American Mathematics Competitions
GRAND STATISTICS
2011 AMC 10 A Results
TOTAL NUMBER of official students taking exam: 70919
Number of unofficial participants: 483
Average score of participants: 67.7
Average score for female students is: 62.2 ( 25692 Students)
Average score for male students is: 73.0 ( 32739 Students)
Average score for unspecified gender is 65.1 ( 12488 Students)
Average score for grade 10 is: 70.5 ( 35727 Students)
Average score for grade 9 is: 62.4 ( 24410 Students)
Average score for grade 8 and below is: 81.3 ( 5018 Students)
Average score with unknown grade: 60.8 ( 5764 Students)
AIME qualifying score = 117.0 or better
Number of AIME qualifers 3128
Number of schools returning results 2451
Average school winning score 101.88
American Mathematics Competitions
GRAND STATISTICS
2011 AMC 12 A Results
TOTAL NUMBER of official students taking exam: 74665
Number of unofficial participants: 472
Average score of participants: 66.8
Average score for female students is: 62.5 ( 26418 Students)
Average score for male students is: 70.0 ( 37477 Students)
Average score for unspecified gender is 66.2 ( 10770 Students)
Average score for grade 13 is: 67.9 ( 66 Students)
Average score for grade 12 is: 67.7 ( 29957 Students)
Average score for grade 11 is: 66.3 ( 34889 Students)
Average score for grade 10 is: 68.3 ( 4469 Students)
Average score for grade 9 is: 65.7 ( 1348 Students)
Average score for grade 8 and below is: 73.8 ( 214 Students)
Average score with unknown grade: 62.8 ( 3722 Students)
AIME qualifying score = 93.0 or better
Number of AIME qualifers 4768
Number of schools returning results 2622
Average school winning score 92.32
Average school team score 250.95
American Mathematics Competitions
GRAND STATISTICS
2011 AMC 10 B Results
TOTAL NUMBER of official students taking exam: 33723
Number of unofficial participants: 371
Average score of participants: 72.2
Average score for female students is: 66.7 ( 12088 Students)
Average score for male students is: 75.9 ( 15097 Students)
Average score for unspecified gender is 73.8 ( 6538 Students)
Average score for grade 10 is: 73.9 ( 16661 Students)
Average score for grade 9 is: 66.6 ( 10249 Students)
Average score for grade 8 and below is: 78.7 ( 3477 Students)
Average score with unknown grade: 74.2 ( 3336 Students)
AIME qualifying score = 117.0 or better
Number of AIME qualifers 2038
Number of schools returning results 1263
Average school winning score 100.13
American Mathematics Competitions
GRAND STATISTICS
2011 AMC 12 B Results
TOTAL NUMBER of official students taking exam: 30846
Number of unofficial participants: 221
Average score of participants: 64.9
Average score for female students is: 58.7 ( 9987 Students)
Average score for male students is: 68.3 ( 15095 Students)
Average score for unspecified gender is 67.0 ( 5764 Students)
Average score for grade 13 is: 70.5 ( 86 Students)
Average score for grade 12 is: 63.7 ( 9959 Students)
Average score for grade 11 is: 63.9 ( 14251 Students)
Average score for grade 10 is: 69.7 ( 2429 Students)
Average score for grade 9 is: 69.7 ( 903 Students)
Average score for grade 8 and below is: 75.9 ( 326 Students)
Average score with unknown grade: 67.6 ( 2892 Students)
AIME qualifying score = 97.5 or better
Number of AIME qualifers 2383
Number of schools returning results 1447
Average school winning score 91.60
Average school team score 238.72
2011 AMC Contest Score Distributions
-----------------------------------------------
score 12A 12B 10A 10B
-----------------------------------------------
150.0 4 5 16 26
148.5
147.0
145.5 1 9 24 5
144.0 7 10 29 60
142.5
141.0 1 3 50 7
139.5 10 29 32
138.0 6 9 46 93
136.5 9 13 57 10
135.0 6 19 81 46
133.5 1 5 33 45
132.0 16 33 182 173
130.5 12 13 97 63
129.0 9 17 104 82
127.5 31 15 159 104
126.0 38 50 355 240
124.5 15 20 172 101
123.0 43 40 246 115
121.5 71 46 323 158
120.0 65 50 483 344
118.5 72 53 242 131
117.0 72 64 400 203
115.5 46 62 332 246
114.0 127 113 636 514
112.5 98 71 419 199
111.0 91 84 460 241
109.5 148 107 454 274
108.0 211 151 732 569
106.5 115 142 454 226
105.0 195 155 551 293
103.5 222 141 577 341
102.0 314 242 781 633
100.5 345 215 540 276
99.0 370 218 654 362
97.5 307 197 660 353
96.0 588 287 920 640
94.5 645 351 699 350
93.0 464 277 728 372
91.5 578 342 713 431
90.0 909 446 1027 690
88.5 870 450 745 367
87.0 937 390 819 436
85.5 1014 399 891 529
84.0 1384 520 1155 796
82.5 1444 518 932 437
81.0 1534 529 1000 482
79.5 1563 455 1092 557
78.0 2047 678 1329 767
76.5 2167 639 1072 548
75.0 2108 607 1189 567
73.5 2306 600 1256 587
72.0 3091 818 1609 893
70.5 2769 716 1252 593
69.0 2767 729 1384 591
67.5 3012 780 1546 659
66.0 3620 1003 1969 921
64.5 3039 804 1539 661
63.0 3013 809 1641 650
61.5 2781 854 1725 706
60.0 3368 1087 2108 1020
58.5 2527 847 1808 687
57.0 2274 873 1778 730
55.5 2201 907 1798 739
54.0 2743 1095 2192 917
52.5 1862 827 1779 654
51.0 1627 806 1772 694
49.5 1561 789 1730 653
48.0 1829 985 2157 864
46.5 1088 760 1514 596
45.0 986 704 1577 547
43.5 847 659 1417 547
42.0 1047 811 1804 721
40.5 539 485 1150 380
39.0 435 421 1068 396
37.5 439 416 1009 380
36.0 526 531 1248 519
34.5 185 243 659 233
33.0 156 209 568 225
31.5 148 170 547 206
30.0 248 292 753 328
28.5 53 101 332 130
27.0 24 68 257 121
25.5 47 65 234 69
24.0 101 119 415 199
22.5 10 33 114 63
21.0 12 23 102 54
19.5 9 27 79 43
18.0 31 49 159 98
16.5 1 11 24 15
15.0 10 23 15
13.5 3 7 21 13
12.0 11 16 65 49
10.5 3 10 3
9.0 2 8 3
7.5 5 6 3
6.0 2 5 17 11
4.5 2 1
3.0 1
1.5
4 1 5 1
American Mathematics Competitions
SCORE DISTRIBUTION
2011 AMC 10 A Results
GENDER and GRADES
score ----gender----------- -----------------grade-----------------
male female ?
American Mathematics Competitions
SCORE DISTRIBUTION
2011 AMC 12 A Results
GENDER and GRADES
score ----gender------------ ---------------------------grade---------------------------
male female ?
American Mathematics Competitions
SCORE DISTRIBUTION
2011 AMC 10 B Results
GENDER and GRADES
score ----gender----------- -----------------grade-----------------
male female ?
American Mathematics Competitions
SCORE DISTRIBUTION
2011 AMC 12 B Results
GENDER and GRADES
score ----gender------------ ---------------------------grade---------------------------
male female ?
American Mathematics Competitions
Analysis
2011 AMC 10 A Results
Table of Item Difficulty for the 2011
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.43 0.61 11.48 84.97* 1.67 0.84 0.01
2 0.36 0.69 1.03 10.35 87.13* 0.41 0.03
3 1.68 4.15 5.84 60.97* 2.94 24.39 0.03
4 58.63* 5.41 6.72 5.00 3.46 20.75 0.03
5 3.88 18.43 55.88* 3.22 2.05 16.50 0.04
6 12.86 10.95 31.27* 17.20 4.52 23.15 0.05
7 5.18 40.38* 44.64 1.32 1.50 6.96 0.02
8 4.74 18.76 61.63* 2.08 2.66 10.11 0.02
9 33.85* 7.43 4.80 5.26 6.28 42.35 0.04
10 5.37 24.77* 5.95 12.24 13.63 38.01 0.03
11 8.35 28.64* 5.93 6.64 3.03 47.38 0.03
12 70.56* 2.41 3.46 6.44 2.71 14.39 0.03
13 28.78* 12.36 12.42 9.38 3.84 33.17 0.05
14 13.07 29.40* 11.96 3.51 3.06 38.97 0.03
15 4.98 6.56 32.34* 4.76 2.54 48.81 0.02
16 16.40 15.68* 3.73 4.38 18.71 41.07 0.03
17 1.65 2.98 65.56* 2.63 1.30 25.86 0.02
18 5.90 4.35 19.35* 11.96 6.49 51.91 0.04
19 5.01 7.14 6.20 4.40 9.39* 67.82 0.03
20 11.08 4.21 8.80 8.93* 11.75 55.17 0.05
21 6.07 6.13 8.32 6.93* 8.35 64.16 0.03
22 4.20 9.00 7.49* 6.11 6.58 66.58 0.03
23 6.60 5.10 18.46* 7.59 8.08 54.11 0.05
24 2.02 3.86 4.77 3.45* 2.72 83.15 0.02
25 2.51 4.08 4.06* 3.98 2.26 83.10 0.02
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
American Mathematics Competitions
Analysis
2011 AMC 12 A Results
Table of Item Difficulty for the 2011
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.32 0.42 7.98 89.73* 1.02 0.52 0.01
2 0.07 0.13 0.65 0.38 98.64* 0.12 0.01
3 0.24 0.52 0.94 7.89 90.10* 0.28 0.03
4 2.26 12.28 73.20* 2.17 1.34 8.73 0.02
5 4.04 14.43 71.92* 1.47 2.10 6.03 0.02
6 81.30* 1.58 2.39 4.48 1.57 8.67 0.02
7 4.86 33.11* 6.28 11.81 11.23 32.68 0.04
8 1.00 2.12 79.88* 1.89 0.91 14.19 0.01
9 5.81 20.35* 8.10 9.21 28.81 27.67 0.04
10 15.17 42.20* 11.63 3.45 2.49 25.03 0.02
11 5.07 4.08 29.21* 17.32 8.34 35.94 0.04
12 4.99 6.35 5.26 18.78* 25.99 38.57 0.05
13 34.67 8.25* 4.52 10.90 2.84 38.80 0.02
14 3.03 5.92 5.52 5.73 9.01* 70.75 0.03
15 11.00* 3.29 15.75 4.07 2.38 63.48 0.03
16 3.55 10.18 8.11* 6.15 7.85 64.13 0.04
17 3.51 4.73 5.65 11.38* 4.72 69.98 0.03
18 3.92 5.59 10.95 24.59* 2.22 52.70 0.04
19 5.07 4.72 9.74* 2.88 1.55 75.99 0.04
20 6.04 11.86 6.83* 3.52 2.40 69.34 0.02
21 1.91* 3.52 3.41 3.54 2.31 85.28 0.03
22 2.12 3.63 4.19* 3.42 1.62 84.98 0.02
23 2.78 3.80 4.75* 2.88 2.07 83.68 0.03
24 4.25 6.07 6.56* 3.71 6.16 73.22 0.03
25 4.54 5.11 4.35 3.14* 9.94 72.88 0.03
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
American Mathematics Competitions
Analysis
2011 AMC 10 B Results
Table of Item Difficulty for the 2011
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 5.63 1.12 90.80* 0.85 0.21 1.39 0.00
2 12.27 2.58 3.59 3.59 75.74* 2.21 0.02
3 77.23* 5.90 3.90 4.59 1.68 6.70 0.01
4 5.79 5.14 65.07* 22.12 0.19 1.68 0.01
5 6.52 4.26 2.54 4.48 57.23* 24.94 0.04
6 78.61* 3.04 3.75 5.49 2.06 7.04 0.01
7 29.67 49.80* 5.36 2.59 4.64 7.92 0.01
8 24.70 67.46* 1.32 1.17 3.19 2.13 0.04
9 11.80 2.65 4.52 45.03* 3.23 32.75 0.02
10 10.68 43.38* 12.72 7.89 6.72 18.58 0.01
11 6.61 3.03 49.19 27.20* 3.45 10.50 0.02
12 40.04* 8.86 2.29 5.37 1.93 41.46 0.04
13 10.23 21.23 7.11 26.56* 8.05 26.80 0.01
14 6.67 6.89 44.52* 5.35 5.05 31.48 0.03
15 6.21 8.21 7.78 8.80 50.59* 18.34 0.06
16 30.32* 10.76 9.85 5.35 2.30 41.40 0.01
17 5.10 4.18 35.11* 9.66 11.15 34.77 0.02
18 1.77 5.34 18.68 20.52 27.08* 26.60 0.02
19 27.24* 10.46 3.70 7.27 11.25 40.02 0.06
20 4.27 16.96 16.53* 4.10 3.46 54.67 0.02
21 11.37 13.25* 6.21 5.31 3.06 60.78 0.03
22 6.96* 7.00 7.58 4.16 3.88 70.39 0.03
23 31.84 6.36 5.73 9.64* 4.08 42.29 0.05
24 7.94 4.98* 8.71 8.30 4.25 65.81 0.03
25 2.39 4.21 6.36 6.47* 4.42 76.15 0.01
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
American Mathematics Competitions
Analysis
2011 AMC 12 B Results
Table of Item Difficulty for the 2011
Tabulation of responses for all Participants
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 2.50 0.82 95.12* 0.61 0.12 0.82 0.01
2 7.42 1.43 2.60 2.82 84.47* 1.23 0.03
3 3.89 5.06 73.42* 16.49 0.10 1.02 0.02
4 4.22 3.16 1.64 3.76 69.35* 17.80 0.06
5 48.44* 2.61 1.87 27.06 12.12 7.87 0.03
6 1.76 5.47 48.33* 5.16 10.02 29.18 0.07
7 8.12 60.76* 3.15 9.53 2.52 15.89 0.02
8 49.94* 7.83 2.92 5.13 1.64 32.48 0.06
9 9.74 14.76 6.77 44.25* 6.92 17.53 0.03
10 2.02 5.51 19.28 22.18 33.62* 17.33 0.06
11 9.63 32.70* 10.14 14.59 5.16 27.73 0.05
12 40.95* 8.56 11.06 5.57 2.17 31.65 0.03
13 10.96 18.85* 6.52 5.79 2.75 55.12 0.02
14 2.40 6.44 4.01 10.93* 8.69 67.48 0.05
15 11.09 13.08 9.05 14.42* 4.35 47.96 0.04
16 4.38 20.24 20.88* 4.36 2.92 47.19 0.03
17 2.73 14.60* 8.51 5.38 6.82 61.92 0.04
18 10.94* 5.85 8.41 4.38 4.43 65.96 0.04
19 8.58 6.38* 8.93 8.90 3.39 63.78 0.03
20 3.49 4.95 6.28* 4.97 3.21 77.05 0.05
21 3.94 5.54 6.83 7.42* 1.49 74.75 0.03
22 2.18 3.73 5.06 5.14* 3.04 80.81 0.05
23 4.57 6.25 9.75* 5.83 3.53 70.01 0.06
24 3.38 3.22* 4.38 4.20 3.41 81.37 0.04
25 3.41 5.66 4.67 3.83* 2.98 79.43 0.02
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
American Mathematics Competitions
Analysis
2011 AMC 10 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 35727 Student(s), Grade 10^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.43 0.55 10.88 85.95* 1.48 0.70 0.01
2 0.31 0.65 0.98 9.90 87.86* 0.29 0.02
3 1.38 3.88 5.28 65.52* 2.83 21.09 0.02
4 62.40* 4.57 6.33 4.51 3.39 18.76 0.03
5 3.29 16.21 60.54* 2.85 2.02 15.03 0.05
6 11.98 11.78 32.12* 17.43 4.87 21.77 0.06
7 3.76 45.79* 43.01 1.09 1.19 5.13 0.02
8 4.58 17.41 64.30* 1.97 2.61 9.11 0.03
9 37.76* 7.24 4.57 4.97 6.98 38.47 0.03
10 5.51 27.30* 5.67 12.29 13.06 36.15 0.02
11 8.67 32.82* 5.35 6.64 2.86 43.63 0.04
12 72.59* 2.12 3.07 6.00 2.55 13.65 0.02
13 29.86* 12.38 12.23 9.06 3.66 32.76 0.04
14 13.53 32.15* 11.41 3.45 2.89 36.54 0.04
15 4.57 5.89 35.08* 4.55 2.47 47.43 0.02
16 16.24 20.64* 3.33 4.15 18.78 36.83 0.04
17 1.48 2.62 67.83* 2.48 1.14 24.43 0.02
18 5.42 4.42 23.89* 12.38 6.60 47.25 0.04
19 4.93 7.05 6.06 4.44 9.26* 68.22 0.03
20 11.93 4.09 9.11 9.40* 11.95 53.44 0.07
21 5.78 6.16 8.29 6.67* 8.12 64.94 0.04
22 4.03 9.19 7.35* 6.19 6.73 66.48 0.02
23 6.48 4.99 19.62* 7.48 7.92 53.46 0.06
24 1.94 4.05 4.94 3.50* 2.81 82.72 0.03
25 2.32 4.09 4.18* 4.19 2.19 83.00 0.02
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 24410 Student(s), Grade 9^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.40 0.69 12.80 83.40* 1.83 0.88 0.00
2 0.44 0.74 1.10 11.31 85.89* 0.49 0.03
3 2.01 4.41 6.78 53.08* 3.10 30.59 0.03
4 51.24* 6.56 7.56 5.78 3.67 25.17 0.02
5 4.85 22.20 47.92* 3.74 2.01 19.27 0.01
6 13.86 10.43 27.85* 17.74 4.39 25.69 0.05
7 7.00 31.45* 49.11 1.62 1.66 9.15 0.01
8 5.17 21.30 56.79* 2.26 2.76 11.70 0.01
9 27.34* 7.79 5.19 5.74 5.67 48.24 0.04
10 5.29 19.93* 6.36 12.37 14.01 42.02 0.02
11 8.12 20.65* 6.75 6.69 3.42 54.35 0.02
12 67.12* 2.82 3.97 7.14 3.06 15.86 0.03
13 25.31* 11.92 12.79 9.95 4.24 35.75 0.05
14 12.43 23.81* 12.40 3.66 3.36 44.33 0.02
15 5.76 7.53 25.76* 5.18 2.72 53.03 0.02
16 17.01 8.87* 3.95 4.65 18.87 46.64 0.02
17 1.89 3.47 61.75* 2.83 1.44 28.61 0.01
18 6.53 4.29 11.44* 11.34 6.33 60.05 0.02
19 5.21 7.36 6.46 4.25 7.74* 68.95 0.03
20 9.51 4.45 8.59 7.68* 11.72 58.02 0.02
21 6.35 6.22 8.19 6.75* 8.19 64.28 0.02
22 4.38 8.25 7.38* 6.05 5.76 68.15 0.03
23 6.81 5.24 15.75* 7.49 8.34 56.33 0.04
24 1.97 3.64 4.40 3.15* 2.41 84.43 0.01
25 2.60 4.08 3.78* 3.58 2.22 83.74 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 5018 Student(s), Grades 8 and Below^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.26 0.26 6.82 90.85* 1.24 0.56 0.02
2 0.18 0.42 0.66 5.10 93.52* 0.10 0.02
3 1.22 4.40 3.47 76.52* 1.51 12.83 0.04
4 76.40* 3.65 4.30 3.67 2.79 9.15 0.04
5 2.25 11.78 70.23* 2.31 2.51 10.88 0.04
6 12.26 7.69 48.72* 11.74 2.31 17.20 0.08
7 5.38 53.39* 31.98 1.10 1.85 6.28 0.02
8 3.19 11.08 75.11* 1.63 2.25 6.70 0.04
9 44.36* 5.68 3.73 4.70 4.76 36.69 0.08
10 4.62 37.35* 4.20 10.24 16.50 27.02 0.06
11 6.10 48.01* 4.11 6.04 1.83 33.88 0.04
12 79.53* 1.77 2.33 5.46 1.59 9.29 0.02
13 44.70* 15.01 10.56 7.09 2.45 20.17 0.02
14 12.83 43.88* 11.34 2.63 2.47 26.80 0.04
15 2.69 5.16 52.03* 3.91 1.87 34.34 0.00
16 13.19 22.62* 4.30 4.50 16.44 38.92 0.02
17 1.08 2.27 74.95* 2.19 1.04 18.45 0.02
18 4.96 3.85 35.73* 10.40 5.82 39.22 0.02
19 4.18 6.40 5.26 4.70 20.84* 58.57 0.04
20 14.25 3.65 7.07 13.65* 9.90 51.39 0.08
21 5.50 5.22 9.25 10.18* 10.70 59.13 0.02
22 4.36 11.76 9.49* 5.18 9.90 59.23 0.08
23 5.98 5.10 27.46* 8.89 7.35 45.12 0.10
24 2.11 3.41 4.90 4.60* 3.13 81.83 0.02
25 2.07 4.05 4.13* 4.13 2.67 82.94 0.02
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 32739 Student(s), MALES
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.37 0.45 7.86 89.45* 1.22 0.65 0.01
2 0.24 0.62 0.82 8.14 89.88* 0.28 0.03
3 1.63 4.58 5.27 66.15* 2.27 20.07 0.03
4 66.04* 4.39 6.60 4.56 3.01 15.37 0.03
5 2.73 15.81 63.80* 2.75 1.98 12.87 0.05
6 11.47 10.74 36.95* 15.02 4.73 21.03 0.06
7 4.73 47.20* 39.97 1.17 1.40 5.49 0.02
8 3.74 15.60 68.26* 1.78 2.51 8.08 0.03
9 37.58* 7.41 4.41 5.23 6.06 39.26 0.05
10 4.97 28.43* 5.63 12.41 14.86 33.66 0.04
11 7.94 34.89* 5.42 6.89 2.84 42.00 0.02
12 77.27* 2.01 2.89 5.71 1.96 10.12 0.05
13 32.23* 12.80 12.66 8.94 3.54 29.77 0.05
14 13.31 35.71* 12.07 3.67 3.10 32.11 0.04
15 3.70 6.23 41.11* 4.87 2.84 41.23 0.02
16 14.87 19.22* 3.96 4.67 18.76 38.48 0.04
17 1.60 2.72 69.96* 2.48 1.18 22.05 0.02
18 5.43 4.20 24.07* 12.58 6.48 47.21 0.04
19 5.00 7.35 6.16 4.82 12.62* 64.00 0.04
20 12.18 4.47 8.83 10.99* 11.38 52.08 0.07
21 6.16 6.41 9.07 8.12* 9.00 61.20 0.04
22 4.11 9.93 8.14* 5.94 7.06 64.78 0.05
23 6.50 5.24 21.74* 8.09 8.16 50.20 0.07
24 2.23 4.28 5.36 4.14* 3.04 80.92 0.04
25 2.65 4.45 4.64* 4.34 2.48 81.43 0.01
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 25692 Student(s), Females
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.50 0.81 16.11 79.39* 2.21 0.97 0.01
2 0.49 0.75 1.19 13.00 84.07* 0.46 0.02
3 1.69 3.57 6.52 55.02* 3.79 29.39 0.02
4 50.76* 6.60 6.73 5.25 3.91 26.72 0.03
5 5.30 21.34 46.98* 3.75 2.21 20.40 0.02
6 14.41 11.24 24.46* 20.16 4.64 25.05 0.04
7 5.59 32.90* 49.98 1.58 1.60 8.33 0.01
8 6.07 22.36 54.11* 2.48 2.85 12.12 0.02
9 29.99* 7.52 5.28 5.41 6.82 44.95 0.02
10 6.03 22.10* 6.16 11.99 12.42 41.29 0.02
11 8.80 22.79* 6.48 6.16 3.22 52.52 0.04
12 63.04* 2.93 4.11 7.26 3.65 19.01 0.01
13 25.44* 11.66 12.02 9.99 4.31 36.54 0.04
14 12.63 22.69* 11.67 3.28 2.98 46.73 0.03
15 6.53 6.95 22.97* 4.71 2.19 56.64 0.01
16 18.09 14.50* 3.26 4.02 18.43 41.69 0.02
17 1.69 3.29 61.47* 2.77 1.42 29.35 0.02
18 6.45 4.68 16.43* 10.98 6.47 54.98 0.02
19 5.12 7.07 6.38 3.86 6.40* 71.14 0.02
20 10.29 3.95 8.82 6.76* 12.86 57.27 0.05
21 5.99 5.97 7.68 5.58* 7.84 66.92 0.02
22 4.41 8.33 7.10* 6.55 6.25 67.34 0.01
23 6.80 5.07 16.06* 7.12 8.09 56.84 0.04
24 1.81 3.58 4.32 2.85* 2.38 85.06 0.01
25 2.38 3.83 3.43* 3.85 2.11 84.39 0.01
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 12488 Student(s), Unknown Gender
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.43 0.62 11.43 84.71* 1.70 1.07 0.04
2 0.39 0.78 1.27 10.71 86.19* 0.62 0.03
3 1.77 4.24 5.96 59.65* 2.93 25.42 0.03
4 55.40* 5.65 6.99 5.64 3.71 22.59 0.02
5 3.97 19.31 53.40* 3.37 1.92 17.99 0.02
6 13.34 10.91 30.37* 16.82 3.73 24.78 0.05
7 5.52 37.86* 45.90 1.19 1.55 7.98 0.01
8 4.64 19.63 59.70* 2.04 2.66 11.31 0.02
9 32.00* 7.31 4.81 5.01 5.73 45.10 0.04
10 5.09 20.68* 6.35 12.28 12.92 42.66 0.02
11 8.53 24.30* 6.11 6.96 3.15 50.89 0.06
12 68.43* 2.41 3.59 6.69 2.75 16.10 0.03
13 26.59* 12.65 12.61 9.28 3.64 35.17 0.06
14 13.37 26.67* 12.26 3.56 3.13 40.98 0.03
15 5.14 6.62 28.60* 4.56 2.47 52.59 0.02
16 16.96 8.82* 4.08 4.37 19.12 46.58 0.06
17 1.72 3.05 62.44* 2.71 1.37 28.70 0.02
18 6.01 4.08 12.99* 12.35 6.58 57.91 0.07
19 4.80 6.72 5.95 4.44 7.08* 71.00 0.02
20 9.83 4.07 8.69 8.02* 10.45 58.93 0.02
21 6.01 5.75 7.65 6.56* 7.73 66.26 0.05
22 4.00 7.95 6.61* 5.66 5.98 69.76 0.04
23 6.49 4.80 14.77* 7.28 7.87 58.74 0.05
24 1.91 3.38 4.19 2.85* 2.59 85.07 0.02
25 2.41 3.63 3.81* 3.31 1.98 84.82 0.05
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 66 Student(s), Grade 13^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.00 0.00 7.58 89.39* 1.52 1.52 0.00
2 0.00 0.00 4.55 0.00 95.45* 0.00 0.00
3 1.52 0.00 1.52 4.55 92.42* 0.00 0.00
4 3.03 9.09 71.21* 9.09 0.00 7.58 0.00
5 4.55 18.18 69.70* 0.00 0.00 7.58 0.00
6 83.33* 1.52 1.52 4.55 0.00 9.09 0.00
7 6.06 36.36* 0.00 12.12 10.61 34.85 0.00
8 1.52 1.52 81.82* 0.00 0.00 15.15 0.00
9 4.55 24.24* 10.61 6.06 33.33 21.21 0.00
10 10.61 45.45* 13.64 1.52 3.03 25.76 0.00
11 3.03 4.55 34.85* 9.09 9.09 39.39 0.00
12 6.06 6.06 6.06 21.21* 22.73 37.88 0.00
13 22.73 13.64* 4.55 9.09 1.52 48.48 0.00
14 1.52 9.09 4.55 1.52 7.58* 75.76 0.00
15 7.58* 4.55 12.12 9.09 1.52 65.15 0.00
16 4.55 12.12 10.61* 7.58 7.58 57.58 0.00
17 1.52 6.06 4.55 10.61* 1.52 75.76 0.00
18 3.03 4.55 9.09 18.18* 3.03 62.12 0.00
19 3.03 12.12 6.06* 1.52 0.00 77.27 0.00
20 3.03 13.64 10.61* 3.03 0.00 69.70 0.00
21 0.00* 6.06 1.52 3.03 0.00 89.39 0.00
22 1.52 1.52 3.03* 3.03 3.03 87.88 0.00
23 3.03 1.52 3.03* 4.55 0.00 87.88 0.00
24 3.03 3.03 1.52* 0.00 7.58 84.85 0.00
25 1.52 3.03 3.03 1.52* 4.55 86.36 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 29957 Student(s), Grade 12^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.34 0.38 7.18 90.70* 0.93 0.45 0.01
2 0.05 0.15 0.69 0.41 98.59* 0.09 0.02
3 0.21 0.51 0.91 7.65 90.47* 0.22 0.03
4 1.94 10.94 75.45* 2.05 1.26 8.35 0.02
5 3.95 13.07 73.65* 1.42 2.13 5.77 0.02
6 82.51* 1.52 2.27 4.10 1.34 8.23 0.03
7 4.64 34.32* 6.29 11.54 10.65 32.51 0.05
8 1.00 2.03 80.19* 1.89 0.84 14.01 0.02
9 5.53 20.24* 7.77 8.99 28.97 28.45 0.05
10 14.43 44.78* 11.32 3.36 2.31 23.78 0.02
11 4.72 3.90 31.56* 17.77 8.33 33.67 0.05
12 5.08 6.35 5.08 18.74* 25.58 39.12 0.05
13 32.09 7.69* 5.02 10.93 2.75 41.49 0.03
14 3.10 5.75 5.64 5.76 9.76* 69.93 0.05
15 10.85* 3.59 15.31 3.82 2.37 64.04 0.04
16 3.46 10.11 8.40* 6.00 7.75 64.23 0.05
17 3.48 4.90 5.52 11.77* 4.81 69.48 0.05
18 3.71 5.34 11.13 25.02* 2.17 52.59 0.04
19 5.24 4.82 9.95* 2.87 1.57 75.50 0.04
20 5.73 12.04 7.18* 3.47 2.22 69.33 0.03
21 2.05* 3.61 3.66 3.44 2.30 84.92 0.03
22 2.18 3.73 4.37* 3.29 1.63 84.77 0.03
23 2.71 3.95 4.86* 2.78 2.01 83.64 0.05
24 4.14 5.82 6.76* 3.48 5.76 74.01 0.04
25 4.22 4.95 4.41 3.13* 8.83 74.42 0.04
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 34889 Student(s), Grade 11^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.29 0.38 8.45 89.38* 1.05 0.45 0.01
2 0.08 0.09 0.61 0.34 98.80* 0.08 0.00
3 0.22 0.52 0.97 7.79 90.23* 0.26 0.03
4 2.30 12.87 72.41* 2.14 1.40 8.87 0.02
5 4.14 15.06 71.13* 1.52 2.04 6.09 0.02
6 80.74* 1.61 2.39 4.66 1.66 8.91 0.02
7 5.01 32.39* 6.32 12.21 11.70 32.34 0.04
8 0.89 2.20 80.14* 1.84 0.91 14.00 0.01
9 5.99 20.05* 8.49 9.57 28.90 26.96 0.04
10 15.85 40.59* 11.70 3.55 2.68 25.60 0.03
11 5.19 4.24 28.08* 17.57 8.41 36.47 0.03
12 4.95 6.49 5.51 18.78* 26.55 37.67 0.05
13 36.62 8.76* 4.28 10.89 2.82 36.61 0.01
14 3.02 6.13 5.43 5.88 8.25* 71.27 0.01
15 11.15* 3.16 16.41 4.32 2.48 62.46 0.02
16 3.65 10.26 7.76* 6.25 8.22 63.81 0.04
17 3.52 4.79 5.91 11.38* 4.83 69.54 0.03
18 4.09 5.86 11.13 24.56* 2.30 52.03 0.03
19 5.07 4.73 9.53* 2.97 1.60 76.07 0.03
20 6.35 12.02 6.60* 3.74 2.55 68.74 0.01
21 1.83* 3.58 3.33 3.52 2.39 85.33 0.02
22 2.10 3.63 4.15* 3.56 1.63 84.90 0.03
23 2.88 3.76 4.78* 3.05 2.15 83.35 0.02
24 4.47 6.48 6.59* 3.82 6.52 72.09 0.02
25 4.80 5.39 4.40 3.17* 11.00 71.21 0.04
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 4469 Student(s), Grade 10^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.25 0.27 7.61 90.76* 0.81 0.31 0.00
2 0.02 0.09 0.47 0.20 99.04* 0.18 0.00
3 0.38 0.47 0.81 6.58 91.47* 0.25 0.04
4 2.69 12.58 72.59* 2.35 1.61 8.19 0.00
5 3.65 14.19 72.66* 1.23 2.04 6.22 0.02
6 82.77* 1.41 2.10 4.30 1.39 8.03 0.00
7 4.45 35.06* 5.68 10.85 11.59 32.36 0.00
8 1.25 1.59 80.89* 1.36 0.76 14.14 0.00
9 5.24 24.12* 6.82 7.63 28.46 27.72 0.00
10 14.32 42.81* 11.32 3.16 2.17 26.23 0.00
11 4.63 3.51 29.65* 13.83 7.09 41.24 0.04
12 4.18 6.02 4.61 19.22* 25.49 40.41 0.07
13 37.14 9.44* 3.09 11.14 2.73 36.43 0.02
14 2.44 4.99 4.83 4.54 10.49* 72.70 0.00
15 11.77* 2.30 14.84 3.49 1.83 65.76 0.00
16 3.18 9.71 8.59* 5.57 6.78 66.17 0.00
17 3.13 3.20 4.18 10.99* 3.78 74.71 0.00
18 3.47 4.32 9.89 24.70* 1.88 55.65 0.09
19 4.01 3.74 10.79* 1.86 1.14 78.47 0.00
20 4.61 11.12 6.51* 2.37 1.83 73.55 0.00
21 1.50* 2.26 2.42 3.22 1.52 89.06 0.02
22 1.14 2.66 3.13* 2.60 1.19 89.28 0.00
23 2.10 2.46 3.24* 2.17 1.92 88.10 0.00
24 3.71 4.59 5.48* 3.33 5.57 77.29 0.02
25 3.85 4.32 3.29 2.60* 9.69 76.26 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 1348 Student(s), Grade 9^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.22 0.45 9.12 88.65* 1.04 0.52 0.00
2 0.00 0.15 0.52 0.45 98.74* 0.15 0.00
3 0.22 0.22 1.19 8.16 89.91* 0.30 0.00
4 3.34 19.44 61.65* 2.08 1.34 12.09 0.07
5 3.49 18.32 67.28* 1.41 1.71 7.79 0.00
6 79.45* 1.56 2.37 4.82 2.60 9.20 0.00
7 4.53 31.75* 5.49 9.79 12.91 35.39 0.15
8 1.04 2.08 76.56* 1.78 0.82 17.73 0.00
9 6.16 22.77* 8.09 8.75 28.93 25.15 0.15
10 13.80 36.13* 12.09 3.41 2.23 32.34 0.00
11 5.86 3.26 23.29* 11.50 7.64 48.44 0.00
12 4.82 4.53 4.60 19.81* 25.52 40.73 0.00
13 35.76 7.72* 3.26 11.05 3.41 38.65 0.15
14 2.37 4.45 3.71 4.30 9.57* 75.59 0.00
15 10.46* 2.08 12.91 4.01 1.63 68.92 0.00
16 3.19 9.64 9.05* 5.79 6.90 65.43 0.00
17 2.82 3.34 4.75 10.53* 3.41 75.15 0.00
18 3.41 4.38 7.94 22.11* 2.37 59.79 0.00
19 4.08 3.12 10.24* 2.30 0.37 79.82 0.07
20 6.01 8.68 7.12* 2.97 1.78 73.37 0.07
21 2.08* 2.89 2.89 3.34 1.26 87.46 0.07
22 2.15 3.26 3.26* 3.34 1.34 86.65 0.00
23 2.08 3.41 3.64* 2.45 1.78 86.65 0.00
24 3.12 5.27 5.12* 4.08 5.93 76.41 0.07
25 4.60 4.15 3.64 2.82* 9.27 75.52 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 214 Student(s), Grades 8 and Below^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.47 0.93 7.94 85.98* 4.21 0.47 0.00
2 0.00 0.00 2.80 0.00 96.26* 0.93 0.00
3 0.00 0.47 0.47 7.94 90.19* 0.93 0.00
4 2.34 13.08 72.43* 3.27 1.40 7.48 0.00
5 3.74 14.02 73.36* 1.40 0.93 6.07 0.47
6 79.44* 2.80 1.40 6.07 3.74 6.54 0.00
7 5.14 45.79* 5.14 7.48 12.62 23.83 0.00
8 0.00 2.80 78.50* 3.74 2.34 12.62 0.00
9 3.74 32.71* 6.07 10.75 22.90 23.83 0.00
10 13.55 49.07* 11.21 1.87 1.87 22.43 0.00
11 6.07 2.80 44.86* 6.07 5.61 34.58 0.00
12 4.67 4.21 5.61 28.04* 22.43 34.11 0.93
13 21.96 18.69* 2.80 10.75 1.87 43.93 0.00
14 1.40 6.07 4.21 3.74 21.03* 63.55 0.00
15 17.76* 2.80 10.28 5.61 1.87 61.68 0.00
16 3.74 8.41 12.62* 8.41 7.48 59.35 0.00
17 4.67 4.21 3.74 20.09* 3.27 64.02 0.00
18 4.21 2.80 6.07 36.45* 0.47 50.00 0.00
19 3.27 1.40 24.30* 1.87 0.93 68.22 0.00
20 6.07 12.62 13.08* 3.27 2.34 62.62 0.00
21 3.74* 3.74 0.93 5.14 2.34 84.11 0.00
22 2.34 2.34 4.21* 3.74 1.87 85.51 0.00
23 0.93 2.80 7.01* 2.34 1.87 85.05 0.00
24 2.34 5.14 7.01* 6.54 2.34 76.64 0.00
25 6.54 3.74 3.27 3.74* 7.01 75.70 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 37477 Student(s), MALES
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.26 0.32 5.29 93.05* 0.75 0.32 0.01
2 0.05 0.13 0.68 0.39 98.67* 0.07 0.01
3 0.19 0.38 0.72 5.88 92.63* 0.18 0.02
4 1.54 10.04 79.30* 1.79 1.27 6.04 0.02
5 2.87 11.71 77.52* 1.30 1.97 4.61 0.02
6 86.07* 1.30 1.96 3.78 1.12 5.76 0.01
7 4.67 37.23* 6.05 12.06 11.83 28.13 0.04
8 0.88 1.86 83.62* 1.71 0.84 11.07 0.01
9 5.56 23.47* 8.24 9.12 26.62 26.96 0.04
10 14.73 49.57* 11.48 3.33 2.44 18.42 0.02
11 4.65 3.62 34.65* 17.65 8.81 30.57 0.05
12 5.44 6.61 5.39 21.83* 26.33 34.36 0.06
13 32.40 10.04* 4.71 11.67 2.69 38.47 0.02
14 3.28 6.53 5.98 6.28 11.60* 66.30 0.02
15 13.06* 3.76 16.11 4.09 2.63 60.33 0.03
16 3.58 10.99 9.13* 5.97 8.11 62.17 0.05
17 3.59 4.97 5.87 13.80* 5.03 66.72 0.02
18 3.45 5.25 11.84 28.35* 2.21 48.87 0.04
19 5.39 5.10 12.31* 3.15 1.69 72.33 0.04
20 5.80 13.35 7.98* 3.75 2.25 66.86 0.01
21 2.26* 3.79 3.83 4.01 2.39 83.71 0.02
22 2.29 3.87 4.79* 3.56 1.64 83.82 0.02
23 2.99 3.99 5.26* 3.08 2.20 82.46 0.02
24 4.11 6.15 6.59* 3.58 5.69 73.85 0.02
25 4.59 5.66 4.60 3.11* 8.85 73.15 0.03
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 26418 Student(s), Females
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.38 0.56 12.04 84.91* 1.42 0.67 0.02
2 0.12 0.10 0.62 0.35 98.70* 0.10 0.02
3 0.31 0.71 1.24 10.72 86.65* 0.34 0.04
4 3.19 15.94 64.14* 2.69 1.47 12.55 0.02
5 5.83 18.54 63.58* 1.73 2.23 8.06 0.03
6 74.75* 1.98 2.93 5.30 2.31 12.69 0.03
7 5.10 28.03* 6.41 11.56 10.80 38.06 0.05
8 1.11 2.43 75.11* 2.12 0.94 18.28 0.02
9 6.06 16.14* 7.86 9.27 32.42 28.20 0.05
10 15.66 32.09* 11.50 3.52 2.65 34.55 0.04
11 5.56 4.81 22.25* 16.62 7.78 42.95 0.03
12 4.45 6.02 5.22 15.24* 25.50 43.52 0.05
13 38.25 6.96* 4.20 10.01 3.03 37.52 0.03
14 2.63 5.04 4.89 4.95 5.49* 76.97 0.03
15 8.51* 2.63 15.67 4.22 2.09 66.86 0.03
16 3.57 9.32 6.93* 6.40 7.87 65.86 0.04
17 3.38 4.57 5.46 9.09* 4.43 73.04 0.05
18 4.65 6.02 9.96 20.29* 2.33 56.72 0.04
19 4.77 4.11 6.44* 2.57 1.39 80.69 0.04
20 6.50 10.27 5.46* 3.32 2.60 71.84 0.02
21 1.46* 3.30 2.82 2.97 2.12 87.30 0.04
22 1.85 3.35 3.44* 3.25 1.67 86.41 0.03
23 2.57 3.58 4.07* 2.82 1.93 85.00 0.04
24 4.50 6.38 6.67* 3.93 6.91 71.56 0.04
25 4.65 4.55 4.04 3.16* 12.24 71.31 0.04
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 A Results
Table of Item Difficulty for the 2011
Tabulation of responses by 10770 Student(s), Unknown Gender
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.38 0.42 7.41 90.00* 0.95 0.84 0.01
2 0.06 0.19 0.63 0.44 98.39* 0.29 0.00
3 0.26 0.52 0.97 7.97 89.77* 0.50 0.01
4 2.47 11.12 74.21* 2.23 1.30 8.67 0.00
5 3.68 13.82 72.87* 1.43 2.22 5.97 0.02
6 80.77* 1.52 2.53 4.90 1.31 8.92 0.05
7 4.90 31.23* 6.78 11.58 10.19 35.29 0.03
8 1.15 2.27 78.54* 1.98 1.07 14.98 0.01
9 6.09 19.84* 8.23 9.35 27.60 28.87 0.02
10 15.50 41.32* 12.48 3.70 2.30 24.70 0.00
11 5.36 3.90 27.34* 17.88 8.10 37.42 0.01
12 4.76 6.25 4.94 16.87* 26.06 41.10 0.02
13 33.80 5.16* 4.61 10.39 2.92 43.10 0.02
14 3.15 5.98 5.47 5.77 8.63* 70.99 0.02
15 9.97* 3.28 14.71 3.64 2.25 66.15 0.01
16 3.40 9.45 7.45* 6.14 6.85 66.69 0.02
17 3.57 4.26 5.33 8.60* 4.39 73.82 0.04
18 3.76 5.75 10.32 22.06* 1.96 56.14 0.02
19 4.71 4.94 8.91* 2.73 1.42 77.22 0.06
20 5.76 10.60 6.17* 3.18 2.44 71.84 0.02
21 1.81* 3.14 3.37 3.31 2.52 85.82 0.04
22 2.20 3.51 3.90* 3.38 1.46 85.54 0.01
23 2.61 3.65 4.61* 2.37 2.01 84.72 0.05
24 4.13 5.00 6.21* 3.61 5.93 75.10 0.01
25 4.09 4.55 4.24 3.21* 8.09 75.79 0.02
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 16661 Student(s), Grade 10^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 4.75 0.98 92.10* 0.81 0.20 1.15 0.00
2 14.51 2.63 3.64 3.73 73.34* 2.14 0.02
3 77.67* 5.78 3.66 4.31 1.68 6.89 0.01
4 5.52 4.86 67.98* 19.98 0.19 1.48 0.01
5 6.62 4.12 2.59 4.86 56.46* 25.31 0.05
6 78.70* 2.83 3.79 6.12 2.05 6.49 0.01
7 28.85 50.36* 5.47 2.75 4.72 7.83 0.02
8 23.61 68.51* 1.27 1.21 3.15 2.20 0.05
9 11.66 2.38 3.89 49.89* 2.87 29.29 0.01
10 10.62 44.32* 12.76 8.12 6.40 17.78 0.00
11 6.37 3.20 49.71 27.06* 3.31 10.34 0.02
12 44.96* 8.19 2.21 4.55 1.83 38.23 0.03
13 11.24 21.85 7.36 27.50* 7.72 24.31 0.02
14 6.57 7.03 45.29* 5.34 4.93 30.82 0.02
15 6.01 7.38 7.42 8.19 54.11* 16.83 0.06
16 33.73* 9.78 10.17 4.64 2.23 39.44 0.01
17 5.05 3.82 38.86* 9.14 11.25 31.87 0.02
18 1.97 5.05 17.51 19.93 30.86* 24.64 0.03
19 31.38* 11.18 3.54 6.90 11.61 35.32 0.07
20 4.26 17.43 18.11* 4.34 3.25 52.59 0.02
21 11.97 13.48* 6.54 5.49 3.21 59.30 0.02
22 7.75* 7.68 7.93 4.24 4.14 68.23 0.04
23 31.64 6.55 5.81 9.44* 4.50 42.01 0.05
24 9.24 4.85* 9.36 9.05 4.28 63.17 0.05
25 2.46 4.36 6.77 7.11* 4.94 74.35 0.01
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 10249 Student(s), Grade 9^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 7.87 1.36 87.80* 1.00 0.25 1.71 0.00
2 10.41 2.72 4.11 4.06 76.10* 2.58 0.02
3 75.37* 6.07 4.41 5.06 1.76 7.33 0.00
4 7.09 5.03 58.43* 27.21 0.20 2.04 0.00
5 6.81 4.52 2.45 4.17 53.53* 28.51 0.02
6 75.76* 3.79 4.02 5.10 2.24 9.07 0.01
7 32.18 45.98* 5.71 2.33 4.76 9.03 0.01
8 28.52 63.45* 1.40 0.91 3.48 2.23 0.01
9 13.16 2.94 4.80 36.17* 3.76 39.16 0.02
10 10.99 36.76* 13.58 8.45 7.45 22.72 0.04
11 7.49 3.00 50.67 23.03* 3.73 12.08 0.01
12 29.12* 9.66 2.38 6.27 2.19 50.31 0.08
13 9.53 22.67 6.58 21.53* 8.60 31.08 0.02
14 7.32 7.21 38.66* 5.22 5.19 36.37 0.03
15 7.40 8.48 7.92 10.82 41.94* 23.38 0.07
16 21.94* 12.38 8.96 6.54 2.21 47.96 0.01
17 5.06 4.50 28.12* 9.83 10.99 41.51 0.00
18 1.50 5.85 20.61 21.67 20.26* 30.10 0.01
19 18.74* 10.06 3.95 7.80 9.98 49.46 0.01
20 4.41 13.81 13.07* 3.52 3.91 61.25 0.02
21 10.13 11.04* 5.65 4.90 2.67 65.59 0.03
22 4.49* 5.67 6.22 3.92 3.45 76.23 0.02
23 32.72 5.98 4.80 7.78* 3.62 45.07 0.04
24 6.14 4.57* 7.27 6.95 4.17 70.91 0.00
25 2.14 3.48 5.31 4.87* 3.54 80.66 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 3477 Student(s), Grades 8 and Below^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 3.31 0.95 93.93* 0.63 0.14 1.04 0.00
2 5.46 1.87 2.44 2.10 87.20* 0.92 0.00
3 83.81* 5.35 2.88 3.51 0.86 3.60 0.00
4 3.85 6.27 69.31* 19.13 0.06 1.35 0.03
5 3.62 3.13 1.90 3.05 73.43* 14.84 0.03
6 87.89* 1.67 2.01 3.57 1.38 3.48 0.00
7 29.48 57.81* 3.16 1.73 2.67 5.12 0.03
8 20.53 73.94* 0.98 1.21 2.04 1.27 0.03
9 9.35 3.05 6.50 43.17* 3.88 33.97 0.09
10 9.52 57.18* 9.95 5.90 5.67 11.79 0.00
11 5.12 2.16 47.11 35.15* 2.76 7.68 0.03
12 42.42* 9.58 2.62 6.15 1.67 37.53 0.03
13 7.13 13.86 7.39 34.45* 7.74 29.42 0.00
14 5.21 5.55 57.75* 4.08 5.35 22.06 0.00
15 4.14 10.64 8.77 6.27 56.80* 13.29 0.09
16 33.42* 11.22 10.32 5.61 2.93 36.50 0.00
17 4.72 4.75 33.25* 12.31 11.25 33.68 0.06
18 1.15 5.09 18.29 21.63 24.62* 29.22 0.00
19 28.93* 8.86 2.82 6.64 12.71 39.95 0.09
20 3.48 22.95 15.19* 3.80 3.42 51.11 0.06
21 8.92 15.27* 5.64 5.75 3.19 61.23 0.00
22 8.14* 5.49 8.34 4.14 3.62 70.26 0.00
23 30.37 6.50 7.39 13.55* 3.36 38.77 0.06
24 5.72 5.26* 7.91 8.23 3.97 68.88 0.03
25 1.78 3.88 6.10 6.15* 3.65 78.43 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 15097 Student(s), MALES
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 4.60 1.04 92.06* 0.97 0.15 1.18 0.00
2 9.62 2.33 3.52 3.62 79.13* 1.77 0.01
3 79.48* 5.88 3.60 3.71 1.68 5.64 0.01
4 4.34 5.48 66.52* 21.92 0.19 1.54 0.00
5 5.59 3.82 2.25 4.23 62.65* 21.40 0.05
6 82.02* 2.72 2.80 5.01 1.68 5.78 0.00
7 30.32 51.88* 5.14 2.25 3.98 6.41 0.02
8 19.63 73.02* 1.20 1.22 2.85 2.06 0.03
9 11.95 2.76 4.79 48.03* 2.97 29.49 0.02
10 9.47 51.28* 11.25 7.48 5.95 14.56 0.01
11 5.35 2.62 49.14 31.25* 2.99 8.62 0.03
12 43.31* 8.29 2.60 5.55 2.16 38.02 0.07
13 11.04 19.61 7.43 31.29* 7.48 23.14 0.02
14 6.58 6.68 49.04* 4.84 5.11 27.73 0.02
15 5.57 7.92 7.52 8.43 53.84* 16.67 0.05
16 33.91* 11.05 10.35 5.74 2.34 36.60 0.01
17 4.72 4.08 38.09* 9.74 11.31 32.04 0.03
18 1.77 5.27 17.98 20.14 29.77* 25.06 0.02
19 31.33* 9.78 3.49 6.82 11.37 37.14 0.07
20 4.54 18.30 18.53* 4.17 3.41 51.02 0.03
21 10.70 14.69* 6.51 6.08 3.35 58.64 0.03
22 8.25* 6.94 8.09 4.66 3.68 68.34 0.04
23 31.20 6.47 6.83 11.29* 3.76 40.37 0.07
24 8.39 5.37* 9.68 9.39 4.66 62.49 0.03
25 2.32 4.46 6.60 7.23* 4.96 74.43 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 12088 Student(s), Females
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 7.34 1.28 88.74* 0.79 0.29 1.56 0.00
2 16.31 3.03 3.80 3.77 70.40* 2.66 0.03
3 73.68* 6.11 4.25 5.77 1.69 8.49 0.01
4 7.92 4.57 62.52* 22.82 0.19 1.97 0.02
5 7.54 4.92 2.71 4.67 50.02* 30.10 0.02
6 73.99* 3.62 4.96 6.06 2.54 8.81 0.02
7 29.44 46.27* 5.93 2.96 5.18 10.20 0.02
8 31.74 59.75* 1.34 1.10 3.75 2.29 0.03
9 11.74 2.63 4.31 40.34* 3.88 37.09 0.01
10 12.22 32.54* 14.32 8.70 7.80 24.41 0.01
11 8.42 3.42 50.37 20.59* 3.92 13.27 0.01
12 34.55* 9.86 1.94 4.91 1.73 46.99 0.02
13 9.39 23.93 6.49 19.54* 8.57 32.06 0.02
14 7.03 7.42 38.63* 5.71 4.96 36.23 0.02
15 7.30 8.25 7.86 9.74 45.39* 21.38 0.08
16 24.46* 10.99 8.98 4.83 2.30 48.43 0.01
17 5.40 4.51 30.97* 9.65 10.68 38.77 0.02
18 1.80 5.58 19.68 21.43 22.96* 28.53 0.02
19 21.79* 11.66 3.91 7.78 10.65 44.18 0.03
20 4.01 14.98 13.54* 3.76 3.58 60.12 0.00
21 11.84 10.99* 5.61 4.45 2.61 64.49 0.02
22 5.27* 6.51 6.55 3.57 4.03 74.05 0.02
23 32.88 6.37 4.29 7.26* 4.54 44.64 0.03
24 6.92 4.19* 7.35 6.73 3.92 70.86 0.03
25 2.36 3.56 5.70 5.20* 3.68 79.50 0.01
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 10 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 6538 Student(s), Unknown Gender
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 4.83 1.02 91.68* 0.70 0.20 1.56 0.00
2 10.92 2.34 3.40 3.20 77.76* 2.37 0.02
3 78.59* 5.57 3.92 4.42 1.67 5.84 0.00
4 5.23 5.38 66.46* 21.26 0.21 1.45 0.00
5 6.78 4.04 2.89 4.70 58.00* 23.57 0.03
6 79.28* 2.72 3.75 5.54 2.05 6.67 0.00
7 28.59 51.53* 4.82 2.69 5.17 7.20 0.00
8 23.40 68.86* 1.58 1.18 2.94 1.99 0.06
9 11.58 2.46 4.28 46.77* 2.62 32.23 0.06
10 10.66 45.21* 13.15 7.33 6.52 17.10 0.03
11 6.18 3.27 47.12 30.09* 3.61 9.71 0.02
12 42.66* 8.35 2.22 5.81 1.76 39.19 0.02
13 9.91 20.01 7.53 28.63* 8.41 25.51 0.00
14 6.24 6.41 44.97* 5.87 5.08 31.39 0.05
15 5.67 8.78 8.23 7.92 52.72* 16.61 0.06
16 32.84* 9.67 10.31 5.41 2.22 39.52 0.03
17 5.45 3.81 35.88* 9.48 11.65 33.71 0.02
18 1.74 5.05 18.42 19.72 28.49* 26.57 0.02
19 27.88* 9.83 3.79 7.37 12.07 38.99 0.06
20 4.10 17.56 17.42* 4.56 3.33 53.00 0.03
21 12.05 14.09* 6.61 5.12 3.23 58.86 0.05
22 7.13* 8.01 8.31 4.10 4.07 68.37 0.02
23 31.37 6.10 5.89 10.22* 3.98 42.40 0.05
24 8.79 5.52* 8.98 8.69 3.88 64.12 0.02
25 2.60 4.83 7.04 7.07* 4.51 73.92 0.03
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 86 Student(s), Grade 13^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 0.00 0.00 97.67* 2.33 0.00 0.00 0.00
2 3.49 0.00 2.33 1.16 93.02* 0.00 0.00
3 2.33 5.81 84.88* 6.98 0.00 0.00 0.00
4 0.00 1.16 0.00 2.33 83.72* 12.79 0.00
5 63.95* 0.00 1.16 23.26 8.14 3.49 0.00
6 2.33 3.49 54.65* 4.65 6.98 27.91 0.00
7 2.33 76.74* 2.33 10.47 1.16 6.98 0.00
8 70.93* 4.65 2.33 2.33 1.16 18.60 0.00
9 8.14 12.79 2.33 62.79* 4.65 9.30 0.00
10 1.16 5.81 15.12 23.26 25.58* 29.07 0.00
11 8.14 36.05* 6.98 11.63 4.65 32.56 0.00
12 52.33* 8.14 5.81 6.98 4.65 22.09 0.00
13 12.79 9.30* 6.98 2.33 2.33 66.28 0.00
14 0.00 2.33 3.49 8.14* 6.98 79.07 0.00
15 4.65 6.98 9.30 10.47* 6.98 61.63 0.00
16 5.81 20.93 12.79* 3.49 4.65 52.33 0.00
17 6.98 10.47* 3.49 3.49 9.30 66.28 0.00
18 4.65* 6.98 9.30 0.00 5.81 73.26 0.00
19 6.98 6.98* 6.98 1.16 2.33 75.58 0.00
20 2.33 3.49 4.65* 1.16 1.16 87.21 0.00
21 2.33 3.49 2.33 3.49* 3.49 84.88 0.00
22 2.33 1.16 3.49 1.16* 2.33 89.53 0.00
23 5.81 3.49 9.30* 1.16 1.16 79.07 0.00
24 5.81 2.33* 2.33 2.33 0.00 87.21 0.00
25 0.00 5.81 3.49 1.16* 1.16 88.37 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 9959 Student(s), Grade 12^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 2.29 0.91 95.17* 0.74 0.12 0.76 0.00
2 5.95 1.63 2.68 3.26 85.22* 1.24 0.02
3 3.49 4.97 73.48* 16.91 0.12 0.98 0.04
4 4.01 3.26 1.83 3.82 68.39* 18.65 0.05
5 47.85* 2.52 1.75 27.13 12.14 8.60 0.02
6 1.82 6.02 43.80* 5.60 10.00 32.68 0.07
7 8.19 60.48* 2.93 9.65 2.61 16.12 0.02
8 47.15* 8.41 3.35 5.39 1.85 33.79 0.05
9 10.32 13.76 6.68 44.57* 6.99 17.65 0.03
10 2.18 6.37 19.46 23.13 29.87* 18.92 0.07
11 9.32 32.37* 9.93 14.75 5.51 28.10 0.02
12 37.18* 8.66 11.29 6.43 2.25 34.15 0.05
13 9.90 17.64* 6.57 4.98 2.40 58.47 0.04
14 2.63 6.45 4.07 9.20* 8.28 69.31 0.06
15 10.60 12.32 8.20 13.10* 4.26 51.45 0.06
16 4.16 18.57 18.56* 4.47 3.07 51.11 0.07
17 2.85 12.68* 8.33 5.59 6.68 63.83 0.03
18 9.34* 5.73 8.07 4.53 4.38 67.93 0.02
19 8.36 6.50* 8.46 8.12 3.47 65.05 0.03
20 3.34 5.09 5.65* 4.92 3.16 77.76 0.07
21 4.10 5.63 6.60 6.24* 1.57 75.86 0.01
22 2.54 3.70 5.01 4.68* 2.97 81.06 0.04
23 4.72 6.38 9.16* 5.76 3.33 70.59 0.06
24 3.38 3.23* 4.26 4.11 3.39 81.58 0.04
25 3.68 5.16 4.51 3.95* 3.10 79.57 0.04
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 14251 Student(s), Grade 11^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 2.80 0.86 94.89* 0.59 0.13 0.72 0.01
2 7.89 1.40 2.63 2.83 84.04* 1.18 0.02
3 4.39 5.11 71.59* 17.77 0.09 1.03 0.01
4 4.63 3.26 1.62 3.61 68.28* 18.53 0.07
5 46.96* 2.60 1.75 28.12 12.57 7.96 0.03
6 1.80 5.49 47.31* 5.17 10.72 29.44 0.08
7 8.71 59.53* 3.22 9.82 2.57 16.13 0.04
8 48.34* 7.89 2.98 5.10 1.56 34.06 0.06
9 9.93 15.89 6.97 42.07* 7.38 17.73 0.03
10 1.88 5.21 20.41 22.55 32.90* 16.97 0.07
11 10.34 31.84* 10.20 14.34 4.99 28.25 0.05
12 39.84* 8.86 11.23 5.40 2.32 32.31 0.03
13 10.71 17.64* 6.55 6.34 2.88 55.87 0.01
14 2.27 6.23 3.82 10.93* 9.36 67.34 0.04
15 11.87 13.15 8.80 13.74* 4.32 48.09 0.04
16 4.45 20.55 20.47* 4.39 2.92 47.20 0.01
17 2.65 13.59* 8.57 5.19 6.76 63.19 0.05
18 10.32* 5.77 8.29 4.42 4.75 66.41 0.04
19 8.32 5.73* 8.58 9.20 3.42 64.70 0.04
20 3.56 4.81 5.86* 4.66 3.32 77.76 0.02
21 3.94 5.40 6.48 7.08* 1.55 75.51 0.04
22 2.11 3.58 4.79 4.76* 2.87 81.83 0.06
23 4.65 6.27 9.06* 5.82 3.50 70.65 0.05
24 3.35 2.95* 4.12 4.03 3.47 82.04 0.03
25 3.52 5.70 4.62 3.40* 2.93 79.83 0.01
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 2429 Student(s), Grade 10^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 2.26 0.41 95.97* 0.33 0.16 0.86 0.00
2 4.86 0.99 2.22 1.93 89.21* 0.78 0.00
3 3.95 5.27 74.85* 15.03 0.08 0.82 0.00
4 2.47 2.39 0.99 2.39 76.82* 14.90 0.04
5 55.70* 1.44 1.15 24.95 11.16 5.56 0.04
6 1.89 4.41 56.69* 3.87 8.23 24.91 0.00
7 6.75 67.68* 1.73 8.52 1.69 13.63 0.00
8 53.36* 6.42 2.14 4.78 1.52 31.78 0.00
9 7.53 12.02 5.31 51.67* 5.89 17.54 0.04
10 1.69 4.69 18.07 20.26 38.74* 16.55 0.00
11 8.40 35.73* 9.35 15.07 4.94 26.39 0.12
12 46.93* 7.62 9.47 4.53 1.19 30.26 0.00
13 11.32 24.17* 5.85 4.94 2.31 51.42 0.00
14 2.14 5.35 3.91 12.02* 7.29 69.21 0.08
15 10.62 13.75 10.37 16.51* 3.99 44.75 0.00
16 3.54 22.56 23.96* 3.42 3.21 43.31 0.00
17 2.51 18.81* 6.75 4.65 5.06 62.21 0.00
18 12.60* 5.80 7.49 3.09 3.46 67.52 0.04
19 7.66 6.92* 9.55 8.15 2.84 64.88 0.00
20 2.92 4.08 6.88* 3.91 2.59 79.58 0.04
21 3.01 4.49 6.67 8.73* 0.78 76.33 0.00
22 1.28 3.33 3.95 4.57* 2.55 84.27 0.04
23 3.75 4.69 11.07* 5.80 3.25 71.39 0.04
24 2.55 2.14* 4.36 3.38 2.51 85.06 0.00
25 2.22 5.02 4.41 3.05* 2.39 82.91 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 903 Student(s), Grade 9^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 3.65 0.78 94.02* 0.22 0.22 1.11 0.00
2 4.43 0.89 2.44 2.33 88.93* 0.89 0.11
3 3.54 5.98 72.65* 16.83 0.22 0.78 0.00
4 2.55 1.66 1.11 2.77 77.08* 14.84 0.00
5 60.91* 1.88 0.78 21.48 8.19 6.76 0.00
6 1.55 4.32 56.48* 3.54 9.08 24.92 0.11
7 5.20 67.44* 2.10 6.20 2.33 16.72 0.00
8 51.83* 6.87 1.66 5.43 1.22 32.89 0.11
9 5.87 12.85 6.53 48.17* 5.76 20.82 0.00
10 1.99 4.65 16.28 18.05 39.09* 19.93 0.00
11 7.20 34.55* 9.08 15.61 4.98 28.57 0.00
12 45.85* 7.42 10.30 4.98 1.44 30.01 0.00
13 10.96 25.03* 4.76 4.98 3.10 51.16 0.00
14 1.77 6.20 2.77 10.63* 6.20 72.31 0.11
15 7.86 15.17 11.30 17.28* 4.65 43.74 0.00
16 4.76 22.70 20.71* 3.21 1.33 47.29 0.00
17 2.21 18.72* 5.87 3.88 5.65 63.46 0.22
18 13.29* 5.20 6.76 2.44 2.77 69.44 0.11
19 7.09 6.64* 9.41 9.75 3.10 64.01 0.00
20 2.33 2.88 6.53* 3.43 2.33 82.39 0.11
21 2.44 5.43 5.09 8.86* 0.66 77.52 0.00
22 1.66 2.88 3.54 4.32* 2.55 85.05 0.00
23 2.99 5.54 11.85* 4.54 2.99 71.98 0.11
24 1.44 2.77* 3.77 2.88 1.55 87.38 0.22
25 1.44 3.65 3.10 3.99* 2.44 85.38 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 326 Student(s), Grades 8 and Below^
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 1.53 0.31 96.01* 0.92 0.61 0.61 0.00
2 2.15 0.61 3.07 0.92 92.64* 0.61 0.00
3 1.23 6.75 80.06* 11.66 0.00 0.31 0.00
4 0.92 1.23 0.92 2.76 84.97* 9.20 0.00
5 64.72* 1.53 0.92 21.17 9.20 2.45 0.00
6 1.23 3.37 67.18* 5.21 5.83 17.18 0.00
7 4.29 79.14* 3.07 6.44 0.61 6.44 0.00
8 64.72* 7.67 2.76 3.99 2.15 18.71 0.00
9 3.68 8.28 5.21 62.27* 5.52 15.03 0.00
10 2.15 4.29 12.27 24.85 44.17* 12.27 0.00
11 6.75 38.34* 8.90 17.48 7.67 20.86 0.00
12 57.98* 6.44 10.12 3.68 1.84 19.63 0.31
13 8.59 27.91* 7.67 6.44 1.84 47.55 0.00
14 1.84 3.37 6.13 15.95* 6.44 66.26 0.00
15 9.20 12.27 14.11 26.38* 4.29 33.74 0.00
16 5.52 28.53 27.30* 2.45 3.37 32.82 0.00
17 3.68 24.54* 5.21 4.91 7.98 53.68 0.00
18 16.26* 3.07 10.43 4.91 4.60 60.43 0.31
19 7.06 11.35* 10.12 9.82 1.84 59.51 0.31
20 2.76 5.21 7.36* 4.29 2.45 77.91 0.00
21 3.68 3.37 5.83 10.74* 1.53 74.85 0.00
22 2.15 2.76 3.99 6.44* 2.45 82.21 0.00
23 5.21 3.99 13.80* 5.52 3.68 67.79 0.00
24 1.84 3.99* 5.21 3.07 3.07 82.82 0.00
25 2.76 7.36 3.07 4.91* 0.31 81.60 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 15095 Student(s), MALES
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 1.96 0.79 95.81* 0.66 0.13 0.65 0.01
2 4.84 1.37 2.47 2.76 87.68* 0.86 0.02
3 2.89 5.17 75.66* 15.38 0.09 0.80 0.01
4 3.30 2.80 1.45 3.15 74.87* 14.39 0.04
5 52.90* 2.08 1.56 25.98 11.22 6.23 0.03
6 1.66 5.23 53.02* 5.09 9.65 25.30 0.07
7 6.91 68.10* 2.61 8.21 2.13 12.03 0.01
8 54.28* 7.60 3.23 5.00 1.52 28.30 0.07
9 9.90 12.50 6.46 51.45* 5.93 13.72 0.03
10 1.95 5.53 18.32 21.46 36.76* 15.91 0.06
11 8.35 37.37* 10.38 15.11 5.35 23.42 0.02
12 45.19* 8.27 11.46 5.66 2.13 27.25 0.03
13 10.22 22.03* 6.72 5.91 2.87 52.22 0.03
14 2.57 6.41 4.23 13.15* 8.53 65.06 0.06
15 10.79 13.92 10.04 15.14* 4.10 45.98 0.03
16 4.29 21.15 22.92* 4.55 2.80 44.27 0.03
17 3.07 17.86* 7.88 5.53 7.01 58.62 0.03
18 12.16* 5.75 8.74 3.93 4.54 64.86 0.02
19 8.79 7.19* 9.96 9.83 3.36 60.83 0.03
20 3.14 4.60 7.02* 4.87 3.11 77.24 0.03
21 3.73 5.57 6.73 8.07* 1.47 74.41 0.02
22 2.08 3.56 5.17 5.55* 3.20 80.40 0.04
23 4.39 6.00 10.84* 5.93 3.39 69.41 0.05
24 3.09 3.29* 4.74 4.18 3.05 81.62 0.03
25 3.29 5.45 5.05 3.90* 2.88 79.40 0.02
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 9987 Student(s), Females
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 3.73 0.93 93.84* 0.47 0.15 0.86 0.01
2 10.58 1.52 2.88 3.05 80.27* 1.65 0.03
3 5.88 4.83 67.62* 20.25 0.12 1.28 0.03
4 5.62 3.93 1.98 4.38 60.20* 23.80 0.10
5 41.35* 3.32 2.10 29.22 13.23 10.74 0.03
6 1.98 6.15 38.03* 5.52 11.24 36.99 0.09
7 10.41 48.62* 3.71 11.82 3.22 22.17 0.04
8 39.69* 8.44 2.74 5.46 1.81 41.81 0.04
9 9.53 18.79 7.15 31.73* 8.79 23.97 0.03
10 1.99 5.58 21.81 23.68 26.23* 20.62 0.09
11 12.18 25.13* 9.45 13.38 4.85 34.95 0.07
12 31.42* 9.18 10.56 5.39 2.30 41.11 0.03
13 11.23 13.07* 6.03 5.38 2.52 61.75 0.02
14 2.16 6.00 3.53 6.96* 8.63 72.66 0.05
15 11.64 11.42 7.14 12.90* 4.71 52.14 0.06
16 4.40 17.98 16.69* 3.94 3.23 53.73 0.03
17 2.26 8.74* 8.84 4.77 6.04 69.28 0.07
18 8.02* 5.73 7.22 4.83 4.37 69.77 0.07
19 7.34 4.59* 7.03 7.03 3.43 70.52 0.06
20 3.88 5.46 4.43* 4.60 3.31 78.25 0.08
21 4.23 5.42 6.36 5.71* 1.52 76.74 0.03
22 2.38 3.74 4.30 3.67* 2.57 83.27 0.06
23 5.04 6.35 7.68* 5.76 3.34 71.76 0.07
24 3.57 2.71* 3.54 3.76 3.98 82.37 0.06
25 3.92 5.57 4.05 3.29* 2.84 80.30 0.03
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
American Mathematics Competitions
Analysis
2011 AMC 12 B Results
Table of Item Difficulty for the 2011
Tabulation of responses by 5764 Student(s), Unknown Gender
Percent of Responses
ITEM A B C D E OMITS ?
____ _____ _____ _____ _____ _____ _____ _____
1 1.79 0.71 95.52* 0.69 0.07 1.21 0.00
2 8.69 1.44 2.45 2.57 83.36* 1.46 0.03
3 3.05 5.20 77.60* 12.89 0.09 1.15 0.02
4 4.23 2.79 1.54 4.27 70.75* 16.34 0.07
5 49.06* 2.78 2.26 26.15 12.54 7.20 0.02
6 1.67 4.91 53.92* 4.75 8.90 25.82 0.03
7 7.32 62.60* 3.61 9.06 2.29 15.11 0.02
8 56.37* 7.37 2.43 4.88 1.65 27.26 0.05
9 9.66 13.71 6.90 47.07* 6.30 16.36 0.00
10 2.24 5.36 17.40 21.46 38.17* 15.35 0.02
11 8.55 33.61* 10.69 15.34 5.22 26.49 0.10
12 46.34* 8.22 10.90 5.66 2.06 26.79 0.03
13 12.44 20.54* 6.82 6.18 2.83 51.20 0.00
14 2.38 7.32 4.29 11.97* 9.21 64.82 0.02
15 10.91 13.76 9.80 15.18* 4.41 45.92 0.02
16 4.61 21.76 22.80* 4.61 2.67 43.51 0.03
17 2.65 16.19* 9.58 6.07 7.67 57.82 0.02
18 12.80* 6.30 9.63 4.77 4.23 62.25 0.02
19 10.18 7.36* 9.51 9.70 3.42 59.84 0.00
20 3.76 5.00 7.53* 5.86 3.31 74.48 0.05
21 4.01 5.69 7.91 8.71* 1.47 72.17 0.03
22 2.06 4.16 6.09 6.59* 3.42 77.64 0.03
23 4.23 6.77 10.48* 5.67 4.23 68.55 0.07
24 3.80 3.90* 4.89 5.03 3.38 78.96 0.03
25 2.85 6.38 4.74 4.58* 3.49 77.97 0.00
(*) Correct Response
(?) Response the computer was unable to read due to incomplete
erasures or two answers marked in the same column
(^) Note: Students who failed to indicate their grade are not
included in this analysis.
