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Missing Title
American Mathematics Competitions
2005 AMC 10 A Results for Missouri
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 1062
Number of unofficial participants: 0
Average score of participants: 72.8
Average score for female students is: 70.6 ( 404 Students)
Average score for male students is: 75.1 ( 567 Students)
Average score for unspecified gender is 68.7 ( 91 Students)
Average score for grade 10 is: 75.7 ( 544 Students)
Average score for grade 9 is: 69.7 ( 451 Students)
Average score for grade 8 and below is: 90.2 ( 11 Students)
Average score with unknown grade: 66.4 ( 56 Students)
AIME qualifying score = 120.0 or better
Number of AIME qualifers 8
Number of schools returning results 36
Average school winning score 103.86
American Mathematics Competitions
2005 AMC 12 A Results for Missouri
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 1280
Number of unofficial participants: 0
Average score of participants: 76.1
Average score for female students is: 73.0 ( 453 Students)
Average score for male students is: 78.4 ( 735 Students)
Average score for unspecified gender is 73.8 ( 92 Students)
Average score for grade 12 is: 78.6 ( 523 Students)
Average score for grade 11 is: 75.4 ( 597 Students)
Average score for grade 10 is: 73.0 ( 62 Students)
Average score for grade 9 is: 67.4 ( 29 Students)
Average score for grade 8 and below is: 48.0 ( 12 Students)
Average score with unknown grade: 74.5 ( 57 Students)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 87
Number of schools returning results 44
Average school winning score 105.08
Average school team score 294.36
American Mathematics Competitions
2005 AMC 10 B Results for Missouri
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 542
Number of unofficial participants: 0
Average score of participants: 72.4
Average score for female students is: 70.1 ( 193 Students)
Average score for male students is: 73.7 ( 328 Students)
Average score for unspecified gender is 72.8 ( 21 Students)
Average score for grade 10 is: 74.1 ( 300 Students)
Average score for grade 9 is: 69.6 ( 234 Students)
Average score for grade 8 and below is: 104.5 ( 5 Students)
Average score with unknown grade: 66.8 ( 3 Students)
AIME qualifying score = 120.0 or better
Number of AIME qualifers 9
Number of schools returning results 22
Average school winning score 104.39
American Mathematics Competitions
2005 AMC 12 B Results for Missouri
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 700
Number of unofficial participants: 0
Average score of participants: 79.5
Average score for female students is: 76.3 ( 257 Students)
Average score for male students is: 81.4 ( 421 Students)
Average score for unspecified gender is 82.3 ( 22 Students)
Average score for grade 13 is: 91.5 ( 1 Student)
Average score for grade 12 is: 79.6 ( 268 Students)
Average score for grade 11 is: 78.8 ( 370 Students)
Average score for grade 10 is: 81.5 ( 45 Students)
Average score for grade 9 is: 90.5 ( 12 Students)
Average score for grade 8 and below is: 91.0 ( 1 Student)
Average score with unknown grade: 75.7 ( 3 Students)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 81
Number of schools returning results 32
Average school winning score 105.81
Average school team score 282.78
2005 State AMC 12 TEAM Score Distribution
-----------------------------------------------
score A B Rank
-----------------------------------------------
401.5 1 1
370.5 1 2
359.5 1 3
359.0 1 4
358.5 1 5
347.0 1 6
346.5 1 7
343.0 1 8
342.0 2 1 9
335.5 1 12
331.5 1 13
329.5 1 14
329.0 1 1 15
328.5 1 17
322.5 1 18
319.5 1 19
319.0 1 20
317.5 1 21
316.5 1 22
315.0 1 23
310.0 2 24
306.0 1 26
305.0 1 1 27
302.5 1 29
302.0 1 30
300.0 1 31
299.0 1 32
298.5 1 33
297.5 2 34
293.0 1 36
292.0 1 37
289.0 1 1 38
286.5 1 40
286.0 1 41
283.5 1 42
282.5 1 43
282.0 1 44
281.0 1 45
279.5 1 1 46
278.0 1 48
276.5 4 49
274.5 1 53
274.0 1 54
273.5 1 55
272.0 1 56
271.5 1 57
269.0 1 58
263.5 1 59
262.0 1 60
260.5 1 61
255.0 1 62
254.0 1 63
252.5 1 64
252.0 1 65
249.0 1 66
248.5 1 67
247.0 1 68
246.5 1 69
245.0 1 70
236.5 1 71
226.0 1 72
213.0 1 73
169.5 1 74
150.0 1 75
91.0 1 76
2005 AMC Contest Score Distributions
-----------------------------------------------
score 12 A 12 B 10 A 10 B
-----------------------------------------------
150.0 1
146.5 2
144.0 1 1
143.0 1
139.5 1
138.0 1
137.0 1
133.5 2
132.0 1
131.0 1
129.0 1
127.5 1 1 1
126.5 2
125.5 1
125.0 1 2
124.0 1 1 1
123.0 2 1
122.5 1
122.0 1
121.5 3 1 1
120.5 1 2
119.5 2 1
118.5 1 2 1
118.0 1 1 1
117.0 1 1
116.0 1 1 1 2
115.5 2
115.0 3
114.5 3
114.0 1
113.5 1 1 2
113.0 1
112.5 2 2 2
112.0 1 2
111.5 4 3 1
111.0 2 3
110.5 1
110.0 3 4 2 5
109.0 4 4 3
108.5 1 1
108.0 2 3 1
107.5 1 2 1 1
106.5 2 7 2 1
106.0 1 2
105.5 8 2 3 3
105.0 2 1
104.5 8 5
104.0 1 4 3 1
103.0 10 6 2
102.5 2
102.0 7 11 2 1
101.5 2 5 1
101.0 9 7 6
100.5 5 3 6 1
100.0 1
99.5 5 4 8 4
99.0 1 1 1
98.5 15 9 2 4
98.0 1 2 5 4
97.5 7 2 1 1
97.0 9 7 6 7
96.5 1 1 2
96.0 11 9 8 4
95.5 3 1 1 1
95.0 24 15 7 6
94.5 4 2 3 6
94.0 3 5 4
93.5 9 6 8 7
93.0 1 2 1
92.5 17 15 8 5
92.0 5 13
91.5 11 12 4 3
91.0 4 3 4 6
90.5 7 5 3 1
90.0 15 12 10 4
89.5 2 3 1 1
89.0 31 27 12 5
88.5 4 2 3 4
88.0 19 8 2 3
87.5 9 7 10 4
87.0 6 6 2 1
86.5 22 9 10 7
86.0 1 2 6 3
85.5 19 14 14 6
85.0 4 6 4 5
84.5 17 7 3 3
84.0 9 8 15 8
83.5 16 5 9 3
83.0 24 15 22 6
82.5 3 3 4 6
82.0 24 10 12 2
81.5 9 6 3 3
81.0 21 6 9 3
80.5 22 12 16 5
80.0 12 7 11 4
79.5 16 9 11 7
79.0 6 7 7 5
78.5 14 9 12 9
78.0 12 10 12 4
77.5 20 4 7 5
77.0 24 13 12 9
76.5 19 4 9 3
76.0 13 16 27 4
75.5 8 8 8 4
75.0 26 10 16 5
74.5 14 8 16 7
74.0 23 7 7 5
73.5 19 5 17 7
73.0 6 7 16 5
72.5 21 4 17 6
72.0 13 6 13 7
71.5 20 8 11 2
71.0 24 18 24 6
70.5 20 5 13 4
70.0 20 7 18 5
69.5 11 9 13 4
69.0 23 3 8 4
68.5 18 4 14 5
68.0 14 6 13 3
67.5 14 2 17 4
67.0 8 5 15 2
66.5 16 4 15 8
66.0 9 5 12 10
65.5 18 4 16 2
65.0 12 3 18 1
64.5 12 6 10 2
64.0 16 7 10 8
63.5 5 3 9 4
63.0 14 3 11 1
62.5 12 3 14 7
62.0 16 3 11 1
61.5 13 7 10 3
61.0 4 2 6 8
60.5 6 3 10 2
60.0 11 7 15 9
59.5 12 5 7 4
59.0 6 4 14 1
58.5 10 4 11 2
58.0 3 5 7 5
57.5 6 2 6 2
57.0 10 1 14 5
56.5 7 3 11 6
56.0 1 2 8 6
55.5 8 3 9 5
55.0 2 1 4 1
54.5 3 2 6 2
54.0 6 7 14 4
53.5 8 2 6 5
53.0 8 1 5 2
52.5 2 2 4 4
52.0 1 3 4
51.5 4 4 6 1
51.0 4 4 5
50.5 4 1 2 5
50.0 5 1 4
49.5 4 3 3 1
49.0 4 3 1 5
48.5 1 1 6 2
48.0 6 4 4 6
47.5 6 1 2 2
47.0 1 1
46.5 3 1 4 3
46.0 2 1 1 3
45.5 2 3 2
45.0 1 1 2 2
44.5 4 1 4 2
44.0 2 1 4 1
43.0 2 2 1
42.5 1 2 2
42.0 10 4 5 9
41.5 1 1 1
41.0 2 2
40.5 1 1 1 2
40.0 1 2
39.5 3
39.0 1 2
38.5 1 1
38.0 1
37.5 1
37.0 1
36.5 1 1 2
36.0 1 8 3
35.5 1
35.0 1 1 3
34.5 1 1
34.0 1 1 2
33.0 2
32.5 1 1 1
31.5 1 1
31.0 1
30.5 1 2
30.0 1 4 3 5
29.5 1
29.0 2 1
28.0 1 1 1
27.0 2
26.0 1 1
25.0 1
24.0 4 2 5 1
19.5 1
18.0 1 1
American Mathematics Competitions
2005 AMC 10 A Results for Missouri
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 7 1
149.0 124.0 1 99.0 1
148.5 123.5 98.5 1 1
148.0 123.0 98.0 3 2
147.5 122.5 1 97.5 1
147.0 122.0 97.0 3 3
146.5 121.5 96.5
146.0 121.0 96.0 5 3
145.5 120.5 2 95.5 1
145.0 120.0 95.0 6 1
144.5 119.5 94.5 2 1
144.0 1 119.0 94.0 3 1
143.5 118.5 2 93.5 6 2
143.0 118.0 1 93.0 1 1
142.5 117.5 92.5 6 2
142.0 117.0 1 92.0 8 5
141.5 116.5 91.5 2 2
141.0 116.0 1 91.0 3 1
140.5 115.5 2 90.5 2
140.0 115.0 90.0 4 3
139.5 114.5 2 1 89.5 1
139.0 114.0 1 89.0 5 6
138.5 113.5 1 88.5 3
138.0 113.0 88.0 2
137.5 112.5 87.5 7 3
137.0 112.0 2 87.0 2
136.5 111.5 86.5 6 4
136.0 111.0 1 1 86.0 5 1
135.5 110.5 1 85.5 9 5
135.0 110.0 2 85.0 3 1
134.5 109.5 84.5 3
134.0 109.0 84.0 8 6
133.5 108.5 1 83.5 7 2
133.0 108.0 83.0 11 11
132.5 107.5 1 82.5 1 3
132.0 107.0 82.0 8 2
131.5 106.5 1 81.5 2 1
131.0 106.0 1 81.0 7 2
130.5 105.5 1 2 80.5 10 6
130.0 105.0 1 80.0 5 5
129.5 104.5 79.5 4 7
129.0 104.0 2 79.0 4 3
128.5 103.5 78.5 9 3
128.0 103.0 78.0 8 3
127.5 1 102.5 1 77.5 4
127.0 102.0 2 77.0 7 4
126.5 101.5 2 2 76.5 5 3
126.0 101.0 4 76.0 13 10
125.5 100.5 3 3 75.5 2 6
American Mathematics Competitions
2005 AMC 10 A Results for Missouri
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 9 5 50.0 25.0
74.5 12 3 49.5 2 1 24.5
74.0 2 3 49.0 1 24.0 2 2
73.5 6 9 48.5 4 23.5
73.0 5 10 48.0 2 2 23.0
72.5 10 7 47.5 22.5
72.0 10 2 47.0 1 22.0
71.5 7 3 46.5 1 3 21.5
71.0 15 6 46.0 1 21.0
70.5 7 6 45.5 2 20.5
70.0 14 3 45.0 1 20.0
69.5 4 9 44.5 3 1 19.5
69.0 1 5 44.0 2 1 19.0
68.5 6 8 43.5 18.5
68.0 6 5 43.0 2 18.0 1
67.5 7 10 42.5 1 1 17.5
67.0 8 6 42.0 4 1 17.0
66.5 9 5 41.5 16.5
66.0 6 5 41.0 1 16.0
65.5 2 13 40.5 1 15.5
65.0 7 9 40.0 1 15.0
64.5 7 2 39.5 14.5
64.0 4 5 39.0 14.0
63.5 4 5 38.5 13.5
63.0 9 2 38.0 1 13.0
62.5 4 7 37.5 12.5
62.0 7 4 37.0 12.0
61.5 6 4 36.5 1 11.5
61.0 2 4 36.0 4 3 11.0
60.5 7 2 35.5 10.5
60.0 8 7 35.0 1 10.0
59.5 2 4 34.5 9.5
59.0 6 7 34.0 9.0
58.5 4 4 33.5 8.5
58.0 2 3 33.0 8.0
57.5 3 3 32.5 1 7.5
57.0 5 6 32.0 7.0
56.5 4 5 31.5 6.5
56.0 3 4 31.0 6.0
55.5 4 4 30.5 5.5
55.0 2 2 30.0 2 1 5.0
54.5 5 29.5 1 4.5
54.0 7 5 29.0 4.0
53.5 2 1 28.5 3.5
53.0 3 1 28.0 1 3.0
52.5 3 1 27.5 2.5
52.0 2 27.0 2.0
51.5 3 3 26.5 1.5
51.0 1 3 26.0 1 1.0
50.5 1 25.5 .5
0.0 0 0
American Mathematics Competitions
2005 AMC 10 A Results for Missouri
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 unknown
---------------------------
144.0 1
143.0 1
127.5 1
125.0 1
124.0 1
122.5 1
120.5 1 1
119.5 1
118.5 2
118.0 1
117.0 1
116.0 1
115.5 1 1
114.5 1 2
114.0 1
113.5 1
112.0 2
111.0 1 1
110.5 1
110.0 1 1
108.5 1
107.5 1
106.5 1 1
106.0 1
105.5 1 2
105.0 1
104.0 2 1
102.5 1 1
102.0 2
101.5 1 1 2 1
101.0 3 3
100.5 6
100.0 1
99.5 8
99.0 1
98.5 2
98.0 2 3
97.5 1
97.0 1 5
96.0 2 6
95.5 1
95.0 4 3
94.5 2 1
94.0 1 3
93.5 1 7
93.0 1 1
92.5 2 6
92.0 6 7
91.5 2 2
91.0 4
90.5 3
90.0 1 2 5 2
89.5 1
89.0 5 6 1
88.5 3
88.0 1 1
87.5 4 6
87.0 1 1
86.5 3 7
86.0 1 5
85.5 4 10
85.0 4
84.5 1 2
84.0 5 10
83.5 4 5
83.0 8 14
82.5 2 2
82.0 5 7
81.5 1 2
81.0 3 6
80.5 6 10
80.0 4 7
79.5 4 7
79.0 1 6
78.5 6 6
78.0 6 6
77.5 4 1 2
77.0 6 6
76.5 6 2 1
76.0 15 11 1
75.5 5 3
75.0 8 6 2
74.5 5 10 1
74.0 5 1 1
73.5 9 7 1
73.0 4 11 1
72.5 11 6
72.0 7 5 1
71.5 6 4 1
71.0 10 12 2
70.5 9 4
70.0 13 5
69.5 1 6 6
69.0 1 2 4 1
68.5 6 8
68.0 6 5 2
67.5 10 7
67.0 5 9 1
66.5 6 8 1
66.0 5 6 1
65.5 10 5 1
65.0 6 10 2
64.5 4 6
64.0 6 4
63.5 5 4
63.0 5 6
62.5 5 7 2
62.0 6 5
61.5 5 5
61.0 5 1
60.5 4 5 1
60.0 7 8
59.5 4 3
59.0 7 6 1
58.5 3 5 3
58.0 5 1 1
57.5 3 3
57.0 6 5 3
56.5 5 5 1
56.0 4 4
55.5 3 6
55.0 3 1
54.5 1 5
54.0 9 5
53.5 4 1 1
53.0 2 2 1
52.5 3 1
52.0 1 1 1
51.5 5 1
51.0 1 3 1
50.5 1 1
49.5 2 1
49.0 1
48.5 2 3 1
48.0 4
47.5 2
47.0 1
46.5 3 1
46.0 1
45.5 2 1
45.0 1 1
44.5 2 2
44.0 1 2 1
43.0 2
42.5 1 1
42.0 2 3
41.0 1 1
40.5 1
40.0 1
38.0 1
36.5 1
36.0 4 3 1
35.0 1
32.5 1
30.0 1 2
29.5 1
28.0 1
26.0 1
24.0 3 1 1
18.0 1
American Mathematics Competitions
2005 AMC 10 A Results for Missouri
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 0.16 0.10 0.27 8.77* 0.45 0.24 0.00
2 0.12 0.12 5.51* 0.05 1.55 2.65 0.00
3 0.01 8.88* 0.29 0.44 0.09 0.28 0.00
4 0.46 1.60* 2.02 0.74 0.51 4.66 0.00
5 5.81* 0.33 3.56 0.10 0.06 0.14 0.00
6 0.21 4.65* 3.42 0.19 0.10 1.42 0.01
7 0.64 3.54* 0.39 0.56 0.72 4.15 0.00
8 1.20 0.32 3.95* 0.12 0.12 4.28 0.00
9 1.05 5.53* 1.05 0.29 0.13 1.95 0.00
10 1.30* 0.35 1.20 0.36 0.13 6.66 0.01
11 0.56 2.32* 0.20 0.72 0.12 6.08 0.00
12 0.31 1.16* 0.57 0.19 0.54 7.23 0.00
13 1.44 0.51 0.25 0.21 0.67* 6.92 0.00
14 0.80 0.51 0.34 0.43 2.16* 5.76 0.00
15 0.38 0.59 0.65 0.90 0.81* 6.66 0.01
16 0.70 0.27 0.69 1.83* 0.12 6.39 0.00
17 0.27 0.21 0.52 1.72* 0.33 6.95 0.00
18 1.73* 2.11 1.24 2.83 0.19 1.89 0.00
19 0.39 0.76 0.75 3.36* 0.70 4.04 0.00
20 0.50* 0.41 0.44 0.50 0.35 7.80 0.00
21 1.40 0.64* 0.27 0.24 0.59 6.85 0.00
22 0.79 0.44 0.26 2.20* 0.57 5.73 0.00
23 0.20 0.42 1.11* 1.06 0.68 6.53 0.00
24 0.94 0.63* 0.18 0.18 0.13 7.93 0.01
25 0.34 0.67 0.74 0.72* 0.14 7.39 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 Missouri
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 3 2
149.0 124.0 1 99.0 1
148.5 123.5 98.5 10 5
148.0 123.0 2 98.0 1
147.5 122.5 97.5 4 3
147.0 122.0 1 97.0 7 1
146.5 121.5 3 96.5 1
146.0 121.0 96.0 7 3
145.5 120.5 1 95.5 3
145.0 120.0 95.0 16 8
144.5 119.5 2 94.5 1 2
144.0 119.0 94.0 1 1
143.5 118.5 1 93.5 4 4
143.0 118.0 1 93.0
142.5 117.5 92.5 12 4
142.0 117.0 92.0 4 1
141.5 116.5 91.5 7 4
141.0 116.0 1 91.0 3 1
140.5 115.5 90.5 5 1
140.0 115.0 90.0 13 2
139.5 114.5 89.5 2
139.0 114.0 89.0 21 8
138.5 113.5 1 88.5 3
138.0 113.0 88.0 11 8
137.5 112.5 2 87.5 6 2
137.0 112.0 87.0 5 1
136.5 111.5 2 86.5 12 10
136.0 111.0 86.0
135.5 110.5 85.5 15 3
135.0 110.0 3 85.0 1 3
134.5 109.5 84.5 7 8
134.0 109.0 2 2 84.0 6 3
133.5 2 108.5 1 83.5 12 3
133.0 108.0 1 1 83.0 17 6
132.5 107.5 1 82.5 3
132.0 1 107.0 82.0 13 8
131.5 106.5 1 81.5 4 3
131.0 106.0 81.0 12 7
130.5 105.5 6 1 80.5 15 7
130.0 105.0 80.0 8 3
129.5 104.5 5 3 79.5 7 9
129.0 104.0 1 79.0 4 2
128.5 103.5 78.5 7 7
128.0 103.0 8 1 78.0 5 6
127.5 1 102.5 77.5 9 9
127.0 102.0 4 2 77.0 14 9
126.5 1 1 101.5 76.5 10 8
126.0 101.0 7 2 76.0 7 4
125.5 100.5 4 1 75.5 6 2
American Mathematics Competitions
2005 AMC 12 A Results for Missouri
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 12 14 50.0 1 4 25.0
74.5 11 2 49.5 2 2 24.5
74.0 10 11 49.0 3 1 24.0 2 2
73.5 10 6 48.5 1 23.5
73.0 3 2 48.0 3 3 23.0
72.5 12 4 47.5 3 2 22.5
72.0 8 5 47.0 22.0
71.5 12 7 46.5 2 21.5
71.0 15 8 46.0 1 21.0
70.5 12 6 45.5 2 20.5
70.0 11 7 45.0 1 20.0
69.5 3 7 44.5 4 19.5
69.0 8 14 44.0 1 1 19.0
68.5 8 7 43.5 18.5
68.0 6 7 43.0 2 18.0
67.5 4 6 42.5 17.5
67.0 5 3 42.0 6 3 17.0
66.5 8 7 41.5 1 16.5
66.0 5 3 41.0 16.0
65.5 7 8 40.5 15.5
65.0 6 6 40.0 15.0
64.5 4 7 39.5 14.5
64.0 9 6 39.0 1 14.0
63.5 1 4 38.5 1 13.5
63.0 10 3 38.0 13.0
62.5 7 4 37.5 12.5
62.0 7 8 37.0 12.0
61.5 10 2 36.5 1 11.5
61.0 3 1 36.0 1 11.0
60.5 3 3 35.5 10.5
60.0 7 4 35.0 1 10.0
59.5 8 4 34.5 1 9.5
59.0 3 3 34.0 1 9.0
58.5 5 5 33.5 8.5
58.0 2 33.0 2 8.0
57.5 4 2 32.5 1 7.5
57.0 3 5 32.0 7.0
56.5 3 2 31.5 6.5
56.0 1 31.0 6.0
55.5 3 4 30.5 5.5
55.0 2 30.0 5.0
54.5 3 29.5 4.5
54.0 3 3 29.0 1 1 4.0
53.5 5 3 28.5 3.5
53.0 6 2 28.0 1 3.0
52.5 2 27.5 2.5
52.0 1 27.0 2.0
51.5 2 1 26.5 1.5
51.0 2 1 26.0 1.0
50.5 1 2 25.5 .5
0.0 0 0
American Mathematics Competitions
2005 AMC 12 A Results for Missouri
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 11 12 13 unknown
---------------------------
133.5 2
132.0 1
127.5 1
126.5 1 1
124.0 1
123.0 1 1
122.0 1
121.5 1 2
120.5 1
119.5 1 1
118.5 1
118.0 1
116.0 1
113.5 1
112.5 1 1
111.5 1 1 2
110.0 3
109.0 4
108.5 1
108.0 1 1
107.5 1
106.5 1 1
105.5 1 4 3
104.5 3 5
104.0 1
103.0 8 2
102.0 2 4 1
101.0 2 7
100.5 3 2
99.5 3 2
99.0 1
98.5 1 6 8
98.0 1
97.5 1 2 4
97.0 1 1 2 5
96.5 1
96.0 4 6 1
95.5 3
95.0 2 10 12
94.5 2 2
94.0 1 1 1
93.5 1 4 3 1
92.5 5 12
92.0 1 2 2
91.5 7 4
91.0 2 2
90.5 1 6
90.0 6 9
89.5 1 1
89.0 1 15 14 1
88.5 4
88.0 1 10 8
87.5 4 4 1
87.0 3 3
86.5 2 13 7
86.0 1
85.5 10 9
85.0 1 3
84.5 2 7 6 2
84.0 4 5
83.5 1 8 6 1
83.0 2 9 12 1
82.5 3
82.0 11 13
81.5 1 5 2 1
81.0 1 11 8 1
80.5 3 11 8
80.0 3 8 1
79.5 6 9 1
79.0 2 4
78.5 1 8 5
78.0 7 5
77.5 1 1 11 5 2
77.0 13 11
76.5 1 4 13 1
76.0 2 4 5 2
75.5 1 4 3
75.0 11 15
74.5 8 5 1
74.0 1 11 9 2
73.5 1 1 11 4 2
73.0 3 2 1
72.5 1 2 8 7 3
72.0 10 3
71.5 1 11 7 1
71.0 1 13 10
70.5 9 9 2
70.0 1 8 10 1
69.5 4 7
69.0 1 16 6
68.5 2 2 10 2 2
68.0 1 2 8 3
67.5 6 4 4
67.0 1 1 3 3
66.5 1 1 11 2 1
66.0 1 1 5 2
65.5 1 3 9 3 2
65.0 1 1 7 3
64.5 2 6 3 1
64.0 9 6 1
63.5 1 2 2
63.0 1 8 4 1
62.5 2 2 8
62.0 3 1 7 4 1
61.5 8 5
61.0 3 1
60.5 3 1 2
60.0 8 3
59.5 1 3 6 2
59.0 2 4
58.5 1 6 3
58.0 1 1 1
57.5 2 1 3
57.0 2 3 3 2
56.5 1 4 2
56.0 1
55.5 1 1 1 2 3
55.0 1 1
54.5 1 2
54.0 4 2
53.5 5 3
53.0 1 4 3
52.5 2
52.0 1
51.5 2 1 1
51.0 2 1 1
50.5 1 1 1 1
50.0 5
49.5 1 3
49.0 1 2 1
48.5 1
48.0 1 1 1 3
47.5 3 2 1
46.5 1 1 1
46.0 2
45.5 2
45.0 1
44.5 1 2 1
44.0 1 1
43.0 1 1
42.0 2 8
41.5 1
40.5 1
39.0 1
38.5 1
36.5 1
36.0 1
35.0 1
34.5 1
34.0 1
33.0 2
32.5 1
30.0 1
29.0 2
28.0 1
24.0 1 2 1
American Mathematics Competitions
2005 AMC 12 A Results for Missouri
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 0.05 0.04 0.07 9.52* 0.16 0.16 0.00
2 0.02 9.44* 0.16 0.23 0.05 0.09 0.01
3 0.35 3.52* 1.26 0.45 0.55 3.87 0.00
4 6.86* 0.38 2.58 0.05 0.04 0.09 0.00
5 0.30 6.20* 2.33 0.11 0.07 1.00 0.00
6 0.48 4.61* 0.23 0.37 0.91 3.39 0.00
7 0.72 0.18 6.42* 0.15 0.08 2.45 0.00
8 0.31 0.41 0.36 1.55* 0.31 7.05 0.00
9 2.78* 0.33 0.91 0.34 0.13 5.50 0.00
10 0.38 2.93* 0.26 0.63 0.11 5.69 0.00
11 0.90 0.41 0.38 0.48 2.94* 4.89 0.00
12 0.86 0.31 0.23 3.27* 1.23 4.10 0.00
13 0.22 0.30 0.39 2.53* 0.39 6.16 0.00
14 0.38 0.35 3.27 1.03* 0.45 4.52 0.00
15 0.25 0.41 1.34* 0.74 0.82 6.43 0.00
16 0.29 0.29 0.80 0.64* 0.36 7.62 0.00
17 1.53* 0.90 1.44 0.34 0.50 5.29 0.00
18 0.38* 0.41 0.39 0.29 0.26 8.28 0.00
19 0.95 1.98* 0.90 0.63 0.76 4.77 0.01
20 0.41 0.14 0.21 0.12 0.26* 8.87 0.00
21 0.56 0.45 0.40* 0.21 0.09 8.29 0.00
22 0.35 0.48* 0.28 0.31 0.17 8.41 0.00
23 0.55 0.52* 0.24 0.25 0.45 7.98 0.00
24 0.13 0.16* 0.17 0.27 0.08 9.20 0.00
25 0.36 0.27 0.25* 0.25 0.09 8.77 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 Missouri
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 125.0 2 100.0
149.5 124.5 99.5 2 1
149.0 124.0 99.0 1
148.5 123.5 98.5 2 2
148.0 123.0 98.0 2 2
147.5 122.5 97.5 1
147.0 122.0 97.0 4 3
146.5 2 121.5 1 96.5 1 1
146.0 121.0 96.0 4
145.5 120.5 95.5 1
145.0 120.0 95.0 2 3
144.5 119.5 94.5 3 2
144.0 1 119.0 94.0
143.5 118.5 1 93.5 2 4
143.0 118.0 93.0 1
142.5 117.5 92.5 3 2
142.0 117.0 1 92.0
141.5 116.5 91.5 3
141.0 116.0 2 91.0 4 2
140.5 115.5 90.5 1
140.0 115.0 90.0 2 2
139.5 114.5 89.5 1
139.0 114.0 89.0 4 1
138.5 113.5 2 88.5 2 2
138.0 113.0 1 88.0 3
137.5 112.5 2 87.5 3 1
137.0 1 112.0 87.0 1
136.5 111.5 1 86.5 5 2
136.0 111.0 3 86.0 3
135.5 110.5 85.5 5 1
135.0 110.0 4 1 85.0 3 2
134.5 109.5 84.5 2 1
134.0 109.0 3 84.0 6 2
133.5 108.5 83.5 3
133.0 108.0 1 83.0 4 1
132.5 107.5 1 82.5 3 3
132.0 107.0 82.0 2
131.5 106.5 1 81.5 2 1
131.0 1 106.0 2 81.0 1 1
130.5 105.5 2 1 80.5 1 4
130.0 105.0 80.0 2 2
129.5 104.5 79.5 5 1
129.0 1 104.0 1 79.0 4 1
128.5 103.5 78.5 1 5
128.0 103.0 1 1 78.0 4
127.5 102.5 77.5 3 2
127.0 102.0 1 77.0 4 5
126.5 101.5 1 76.5 3
126.0 101.0 76.0 2 2
125.5 100.5 1 75.5 3
American Mathematics Competitions
2005 AMC 10 B Results for Missouri
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 4 1 50.0 2 2 25.0 1
74.5 3 4 49.5 1 24.5
74.0 1 2 49.0 2 3 24.0 1
73.5 3 4 48.5 1 23.5
73.0 4 1 48.0 5 23.0
72.5 3 3 47.5 1 1 22.5
72.0 4 2 47.0 1 22.0
71.5 1 1 46.5 2 1 21.5
71.0 4 1 46.0 1 2 21.0
70.5 3 1 45.5 2 20.5
70.0 3 2 45.0 1 1 20.0
69.5 1 3 44.5 2 19.5 1
69.0 4 44.0 1 19.0
68.5 1 4 43.5 18.5
68.0 3 43.0 1 18.0
67.5 2 2 42.5 2 17.5
67.0 1 1 42.0 7 2 17.0
66.5 6 2 41.5 1 16.5
66.0 8 2 41.0 1 1 16.0
65.5 1 1 40.5 1 1 15.5
65.0 1 40.0 1 15.0
64.5 2 39.5 2 1 14.5
64.0 6 2 39.0 1 1 14.0
63.5 3 1 38.5 13.5
63.0 1 38.0 13.0
62.5 4 3 37.5 1 12.5
62.0 1 37.0 12.0
61.5 1 2 36.5 1 1 11.5
61.0 6 2 36.0 2 1 11.0
60.5 1 1 35.5 1 10.5
60.0 5 4 35.0 1 2 10.0
59.5 4 34.5 1 9.5
59.0 1 34.0 2 9.0
58.5 2 33.5 8.5
58.0 2 3 33.0 8.0
57.5 1 1 32.5 1 7.5
57.0 2 2 32.0 7.0
56.5 2 4 31.5 1 6.5
56.0 4 1 31.0 1 6.0
55.5 2 3 30.5 1 1 5.5
55.0 1 30.0 3 2 5.0
54.5 1 1 29.5 4.5
54.0 3 1 29.0 4.0
53.5 3 2 28.5 3.5
53.0 1 1 28.0 1 3.0
52.5 2 2 27.5 2.5
52.0 1 2 27.0 2 2.0
51.5 1 26.5 1.5
51.0 26.0 1 1.0
50.5 5 25.5 .5
0.0 0 0
American Mathematics Competitions
2005 AMC 10 B Results for Missouri
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 unknown
---------------------------
146.5 1 1
144.0 1
137.0 1
131.0 1
129.0 1
125.0 1 1
121.5 1
118.5 1
117.0 1
116.0 1 1
113.5 1 1
113.0 1
112.5 2
111.5 1
111.0 1 1 1
110.0 1 4
109.0 2 1
108.0 1
107.5 1
106.5 1
106.0 1 1
105.5 2 1
104.0 1
103.0 2
102.0 1
101.5 1
100.5 1
99.5 1 3
99.0 1
98.5 3 1
98.0 1 3
97.5 1
97.0 2 5
96.5 1 1
96.0 1 3
95.5 1
95.0 5 1
94.5 6
93.5 3 4
93.0 1
92.5 2 3
91.5 2 1
91.0 1 2 3
90.5 1
90.0 1 3
89.5 1
89.0 3 2
88.5 1 3
88.0 2 1
87.5 1 3
87.0 1
86.5 4 3
86.0 1 2
85.5 2 4
85.0 2 3
84.5 1 2
84.0 2 6
83.5 1 2
83.0 5 1
82.5 3 3
82.0 2
81.5 3
81.0 1 2
80.5 4 1
80.0 1 2 1
79.5 2 5
79.0 1 2 2
78.5 5 4
78.0 3 1
77.5 4 1
77.0 1 8
76.5 3
76.0 1 3
75.5 2 2
75.0 2 3
74.5 1 6
74.0 1 4
73.5 4 3
73.0 3 2
72.5 3 2 1
72.0 4 3
71.5 2
71.0 4 2
70.5 3 1
70.0 2 3
69.5 2 2
69.0 2 2
68.5 4 1
68.0 2 1
67.5 4
67.0 2
66.5 2 6
66.0 6 4
65.5 2
65.0 1
64.5 1 1
64.0 3 5
63.5 1 3
63.0 1
62.5 5 2
62.0 1
61.5 2 1
61.0 2 6
60.5 2
60.0 3 6
59.5 2 2
59.0 1
58.5 1 1
58.0 1 4
57.5 2
57.0 4 1
56.5 1 5
56.0 2 4
55.5 2 3
55.0 1
54.5 2
54.0 2 2
53.5 2 3
53.0 2
52.5 1 3
52.0 3 1
51.5 1
50.5 1 4
50.0 3 1
49.5 1
49.0 3 2
48.5 2
48.0 2 3 1
47.5 1 1
47.0 1
46.5 3
46.0 2 1
45.5 1 1
45.0 1 1
44.5 1 1
44.0 1
43.0 1
42.5 1 1
42.0 5 4
41.5 1
41.0 1 1
40.5 2
40.0 2
39.5 2 1
39.0 2
37.5 1
36.5 2
36.0 2 1
35.5 1
35.0 1 2
34.5 1
34.0 2
32.5 1
31.5 1
31.0 1
30.5 1 1
30.0 5
28.0 1
27.0 2
26.0 1
25.0 1
24.0 1
19.5 1
American Mathematics Competitions
2005 AMC 10 B Results for Missouri
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 7.75* 0.33 0.65 0.41 0.70 0.17 0.00
2 0.20 0.42 0.28 7.45* 0.44 1.20 0.00
3 0.02 0.70 2.86 5.07* 0.83 0.52 0.00
4 1.07 0.15 0.52 3.62* 0.30 4.35 0.00
5 0.17 0.07 7.99* 0.26 0.87 0.65 0.00
6 0.17 8.01* 0.37 0.39 0.30 0.77 0.00
7 0.79 1.42* 0.46 1.33 0.79 5.20 0.00
8 4.94* 0.41 1.22 0.09 0.15 3.19 0.00
9 0.61 0.46 3.01 4.23* 0.63 1.07 0.00
10 1.44* 0.79 0.70 0.52 0.42 6.13 0.00
11 0.48 0.89 0.24 1.73 1.72* 4.94 0.00
12 0.65 1.57 0.59 0.31 0.39* 6.49 0.00
13 0.72 0.70 1.90* 1.46 0.41 4.82 0.00
14 0.44 0.26 1.81* 2.29 0.65 4.56 0.00
15 1.25 0.83 0.74 4.39* 0.70 2.07 0.02
16 0.54 0.92 0.77 0.50* 0.13 7.14 0.00
17 0.66 2.12* 1.22 0.54 0.33 5.13 0.00
18 0.54 4.78 0.94 1.97* 0.57 1.20 0.00
19 0.55 4.91* 0.76 0.68 0.65 2.45 0.00
20 0.87 0.39 1.37* 0.48 0.28 6.59 0.04
21 0.39* 0.44 0.57 0.46 0.24 7.90 0.00
22 0.98 1.11 0.52* 0.31 0.46 6.62 0.00
23 2.44 0.55 0.61* 0.44 0.30 5.66 0.00
24 0.50 0.35 0.33 0.63 1.03* 7.16 0.00
25 0.31 0.52 2.82* 0.52 0.28 5.55 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 Missouri
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 3 1
149.0 124.0 1 99.0
148.5 123.5 98.5 8
148.0 123.0 1 98.0 2
147.5 122.5 97.5 2
147.0 122.0 97.0 6 1
146.5 121.5 1 96.5 1
146.0 121.0 96.0 6 1
145.5 120.5 95.5 1
145.0 120.0 95.0 6 7
144.5 119.5 94.5 2
144.0 119.0 94.0 4 1
143.5 118.5 93.5 4 2
143.0 118.0 1 93.0 1
142.5 117.5 92.5 12 2
142.0 117.0 92.0
141.5 116.5 91.5 5 6
141.0 116.0 1 91.0 3
140.5 115.5 90.5 2 3
140.0 115.0 1 2 90.0 9 3
139.5 1 114.5 89.5 2
139.0 114.0 89.0 18 9
138.5 113.5 88.5 1 1
138.0 1 113.0 88.0 7 1
137.5 112.5 2 87.5 7
137.0 112.0 1 87.0 3 3
136.5 111.5 2 86.5 8 1
136.0 111.0 86.0 2
135.5 110.5 85.5 9 4
135.0 110.0 3 85.0 4 1
134.5 109.5 84.5 3 4
134.0 109.0 3 1 84.0 5 3
133.5 108.5 83.5 3 2
133.0 108.0 2 1 83.0 10 5
132.5 107.5 2 82.5 2 1
132.0 107.0 82.0 6 4
131.5 106.5 6 81.5 3 3
131.0 106.0 81.0 4 2
130.5 105.5 1 1 80.5 5 7
130.0 105.0 1 1 80.0 4 3
129.5 104.5 3 2 79.5 5 4
129.0 104.0 4 79.0 4 2
128.5 103.5 78.5 3 6
128.0 103.0 4 2 78.0 7 3
127.5 1 102.5 77.5 2 2
127.0 102.0 9 2 77.0 7 6
126.5 101.5 2 76.5 4
126.0 101.0 6 1 76.0 7 9
125.5 1 100.5 2 1 75.5 3 5
American Mathematics Competitions
2005 AMC 12 B Results for Missouri
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 5 4 50.0 1 25.0
74.5 3 5 49.5 3 24.5
74.0 5 2 49.0 2 1 24.0 2
73.5 2 3 48.5 1 23.5
73.0 4 3 48.0 4 23.0
72.5 2 2 47.5 1 22.5
72.0 5 1 47.0 22.0
71.5 3 5 46.5 1 21.5
71.0 8 10 46.0 1 21.0
70.5 2 3 45.5 20.5
70.0 4 2 45.0 1 20.0
69.5 5 4 44.5 1 19.5
69.0 1 2 44.0 1 19.0
68.5 2 2 43.5 18.5
68.0 4 2 43.0 18.0 1
67.5 1 1 42.5 1 17.5
67.0 5 42.0 4 17.0
66.5 3 1 41.5 1 16.5
66.0 3 2 41.0 16.0
65.5 1 3 40.5 1 15.5
65.0 2 40.0 15.0
64.5 2 4 39.5 14.5
64.0 3 4 39.0 14.0
63.5 1 2 38.5 1 13.5
63.0 1 2 38.0 13.0
62.5 2 37.5 12.5
62.0 3 37.0 1 12.0
61.5 5 2 36.5 11.5
61.0 1 36.0 11.0
60.5 3 35.5 10.5
60.0 2 5 35.0 10.0
59.5 3 1 34.5 9.5
59.0 1 3 34.0 9.0
58.5 3 1 33.5 8.5
58.0 3 2 33.0 8.0
57.5 2 32.5 7.5
57.0 1 32.0 7.0
56.5 3 31.5 1 6.5
56.0 1 1 31.0 6.0
55.5 1 2 30.5 1 5.5
55.0 1 30.0 3 1 5.0
54.5 2 29.5 4.5
54.0 4 3 29.0 1 4.0
53.5 2 28.5 3.5
53.0 1 28.0 3.0
52.5 2 27.5 2.5
52.0 27.0 2.0
51.5 2 1 26.5 1.5
51.0 2 2 26.0 1.0
50.5 1 25.5 .5
0.0 0 0
American Mathematics Competitions
2005 AMC 12 B Results for Missouri
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 11 12 13 unknown
---------------------------
150.0 1
139.5 1
138.0 1
127.5 1
125.5 1
124.0 1
123.0 1
121.5 1
118.0 1
116.0 1
115.0 1 2
112.5 1 1
112.0 1
111.5 3
110.0 2 2
109.0 1 1 2
108.0 1 1 1
107.5 2
106.5 2 2 3
105.5 2
105.0 1 1
104.5 1 3 1
104.0 1 1 2
103.0 2 2 2
102.0 7 4
101.5 1 1
101.0 1 3 3
100.5 3
99.5 2 2
98.5 1 6 2
98.0 2
97.5 1 1
97.0 1 5 1
96.5 1
96.0 5 4
95.5 1
95.0 1 4 9 1
94.5 1 1
94.0 3 2
93.5 3 3
93.0 1
92.5 7 8
91.5 6 5 1
91.0 1 1 1
90.5 1 1 2 1
90.0 4 8
89.5 2 1
89.0 2 3 11 11
88.5 2
88.0 6 2
87.5 3 4
87.0 2 3 1
86.5 1 5 3
86.0 2
85.5 1 7 6
85.0 4 2
84.5 1 5 1
84.0 1 1 6
83.5 1 2 2
83.0 2 9 4
82.5 2 1
82.0 1 7 2
81.5 2 4
81.0 2 3 1
80.5 2 6 4
80.0 1 3 3
79.5 6 3
79.0 6 1
78.5 1 6 2
78.0 1 5 4
77.5 2 2
77.0 9 4
76.5 1 1 2
76.0 11 5
75.5 4 4
75.0 8 2
74.5 5 3
74.0 3 4
73.5 4 1
73.0 3 4
72.5 2 2
72.0 4 2
71.5 3 5
71.0 13 5
70.5 1 1 3
70.0 2 4 1
69.5 4 4 1
69.0 1 2
68.5 1 3
68.0 1 5
67.5 1 1
67.0 1 4
66.5 3 1
66.0 3 2
65.5 1 1 2
65.0 3
64.5 3 3
64.0 1 3 3
63.5 3
63.0 1 2
62.5 2 1
62.0 2 1
61.5 1 2 4
61.0 1 1
60.5 2 1
60.0 4 3
59.5 4 1
59.0 2 2
58.5 2 2
58.0 3 2
57.5 1 1
57.0 1
56.5 2 1
56.0 2
55.5 1 2
55.0 1
54.5 1 1
54.0 1 2 4
53.5 1 1
53.0 1
52.5 2
51.5 1 3
51.0 2 2
50.5 1
50.0 1
49.5 2 1
49.0 3
48.5 1
48.0 3 1
47.5 1
46.5 1
46.0 1
45.0 1
44.5 1
44.0 1
42.5 1
42.0 2 2
41.5 1
40.5 1
38.5 1
37.0 1
34.0 1
31.5 1
30.5 1
30.0 2 2
29.0 1
24.0 2
18.0 1
American Mathematics Competitions
2005 AMC 12 B Results for Missouri
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 8.89* 0.27 0.27 0.10 0.31 0.16 0.00
2 0.04 0.19 0.23 8.60* 0.30 0.64 0.00
3 0.06 0.10 8.67* 0.17 0.49 0.51 0.00
4 0.13 8.53* 0.19 0.24 0.26 0.64 0.01
5 6.71* 0.16 0.77 0.03 0.13 2.20 0.00
6 2.63* 0.87 0.57 0.41 0.39 5.13 0.00
7 0.69 1.43 0.29 2.40* 0.50 4.70 0.00
8 0.91 1.63 3.61* 0.04 1.26 2.54 0.00
9 0.43 6.90* 0.34 0.50 0.34 1.47 0.01
10 0.11 0.53 0.11 2.21 2.80* 4.23 0.00
11 1.30 1.11 0.73 4.37* 0.44 2.04 0.00
12 0.31 0.64 0.81 0.80* 0.09 7.34 0.00
13 0.41 0.24 0.37 1.76* 0.21 7.00 0.00
14 0.86 0.96 0.71 0.24 1.04* 6.19 0.00
15 0.67 0.37 0.51 4.27* 0.43 3.74 0.00
16 0.31 0.27 0.63 0.71* 0.23 7.84 0.00
17 0.37 0.56* 0.30 0.07 0.69 8.01 0.00
18 1.51 0.43 0.54* 0.37 0.24 6.90 0.00
19 0.20 0.27 0.23 0.39 1.60* 7.31 0.00
20 0.29 0.33 3.59* 0.56 2.00 3.24 0.00
21 0.21 0.34 0.53* 0.33 0.17 8.41 0.00
22 0.41 0.67 0.24 0.20 0.20* 8.27 0.00
23 0.14 0.19* 0.21 0.16 0.11 9.19 0.00
24 0.39* 0.27 0.37 0.24 0.21 8.51 0.00
25 0.34* 0.21 0.47 0.19 0.47 8.31 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
