2nd exam done! Yesterday, thousands of middle school and high school students participated in this year’s AMC 10B and 12B Competition.

The problems can now be discussed! See below for answer keys and concepts tested for every problem on the 2023 AMC 10B and AMC 12B held on November 14th, 2023.

2023 AMC 10B Answers

1

C

arithmetic: word problems and fractions

2

B

arithmetic: percentages, discounts, and taxes

3

D

geometry: circles, inscribed triangles, and Pythagorean triples

4

C

arithmetic: units, conversions, and areas

5

A

algebra: sums, logic, and systems of equations

6

E

number theory: sequences, patterns, and parity

7

B

geometry: squares, triangles, angles, and rotations

8

A

number theory: powers, units digits, and patterns

9

B

algebra: difference of squares and inequalities

10

C

careful thinking, logic, and games

11

B

algebra and number theory: Diophantine equations and patterns

12

C

algebra: polynomials, end behavior, and patterns

13

B

algebra and geometry: areas, absolute values, and symmetry

14

C

algebra and number theory: Diophantine equations, factoring, and squares

15

C

number theory: perfect squares, prime factorization, and grouping

16

E

combinatorics: counting, careful thinking, and subsets

17

D

geometry and algebra: distances in 3D, edges, surfaces areas, volumes, and Vieta’s formulas

18

E

number theory: Diophantine equations, careful thinking, and GCDs

19

B

combinatorics: geometry probability, law of total probability, and cases

20

A

geometry: spheres, circles, squares, and perimeter

21

E

combinatorics: probability, states, and patterns

22

B

algebra: equations and the floor function

23

B

algebra and number theory: arithmetic series and modular arithmetic

24

E

algebra and geometry: vectors, transformations, and perimeter

25

B

geometry: similar polygons, area ratios, and the Golden ratio

2023 AMC 12B Answers

1

C

arithmetic: word problems and fractions

2

B

arithmetic: percentages, discounts, and taxes

3

D

geometry: circles, inscribed triangles, and Pythagorean triples

4

C

arithmetic: units, conversions, and areas

5

C

careful thinking, logic, and games

6

C

algebra: polynomials, end behavior, and patterns

7

E

algebra: logarithms, domains, and inequalities

8

D

combinatorics: subsets, patterns, and the Fibonacci sequence

9

B

algebra and geometry: areas, absolute values, and symmetry

10

E

geometry: circles, equations, and lines

11

D

geometry: trapezoids, area formulas, maximization, and AM-GM

12

E

algebra: complex numbers, modulii, and equations

13

D

geometry and algebra: distances in 3D, edges, surfaces areas, volumes, and Vieta’s formulas

14

A

algebra: polynomials, factors, and Vieta’s formula

15

E

number theory: Diophantine equations, careful thinking, and GCDs

16

D

number theory: GCDs and Bezout’s identity

17

E

geometry: triangles, law of cosines, and areas

18

A

algebra: averages vs totals, careful thinking, and Simpson’s paradox

19

E

combinatorics: probability, states, and patterns

20

E

combinatorics and geometry: geometric probability, angles, and trigonometry

21

E

geometry: cones, frustrums, similar triangles, and tangents

22

E

algebra: functional equations, logic, and factoring

23

A

combinatorics: careful thinking, cases, and stars and bars

24

C

number theory: prime factorizations, GCDs, and LCMs

25

B

geometry: similar polygons, area ratios, and the Golden ratio

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

4

4

10

5

12

6

13

9

17

13

18

15

21

19

25

25

Want to see the problems? The 2023 AMC 10B and 12B 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.