{"id":2625,"date":"2023-11-09T09:25:56","date_gmt":"2023-11-09T17:25:56","guid":{"rendered":"https:\/\/areteem.org\/blog\/?p=2625"},"modified":"2023-11-15T15:00:08","modified_gmt":"2023-11-15T23:00:08","slug":"2023-amc-10a-amc-12a-answer-key-released","status":"publish","type":"post","link":"https:\/\/areteem.org\/blog\/2023-amc-10a-amc-12a-answer-key-released\/","title":{"rendered":"2023 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.<\/p>\n\n\n\n

The problems can now be discussed! See below for answer keys and concepts tested for every problem on the 2023 AMC 10A and AMC 12A held on November 8th, 2023.<\/p>\n\n\n\n

2023 AMC 10A Answers<\/strong><\/p>\n\n

\n
1<\/strong><\/div>\n
E<\/strong><\/div>\n
algebra: motion and ratios<\/div>\n<\/div>\n
\n
2<\/strong><\/div>\n
A<\/strong><\/div>\n
arithmetic: fractions and equations<\/div>\n<\/div>\n
\n
3<\/strong><\/div>\n
A<\/strong><\/div>\n
number theory: primes, perfect squares, and counting<\/div>\n<\/div>\n
\n
4<\/strong><\/div>\n
D<\/strong><\/div>\n
geometry: perimeters and inequalities<\/div>\n<\/div>\n
\n
5<\/strong><\/div>\n
E<\/strong><\/div>\n
number theory: prime factorization and digits<\/div>\n<\/div>\n
\n
6<\/strong><\/div>\n
D<\/strong><\/div>\n
arithmetic: careful thinking and sums<\/div>\n<\/div>\n
\n
7<\/strong><\/div>\n
B<\/strong><\/div>\n
probability: dice rolls, sums, and cases<\/div>\n<\/div>\n
\n
8<\/strong><\/div>\n
D<\/strong><\/div>\n
algebra: conversions, slopes, and linear functions<\/div>\n<\/div>\n
\n
9<\/strong><\/div>\n
E<\/strong><\/div>\n
careful thinking, logic, and number of days in months<\/div>\n<\/div>\n
\n
10<\/strong><\/div>\n
D<\/strong><\/div>\n
algebra: equations and averages<\/div>\n<\/div>\n
\n
11<\/strong><\/div>\n
C<\/strong><\/div>\n
geometry and algebra: areas, equations, quadratics, and ratios<\/div>\n<\/div>\n
\n
12<\/strong><\/div>\n
B<\/strong><\/div>\n
number theory: divisibility, place values, and multiples<\/div>\n<\/div>\n
\n
13<\/strong><\/div>\n
C<\/strong><\/div>\n
geometry: optimization and special triangles<\/div>\n<\/div>\n<\/div>
\n
14<\/strong><\/div>\n
B<\/strong><\/div>\n
combinatorics and number theory: probability, number of factors, and careful thinking<\/div>\n<\/div>\n
\n
15<\/strong><\/div>\n
E<\/strong><\/div>\n
geometry and algebra: circles, areas, and arithmetic sequences<\/div>\n<\/div>\n
\n
16<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra and number theory: ratios, equations, and multiples<\/div>\n<\/div>\n
\n
17<\/strong><\/div>\n
A<\/strong><\/div>\n
geometry and algebra: Pythagorean triples<\/div>\n<\/div>\n
\n
18<\/strong><\/div>\n
D<\/strong><\/div>\n
geometry: 3D solids, vertices, faces, and edges<\/div>\n<\/div>\n
\n
19<\/strong><\/div>\n
E<\/strong><\/div>\n
geometry and algebra: rotations, circles, chords, and lines<\/div>\n<\/div>\n
\n
20<\/strong><\/div>\n
D<\/strong><\/div>\n
combinatorics: counting, cases, and logic<\/div>\n<\/div>\n
\n
21<\/strong><\/div>\n
D<\/strong><\/div>\n
algebra: polynomials, roots, and transformations<\/div>\n<\/div>\n
\n
22<\/strong><\/div>\n
D<\/strong><\/div>\n
geometry: circles and tangents<\/div>\n<\/div>\n
\n
23<\/strong><\/div>\n
C<\/strong><\/div>\n
number theory and algebra: factors and Diophantine equations<\/div>\n<\/div>\n
\n
24<\/strong><\/div>\n
C<\/strong><\/div>\n
geometry: areas, regular hexagons, and similarity<\/div>\n<\/div>\n
\n
25<\/strong><\/div>\n
A<\/strong><\/div>\n
combinatorics and geometry: probability, symmetry, and 3D solids<\/div>\n<\/div>\n<\/div><\/div>\n\n

2023 AMC 12A Answers<\/strong><\/p>\n\n

\n
1<\/strong><\/div>\n
E<\/strong><\/div>\n
algebra: motion and ratios<\/div>\n<\/div>\n
\n
2<\/strong><\/div>\n
A<\/strong><\/div>\n
arithmetic: fractions and equations<\/div>\n<\/div>\n
\n
3<\/strong><\/div>\n
A<\/strong><\/div>\n
number theory: primes, perfect squares, and counting<\/div>\n<\/div>\n
\n
4<\/strong><\/div>\n
E<\/strong><\/div>\n
number theory: prime factorization and digits<\/div>\n<\/div>\n
\n
5<\/strong><\/div>\n
B<\/strong><\/div>\n
probability: dice rolls, sums, and cases<\/div>\n<\/div>\n
\n
6<\/strong><\/div>\n
D<\/strong><\/div>\n
algebra: logarithms and midpoints<\/div>\n<\/div>\n
\n
7<\/strong><\/div>\n
E<\/strong><\/div>\n
careful thinking, logic, and number of days in months<\/div>\n<\/div>\n
\n
8<\/strong><\/div>\n
D<\/strong><\/div>\n
algebra: equations and averages<\/div>\n<\/div>\n
\n
9<\/strong><\/div>\n
C<\/strong><\/div>\n
geometry and algebra: areas, equations, quadratics, and ratios<\/div>\n<\/div>\n
\n
10<\/strong><\/div>\n
D<\/strong><\/div>\n
algebra: algebraic identities and substitution<\/div>\n<\/div>\n
\n
11<\/strong><\/div>\n
C<\/strong><\/div>\n
algebra and geometry: slopes, angles, trigonometry, and Law of Cosines<\/div>\n<\/div>\n
\n
12<\/strong><\/div>\n
D<\/strong><\/div>\n
algebra: difference of cubes, series, and sum of n squares<\/div>\n<\/div>\n
\n
13<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra and number theory: ratios, equations, and multiples<\/div>\n<\/div>\n<\/div>
\n
14<\/strong><\/div>\n
E<\/strong><\/div>\n
algebra: complex numbers, conjugates, roots of unity, and polynomial equations<\/div>\n<\/div>\n
\n
15<\/strong><\/div>\n
A<\/strong><\/div>\n
geometry: reflections and basic trigonometry<\/div>\n<\/div>\n
\n
16<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra: complex numbers, quadratics, and careful thinking<\/div>\n<\/div>\n
\n
17<\/strong><\/div>\n
E<\/strong><\/div>\n
combinatorics: probability, law of total probability, and patterns<\/div>\n<\/div>\n
\n
18<\/strong><\/div>\n
D<\/strong><\/div>\n
geometry: circles and tangents<\/div>\n<\/div>\n
\n
19<\/strong><\/div>\n
C<\/strong><\/div>\n
algebra: logarithms, change of base, and equations<\/div>\n<\/div>\n
\n
20<\/strong><\/div>\n
C<\/strong><\/div>\n
number theory: sums, patterns, and modular arithmetic<\/div>\n<\/div>\n
\n
21<\/strong><\/div>\n
A<\/strong><\/div>\n
combinatorics and geometry: probability, symmetry, and 3D solids<\/div>\n<\/div>\n
\n
22<\/strong><\/div>\n
B<\/strong><\/div>\n
number theory and algebra: prime factorization and functions<\/div>\n<\/div>\n
\n
23<\/strong><\/div>\n
B<\/strong><\/div>\n
algebra: factoring and completing the square<\/div>\n<\/div>\n
\n
24<\/strong><\/div>\n
C<\/strong><\/div>\n
combinatorics and number theory: subsets, patterns, and modular arithmetic<\/div>\n<\/div>\n
\n
25<\/strong><\/div>\n
C<\/strong><\/div>\n
algebra: trigonometric identities and patterns<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n

In total, 11 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>
3<\/td>3<\/td><\/tr>
5<\/td>4<\/td><\/tr>
7<\/td>5<\/td><\/tr>
9<\/td>7<\/td><\/tr>
10<\/td>8<\/td><\/tr>
11<\/td>9<\/td><\/tr>
16<\/td>13<\/td><\/tr>
22<\/td>18<\/td><\/tr>
25<\/td>21<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Want to see the problems?<\/strong> The 2023 AMC 10A and 12A problems are 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 2023 AMC 10A and 12A Exams held November 8, 2023 are available now. See all the answers and problem types from the exams!<\/p>\n","protected":false},"author":11,"featured_media":2629,"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":"\n2023 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\/2023-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=\"2023 AMC 10A & AMC 12A Answer Key Released - Areteem Institute Blog\" \/>\n<meta property=\"og:description\" content=\"Answers to the 2023 AMC 10A and 12A Exams held November 8, 2023 are available now. See all the answers and problem types from the exams!\" \/>\n<meta property=\"og:url\" content=\"https:\/\/areteem.org\/blog\/2023-amc-10a-amc-12a-answer-key-released\/\" \/>\n<meta property=\"og:site_name\" content=\"Areteem Institute Blog\" \/>\n<meta property=\"article:published_time\" content=\"2023-11-09T17:25:56+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-11-15T23:00:08+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/areteem.org\/blog\/wp-content\/uploads\/2023\/11\/2023_Key_AMC10A12A.png\" \/>\n\t<meta property=\"og:image:width\" content=\"560\" \/>\n\t<meta property=\"og:image:height\" content=\"315\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\">\n\t<meta name=\"twitter:data1\" content=\"3 minutes\">\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/areteem.org\/blog\/#website\",\"url\":\"https:\/\/areteem.org\/blog\/\",\"name\":\"Areteem Institute Blog\",\"description\":\"Challenging Talented Minds\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":\"https:\/\/areteem.org\/blog\/?s={search_term_string}\",\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/areteem.org\/blog\/2023-amc-10a-amc-12a-answer-key-released\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/areteem.org\/blog\/wp-content\/uploads\/2023\/11\/2023_Key_AMC10A12A.png\",\"width\":560,\"height\":315},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/areteem.org\/blog\/2023-amc-10a-amc-12a-answer-key-released\/#webpage\",\"url\":\"https:\/\/areteem.org\/blog\/2023-amc-10a-amc-12a-answer-key-released\/\",\"name\":\"2023 AMC 10A & AMC 12A Answer Key Released - Areteem Institute Blog\",\"isPartOf\":{\"@id\":\"https:\/\/areteem.org\/blog\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/areteem.org\/blog\/2023-amc-10a-amc-12a-answer-key-released\/#primaryimage\"},\"datePublished\":\"2023-11-09T17:25:56+00:00\",\"dateModified\":\"2023-11-15T23:00:08+00:00\",\"author\":{\"@id\":\"https:\/\/areteem.org\/blog\/#\/schema\/person\/02237852b45e7c235c18cdedabc005ba\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/areteem.org\/blog\/2023-amc-10a-amc-12a-answer-key-released\/\"]}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/areteem.org\/blog\/#\/schema\/person\/02237852b45e7c235c18cdedabc005ba\",\"name\":\"John Lensmire\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/areteem.org\/blog\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/31ef7aa2dde40e811a9678448e86a934?s=96&d=mm&r=g\",\"caption\":\"John Lensmire\"},\"description\":\"Lifelong learner in math and science. Director of Curriculum and Instruction at Areteem Institute.\",\"sameAs\":[\"http:\/\/www.areteem.org\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","_links":{"self":[{"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/posts\/2625"}],"collection":[{"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/comments?post=2625"}],"version-history":[{"count":4,"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/posts\/2625\/revisions"}],"predecessor-version":[{"id":2644,"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/posts\/2625\/revisions\/2644"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/media\/2629"}],"wp:attachment":[{"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/media?parent=2625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/categories?post=2625"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/areteem.org\/blog\/wp-json\/wp\/v2\/tags?post=2625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}