Middle school and high school students competed across the world in the AMC 10B and 12B Competition yesterday! Congrats to all who participated!

The problems can now be discussed! See below for answer keys and concepts tested for every problem on the 2022 AMC 10B and AMC 12B held on November 16th, 2022.

AMC 10B Answers

1

A

algebra: absolute values and arithmetic

2

D

geometry: areas and Pythagorean triples

3

D

combinatorics: counting, digits, and cases

4

A

arithmetic: units and conversions

5

B

algebra and arithmetic: radicals, fractions, and difference of squares

6

A

arithmetic and number theory: primes, multiplication, and factoring

7

B

algebra: quadratics, Vieta’s theorem, and factors

8

B

number theory: multiples, patterns, and counting

9

D

algebra: sums, factorials, and patterns

10

D

algebra: statistics (mean, median, and mode) and equations

11

B

logic: equivalent statements and negation

12

C

combinatorics: probability, dice sums, and complementary counting

13

E

algebra and number theory: primes, factoring, and prime factorizations

14

B

combinatorics: subsets, logic, and sums

15

D

algebra: arithmetic sequences and series

16

D

geometry: areas, similar triangles, Pythagorean triples

17

C

number theory: divisibility, modular arithmetic, patterns

18

B

algebra and combinatorics: systems of equations, cases, and counting

19

C

combinatorics: counting, thinking carefully, and cases

20

D

geometry: angles, parallelograms, and cyclic quadrilaterals

21

E

algebra: polynomials, quotients and remainders, and systems of equations

22

E

geometry: tangent circles and graphs

23

C

combinatorics: geometric probability, law of total probability

24

B

algebra: slopes, absolute values, and inequalities

25

A

number theory: modular arithmetic and patterns

AMC 12B Answers

1

A

algebra: absolute values and arithmetic

2

D

geometry: areas and Pythagorean triples

3

A

arithmetic and number theory: primes, multiplication, and factoring

4

B

algebra: quadratics, Vieta’s theorem, and factors

5

B

geometry: coordinates and rotations

6

B

number theory: multiples, patterns, and counting

7

D

algebra: statistics (mean, median, and mode) and equations

8

D

algebra: factoring, conics, and graphing

9

B

algebra: arithmetic sequences and logarithms

10

D

geometry: hexagons, perimeter, and Law of Cosines

11

E

algebra: complex numbers, polar form, and De Moivre’s Theorem

12

D

combinatorics: probability and cases

13

D

geometry: areas, similar triangles, Pythagorean triples

14

E

geometry and algebra: intercepts, trigonometry, and identities

15

C

number theory: divisibility, modular arithmetic, patterns

16

C

algebra: logarithms, simplification, and substitution

17

D

combinatorics: careful thinking, symmetry, and permutations

18

C

combinatorics: counting, thinking carefully, and cases

19

A

geometry: medians, centroids, and Law of Cosines

20

E

algebra: polynomials, quotients and remainders, and systems of equations

21

E

geometry: tangent circles and graphs

22

C

combinatorics: geometric probability, law of total probability

23

A

number theory: modular arithmetic and patterns

24

C

geometry and algebra: diagonals, complex numbers, and roots of unity

25

B

geometry: areas, regular polygons, Law of Sines

In total, 13 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

6

3

7

4

8

6

10

7

16

13

17

15

19

18

21

20

22

21

23

22

25

23

Want reviews of past AMC 10 and 12 questions questions? Check out our AMC 10+12 contest page. Click here for more information. The 2022 AMC 10B and 12B problems will also be 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.