American Mathematics Competitions
2009 AMC 10 A Results for Massachusetts
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 3110
Number of unofficial participants: 30
Average score of participants: 69.5
Average score for female students is: 64.3 ( 1023 Students)
Average score for male students is: 73.3 ( 1452 Students)
Average score for unspecified gender is 69.4 ( 635 Students)
Average score for grade 10 is: 70.0 ( 1463 Students)
Average score for grade 9 is: 66.1 ( 1156 Students)
Average score for grade 8 and below is: 81.1 ( 236 Students)
Average score with unknown grade: 71.6 ( 255 Students)
AIME qualifying score = 120.0 or better
Number of AIME qualifers 86
Number of schools returning results 101
Average school winning score 111.43
American Mathematics Competitions
2009 AMC 12 A Results for Massachusetts
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 2492
Number of unofficial participants: 60
Average score of participants: 69.7
Average score for female students is: 65.0 ( 841 Students)
Average score for male students is: 73.3 ( 1140 Students)
Average score for unspecified gender is 69.6 ( 511 Students)
Average score for grade 13 is: 81.8 ( 4 Students)
Average score for grade 12 is: 70.6 ( 953 Students)
Average score for grade 11 is: 69.0 ( 1185 Students)
Average score for grade 10 is: 72.4 ( 101 Students)
Average score for grade 9 is: 72.7 ( 29 Students)
Average score for grade 8 and below is: 91.1 ( 4 Students)
Average score with unknown grade: 67.9 ( 216 Students)
AIME qualifying score = 97.5 or better
Number of AIME qualifers 195
Number of schools returning results 92
Average school winning score 101.67
Average school team score 281.79
American Mathematics Competitions
2009 AMC 10 B Results for Massachusetts
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 639
Number of unofficial participants: 0
Average score of participants: 79.5
Average score for female students is: 74.7 ( 191 Students)
Average score for male students is: 85.6 ( 232 Students)
Average score for unspecified gender is 77.2 ( 216 Students)
Average score for grade 10 is: 79.0 ( 274 Students)
Average score for grade 9 is: 81.0 ( 137 Students)
Average score for grade 8 and below is: 90.9 ( 71 Students)
Average score with unknown grade: 74.0 ( 157 Students)
AIME qualifying score = 120.0 or better
Number of AIME qualifers 54
Number of schools returning results 37
Average school winning score 120.32
American Mathematics Competitions
2009 AMC 12 B Results for Massachusetts
GRAND STATISTICS
TOTAL NUMBER of official students taking exam: 873
Number of unofficial participants: 0
Average score of participants: 76.1
Average score for female students is: 68.7 ( 242 Students)
Average score for male students is: 80.7 ( 371 Students)
Average score for unspecified gender is 76.3 ( 260 Students)
Average score for grade 13 is: 112.5 ( 1 Student)
Average score for grade 12 is: 78.0 ( 260 Students)
Average score for grade 11 is: 74.3 ( 368 Students)
Average score for grade 10 is: 87.9 ( 54 Students)
Average score for grade 9 is: 84.4 ( 20 Students)
Average score for grade 8 and below is: 98.5 ( 6 Students)
Average score with unknown grade: 71.1 ( 164 Students)
AIME qualifying score = 100.0 or better
Number of AIME qualifers 125
Number of schools returning results 42
Average school winning score 109.86
Average school team score 301.11
2009 State AMC 12 TEAM Score Distribution
-----------------------------------------------
score A B Rank
-----------------------------------------------
418.5 1 1
390.0 1 1 2
388.5 1 4
387.0 1 5
384.0 1 6
381.0 1 7
376.5 1 8
372.0 1 9
367.5 1 10
364.5 2 11
360.0 1 13
352.5 1 14
351.0 1 15
348.0 2 1 16
340.5 1 1 19
337.5 2 21
334.5 1 23
331.5 1 24
330.0 2 25
328.5 1 3 27
325.5 1 31
322.5 1 32
321.0 1 33
319.5 2 1 34
318.0 3 37
315.0 2 40
313.5 1 2 42
310.5 1 45
309.0 1 1 46
307.5 1 1 48
306.0 1 50
304.5 1 51
303.0 3 52
301.5 1 55
300.0 2 2 56
298.5 1 60
297.0 2 61
295.5 2 63
294.0 1 65
289.5 1 66
288.0 1 2 67
286.5 3 70
285.0 4 1 73
283.5 1 78
277.5 1 79
276.0 5 80
274.5 2 85
273.0 1 87
270.0 2 1 88
268.5 1 91
267.0 1 92
264.0 1 93
261.0 1 94
258.0 1 1 95
256.5 1 1 97
255.0 2 99
253.5 1 101
250.5 1 102
249.0 2 103
247.5 2 105
244.5 1 107
243.0 1 108
241.5 1 109
240.0 1 110
238.5 3 111
237.0 2 114
235.5 2 1 116
234.0 2 119
232.5 1 121
229.5 1 122
228.0 1 123
226.5 1 124
225.0 1 125
223.5 1 126
220.5 1 127
219.0 1 128
213.0 1 129
205.5 1 130
132.0 1 131
115.5 1 132
99.0 1 133
79.5 1 134
2009 AMC Contest Score Distributions
-----------------------------------------------
score 12 A 12 B 10 A 10 B
-----------------------------------------------
150.0 1 1 4 4
145.5 1 1 2
144.0 1 2 2
141.0 2 1
139.5 1 3 5
138.0 4 2
136.5 1 3 1
135.0 2 2 3
133.5 5 4
132.0 3 1 9 6
130.5 1 2 1
129.0 2 2 5 1
127.5 8 1
126.0 2 3 9 4
124.5 1 1 4 4
123.0 4 3 6 6
121.5 3 3 10 3
120.0 3 3 9 5
118.5 2 3 7 4
117.0 4 9 6 4
115.5 6 4 13 2
114.0 7 4 14 6
112.5 8 4 8 5
111.0 9 3 17 4
109.5 8 6 11 2
108.0 14 13 21 8
106.5 8 11 15 6
105.0 13 7 18 6
103.5 18 11 24 4
102.0 6 11 16 9
100.5 21 19 26 5
99.0 23 18 28 12
97.5 22 18 20 11
96.0 26 10 41 11
94.5 42 21 28 4
93.0 24 15 32 3
91.5 25 12 37 8
90.0 43 15 62 18
88.5 37 18 47 10
87.0 45 16 38 7
85.5 43 22 45 16
84.0 50 21 71 19
82.5 66 26 52 12
81.0 59 19 71 24
79.5 48 25 65 16
78.0 72 26 86 22
76.5 71 20 79 13
75.0 59 17 75 16
73.5 73 24 76 12
72.0 95 23 99 19
70.5 74 27 72 19
69.0 111 19 86 14
67.5 81 15 88 21
66.0 96 26 111 26
64.5 85 33 86 17
63.0 101 25 93 17
61.5 91 23 91 19
60.0 96 27 97 17
58.5 82 17 76 9
57.0 61 12 79 12
55.5 52 10 80 7
54.0 66 20 121 11
52.5 57 11 79 4
51.0 36 15 68 11
49.5 48 14 59 10
48.0 40 15 72 11
46.5 36 8 56 4
45.0 20 18 41 7
43.5 25 11 48 5
42.0 35 11 65 10
40.5 17 3 23 5
39.0 17 6 17 1
37.5 13 1 32 4
36.0 16 3 28 2
34.5 7 6 19 2
33.0 7 11 1
31.5 5 4 11
30.0 17 32
28.5 7 2
27.0 5 4
25.5 2 6
24.0 8 1 12
22.5 1 2
21.0 1 1
19.5 1 4
18.0 3
16.5 1 1
13.5 1
12.0 1
6.0 1
American Mathematics Competitions
2009 AMC 10 A Results for Massachusetts
SCORE DISTRIBUTION
score ----gender----------- -----------grade-----------------
male female ? <=6 7 8 9 10 ?
----------------------------------------------------------------------------------------
150.0 3 1 1 1 2
145.5 1 1
144.0 2 1 1
141.0 2 2
139.5 3 1 1 1
138.0 3 1 2 2
136.5 1 1
135.0 1 1 1
133.5 3 1 2 3
132.0 7 3 1 3 2
130.5 1 1 1 1
129.0 3 2 1 2
127.5 7 1 4 3
126.0 6 1 2 3 3 1
124.5 2 2 1 3
123.0 4 2 1 3
121.5 6 2 3 3 3 1
120.0 6 2 1 3 5
118.5 4 1 1 3 2 1
117.0 4 1 3 3
115.5 6 5 2 5 6
114.0 10 2 1 3 2 6 2
112.5 4 3 1 1 5 1
111.0 9 5 1 1 5 8 2
109.5 7 3 1 5 4 1
108.0 17 1 2 2 3 6 7 1
106.5 11 3 1 2 5 7
105.0 10 4 1 1 9 6 1
103.5 11 7 2 5 13 4
102.0 7 2 1 2 1 11 1
100.5 17 4 3 4 16 3
99.0 18 6 1 6 6 14 1
97.5 11 5 2 2 4 10 2
96.0 24 7 1 2 14 20 4
94.5 16 8 2 1 8 16 1
93.0 20 5 1 5 12 11 3
91.5 20 9 2 5 24 6
90.0 34 16 1 1 6 15 32 7
88.5 28 14 3 11 32 1
87.0 20 9 1 1 4 11 18 3
85.5 27 6 3 2 12 23 5
84.0 42 17 3 3 5 24 31 5
82.5 28 13 1 4 17 25 5
81.0 34 18 1 2 4 23 34 7
79.5 26 18 4 20 30 11
78.0 49 18 2 1 7 29 42 5
76.5 34 29 2 2 28 40 7
75.0 39 24 1 3 3 19 42 7
73.5 34 21 1 1 1 28 37 8
72.0 46 30 5 31 54 9
70.5 33 22 1 1 28 31 11
69.0 42 25 2 2 1 36 38 7
67.5 44 31 1 2 40 37 8
66.0 53 38 2 2 5 33 59 10
64.5 40 30 2 4 36 38 6
63.0 42 38 1 2 43 41 6
61.5 33 37 3 1 34 45 8
60.0 36 37 1 1 2 43 39 11
58.5 26 25 1 3 30 29 13
57.0 27 34 2 3 33 34 7
55.5 34 30 1 1 34 39 5
54.0 64 37 2 5 52 54 8
52.5 28 36 1 38 37 3
51.0 26 28 2 2 35 24 5
49.5 17 33 1 1 25 30 2
48.0 36 26 1 1 3 31 32 4
46.5 21 25 1 1 28 25 1
45.0 17 15 1 22 16 2
43.5 17 23 2 24 18 4
42.0 21 29 2 29 29 5
40.5 7 12 10 13
39.0 7 4 11 6
37.5 10 13 10 16 6
36.0 13 11 2 7 18 1
34.5 3 12 1 2 7 8 1
33.0 2 6 6 4 1
31.5 2 8 5 5 1
30.0 11 12 4 15 13
28.5 1 1 2
27.0 2 2 2 2
25.5 2 3 1 5
24.0 4 7 1 8 3
22.5 2 2
19.5 1 3 1 3
18.0 3 1 2
16.5 1 1
6.0 1 1
American Mathematics Competitions
2009 AMC 10 A Results for Massachusetts
Analysis
Table of Item Difficulty for the 2009
American Mathematics Competitions 10/12
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.23 0.58 0.32 6.62 91.70* 0.55 0.00
2 92.35* 1.93 1.06 1.19 1.61 1.83 0.03
3 1.70 8.39 76.01* 5.85 2.99 5.05 0.00
4 33.73* 6.37 5.59 8.20 14.73 31.38 0.00
5 9.74 5.43 5.47 3.57 54.12* 21.64 0.03
6 63.57* 3.41 7.49 3.73 1.22 20.55 0.03
7 5.88 4.05 32.99* 3.86 29.87 23.34 0.00
8 7.81 79.58* 3.54 1.35 1.70 5.98 0.03
9 7.75 25.40* 8.17 5.08 1.19 52.38 0.03
10 4.12 24.50* 5.50 10.80 2.15 52.93 0.00
11 2.41 2.70 4.37 61.58* 1.83 27.11 0.00
12 4.98 6.27 30.93* 7.52 7.88 42.41 0.00
13 20.39 5.21 4.15 10.90 18.30* 41.03 0.03
14 42.64* 1.32 5.69 3.79 10.90 35.63 0.03
15 2.19 3.73 4.66 6.69 48.84* 33.83 0.06
16 23.70 5.05 3.67 14.08* 4.82 48.65 0.03
17 3.99 11.06 9.36* 2.70 4.63 68.20 0.06
18 16.78 12.54 7.62 19.58* 7.01 36.43 0.03
19 5.21 12.96* 8.55 8.17 1.90 63.18 0.03
20 7.11 8.30 8.17 38.91* 2.48 35.02 0.03
21 3.31 2.51 12.86* 3.92 2.89 74.47 0.03
22 5.56 5.50 29.61 7.68* 2.99 48.59 0.06
23 3.95 3.18 5.05 2.83 9.39* 75.50 0.10
24 7.27 12.89 7.65* 4.53 7.23 60.42 0.00
25 7.04 5.37* 5.82 4.15 3.83 73.79 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
2009 AMC 12 A Results for Massachusetts
SCORE DISTRIBUTION
score ----gender----------- -----------grade-----------------
male female ? <=6 7 8 9 10 11 12 13 ?
----------------------------------------------------------------------------------------
150.0 1 1
145.5 1 1
144.0 1 1
139.5 1
136.5 1 1
135.0 2 1 1
132.0 2 1 1 2
130.5 1
129.0 2 2
126.0 2 1 1
124.5 1 1
123.0 3 1 2 2
121.5 3 2 1
120.0 1 1 3
118.5 1 1 2
117.0 3 2 1 1
115.5 4 1 3 1 1
114.0 4 1 2 2 3
112.5 5 4 2 2
111.0 8 1 1 5 3
109.5 5 1 1 5 1 1
108.0 6 7 1 6 7
106.5 4 4 1 1 4 2
105.0 6 3 3 5 5
103.5 10 6 1 9 8
102.0 4 2 3 1
100.5 12 5 10 10 1
99.0 18 2 1 2 7 12 1
97.5 11 3 1 1 9 10 1
96.0 14 6 1 10 12 3
94.5 21 13 2 19 18 3
93.0 14 6 2 9 12 1
91.5 14 5 1 15 9
90.0 24 8 2 21 14 1 5
88.5 28 7 1 2 19 14 1
87.0 23 11 1 24 16 4
85.5 23 12 1 19 18 1 4
84.0 31 12 2 25 20 3
82.5 36 13 1 4 22 29 10
81.0 27 18 2 1 29 24 3
79.5 23 15 1 28 15 4
78.0 35 28 2 34 30 6
76.5 37 22 1 2 32 30 6
75.0 29 15 1 1 28 19 10
73.5 35 15 2 36 23 12
72.0 46 32 2 1 48 37 7
70.5 37 25 1 7 31 31 4
69.0 48 33 3 3 46 47 12
67.5 39 28 1 3 39 32 6
66.0 39 31 2 3 44 33 14
64.5 37 34 1 1 41 37 5
63.0 46 33 3 3 42 45 8
61.5 41 30 1 1 53 28 8
60.0 34 39 2 4 35 43 12
58.5 29 40 49 29 4
57.0 24 23 1 2 38 16 4
55.5 22 21 4 28 17 3
54.0 23 27 2 30 25 9
52.5 19 28 3 27 22 5
51.0 15 15 3 21 10 2
49.5 18 20 1 2 21 20 4
48.0 16 16 1 1 19 14 5
46.5 11 17 2 19 12 3
45.0 7 7 11 7 2
43.5 12 13 2 12 11
42.0 9 17 1 1 18 8 7
40.5 2 11 2 9 6
39.0 7 7 1 8 7 1
37.5 5 4 1 5 6 1
36.0 4 9 8 6 1 1
34.5 2 4 2 3 1 1
33.0 1 5 5 1 1
31.5 1 2 2 1 2
30.0 7 6 2 5 8 2
28.5 1 6 4 3
27.0 2 3 1 2 2
25.5 2 2
24.0 1 5 1 4 3
22.5 1 1
21.0 1 1
19.5 1 1
16.5 1 1
13.5 1 1
American Mathematics Competitions
2009 AMC 12 A Results for Massachusetts
Analysis
Table of Item Difficulty for the 2009
American Mathematics Competitions 10/12
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 89.37* 6.86 0.72 0.44 1.48 1.08 0.04
2 0.88 4.17 89.53* 2.85 1.36 1.20 0.00
3 5.18 82.46* 2.57 4.49 2.69 2.53 0.08
4 95.26* 0.64 0.52 0.96 1.44 1.16 0.00
5 1.65 1.81 2.17 85.23* 1.32 7.78 0.04
6 20.14 5.30 3.53 11.44 39.89* 19.62 0.08
7 2.37 31.10* 5.38 3.09 2.57 55.42 0.08
8 64.21* 1.40 5.38 3.33 8.47 17.22 0.00
9 2.45 4.09 4.65 37.08* 5.74 45.91 0.08
10 3.13 5.74 42.46* 8.31 6.34 33.95 0.08
11 1.97 2.73 3.01 5.70 70.87* 15.57 0.16
12 12.36 30.18* 5.62 6.86 2.73 42.26 0.00
13 8.83 10.83 13.16 21.23* 5.66 40.17 0.12
14 3.45 7.87* 7.95 9.51 5.30 65.93 0.00
15 6.90 4.21 6.90 29.78* 4.86 47.35 0.00
16 11.96 7.10 6.70 8.75* 3.57 61.92 0.00
17 5.74 3.89 9.51* 3.89 6.30 70.67 0.00
18 13.12 6.34* 4.70 2.93 4.17 68.74 0.00
19 7.26 6.30 9.07* 6.10 5.58 65.57 0.12
20 2.53 2.65 6.34 3.57 9.91* 75.00 0.00
21 4.65 3.85 5.66* 3.21 3.61 79.01 0.00
22 3.05 3.65 3.69 4.17 2.53* 82.91 0.00
23 1.40 2.81 4.25 2.93* 1.20 87.40 0.00
24 6.94 4.41 3.33 3.65 1.89* 79.70 0.08
25 2.89* 3.57 4.21 5.14 6.66 77.53 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
2009 AMC 10 B Results for Massachusetts
SCORE DISTRIBUTION
score ----gender----------- -----------grade-----------------
male female ? <=6 7 8 9 10 ?
----------------------------------------------------------------------------------------
150.0 3 1 3
145.5 2 1 1
144.0 2 1 1
141.0 1 1
139.5 5 1 1 3
138.0 1 2
135.0 1 2 3
133.5 2 1 1 1 1
132.0 4 2 3 2 1
130.5 1 1
129.0 1 1
127.5 1 1
126.0 1 1 1 1 1 1
124.5 2 2 1 2 1
123.0 2 2 1 2 3
121.5 1 2 2 1
120.0 1 1 2 1 1 1
118.5 2 1 2 1
117.0 1 2 2 1 1
115.5 2 1 1
114.0 5 1 5
112.5 1 1 2 1 2
111.0 3 1 1 1 2
109.5 1 1 2
108.0 5 1 2 2 1 1 2
106.5 4 1 1 4 1
105.0 4 2 1 1 4
103.5 1 1 1 2 1
102.0 5 1 1 4 3
100.5 3 1 1 1 2 1
99.0 5 1 2 4 3 3
97.5 2 2 3 2 6
96.0 9 3 3 3 2
94.5 2 3 1
93.0 1 1 2 1
91.5 3 2 1 1 1 2 3
90.0 6 3 2 1 3 6 6
88.5 6 4 2 1 7
87.0 2 1 1 1 3 2
85.5 7 4 1 2 9 4
84.0 3 6 1 2 3 7 6
82.5 8 2 1 2 8 1
81.0 5 9 1 1 4 9 9
79.5 5 6 2 10 4
78.0 7 10 1 1 9 8 3
76.5 3 4 1 2 2 4 4
75.0 3 7 3 10 3
73.5 3 5 1 2 4 5
72.0 7 8 6 10 3
70.5 6 5 8 4 7
69.0 6 2 2 9 3
67.5 5 7 1 5 7 8
66.0 8 10 3 7 9 7
64.5 9 3 2 1 10 4
63.0 3 8 5 8 4
61.5 8 3 1 1 1 2 7 7
60.0 4 8 1 1 2 9 4
58.5 1 3 1 3 5
57.0 4 4 2 5 5
55.5 1 1 1 1 5
54.0 4 5 3 6 2
52.5 2 4
51.0 3 6 1 3 5 2
49.5 2 1 3 1 6
48.0 5 2 1 1 1 3 3 2
46.5 4 4
45.0 1 4 4 1 2
43.5 2 2 3
42.0 2 4 1 1 2 4 2
40.5 4 5
39.0 1 1
37.5 1 3 2 2
36.0 2 1 1
34.5 1 1 1
33.0 1 1
21.0 1 1
American Mathematics Competitions
2009 AMC 10 B Results for Massachusetts
Analysis
Table of Item Difficulty for the 2009
American Mathematics Competitions 10/12
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.47 78.40* 5.63 11.89 1.88 1.72 0.00
2 0.63 0.78 94.99* 0.63 0.31 2.66 0.00
3 0.63 2.19 81.53* 11.11 0.94 3.60 0.00
4 1.10 1.88 79.97* 9.86 0.78 6.42 0.00
5 5.95 1.88 16.28 66.04* 1.41 8.45 0.00
6 0.94 1.72 4.07 79.81* 2.19 11.27 0.00
7 8.92 14.55 61.35* 6.73 4.07 4.23 0.16
8 3.44 50.39* 8.61 18.78 3.91 14.87 0.00
9 48.51* 2.97 5.16 8.76 2.97 31.61 0.00
10 6.73 1.10 3.29 3.76 57.12* 28.01 0.00
11 69.64* 5.32 2.82 3.44 2.19 16.59 0.00
12 36.31* 11.74 7.36 12.52 8.45 23.63 0.00
13 2.97 13.93 48.98* 7.04 6.89 20.19 0.00
14 7.04 20.03 20.03 20.50* 7.67 24.73 0.00
15 5.01 6.26 3.13 4.54 58.84* 22.22 0.00
16 3.76 19.72* 1.88 4.38 5.32 64.95 0.00
17 14.08 9.08 31.30* 2.19 0.16 43.19 0.00
18 2.66 5.32 5.79 21.60* 2.82 61.82 0.00
19 27.23* 16.28 9.86 6.73 5.32 34.43 0.16
20 4.07 20.34* 6.57 2.19 1.56 65.26 0.00
21 6.57 14.71 4.38 16.90* 2.66 54.62 0.16
22 2.97 8.61* 3.76 3.44 2.35 78.87 0.00
23 3.13 7.51 12.21* 4.23 4.54 68.39 0.00
24 18.47* 2.97 2.50 3.29 4.69 68.08 0.00
25 15.49 12.83* 7.67 4.54 3.29 56.18 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
2009 AMC 12 B Results for Massachusetts
SCORE DISTRIBUTION
score ----gender----------- -----------grade-----------------
male female ? <=6 7 8 9 10 11 12 13 ?
----------------------------------------------------------------------------------------
150.0 1 1
136.5 1 1 1 1 1
132.0 1 1
129.0 1 1 1 1
126.0 1 2 1
124.5 1 1
123.0 2 1 2
121.5 2 1 1 2
120.0 2 1 1 1 1
118.5 2 1 2
117.0 4 2 1 4 3 1
115.5 2 1 2 1
114.0 3 1 1 2 1
112.5 3 1 2 1
111.0 3 1 1 1
109.5 2 2 1 1 1 2 1
108.0 7 3 1 7 5
106.5 9 1 2 5 4
105.0 2 3 1 4 1 1
103.5 6 2 1 4 5 1
102.0 8 1 1 3 6
100.5 8 5 2 8 8 1
99.0 6 5 2 8 4 4
97.5 9 2 1 1 7 5 4
96.0 2 1 1 1 3 4 1
94.5 15 1 1 9 7 3
93.0 6 5 1 8 4 2
91.5 11 1 2 7 3
90.0 8 2 1 1 6 4 3
88.5 11 3 1 1 7 6 3
87.0 4 4 2 10 2 2
85.5 9 7 6 12 4
84.0 11 5 2 1 8 5 5
82.5 12 8 1 1 4 6 9 5
81.0 9 3 1 1 5 8 4
79.5 9 6 1 10 7 7
78.0 11 6 11 9 6
76.5 6 6 2 5 8 5
75.0 11 2 1 2 5 6 3
73.5 8 10 3 8 7 6
72.0 7 6 9 5 9
70.5 13 4 1 12 8 6
69.0 9 4 8 5 6
67.5 5 5 9 3 3
66.0 13 6 2 9 8 7
64.5 20 5 2 13 11 7
63.0 9 5 1 2 9 7 6
61.5 9 8 2 8 6 7
60.0 11 7 3 12 5 7
58.5 2 7 1 6 5 5
57.0 4 6 1 5 4 2
55.5 4 4 8 1 1
54.0 9 8 1 11 6 2
52.5 1 6 5 3 3
51.0 7 4 8 4 3
49.5 4 5 1 1 5 3 4
48.0 4 8 9 3 3
46.5 1 6 4 3 1
45.0 4 10 11 5 2
43.5 6 5 4 2
42.0 1 9 1 7 2 1
40.5 1 2 3
39.0 1 4 4 2
37.5 1 1
36.0 1 1 2 1
34.5 1 1 1 1 4
31.5 1 3 3 1
24.0 1 1
12.0 1 1
American Mathematics Competitions
2009 AMC 12 B Results for Massachusetts
Analysis
Table of Item Difficulty for the 2009
American Mathematics Competitions 10/12
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.57 85.91* 4.58 6.87 1.83 0.11 0.11
2 0.57 1.60 83.96* 11.57 0.46 1.83 0.00
3 5.38 0.80 12.60 76.63* 1.26 3.09 0.23
4 1.72 1.60 84.54* 8.82 1.37 1.95 0.00
5 0.80 0.92 3.21 86.60* 2.18 6.30 0.00
6 8.02 11.80 69.99* 5.38 2.41 2.18 0.23
7 2.98 64.95* 7.10 15.69 2.86 6.41 0.00
8 3.78 4.12 1.95 2.18 74.91* 13.06 0.00
9 61.97* 4.12 2.52 6.41 0.57 24.40 0.00
10 49.14* 14.78 9.39 5.84 2.63 18.10 0.11
11 2.98 24.74 18.21 26.46* 7.67 19.82 0.11
12 3.09 2.75 3.21 2.52 42.84* 45.59 0.00
13 3.44 4.12 5.15 31.27* 6.99 48.91 0.11
14 8.36 7.22 45.82* 1.26 0.80 36.43 0.11
15 1.37 52.00* 5.96 5.84 4.58 30.24 0.00
16 2.52 8.25* 3.78 2.63 1.26 81.56 0.00
17 17.64 20.62* 7.56 4.58 5.38 44.10 0.11
18 4.70 7.79 14.09* 5.04 4.58 63.80 0.00
19 1.49 2.75 3.09 1.60 6.30* 84.77 0.00
20 3.21 3.44 4.35* 2.06 2.52 84.42 0.00
21 8.25* 3.67 4.01 9.16 17.07 57.85 0.00
22 2.18 2.41 4.70* 4.70 0.69 85.22 0.11
23 1.83 2.98 2.86 3.78* 2.06 86.48 0.00
24 6.19 5.04* 3.09 3.67 1.15 80.87 0.00
25 5.84 2.63 4.12 2.29 3.21* 81.90 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column