American Mathematics Competitions
2005 AMC 10 A Results for Montana
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 657
Number of unofficial participants: 0
Average score of participants: 67.0
Average score for female students is: 66.5 ( 325 Students)
Average score for male students is: 67.9 ( 293 Students)
Average score for unspecified gender is 64.4 ( 39 Students)
Average score for grade 10 is: 69.3 ( 321 Students)
Average score for grade 9 is: 64.8 ( 317 Students)
Average score for grade 8 and below is: 67.9 ( 13 Students)
Average score with unknown grade: 64.7 ( 6 Students)
AIME qualifying score = 120.0 or better
Number of AIME qualifers 0
Number of schools returning results 15
Average school winning score 93.63
American Mathematics Competitions
2005 AMC 12 A Results for Montana
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 932
Number of unofficial participants: 0
Average score of participants: 71.9
Average score for female students is: 69.7 ( 419 Students)
Average score for male students is: 73.8 ( 478 Students)
Average score for unspecified gender is 72.4 ( 35 Students)
Average score for grade 13 is: 76.5 ( 1 Student)
Average score for grade 12 is: 74.4 ( 351 Students)
Average score for grade 11 is: 70.1 ( 444 Students)
Average score for grade 10 is: 71.4 ( 95 Students)
Average score for grade 9 is: 72.2 ( 29 Students)
Average score for grade 8 and below is: 51.8 ( 2 Students)
Average score with unknown grade: 70.4 ( 10 Students)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 27
Number of schools returning results 20
Average school winning score 99.95
Average school team score 282.50
American Mathematics Competitions
2005 AMC 10 B Results for Montana
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 151
Number of unofficial participants: 0
Average score of participants: 68.1
Average score for female students is: 67.5 ( 79 Students)
Average score for male students is: 68.5 ( 66 Students)
Average score for unspecified gender is 71.0 ( 6 Students)
Average score for grade 10 is: 68.0 ( 94 Students)
Average score for grade 9 is: 68.2 ( 57 Students)
AIME qualifying score = 120.0 or better
Number of AIME qualifers 0
Number of schools returning results 8
Average school winning score 89.06
American Mathematics Competitions
2005 AMC 12 B Results for Montana
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 183
Number of unofficial participants: 0
Average score of participants: 77.3
Average score for female students is: 76.3 ( 97 Students)
Average score for male students is: 78.9 ( 83 Students)
Average score for unspecified gender is 66.5 ( 3 Students)
Average score for grade 12 is: 78.6 ( 92 Students)
Average score for grade 11 is: 76.0 ( 90 Students)
Average score for grade 10 is: 89.0 ( 1 Student)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 2
Number of schools returning results 8
Average school winning score 95.19
Average school team score 271.19
2005 State AMC 12 TEAM Score Distribution
-----------------------------------------------
score A B Rank
-----------------------------------------------
327.0 1 1
320.5 1 2
317.5 1 3
308.0 1 4
306.5 1 5
306.0 1 6
305.5 1 7
304.0 1 8
300.5 1 9
294.0 1 10
291.0 1 11
286.5 1 12
284.0 1 13
281.0 1 14
280.0 1 15
275.5 1 16
269.5 1 17
268.5 1 18
267.5 1 19
266.0 1 20
261.5 1 21
261.0 1 22
258.5 1 23
257.0 1 24
247.5 1 25
234.0 1 26
223.5 1 27
217.5 1 28
2005 AMC Contest Score Distributions
-----------------------------------------------
score 12 A 12 B 10 A 10 B
-----------------------------------------------
114.5 1
112.5 2
111.5 1
109.0 3
108.0 1 1
106.5 1
105.5 4
104.5 4
104.0 1 1
102.0 3
101.5 1
101.0 4 1
100.5 2
100.0 1
99.5 2 1 3 1
98.5 8 2 2
98.0 2
97.5 3 1
97.0 3 1 1
96.0 1 1 1
95.0 8 2 2 1
94.0 5 3
93.5 1 1 1
93.0 2
92.5 7 4 2
92.0 1 1
91.5 10 5 4 2
91.0 2 1 2
90.5 4 2 1 1
90.0 5 3 4 2
89.5 2 1
89.0 13 5 3 2
88.5 2 1
88.0 9 3 4
87.5 3 3 1
87.0 3 1 2
86.5 7 4 5 3
86.0 1
85.5 12 7 10 1
85.0 3 1 1
84.5 16 5 7 1
84.0 9 2 3 1
83.5 7 1 1
83.0 23 7 7 2
82.5 3 1 4 1
82.0 16 5 10 4
81.5 6 3 6 4
81.0 15 4 5 1
80.5 10 4 7 1
80.0 10 3 2 1
79.5 17 6 13 1
79.0 2 3
78.5 20 2 11 1
78.0 9 1 7
77.5 11 3 5 1
77.0 16 6 7 3
76.5 5 2 5 1
76.0 19 5 13 2
75.5 11 3 1 2
75.0 21 1 23 1
74.5 6 4 6 4
74.0 25 1 4 1
73.5 10 4 14 3
73.0 3 2 2 2
72.5 26 2 21 1
72.0 6 6 2
71.5 23 4 8 1
71.0 14 9 10 6
70.5 13 6 1
70.0 22 2 11 4
69.5 6 1 3 4
69.0 25 1 18 4
68.5 13 1 4 6
68.0 12 9 2
67.5 22 1 7 1
67.0 6 1 7 1
66.5 19 9 1
66.0 5 13 3
65.5 20 12 1
65.0 14 3 10 3
64.5 13 2 12 1
64.0 12 3 12 2
63.5 6 8 3
63.0 13 13 2
62.5 6 10 1
62.0 12 6 2
61.5 15 7 2
61.0 6 2 7 1
60.5 9 4 9 1
60.0 8 7 2
59.5 13 14 2
59.0 9 1 8 3
58.5 2 1 10 2
58.0 5 1 7 2
57.5 10 1 1
57.0 6 2 8 2
56.5 4 1 7 1
56.0 1 1 6
55.5 7 11
55.0 2 1 3
54.5 2 6
54.0 5 1 6 3
53.5 6 3
53.0 7 2 4 3
52.5 6 1 3 3
52.0 4 7
51.5 4 2 5 1
51.0 3 3
50.5 5 1 6 1
50.0 2 6
49.5 2 1 4
49.0 3 4 1
48.5 2 1
48.0 4 6 2
47.5 1 3
47.0 2 2 2
46.5 5 3
46.0 1 1 1
45.5 4
45.0 2 1
44.5 3 1
44.0 5 1
43.5 1
43.0 3 2
42.5 2
42.0 2 1
41.5 1
41.0 1
40.5 2 3
40.0 1
39.5 2
39.0 1 1
38.5 1 1
38.0 1 1
37.5 4
37.0 3 1
36.0 1 1
35.5 1
35.0 1
34.5 1
34.0 1
33.5 1 1
32.5 2 1 1
32.0 1
31.5 1
30.5 1 1
30.0 1 2 1
29.5 1
28.5 2
27.0 1
26.0 1
25.0 1
24.0 1
23.0 1
21.0 1
19.5 1
18.0 2 1
American Mathematics Competitions
2005 AMC 10 A Results for Montana
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
150.0 125.0 100.0 1
149.5 124.5 99.5 2 1
149.0 124.0 99.0
148.5 123.5 98.5 1
148.0 123.0 98.0
147.5 122.5 97.5
147.0 122.0 97.0 1
146.5 121.5 96.5
146.0 121.0 96.0 1
145.5 120.5 95.5
145.0 120.0 95.0 2
144.5 119.5 94.5
144.0 119.0 94.0
143.5 118.5 93.5 1
143.0 118.0 93.0 1 1
142.5 117.5 92.5 1 1
142.0 117.0 92.0 1
141.5 116.5 91.5 3 1
141.0 116.0 91.0 2
140.5 115.5 90.5 1
140.0 115.0 90.0 1 3
139.5 114.5 1 89.5 2
139.0 114.0 89.0 2 1
138.5 113.5 88.5
138.0 113.0 88.0 4
137.5 112.5 87.5 1
137.0 112.0 87.0 1 1
136.5 111.5 86.5 2 3
136.0 111.0 86.0 1
135.5 110.5 85.5 6 4
135.0 110.0 85.0 1
134.5 109.5 84.5 3 4
134.0 109.0 84.0 3
133.5 108.5 83.5 1
133.0 108.0 83.0 3 3
132.5 107.5 82.5 4
132.0 107.0 82.0 5 5
131.5 106.5 81.5 4
131.0 106.0 81.0 1 4
130.5 105.5 80.5 3 4
130.0 105.0 80.0 2
129.5 104.5 79.5 7 5
129.0 104.0 1 79.0 1 1
128.5 103.5 78.5 7 3
128.0 103.0 78.0 4 3
127.5 102.5 77.5 3 2
127.0 102.0 77.0 4 3
126.5 101.5 76.5 4 1
126.0 101.0 76.0 8 4
125.5 100.5 75.5 1
American Mathematics Competitions
2005 AMC 10 A Results for Montana
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 10 12 50.0 3 3 25.0 1
74.5 3 2 49.5 2 2 24.5
74.0 2 2 49.0 1 3 24.0
73.5 3 9 48.5 23.5
73.0 2 48.0 4 2 23.0 1
72.5 9 11 47.5 1 2 22.5
72.0 3 2 47.0 1 22.0
71.5 3 5 46.5 1 2 21.5
71.0 4 5 46.0 1 21.0
70.5 1 4 45.5 1 3 20.5
70.0 4 7 45.0 1 1 20.0
69.5 1 2 44.5 19.5
69.0 9 9 44.0 19.0
68.5 1 3 43.5 1 18.5
68.0 6 2 43.0 1 1 18.0 1
67.5 4 3 42.5 1 17.5
67.0 2 5 42.0 1 17.0
66.5 5 4 41.5 1 16.5
66.0 5 7 41.0 1 16.0
65.5 7 4 40.5 1 2 15.5
65.0 2 7 40.0 15.0
64.5 7 3 39.5 2 14.5
64.0 6 5 39.0 14.0
63.5 2 6 38.5 1 13.5
63.0 4 9 38.0 13.0
62.5 5 5 37.5 4 12.5
62.0 1 4 37.0 12.0
61.5 2 5 36.5 11.5
61.0 5 1 36.0 1 11.0
60.5 1 8 35.5 10.5
60.0 3 4 35.0 1 10.0
59.5 3 11 34.5 9.5
59.0 5 3 34.0 9.0
58.5 5 4 33.5 1 8.5
58.0 3 4 33.0 8.0
57.5 1 32.5 1 7.5
57.0 4 4 32.0 7.0
56.5 4 3 31.5 6.5
56.0 2 3 31.0 6.0
55.5 4 6 30.5 1 5.5
55.0 1 2 30.0 1 1 5.0
54.5 3 2 29.5 1 4.5
54.0 2 3 29.0 4.0
53.5 2 28.5 1 3.5
53.0 4 28.0 3.0
52.5 1 2 27.5 2.5
52.0 2 4 27.0 1 2.0
51.5 4 1 26.5 1.5
51.0 2 26.0 1 1.0
50.5 2 3 25.5 .5
0.0 0 0
American Mathematics Competitions
2005 AMC 10 A Results for Montana
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 unknown
---------------------------
114.5 1
104.0 1
100.0 1
99.5 1 2
98.5 1 1
97.0 1
96.0 1
95.0 2
93.5 1
93.0 2
92.5 2
92.0 1
91.5 2 2
91.0 2
90.5 1
90.0 1 1 2
89.5 1 1
89.0 3
88.0 2 2
87.5 1
87.0 1 1
86.5 5
86.0 1
85.5 2 8
85.0 1
84.5 4 3
84.0 3
83.5 1
83.0 3 4
82.5 4
82.0 5 5
81.5 4 2
81.0 1 4
80.5 2 5
80.0 2
79.5 2 6 5
79.0 1 2
78.5 7 4
78.0 3 4
77.5 1 4
77.0 2 5
76.5 2 3
76.0 5 8
75.5 1
75.0 1 14 8
74.5 3 3
74.0 2 2
73.5 6 8
73.0 1 1
72.5 2 8 11
72.0 3 3
71.5 4 4
71.0 6 3 1
70.5 3 3
70.0 5 6
69.5 2 1
69.0 10 8
68.5 1 3
68.0 5 4
67.5 2 5
67.0 5 2
66.5 5 4
66.0 10 3
65.5 1 7 3 1
65.0 2 7 1
64.5 6 6
64.0 8 3 1
63.5 4 4
63.0 6 7
62.5 7 3
62.0 4 2
61.5 4 2 1
61.0 3 3 1
60.5 1 5 3
60.0 3 4
59.5 7 7
59.0 7 1
58.5 5 5
58.0 4 3
57.5 1
57.0 5 3
56.5 1 1 5
56.0 4 2
55.5 7 4
55.0 2 1
54.5 2 4
54.0 3 3
53.5 1 2
53.0 4
52.5 1 2
52.0 4 3
51.5 3 2
51.0 2 1
50.5 1 5
50.0 2 4
49.5 1 2 1
49.0 4
48.5 1
48.0 4 2
47.5 3
47.0 1 1
46.5 2 1
46.0 1
45.5 4
45.0 1 1
43.5 1
43.0 1 1
42.5 2
42.0 1
41.5 1
41.0 1
40.5 2 1
39.5 1 1
39.0 1
38.5 1
37.5 3 1
36.0 1
35.0 1
33.5 1
32.5 1
30.5 1
30.0 2
29.5 1
28.5 1 1
27.0 1
26.0 1
25.0 1
23.0 1
18.0 1
American Mathematics Competitions
2005 AMC 10 A Results for Montana
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 0.30 0.15 0.40 8.26* 0.49 0.40 0.00
2 0.21 0.08 3.81* 0.14 1.75 4.02 0.00
3 0.08 8.33* 0.44 0.56 0.15 0.44 0.00
4 0.62 0.64* 2.25 0.56 0.53 5.39 0.00
5 4.69* 0.52 4.44 0.05 0.06 0.24 0.00
6 0.32 3.58* 4.35 0.09 0.06 1.60 0.00
7 0.79 2.82* 0.38 0.59 0.84 4.58 0.00
8 1.40 0.44 2.62* 0.03 0.08 5.43 0.00
9 1.17 5.18* 1.37 0.21 0.18 1.89 0.00
10 0.67* 0.52 1.07 0.40 0.08 7.28 0.00
11 0.41 1.81* 0.37 0.67 0.09 6.65 0.00
12 0.30 0.47* 0.32 0.23 0.59 8.08 0.00
13 1.35 0.72 0.30 0.44 0.50* 6.68 0.00
14 0.79 0.47 0.41 0.46 1.61* 6.26 0.00
15 0.26 0.65 0.56 0.78 0.64* 7.11 0.00
16 0.78 0.53 0.56 1.43* 0.21 6.48 0.00
17 0.21 0.29 0.50 1.57* 0.47 6.96 0.00
18 1.84* 1.72 1.04 2.66 0.24 2.48 0.02
19 0.32 0.68 0.76 2.40* 0.65 5.16 0.02
20 0.23* 0.33 0.53 0.46 0.27 8.17 0.00
21 1.35 0.55* 0.24 0.40 0.67 6.79 0.00
22 0.75 0.32 0.30 1.35* 0.41 6.86 0.00
23 0.29 0.55 0.94* 0.68 0.59 6.94 0.00
24 0.81 0.37* 0.30 0.21 0.11 8.20 0.00
25 0.55 0.67 0.73 0.64* 0.11 7.31 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 Montana
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 1 1
149.0 124.0 99.0
148.5 123.5 98.5 7
148.0 123.0 98.0 1 1
147.5 122.5 97.5 1 1
147.0 122.0 97.0 3
146.5 121.5 96.5
146.0 121.0 96.0 1
145.5 120.5 95.5
145.0 120.0 95.0 7 1
144.5 119.5 94.5
144.0 119.0 94.0 3 2
143.5 118.5 93.5 1
143.0 118.0 93.0
142.5 117.5 92.5 6 1
142.0 117.0 92.0 1
141.5 116.5 91.5 5 4
141.0 116.0 91.0
140.5 115.5 90.5 3 1
140.0 115.0 90.0 3 2
139.5 114.5 89.5
139.0 114.0 89.0 5 8
138.5 113.5 88.5 1 1
138.0 113.0 88.0 5 4
137.5 112.5 1 87.5 2 1
137.0 112.0 87.0 2
136.5 111.5 1 86.5 5 2
136.0 111.0 86.0
135.5 110.5 85.5 5 7
135.0 110.0 85.0 1 2
134.5 109.5 84.5 6 9
134.0 109.0 2 1 84.0 7 2
133.5 108.5 83.5 3 3
133.0 108.0 1 83.0 13 9
132.5 107.5 82.5 2 1
132.0 107.0 82.0 9 7
131.5 106.5 1 81.5 6
131.0 106.0 81.0 9 6
130.5 105.5 4 80.5 7 3
130.0 105.0 80.0 5 5
129.5 104.5 2 2 79.5 8 8
129.0 104.0 1 79.0
128.5 103.5 78.5 14 6
128.0 103.0 78.0 6 2
127.5 102.5 77.5 5 6
127.0 102.0 2 1 77.0 10 6
126.5 101.5 1 76.5 4 1
126.0 101.0 4 76.0 9 10
125.5 100.5 1 1 75.5 6 5
American Mathematics Competitions
2005 AMC 12 A Results for Montana
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 14 5 50.0 2 25.0
74.5 4 2 49.5 1 1 24.5
74.0 9 13 49.0 1 2 24.0 1
73.5 2 8 48.5 1 1 23.5
73.0 2 1 48.0 1 3 23.0
72.5 8 17 47.5 1 22.5
72.0 4 2 47.0 2 22.0
71.5 16 6 46.5 1 4 21.5
71.0 6 8 46.0 1 21.0
70.5 3 9 45.5 20.5
70.0 10 12 45.0 20.0
69.5 4 1 44.5 1 1 19.5 1
69.0 12 13 44.0 4 1 19.0
68.5 5 7 43.5 18.5
68.0 6 6 43.0 2 1 18.0 1 1
67.5 10 12 42.5 17.5
67.0 3 3 42.0 1 1 17.0
66.5 8 10 41.5 16.5
66.0 4 1 41.0 16.0
65.5 5 14 40.5 1 1 15.5
65.0 7 5 40.0 15.0
64.5 6 6 39.5 14.5
64.0 6 6 39.0 1 14.0
63.5 4 2 38.5 1 13.5
63.0 5 8 38.0 1 13.0
62.5 5 1 37.5 12.5
62.0 3 9 37.0 2 12.0
61.5 10 4 36.5 11.5
61.0 4 2 36.0 1 11.0
60.5 6 3 35.5 10.5
60.0 3 4 35.0 10.0
59.5 6 6 34.5 1 9.5
59.0 3 6 34.0 1 9.0
58.5 1 1 33.5 1 8.5
58.0 1 4 33.0 8.0
57.5 6 4 32.5 2 7.5
57.0 6 32.0 7.0
56.5 3 1 31.5 6.5
56.0 1 31.0 6.0
55.5 3 4 30.5 1 5.5
55.0 2 30.0 1 5.0
54.5 1 1 29.5 4.5
54.0 2 3 29.0 4.0
53.5 4 2 28.5 3.5
53.0 5 2 28.0 3.0
52.5 3 2 27.5 2.5
52.0 1 3 27.0 2.0
51.5 1 3 26.5 1.5
51.0 2 1 26.0 1.0
50.5 1 3 25.5 .5
0.0 0 0
American Mathematics Competitions
2005 AMC 12 A Results for Montana
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 11 12 13 unknown
---------------------------
112.5 1 1
111.5 1
109.0 1 2
108.0 1
106.5 1
105.5 1 1 2
104.5 1 3
104.0 1
102.0 2 1
101.5 1
101.0 2 2
100.5 1 1
99.5 1 1
98.5 5 3
98.0 1 1
97.5 1 1 1
97.0 3
96.0 1
95.0 1 1 6
94.0 2 3
93.5 1
92.5 1 2 4
92.0 1
91.5 1 2 3 4
91.0 2
90.5 2 2
90.0 2 3
89.0 7 6
88.5 1 1
88.0 5 4
87.5 1 2
87.0 1 2
86.5 5 2
85.5 1 6 5
85.0 1 1 1
84.5 3 7 6
84.0 1 3 5
83.5 1 4 1 1
83.0 2 8 13
82.5 3
82.0 8 8
81.5 1 2 3
81.0 1 3 5 6
80.5 1 6 3
80.0 2 2 5 1
79.5 1 11 5
78.5 1 9 10
78.0 1 7 1
77.5 1 1 9
77.0 1 4 11
76.5 1 1 2 1
76.0 1 4 10 4
75.5 1 7 3
75.0 1 2 9 9
74.5 3 3
74.0 1 4 10 9 1
73.5 2 1 6 1
73.0 3
72.5 3 10 13
72.0 2 4
71.5 3 1 13 5 1
71.0 1 9 3 1
70.5 2 1 5 4 1
70.0 13 9
69.5 5 1
69.0 1 3 12 9
68.5 8 5
68.0 1 5 6
67.5 3 9 10
67.0 1 2 2 1
66.5 1 1 12 5
66.0 2 3
65.5 5 7 7 1
65.0 1 7 6
64.5 1 1 7 3 1
64.0 1 8 2 1
63.5 3 1 2
63.0 3 4 6
62.5 2 3 1
62.0 1 1 4 6
61.5 1 10 4
61.0 2 4
60.5 1 7 1
60.0 6 2
59.5 2 6 4 1
59.0 1 7 1
58.5 1 1
58.0 1 3 1
57.5 1 3 5 1
57.0 1 3 2
56.5 1 3
56.0 1
55.5 1 4 2
55.0 2
54.5 1 1
54.0 2 3
53.5 3 3
53.0 5 2
52.5 3 2 1
52.0 2 2
51.5 1 2 1
51.0 2 1
50.5 1 3 1
50.0 1 1
49.5 1 1
49.0 2 1
48.5 1 1
48.0 1 1 1 1
47.5 1
47.0 2
46.5 1 3 1
46.0 1
44.5 3
44.0 4 1
43.0 1 2
42.0 1 1
40.5 2
40.0 1
39.0 1
38.5 1
38.0 1
37.0 3
36.0 1
34.5 1
34.0 1
33.5 1
32.5 1 1
30.5 1
30.0 1
24.0 1
19.5 1
18.0 1 1
American Mathematics Competitions
2005 AMC 12 A Results for Montana
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 0.10 0.06 9.36* 0.17 0.26 0.00
2 0.03 9.24* 0.31 0.30 0.03 0.09 0.00
3 0.36 2.11* 1.73 0.46 0.42 4.91 0.00
4 5.92* 0.41 3.54 0.04 0.02 0.06 0.00
5 0.32 5.26* 3.09 0.12 0.08 1.14 0.00
6 0.54 3.89* 0.38 0.31 0.75 4.13 0.00
7 0.65 0.17 5.48* 0.13 0.06 3.50 0.00
8 0.19 0.42 0.18 1.18* 0.27 7.76 0.00
9 1.77* 0.47 0.99 0.27 0.17 6.33 0.00
10 0.35 2.12* 0.11 0.62 0.12 6.67 0.00
11 0.85 0.53 0.28 0.47 2.20* 5.68 0.00
12 1.06 0.25 0.23 2.16* 1.18 5.13 0.00
13 0.20 0.19 0.50 2.18* 0.31 6.61 0.00
14 0.28 0.52 3.25 0.69* 0.48 4.79 0.00
15 0.14 0.29 1.28* 0.75 0.80 6.74 0.00
16 0.20 0.29 0.60 0.44* 0.41 8.06 0.00
17 1.35* 1.28 1.13 0.43 0.36 5.45 0.00
18 0.18* 0.26 0.23 0.27 0.21 8.85 0.00
19 0.97 1.65* 1.01 0.52 0.91 4.95 0.00
20 0.34 0.08 0.10 0.14 0.06* 9.28 0.00
21 0.42 0.41 0.17* 0.11 0.09 8.81 0.00
22 0.30 0.29* 0.26 0.38 0.24 8.54 0.00
23 0.52 0.16* 0.18 0.12 0.43 8.59 0.00
24 0.03 0.16* 0.10 0.15 0.06 9.50 0.00
25 0.33 0.18 0.15* 0.20 0.14 8.99 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 Montana
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 1
149.0 124.0 99.0
148.5 123.5 98.5
148.0 123.0 98.0
147.5 122.5 97.5
147.0 122.0 97.0 1
146.5 121.5 96.5
146.0 121.0 96.0
145.5 120.5 95.5
145.0 120.0 95.0 1
144.5 119.5 94.5
144.0 119.0 94.0
143.5 118.5 93.5
143.0 118.0 93.0
142.5 117.5 92.5
142.0 117.0 92.0
141.5 116.5 91.5 2
141.0 116.0 91.0
140.5 115.5 90.5 1
140.0 115.0 90.0 1 1
139.5 114.5 89.5 1
139.0 114.0 89.0 2
138.5 113.5 88.5 1
138.0 113.0 88.0
137.5 112.5 87.5
137.0 112.0 87.0
136.5 111.5 86.5 2 1
136.0 111.0 86.0
135.5 110.5 85.5 1
135.0 110.0 85.0
134.5 109.5 84.5 1
134.0 109.0 84.0 1
133.5 108.5 83.5 1
133.0 108.0 83.0 1
132.5 107.5 82.5 1
132.0 107.0 82.0 2 2
131.5 106.5 81.5 2 2
131.0 106.0 81.0 1
130.5 105.5 80.5 1
130.0 105.0 80.0 1
129.5 104.5 79.5 1
129.0 104.0 79.0
128.5 103.5 78.5 1
128.0 103.0 78.0
127.5 102.5 77.5 1
127.0 102.0 77.0 2 1
126.5 101.5 76.5 1
126.0 101.0 76.0 1
125.5 100.5 75.5 2
American Mathematics Competitions
2005 AMC 10 B Results for Montana
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 1 50.0 25.0
74.5 2 2 49.5 24.5
74.0 49.0 1 24.0
73.5 3 48.5 23.5
73.0 1 1 48.0 1 1 23.0
72.5 1 47.5 22.5
72.0 1 1 47.0 2 22.0
71.5 1 46.5 21.5
71.0 2 3 46.0 21.0 1
70.5 1 45.5 20.5
70.0 1 3 45.0 1 20.0
69.5 1 2 44.5 1 19.5
69.0 1 3 44.0 19.0
68.5 4 2 43.5 18.5
68.0 1 1 43.0 18.0
67.5 1 42.5 17.5
67.0 1 42.0 17.0
66.5 1 41.5 16.5
66.0 3 41.0 16.0
65.5 1 40.5 15.5
65.0 1 2 40.0 15.0
64.5 1 39.5 14.5
64.0 1 1 39.0 14.0
63.5 2 1 38.5 13.5
63.0 2 38.0 1 13.0
62.5 1 37.5 12.5
62.0 1 1 37.0 1 12.0
61.5 1 1 36.5 11.5
61.0 1 36.0 11.0
60.5 1 35.5 1 10.5
60.0 2 35.0 10.0
59.5 2 34.5 9.5
59.0 2 1 34.0 9.0
58.5 2 33.5 8.5
58.0 2 33.0 8.0
57.5 1 32.5 7.5
57.0 1 1 32.0 1 7.0
56.5 1 31.5 1 6.5
56.0 31.0 6.0
55.5 30.5 5.5
55.0 30.0 1 5.0
54.5 29.5 4.5
54.0 1 2 29.0 4.0
53.5 28.5 3.5
53.0 1 2 28.0 3.0
52.5 2 27.5 2.5
52.0 27.0 2.0
51.5 1 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 10 B Results for Montana
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 unknown
---------------------------
99.5 1
97.0 1
95.0 1
91.5 2
90.5 1
90.0 2
89.5 1
89.0 1 1
88.5 1
86.5 1 2
85.5 1
84.5 1
84.0 1
83.5 1
83.0 2
82.5 1
82.0 3 1
81.5 2 2
81.0 1
80.5 1
80.0 1
79.5 1
78.5 1
77.5 1
77.0 2 1
76.5 1
76.0 1 1
75.5 1 1
75.0 1
74.5 1 3
74.0 1
73.5 3
73.0 2
72.5 1
72.0 2
71.5 1
71.0 2 4
70.5 1
70.0 4
69.5 3 1
69.0 2 2
68.5 6
68.0 1 1
67.5 1
67.0 1
66.5 1
66.0 2 1
65.5 1
65.0 2 1
64.5 1
64.0 1 1
63.5 3
63.0 1 1
62.5 1
62.0 2
61.5 2
61.0 1
60.5 1
60.0 1 1
59.5 1 1
59.0 1 2
58.5 1 1
58.0 1 1
57.5 1
57.0 2
56.5 1
54.0 1 2
53.0 3
52.5 1 2
51.5 1
50.5 1
49.0 1
48.0 2
47.0 2
45.0 1
44.5 1
38.0 1
37.0 1
35.5 1
32.0 1
31.5 1
30.0 1
21.0 1
American Mathematics Competitions
2005 AMC 10 B Results for Montana
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 7.68* 0.33 0.46 0.40 0.99 0.13 0.00
2 0.20 0.40 0.26 7.28* 0.33 1.52 0.00
3 0.13 1.19 3.84 3.44* 0.86 0.53 0.00
4 0.93 0.20 0.93 1.52* 0.26 6.16 0.00
5 0.07 0.07 8.01* 0.20 1.13 0.53 0.00
6 0.20 8.08* 0.20 0.33 0.20 0.99 0.00
7 0.46 0.46* 0.73 1.06 0.46 6.82 0.00
8 4.30* 0.20 1.46 0.20 0.20 3.64 0.00
9 0.53 0.33 3.11 3.64* 0.73 1.66 0.00
10 0.66* 0.93 1.06 0.40 0.26 6.69 0.00
11 0.33 0.60 0.07 1.85 0.73* 6.42 0.00
12 0.60 1.52 0.33 0.13 0.07* 7.35 0.00
13 0.40 0.99 0.93* 1.13 0.53 6.03 0.00
14 0.20 0.33 0.93* 2.72 0.33 5.50 0.00
15 1.13 0.66 0.33 4.30* 0.93 2.65 0.00
16 0.13 0.60 0.66 0.26* 0.07 8.28 0.00
17 0.93 0.99* 0.93 0.53 0.33 6.29 0.00
18 0.46 5.23 0.86 1.46* 0.60 1.32 0.07
19 0.53 4.50* 0.73 0.66 0.46 3.11 0.00
20 0.93 0.26 0.60* 0.46 0.26 7.48 0.00
21 0.07* 0.66 0.20 0.26 0.00 8.81 0.00
22 1.06 0.53 0.00* 0.13 0.46 7.81 0.00
23 2.45 0.60 0.26* 0.33 0.26 6.09 0.00
24 0.20 0.07 0.46 0.46 0.73* 8.08 0.00
25 0.33 0.40 2.32* 0.13 0.26 6.56 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 Montana
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 1
149.0 124.0 99.0
148.5 123.5 98.5 2
148.0 123.0 98.0
147.5 122.5 97.5 1
147.0 122.0 97.0
146.5 121.5 96.5
146.0 121.0 96.0 1
145.5 120.5 95.5
145.0 120.0 95.0 1 1
144.5 119.5 94.5
144.0 119.0 94.0 3
143.5 118.5 93.5 1
143.0 118.0 93.0
142.5 117.5 92.5 1 3
142.0 117.0 92.0
141.5 116.5 91.5 1 4
141.0 116.0 91.0 1
140.5 115.5 90.5 1 1
140.0 115.0 90.0 2 1
139.5 114.5 89.5
139.0 114.0 89.0 3 2
138.5 113.5 88.5
138.0 113.0 88.0 3
137.5 112.5 87.5 3
137.0 112.0 87.0 1
136.5 111.5 86.5 2 2
136.0 111.0 86.0
135.5 110.5 85.5 3 4
135.0 110.0 85.0 1
134.5 109.5 84.5 1 3
134.0 109.0 84.0 1 1
133.5 108.5 83.5
133.0 108.0 1 83.0 4 3
132.5 107.5 82.5 1
132.0 107.0 82.0 4 1
131.5 106.5 81.5 1 2
131.0 106.0 81.0 2 2
130.5 105.5 80.5 2 2
130.0 105.0 80.0 3
129.5 104.5 79.5 4 2
129.0 104.0 79.0 2
128.5 103.5 78.5 2
128.0 103.0 78.0 1
127.5 102.5 77.5 2 1
127.0 102.0 77.0 4 2
126.5 101.5 76.5 2
126.0 101.0 1 76.0 4 1
125.5 100.5 75.5 1 2
American Mathematics Competitions
2005 AMC 12 B Results for Montana
SCORE DISTRIBUTION
GENDER
Score # Students Score # Students Score # Students
male female male female male female
75.0 1 50.0 25.0
74.5 1 3 49.5 1 24.5
74.0 1 49.0 24.0
73.5 4 48.5 23.5
73.0 1 1 48.0 23.0
72.5 1 1 47.5 22.5
72.0 47.0 22.0
71.5 4 46.5 21.5
71.0 2 6 46.0 1 21.0
70.5 45.5 20.5
70.0 1 1 45.0 20.0
69.5 1 44.5 19.5
69.0 1 44.0 19.0
68.5 1 43.5 18.5
68.0 43.0 18.0
67.5 1 42.5 17.5
67.0 1 42.0 17.0
66.5 41.5 16.5
66.0 41.0 16.0
65.5 40.5 15.5
65.0 2 1 40.0 15.0
64.5 1 1 39.5 14.5
64.0 2 1 39.0 14.0
63.5 38.5 13.5
63.0 38.0 13.0
62.5 37.5 12.5
62.0 37.0 12.0
61.5 36.5 11.5
61.0 1 1 36.0 11.0
60.5 4 35.5 10.5
60.0 35.0 10.0
59.5 34.5 9.5
59.0 1 34.0 9.0
58.5 1 33.5 8.5
58.0 1 33.0 8.0
57.5 32.5 1 7.5
57.0 2 32.0 7.0
56.5 1 31.5 6.5
56.0 1 31.0 6.0
55.5 30.5 5.5
55.0 1 30.0 5.0
54.5 29.5 4.5
54.0 1 29.0 4.0
53.5 28.5 3.5
53.0 2 28.0 3.0
52.5 1 27.5 2.5
52.0 27.0 2.0
51.5 1 1 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 Montana
SCORE DISTRIBUTION
score -----------grade-----------
6 7 8 9 10 11 12 13 unknown
---------------------------
108.0 1
101.0 1
99.5 1
98.5 2
97.5 1
96.0 1
95.0 1 1
94.0 1 2
93.5 1
92.5 3 1
91.5 2 3
91.0 1
90.5 2
90.0 1 2
89.0 1 1 3
88.0 2 1
87.5 1 2
87.0 1
86.5 3 1
85.5 2 5
85.0 1
84.5 2 3
84.0 2
83.0 5 2
82.5 1
82.0 4 1
81.5 2 1
81.0 1 3
80.5 2 2
80.0 1 2
79.5 4 2
79.0 1 1
78.5 1 1
78.0 1
77.5 3
77.0 2 4
76.5 2
76.0 1 4
75.5 3
75.0 1
74.5 1 3
74.0 1
73.5 2 2
73.0 1 1
72.5 1 1
71.5 1 3
71.0 3 6
70.0 1 1
69.5 1
69.0 1
68.5 1
67.5 1
67.0 1
65.0 2 1
64.5 1 1
64.0 1 2
61.0 2
60.5 1 3
59.0 1
58.5 1
58.0 1
57.0 1 1
56.5 1
56.0 1
55.0 1
54.0 1
53.0 2
52.5 1
51.5 1 1
50.5 1
49.5 1
46.0 1
44.0 1
32.5 1
American Mathematics Competitions
2005 AMC 12 B Results for Montana
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 8.42* 0.33 0.38 0.33 0.55 0.00 0.00
2 0.00 0.22 0.16 8.63* 0.22 0.77 0.00
3 0.16 0.00 8.85* 0.22 0.22 0.55 0.00
4 0.16 8.69* 0.11 0.16 0.27 0.60 0.00
5 6.99* 0.05 0.49 0.00 0.16 2.30 0.00
6 1.58* 1.04 0.55 0.22 0.33 6.28 0.00
7 1.09 1.53 0.11 1.26* 0.33 5.68 0.00
8 1.58 1.80 2.90* 0.11 0.87 2.73 0.00
9 0.49 6.17* 0.38 0.55 0.44 1.97 0.00
10 0.11 0.38 0.16 2.73 1.53* 5.08 0.00
11 1.86 0.77 0.60 3.66* 0.60 2.51 0.00
12 0.27 0.66 0.49 0.11* 0.00 8.47 0.00
13 0.05 0.22 0.11 0.16* 0.16 9.29 0.00
14 0.33 1.26 0.38 0.38 0.49* 7.16 0.00
15 0.60 0.16 0.38 4.15* 0.60 4.10 0.00
16 0.05 0.11 0.27 0.16* 0.16 9.23 0.00
17 0.00 0.27* 0.38 0.11 0.33 8.91 0.00
18 1.37 0.22 0.33* 0.27 0.33 7.49 0.00
19 0.11 0.16 0.22 0.16 1.64* 7.70 0.00
20 0.22 0.38 3.99* 0.49 1.64 3.28 0.00
21 0.16 0.11 0.27* 0.05 0.11 9.29 0.00
22 0.77 0.49 0.05 0.22 0.05* 8.42 0.00
23 0.00 0.05* 0.11 0.05 0.05 9.73 0.00
24 0.27* 0.00 0.22 0.16 0.05 9.29 0.00
25 0.05* 0.22 0.05 0.38 0.44 8.85 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column