Yesterday, thousands of middle school and high school students participated in this year’s AMC 10B and 12B Competition (including some students at Areteem Headquarters seen below).

The problems can now be discussed! See below for answer keys for both the 2020 AMC 10B and AMC 12B questions as well as the concepts tested on each problem.

AMC 10B Answers

1

D

arithmetic and negative numbers

2

E

geometry: cubes and volumes

3

E

algebra: ratios

4

D

geometry and number theory: primes numbers and angles in triangles

5

B

combinatorics: permutations with repeated objects

6

B

motion and palindromes

7

A

number theory: LCMs and perfect squares

8

D

geometry: right triangles and areas

9

D

number theory: diophantine equations

10

C

geometry: cones and volumes, lateral surfaces

11

D

combinatorics: probability

12

D

number theory: place values and arithmetic

13

B

geometry: coordinates and patterns

14

D

geometry: areas, hexagons, and circles

15

D

combinatorics: patterns and multiples

16

A

logic and game theory

17

C

combinatorics: cases and logic

18

B

combinatorics: probability and repetition

19

A

number theory: computation and modular arithmetic

20

B

geometry: volumes, prisms, cylinders, and spheres

21

B

geometry: areas, squares, right triangles

22

D

number theory: remainders, divisibility, and factoring

23

C

geometry: composing transformations

24

C

number theory: floor function and equations

25

A

combinatorics: permutations of products, cases, and patterns

AMC 12B Answers

1

C

arithmetic and square roots

2

A

algebra: arithmetic and factoring

3

E

algebra: ratios

4

D

geometry and number theory: primes numbers and angles in triangles

5

C

algebra: ratios and equations

6

D

number theory: factoring and simplifying

7

C

geometry: slopes, angles, and trigonometry

8

D

number theory: diophantine equations

9

C

geometry: cones and volumes, lateral surfaces

10

B

geometry: squares, inscribed circles, and power of a point

11

D

geometry: areas, hexagons, and circles

12

E

geometry: circles, chords, and power of a point

13

D

algebra: logarithms and square roots

14

A

logic and game theory

15

C

combinatorics: cases and logic

16

B

combinatorics: probability and repetition

17

C

algebra: polynomials, roots, and complex numbers

18

B

geometry: areas, squares, right triangles

19

C

geometry: composing transformations

20

D

combinatorics: probability, coloring cubes

21

C

number theory: floor function and equations

22

C

algebra: maximums, AM-GM inequality

23

B

algebra: complex numbers and polar coordinates

24

A

combinatorics: permutations of products, cases, and patterns

25

B

combinatorics: geometric probability, trigonometric functions, and maximums

In total 12 questions appeared on both the AMC 10B and AMC 12B. They are listed below:

AMC 10B

AMC 12B

3

3

4

4

9

8

10

9

14

11

16

14

17

15

18

16

21

18

23

19

24

21

25

24

Starting to prep for the AIME? Join one of Areteem’s AIME Prep courses to prepare for next month’s AIME. Click here for more details and registration. For answers to this year’s AMC 10A and 12A exams, click here. The 2020 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.