Yesterday, thousands of middle school and high school students participated in this year’s AMC 10A and 12A Competition. It was great to be able to have students back onsite taking the exam!

The problems can now be discussed! See below for answer keys and concepts tested for every problem on the 2022 AMC 10A and AMC 12A held on November 10th, 2022.

AMC 10A Answers

1

D

arithmetic, fractions, and reciprocals

2

B

speeds, ratios, and estimation

3

E

algebra: multiples, differences, and linear equations

4

E

rates, units, and conversions

5

C

geometry: polygons, perimeter, and special triangles

6

A

algebra: absolute values and square roots

7

B

number theory: GCDs, LCMs, and factors

8

D

algebra: averages and multiples

9

D

combinatorics: counting carefully

10

E

geometry: diagonals and Pythagorean theorem

11

C

algebra: rules of exponents and radicals

12

A

combinatorics: logic and expressions

13

C

geometry: angle bisectors, parallel lines, and trapezoids

14

E

combinatorics: counting, logic, and careful thinking

15

D

geometry: circles, triangles, and Pythagorean triples

16

D

algebra: polynomials and Vieta’s theorem

17

D

algebra and number theory: repeated decimals and Diophantine equations

18

A

geometry: transformations, rotations, and multiples

19

C

number theory and algebra: harmonic series, LCMs, and remainders

20

E

algebra: arithmetic and geometric sequences, differences, and equations

21

B

geometry: solid geometry, polygons, and symmetry

22

D

combinatorics: careful thinking, subsets, and complementary counting

23

B

geometry: trapezoids, Pythagorean theorem, and coordinates

24

E

combinatorics: permutations, partitions, and cases

25

B

algebra and geometry: lattice points, “areas”, ratios, and equations

AMC 12A Answers

1

D

arithmetic, fractions, and reciprocals

2

E

algebra: multiples, differences, and linear equations

3

B

geometry: areas and perimeters

4

B

number theory: GCDs, LCMs, and factors

5

C

combinatorics: lattice points, counting, and symmetry

6

D

algebra: averages and multiples

7

D

combinatorics: counting carefully

8

A

algebra: exponents, radicals, and geometric series

9

A

combinatorics: logic and expressions

10

E

combinatorics: counting and careful thinking

11

E

algebra: rules of logarithms and equations

12

B

geometry: 3D geometry, angles, law of cosines

13

A

algebra and geometry: complex numbers, magnitudes, and areas

14

C

algebra: logarithms, substitutions, and factoring

15

D

algebra: polynomials and Vieta’s theorem

16

D

number theory: factors and perfect squares

17

A

algebra: trigonometry, identities, and graphing

18

A

geometry: transformations, rotations, and multiples

19

D

combinatorics: careful thinking, subsets, and complementary counting

20

B

geometry: trapezoids, Pythagorean theorem, and coordinates

21

E

algebra: polynomials, quotients and remainders, and roots of unity

22

A

geometry and algebra: complex numbers, conjugates, and areas

23

D

number theory and algebra: LCMs, GCDs, and harmonic numbers

24

E

combinatorics: permutations, partitions, and cases

25

E

geometry and number theory: circles, tangents, Pythagorean triples, and factors

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

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.