# 2023 AMC 10A & AMC 12A Answer Key Released

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Yesterday, thousands of middle school and high school students participated in this year’s AMC 10A and 12A Competition.

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.

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

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

In total, 11 questions of the same questions appeared on both the AMC 10A and AMC 12A. They are listed below:

Want to see the problems? The 2023 AMC 10A and 12A problems are available on the ZIML site along with previous exams. Click here for AMC 10 and here for AMC 12.

Starting to prep for the AIME? 8 Week Preparation Courses start soon! Click here for more details and registration.

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.