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.

2023 AMC 10A Answers

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

2023 AMC 12A Answers

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:

AMC 10A

AMC 12A

1

1

2

2

3

3

5

4

7

5

9

7

10

8

11

9

16

13

22

18

25

21

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.

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.