1
146.0 121.0 96.0 2
145.5 120.5 1 95.5 1 1
145.0 120.0 95.0 4
144.5 119.5 1 94.5 2
144.0 119.0 94.0
143.5 118.5 93.5 3 1
143.0 118.0 93.0 1 1
142.5 117.5 92.5 2
142.0 117.0 1 92.0 1
141.5 116.5 91.5 2 1
141.0 116.0 2 91.0 1
140.5 1 115.5 1 1 90.5 2
140.0 115.0 90.0 3 1
139.5 114.5 89.5 3
139.0 114.0 1 89.0 1
138.5 113.5 1 88.5 2
138.0 1 113.0 1 88.0
137.5 112.5 1 87.5 2 1
137.0 2 112.0 1 87.0 2
136.5 111.5 86.5
136.0 111.0 1 2 86.0 5 2
135.5 110.5 85.5 1
135.0 110.0 1 1 85.0 1 2
134.5 1 109.5 84.5 2
134.0 109.0 84.0 1 2
133.5 1 108.5 83.5 4 1
133.0 108.0 83.0 4
132.5 1 107.5 82.5 2
132.0 1 107.0 82.0 2
131.5 106.5 1 81.5 2
131.0 106.0 81.0 1
130.5 105.5 80.5 3 1
130.0 1 105.0 1 80.0 2 2
129.5 104.5 79.5 2 1
129.0 104.0 1 79.0 6
128.5 103.5 78.5 2 1
128.0 103.0 1 78.0 2 3
127.5 102.5 77.5 1 1
127.0 102.0 77.0 2 3
126.5 101.5 3 76.5 2 1
126.0 1 101.0 1 76.0 4
125.5 100.5 2 1 75.5 1
American Mathematics Competitions
2006 AMC 10 B Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 4 50.0 3 2 25.0 1
74.5 7 4 49.5 4 1 24.5
74.0 1 6 49.0 4 2 24.0 2 4
73.5 1 2 48.5 1 4 23.5 1
73.0 2 48.0 4 4 23.0
72.5 3 3 47.5 2 22.5
72.0 4 47.0 2 3 22.0
71.5 2 1 46.5 2 3 21.5
71.0 6 2 46.0 1 2 21.0
70.5 2 45.5 2 3 20.5 1
70.0 5 4 45.0 1 1 20.0
69.5 5 4 44.5 1 19.5
69.0 4 1 44.0 2 3 19.0
68.5 6 4 43.5 1 18.5 1
68.0 6 43.0 3 18.0 3
67.5 4 1 42.5 3 17.5
67.0 1 42.0 3 2 17.0
66.5 5 4 41.5 1 3 16.5
66.0 7 1 41.0 1 16.0
65.5 1 1 40.5 1 2 15.5
65.0 3 1 40.0 1 1 15.0
64.5 4 2 39.5 14.5 1
64.0 3 2 39.0 2 1 14.0
63.5 5 3 38.5 2 13.5
63.0 3 3 38.0 2 1 13.0
62.5 3 2 37.5 1 12.5
62.0 3 37.0 1 3 12.0
61.5 3 3 36.5 1 11.5
61.0 2 2 36.0 3 3 11.0 1
60.5 2 3 35.5 3 1 10.5
60.0 2 5 35.0 10.0
59.5 5 34.5 1 9.5
59.0 5 2 34.0 2 9.0
58.5 3 33.5 1 8.5
58.0 2 33.0 1 8.0
57.5 2 2 32.5 7.5 1
57.0 2 2 32.0 1 7.0
56.5 5 9 31.5 1 6.5
56.0 2 6 31.0 1 6.0
55.5 2 1 30.5 2 5.5
55.0 3 4 30.0 2 1 5.0
54.5 2 3 29.5 2 1 4.5
54.0 7 4 29.0 1 4.0
53.5 2 4 28.5 1 3.5
53.0 1 5 28.0 1 3.0
52.5 2 4 27.5 2.5
52.0 5 3 27.0 2.0
51.5 1 3 26.5 1 1.5
51.0 2 2 26.0 1.0
50.5 2 1 25.5 1 .5
0.0 0 0
American Mathematics Competitions
2006 AMC 10 B Results for Michigan
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 unknown
---------------------------
150.0 1
146.5 1
140.5 1
138.0 1
137.0 1 1
134.5 1
133.5 1
132.5 1
132.0 1
130.0 1
126.0 1
124.0 2
123.0 1 1
122.0 1
121.5 1 2
120.5 1
119.5 1
117.0 1 1
116.0 2
115.5 1 1
114.0 1
113.5 1
113.0 1
112.5 1
112.0 1
111.0 1 1 1
110.0 2 1
107.0 1
106.5 1
105.5 1
105.0 1
104.0 1
103.0 1
101.5 1 1 1
101.0 1
100.5 1 2
99.5 1
99.0 1 2
98.5 1
98.0 1 1 2 1
97.0 1 3
96.5 1
96.0 1 1
95.5 1 1
95.0 1 1 2
94.5 1 1 1
93.5 1 1 2 1 1
93.0 2
92.5 2
92.0 1
91.5 1 2
91.0 1
90.5 1 1 1
90.0 1 1 2
89.5 1 1 2
89.0 1
88.5 1 1
87.5 1 2
87.0 1 1 1
86.0 1 1 5
85.5 1
85.0 1 2
84.5 2
84.0 3
83.5 2 3
83.0 1 3
82.5 2
82.0 1 1
81.5 1 1 1
81.0 1
80.5 1 3
80.0 1 1 1 1
79.5 2 1
79.0 5 1 1
78.5 1 2
78.0 1 4
77.5 2
77.0 2 3
76.5 3
76.0 2 2
75.5 1
75.0 1 3
74.5 1 4 6
74.0 1 2 5
73.5 2 2
73.0 1 1
72.5 2 4
72.0 3 1
71.5 2 1
71.0 1 2 6
70.5 1 1 1
70.0 5 6
69.5 3 6 1
69.0 2 1 2
68.5 1 6 4
68.0 3 2 1
67.5 3 2
67.0 2
66.5 1 4 5
66.0 3 6
65.5 1 1
65.0 2 2
64.5 3 3
64.0 5
63.5 2 6
63.0 4 2
62.5 3 3
62.0 1 2
61.5 2 4
61.0 3 2
60.5 1 5 1
60.0 6 2
59.5 1 3 1
59.0 3 5
58.5 2 1
58.0 2
57.5 1 3
57.0 2 2
56.5 1 6 7
56.0 1 6 1
55.5 1 2
55.0 3 4
54.5 2 3
54.0 5 6
53.5 1 4 1
53.0 6
52.5 3 3 1
52.0 5 3
51.5 4
51.0 2 1 2
50.5 3 1
50.0 3 3
49.5 1 3 1
49.0 2 4
48.5 3 1 2
48.0 1 5 1 1
47.5 1 1
47.0 3 2
46.5 3 2
46.0 1 2
45.5 3 3
45.0 2 1
44.5 1
44.0 3 1 1
43.5 1
43.0 3
42.5 3
42.0 1 4 1
41.5 1 1 2
41.0 1
40.5 2 1
40.0 2
39.0 1 2
38.5 1 1
38.0 4
37.5 1
37.0 2 2
36.5 2
36.0 3 3
35.5 1 1 2
34.5 1
34.0 1 1
33.5 1
33.0 1
32.0 1
31.5 1
31.0 1
30.5 1 1
30.0 2 2 1
29.5 2 1
29.0 1
28.5 1
28.0 1
26.5 1
25.5 1
25.0 1
24.0 1 3 3
23.5 1
20.5 1
18.5 1
18.0 1 2
14.5 1
11.0 1
7.5 1
American Mathematics Competitions
2006 AMC 10 B Results for Michigan
Analysis
Table of Item Difficulty for the 2006
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.88 0.53 5.67* 1.52 0.94 0.47 0.00
2 5.23* 0.63 0.11 0.20 0.36 3.47 0.00
3 7.89* 0.14 0.05 1.28 0.48 0.16 0.00
4 1.42 2.02 0.52 3.23* 1.92 0.89 0.00
5 0.92 4.75* 2.31 0.48 0.16 1.38 0.00
6 0.59 0.25 3.42 3.20* 0.45 2.08 0.00
7 2.36* 1.66 1.17 1.36 0.80 2.66 0.00
8 1.72 1.14* 0.47 1.52 0.81 4.34 0.00
9 0.11 7.83* 0.13 0.11 1.22 0.59 0.02
10 2.98* 0.48 1.38 0.23 2.30 2.61 0.02
11 0.34 0.64 3.27* 0.61 0.42 4.72 0.00
12 0.42 0.44 0.33 0.59 4.31* 3.91 0.00
13 1.02 0.31 2.38 0.98 2.66* 2.66 0.00
14 0.27 0.39 0.53 1.16* 0.17 7.48 0.00
15 0.81 0.58 2.47* 0.55 0.47 5.13 0.00
16 2.50 0.75 1.84 0.89 1.70* 2.31 0.00
17 3.08 1.25 1.84 2.52* 0.16 1.16 0.00
18 0.86 0.59 1.17 0.52 1.25* 5.61 0.00
19 0.45* 0.75 0.55 0.41 0.28 7.56 0.00
20 0.53 0.47 0.56 0.78 1.25* 6.41 0.00
21 0.91 0.38 1.25* 2.02 0.89 4.56 0.00
22 0.31 0.77 2.00 1.23* 0.23 5.44 0.02
23 0.47 1.22 0.38 0.55* 0.36 7.03 0.00
24 0.38 1.34* 0.89 0.36 0.36 6.67 0.00
25 0.27 2.36* 0.33 2.14 0.50 4.41 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
2006 AMC 12 B Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 125.0 100.0
149.5 124.5 99.5 5 3
149.0 124.0 2 1 99.0 1 1
148.5 123.5 98.5 7 5
148.0 123.0 2 98.0 3 3
147.5 122.5 97.5 1 1
147.0 122.0 97.0 4 2
146.5 121.5 96.5 1
146.0 121.0 96.0 7 2
145.5 120.5 4 95.5 1
145.0 120.0 95.0 17 8
144.5 119.5 3 94.5 4 2
144.0 119.0 1 94.0 1 3
143.5 118.5 4 1 93.5 10 4
143.0 118.0 93.0 1
142.5 117.5 92.5 5 5
142.0 117.0 3 1 92.0 1
141.5 116.5 91.5 2 2
141.0 116.0 2 1 91.0 6 2
140.5 115.5 90.5 1
140.0 115.0 2 2 90.0 10 4
139.5 114.5 2 89.5 1
139.0 114.0 1 89.0 20 7
138.5 113.5 88.5 3
138.0 1 113.0 88.0 12 4
137.5 112.5 3 1 87.5 10 2
137.0 112.0 2 87.0 5
136.5 111.5 8 2 86.5 9 3
136.0 1 111.0 4 86.0 2
135.5 110.5 85.5 1 4
135.0 110.0 1 1 85.0 1 3
134.5 109.5 84.5 2 4
134.0 109.0 6 1 84.0 3 6
133.5 1 108.5 1 83.5 1 2
133.0 108.0 4 5 83.0 9 4
132.5 1 107.5 1 82.5 3 1
132.0 107.0 82.0 6 3
131.5 106.5 4 2 81.5 5 3
131.0 1 106.0 1 81.0 5 3
130.5 105.5 8 4 80.5 4 3
130.0 3 105.0 1 80.0 1 1
129.5 104.5 6 3 79.5 4 1
129.0 3 1 104.0 1 1 79.0 2 2
128.5 103.5 78.5 1 3
128.0 103.0 4 3 78.0 3 4
127.5 102.5 1 77.5 1 3
127.0 102.0 8 5 77.0 3 3
126.5 5 101.5 3 76.5 3 1
126.0 101.0 10 6 76.0 5 6
125.5 3 100.5 4 2 75.5 3
American Mathematics Competitions
2006 AMC 12 B Results for Michigan
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 2 3 50.0 25.0
74.5 4 2 49.5 1 24.5
74.0 1 2 49.0 1 24.0 1
73.5 2 2 48.5 2 23.5
73.0 4 3 48.0 3 23.0
72.5 1 2 47.5 22.5
72.0 6 2 47.0 1 22.0
71.5 5 4 46.5 1 21.5
71.0 7 46.0 1 21.0
70.5 3 1 45.5 20.5
70.0 4 2 45.0 1 20.0
69.5 44.5 1 2 19.5
69.0 1 5 44.0 1 19.0
68.5 4 2 43.5 1 18.5
68.0 1 2 43.0 1 18.0
67.5 1 2 42.5 1 17.5
67.0 4 42.0 2 4 17.0
66.5 4 1 41.5 16.5
66.0 3 3 41.0 16.0
65.5 2 4 40.5 1 15.5
65.0 7 40.0 1 15.0
64.5 1 4 39.5 14.5
64.0 1 2 39.0 1 14.0
63.5 3 38.5 2 13.5
63.0 3 1 38.0 13.0
62.5 3 1 37.5 12.5
62.0 1 37.0 12.0
61.5 36.5 11.5
61.0 3 36.0 2 11.0
60.5 1 2 35.5 10.5
60.0 3 2 35.0 10.0
59.5 1 1 34.5 1 9.5
59.0 2 1 34.0 9.0
58.5 1 33.5 1 8.5 1
58.0 1 2 33.0 8.0
57.5 32.5 7.5
57.0 32.0 7.0
56.5 1 1 31.5 1 6.5
56.0 1 1 31.0 6.0
55.5 2 30.5 1 5.5
55.0 30.0 1 1 5.0
54.5 2 1 29.5 4.5
54.0 6 2 29.0 4.0
53.5 28.5 3.5
53.0 3 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 1 26.0 1.0
50.5 25.5 .5
0.0 0 0
American Mathematics Competitions
2006 AMC 12 B Results for Michigan
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 11 12 13 unknown
---------------------------
138.0 1
136.0 1
133.5 1
132.5 1
131.0 1
130.0 1 2
129.0 2 1 1
126.5 1 3 1
125.5 1 1 1
124.0 1 1 1
123.0 1 1
120.5 1 2 1 1
119.5 1 3
119.0 1
118.5 2 2 1
117.0 1 2 1
116.0 1 1 1
115.0 1 3
114.5 1 1
114.0 1
112.5 1 1 2 1
112.0 1 1
111.5 1 1 1 3 4
111.0 1 2 1
110.0 1 1
109.0 1 1 5
108.5 1
108.0 1 1 1 1 4 1
107.5 1
106.5 1 5
106.0 1
105.5 1 3 3 7 2
105.0 1
104.5 1 1 2 5 1
104.0 2
103.0 1 5 2
102.5 1
102.0 3 4 6
101.5 1 1 1 1
101.0 1 1 7 7 1
100.5 1 1 2 2
99.5 1 4 3
99.0 1 1
98.5 1 1 5 5
98.0 1 1 3 1
97.5 2
97.0 1 2 3
96.5 1
96.0 1 2 5 5 2
95.5 1
95.0 1 2 9 13
94.5 1 4 1
94.0 2 1 1
93.5 2 2 5 5 1
93.0 1
92.5 1 4 5 5
92.0 1
91.5 1 3 1
91.0 2 6 2 1
90.5 1
90.0 1 9 4
89.5 1
89.0 1 2 4 9 12 5
88.5 3
88.0 1 8 8
87.5 1 6 5 1
87.0 1 3 1
86.5 1 8 3 2
86.0 1 1
85.5 1 4
85.0 1 3
84.5 5 1
84.0 1 5 4
83.5 1 2
83.0 2 8 3 2
82.5 1 1 2
82.0 1 4 4 1
81.5 1 3 4
81.0 5 3
80.5 3 4
80.0 1 1
79.5 2 2 1
79.0 3 1
78.5 4
78.0 2 4 2
77.5 1 3
77.0 1 5 1 1
76.5 4 1
76.0 2 5 4
75.5 2 1
75.0 5 1
74.5 1 4 4 1
74.0 3 1
73.5 2 3
73.0 3 4
72.5 4 1
72.0 2 3 3
71.5 3 6
71.0 2 3 1 1
70.5 1 3
70.0 3 2 1
69.0 3 3
68.5 1 3 2
68.0 2 1
67.5 1 2
67.0 1 4
66.5 3 1 1
66.0 1 3 2
65.5 1 2 3
65.0 1 6
64.5 3 1 1
64.0 1 2 1
63.5 1 1 1
63.0 2 1 1
62.5 3 1
62.0 1
61.0 3
60.5 3
60.0 1 1 3
59.5 2
59.0 1 1 1
58.5 1 1
58.0 1 2
57.5 1
56.5 2
56.0 1 1
55.5 2
54.5 3
54.0 3 5
53.0 3 1
52.5 1
52.0 1
51.0 1
49.5 1
49.0 1 1
48.5 2
48.0 1 2
47.0 1
46.5 1
46.0 1
45.0 1
44.5 2 1
44.0 1
43.5 1
43.0 1
42.5 1
42.0 2 4
40.5 1
40.0 1
39.0 1
38.5 1 1
36.0 1 1
34.5 1
33.5 1
31.5 1
30.5 1
30.0 1 1
24.0 1
8.5 1
American Mathematics Competitions
2006 AMC 12 B Results for Michigan
Analysis
Table of Item Difficulty for the 2006
American High School Mathematics Examination
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.45 0.26 8.03* 0.80 0.24 0.22 0.00
2 7.76* 0.39 0.08 0.10 0.27 1.40 0.00
3 8.61* 0.24 0.05 0.80 0.18 0.12 0.00
4 9.19* 0.35 0.09 0.19 0.06 0.12 0.00
5 7.47* 0.71 0.30 0.26 0.18 1.09 0.00
6 0.10 8.68* 0.13 0.03 0.58 0.49 0.00
7 0.46 8.39* 0.45 0.36 0.03 0.31 0.00
8 0.19 0.28 0.24 0.30 7.11* 1.86 0.01
9 0.45 4.67* 0.46 0.84 0.50 3.07 0.01
10 3.51* 0.40 1.04 0.17 2.43 2.46 0.00
11 0.68 0.14 1.39 0.84 4.79* 2.16 0.00
12 0.66 0.57 0.50 1.45* 0.53 6.30 0.00
13 0.69 0.58 3.41* 0.23 0.40 4.69 0.00
14 0.23 0.60 1.85 2.24* 0.22 4.86 0.00
15 0.23 2.26* 0.91 0.40 0.19 6.00 0.00
16 0.23 0.28 1.56* 0.30 0.28 7.35 0.00
17 0.73 0.28 1.71* 1.22 0.59 5.46 0.00
18 0.37 0.99* 1.41 0.41 0.24 6.57 0.00
19 0.14 2.28* 0.21 1.40 0.45 5.53 0.00
20 0.22 0.41 0.51* 0.13 0.66 8.07 0.00
21 0.27 0.23 0.33* 0.13 0.04 9.00 0.00
22 0.19 0.39* 0.53 0.22 0.06 8.61 0.00
23 0.23 0.31 0.50 0.33 0.12* 8.51 0.00
24 0.15 0.19 0.30* 0.26 0.19 8.91 0.00
25 0.13 0.21* 0.22 0.41 0.14 8.89 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
