{"id":2366,"date":"2021-11-11T10:16:11","date_gmt":"2021-11-11T18:16:11","guid":{"rendered":"https:\/\/areteem.org\/blog\/?p=2366"},"modified":"2021-11-11T11:04:31","modified_gmt":"2021-11-11T19:04:31","slug":"202122-amc-10a-amc-12a-answer-key-released","status":"publish","type":"post","link":"https:\/\/areteem.org\/blog\/202122-amc-10a-amc-12a-answer-key-released\/","title":{"rendered":"2021-22 AMC 10A & AMC 12A Answer Key Released"},"content":{"rendered":"\n

Yesterday, thousands of middle school and high school students participated in this year’s AMC 10A and 12A Competition. Hopefully everyone was able to take the exam safely, whether they took it online or in school!<\/p>\n\n\n\n

The problems can now be discussed! See below for answer keys for both the Fall 2021-22 AMC 10A and AMC 12A questions as well as the concepts tested on each problem.<\/p>\n\n\n\n

AMC 10A Answers<\/strong><\/p>\n\n

\n
1<\/strong><\/div>\n
C<\/strong><\/div>\n
arithmetic and factors<\/div>\n<\/div>\n
\n
2<\/strong><\/div>\n
E<\/strong><\/div>\n
geometry: areas, rectangles, and logic<\/div>\n<\/div>\n
\n
3<\/strong><\/div>\n
D<\/strong><\/div>\n
geometry: volumes of cubes and spheres and approximations<\/div>\n<\/div>\n
\n
4<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra: rates and average speeds<\/div>\n<\/div>\n
\n
5<\/strong><\/div>\n
E<\/strong><\/div>\n
number theory: primes, digits, and divisibility<\/div>\n<\/div>\n
\n
6<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra: rates, ratios, and careful thinking<\/div>\n<\/div>\n
\n
7<\/strong><\/div>\n
D<\/strong><\/div>\n
geometry: angles in triangles and squares<\/div>\n<\/div>\n
\n
8<\/strong><\/div>\n
B<\/strong><\/div>\n
number theory and algebra: digits and sums<\/div>\n<\/div>\n
\n
9<\/strong><\/div>\n
E<\/strong><\/div>\n
combinatorics: probability<\/div>\n<\/div>\n
\n
10<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra: averages and weighted averages<\/div>\n<\/div>\n
\n
11<\/strong><\/div>\n
A<\/strong><\/div>\n
algebra: rates and relative motion<\/div>\n<\/div>\n
\n
12<\/strong><\/div>\n
D<\/strong><\/div>\n
number theory: number bases and modular arithmetic<\/div>\n<\/div>\n
\n
13<\/strong><\/div>\n
D<\/strong><\/div>\n
combinatorics: probability and combinations<\/div>\n<\/div>\n<\/div>
\n
14<\/strong><\/div>\n
D<\/strong><\/div>\n
algebra: graphing, absolute values, parabolas<\/div>\n<\/div>\n
\n
15<\/strong><\/div>\n
C<\/strong><\/div>\n
geometry: circles, tangent lines, and circumcircles<\/div>\n<\/div>\n
\n
16<\/strong><\/div>\n
D<\/strong><\/div>\n
algebra: absolute values, floor functions, and symmetry<\/div>\n<\/div>\n
\n
17<\/strong><\/div>\n
D<\/strong><\/div>\n
geometry: regular hexagons, planes, and similarity<\/div>\n<\/div>\n
\n
18<\/strong><\/div>\n
C<\/strong><\/div>\n
combinatorics: cases, careful thinking, and symmetry<\/div>\n<\/div>\n
\n
19<\/strong><\/div>\n
A<\/strong><\/div>\n
geometry: areas, circular regions, and careful thinking<\/div>\n<\/div>\n
\n
20<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra: quadratics and discriminants<\/div>\n<\/div>\n
\n
21<\/strong><\/div>\n
E<\/strong><\/div>\n
combinatorics: arrangements and probability<\/div>\n<\/div>\n
\n
22<\/strong><\/div>\n
B<\/strong><\/div>\n
geometry: solid geometry, circles, and equilateral triangles<\/div>\n<\/div>\n
\n
23<\/strong><\/div>\n
D<\/strong><\/div>\n
number theory: prime factorizations, number of factors, and patterns<\/div>\n<\/div>\n
\n
24<\/strong><\/div>\n
E<\/strong><\/div>\n
combinatorics: cases and careful thinking<\/div>\n<\/div>\n
\n
25<\/strong><\/div>\n
A<\/strong><\/div>\n
algebra: quadratics, polynomials, and roots<\/div>\n<\/div>\n<\/div><\/div>\n\n

AMC 12A Answers<\/strong><\/p>\n\n

\n
1<\/strong><\/div>\n
C<\/strong><\/div>\n
arithmetic and factors<\/div>\n<\/div>\n
\n
2<\/strong><\/div>\n
E<\/strong><\/div>\n
geometry: areas, rectangles, and logic<\/div>\n<\/div>\n
\n
3<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra: rates and average speeds<\/div>\n<\/div>\n
\n
4<\/strong><\/div>\n
E<\/strong><\/div>\n
number theory: primes, digits, and divisibility<\/div>\n<\/div>\n
\n
5<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra: rates, ratios, and careful thinking<\/div>\n<\/div>\n
\n
6<\/strong><\/div>\n
D<\/strong><\/div>\n
geometry: angles in triangles and squares<\/div>\n<\/div>\n
\n
7<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra: averages and weighted averages<\/div>\n<\/div>\n
\n
8<\/strong><\/div>\n
D<\/strong><\/div>\n
number theory: prime factorizations and least common multiples<\/div>\n<\/div>\n
\n
9<\/strong><\/div>\n
E<\/strong><\/div>\n
algebra and geometry: surface area, prisms, and logarithms<\/div>\n<\/div>\n
\n
10<\/strong><\/div>\n
D<\/strong><\/div>\n
number theory: number bases and modular arithmetic<\/div>\n<\/div>\n
\n
11<\/strong><\/div>\n
E<\/strong><\/div>\n
geometry: circles, chords, and power of a point<\/div>\n<\/div>\n
\n
12<\/strong><\/div>\n
C<\/strong><\/div>\n
combinatorics and algebra: binomial expansion and binomial theorem<\/div>\n<\/div>\n
\n
13<\/strong><\/div>\n
A<\/strong><\/div>\n
geometry and algebra: slopes, lines, and angle bisector theorem<\/div>\n<\/div>\n<\/div>
\n
14<\/strong><\/div>\n
E<\/strong><\/div>\n
geometry: areas, congruent triangles, and Law of Cosines<\/div>\n<\/div>\n
\n
15<\/strong><\/div>\n
D<\/strong><\/div>\n
algebra: polynomials, complex roots, and Vieta’s theorem<\/div>\n<\/div>\n
\n
16<\/strong><\/div>\n
B<\/strong><\/div>\n
combinatorics: pigeonhole principle and worst-case scenarios<\/div>\n<\/div>\n
\n
17<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra: quadratics and discriminants<\/div>\n<\/div>\n
\n
18<\/strong><\/div>\n
E<\/strong><\/div>\n
combinatorics: arrangements and probability<\/div>\n<\/div>\n
\n
19<\/strong><\/div>\n
B<\/strong><\/div>\n
geometry: trigonometry, identities, and quadratics<\/div>\n<\/div>\n
\n
20<\/strong><\/div>\n
D<\/strong><\/div>\n
number theory: prime factorizations, number of factors, and patterns<\/div>\n<\/div>\n
\n
21<\/strong><\/div>\n
C<\/strong><\/div>\n
geometry: similar triangles, trapezoids, and algebra<\/div>\n<\/div>\n
\n
22<\/strong><\/div>\n
D<\/strong><\/div>\n
combinatorics: cases and complementary counting<\/div>\n<\/div>\n
\n
23<\/strong><\/div>\n
A<\/strong><\/div>\n
algebra: quadratics, polynomials, and roots<\/div>\n<\/div>\n
\n
24<\/strong><\/div>\n
E<\/strong><\/div>\n
geometry and algebra: quadrilaterals, arithmetic sequences, and equations<\/div>\n<\/div>\n
\n
25<\/strong><\/div>\n
E<\/strong><\/div>\n
number theory and combinatorics: modular arithmetic, residue classes, inclusion-exclusion<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n

In total, 12 questions of the same questions appeared on both the AMC 10A and AMC 12A. They are listed below:<\/p>\n\n\n\n

AMC 10A<\/strong><\/td>AMC 12A<\/strong><\/td><\/tr>
1<\/td>1<\/td><\/tr>
2<\/td>2<\/td><\/tr>
4<\/td>3<\/td><\/tr>
5<\/td>4<\/td><\/tr>
6<\/td>5<\/td><\/tr>
7<\/td>6<\/td><\/tr>
10<\/td>7<\/td><\/tr>
12<\/td>10<\/td><\/tr>
20<\/td>17<\/td><\/tr>
21<\/td>18<\/td><\/tr>
23<\/td>20<\/td><\/tr>
25<\/td>23<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Want full solutions to all the 2021 AMC 10A & 12A questions?<\/strong> Our full solutions review video has you covered! Registration and solutions will be available on Friday, November 12th. Click here for registration.<\/a> The 2021 AMC 10A and 12A problems will also be available on the ZIML site along with previous exams. Click here for AMC 10<\/a> and here for AMC 12<\/a>.<\/p>\n\n\n\n

Starting to prep for the AIME?<\/strong> 8 Week Preparation Courses start soon! Click here for more details and registration<\/a>.<\/p>\n\n\n\n

The AMC 10 and 12 exams are administered by the Mathematical Association of America (MAA). For general information about the AMC 10 and 12, click here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Answers to the 2021-22 AMC 10A and 12A Exams are available now. See all the answers and problem types from the exams!<\/p>\n","protected":false},"author":11,"featured_media":2368,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[87],"tags":[123,125,126,137,147,148,151,152],"yoast_head":"\n2021-22 AMC 10A & AMC 12A Answer Key Released - Areteem Institute Blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/areteem.org\/blog\/202122-amc-10a-amc-12a-answer-key-released\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"2021-22 AMC 10A & AMC 12A Answer Key Released - Areteem Institute Blog\" \/>\n<meta property=\"og:description\" content=\"Answers to the 2021-22 AMC 10A and 12A Exams are available now. 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