Yesterday, thousands of middle school and high school students participated in this year’s AMC 10B and 12B Competition. Hopefully everyone was able to take the exam safely, whether they took it online or in school!

The problems can now be discussed! See below for answer keys for both the 2021 AMC 10B and AMC 12B questions as well as the concepts tested on each problem.

AMC 10B Answers

1

D

algebra: absolute values and inequalities

2

D

arithmetic: square roots

3

C

arithmetic: percentages

4

B

arithmetic: careful thinking and calculation

5

B

number theory: factors and multiples

6

C

algebra: ratios and averages

7

D

geometry: circles, areas, and logic

8

A

patterns and sequences

9

D

geometry: coordinates and transformations

10

A

geometry: cones, cylinders, and volumes

11

D

geometry and counting: squares

12

C

number theory: factors and ratios

13

B

number theory: number bases and place values

14

B

geometry: circles, chords and parallel lines

15

B

algebra: factoring, polynomials, and substitution

16

C

combinatorics: counting and divisibility

17

C

logic and careful thinking

18

C

combinatorics: probability and independence

19

D

algebra: sets, averages, and system of equations

20

D

geometry: pentagons, triangles, and symmetry

21

A

geometry: Pythagorean theorem and similar triangles

22

D

combinatorics: probability and inclusion-exclusion

23

C

combinatorics: geometric probability and areas

24

B

games, strategies, and symmetry

25

E

algebra: lattice points, slopes, and patterns

AMC 12B Answers

1

D

algebra: absolute values and inequalities

2

B

arithmetic: careful thinking and calculation

3

A

algebra: fractions and equations

4

C

algebra: ratios and averages

5

D

geometry: coordinates and transformations

6

A

geometry: cones, cylinders, and volumes

7

C

number theory: factors and ratios

8

B

geometry: circles, chords and parallel lines

9

D

arithmetic: rules of logarithms

10

E

algebra: completing the rectangle

11

D

geometry: similar triangles and altitudes

12

D

algebra: sets, averages, and system of equations

13

D

algebra: trigonometry and identities

14

A

geometry: pyramids, distance, and volume

15

D

geometry: pentagons, triangles, and symmetry

16

A

algebra: polynomials and Vieta’s theorem

17

B

geometry: areas, trapezoids, and triangles

18

A

algebra: complex numbers, moduli, conjugates

19

B

probability: dice rolls, cases, and patterns

20

A

algebra: polynomials, roots of unity

21

D

algebra: exponents, logarithms, and equations

22

B

games, strategies, and symmetry

23

A

combinatorics: cases, patterns, and infinite geometric sums

24

A

geometry: projections, parallelograms, and cyclic quadrilaterals

25

E

algebra: lattice points, slopes, and patterns

In total, 11 questions appeared on both the AMC 10B and AMC 12B. They are listed below:

AMC 10B

AMC 12B

1

1

4

2

6

4

9

5

10

6

12

7

14

8

19

12

20

15

24

22

25

25

Want full solutions to all the 2021 AMC 10A & 12A questions? Our full solutions review video has you covered! Click here for registration.

The 2021 AMC 10A, 10B, 12A, and 12B problems are all 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.