Yesterday, thousands of middle school and high school students participated in this year’s AMC 10A and 12A 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 10A and AMC 12A questions as well as the concepts tested on each problem.

AMC 10A Answers

1

D

arithmetic and exponents

2

C

algebra: ratios

3

D

number theory: place values and arithmetic

4

D

algebra: arithmetic sequences with motion

5

B

algebra: averages

6

A

algebra: motion

7

D

logic and cases

8

E

number theory: place values and repeating decimals

9

D

algebra: factoring and minimums

10

C

algebra: factoring and differences of squares

11

E

number theory: bases and divisibility

12

E

geometry: volumes and cones

13

C

geometry: volumes and pyramids

14

A

algebra: polynomials and Vieta’s theorem

15

C

algebra and combinatorics: quadratics and cases

16

C

algebra: arithmetic and medians

17

D

geometry: areas and trapezoids

18

E

number theory and algebra: prime factorizations and functions

19

E

algebra and geometry: absolute values, graphing, circles and areas

20

D

combinatorics: cases and logic

21

C

geometry: hexagons, equilateral triangles, and area

22

B

algebra and number theory: Diophantine equations

23

D

combinatorics: cases and total probability

24

D

geometry and algebra: graphing, areas, parallelograms

25

E

combinatorics: cases and symmetry

AMC 12A Answers

1

B

arithmetic and exponents

2

D

algebra and logic: square roots

3

D

number theory: place values and arithmetic

4

D

logic and cases

5

E

number theory: place values and repeating decimals

6

C

combinatorics: probability

7

D

algebra: factoring and minimums

8

C

number theory: sequences, parity, and patterns

9

C

algebra: factoring and differences of squares

10

E

geometry: volumes and cones

11

C

geometry: coordinates, reflections, and distance

12

A

algebra: polynomials and Vieta’s theorem

13

B

algebra: complex numbers and powers

14

E

algebra: logarithms, sums and summation notation, patterns

15

D

combinatorics: groups and cases

16

C

algebra: arithmetic and medians

17

D

geometry: areas and trapezoids

18

E

number theory and algebra: prime factorizations and functions

19

C

algebra: trigonometric functions

20

B

algebra and geometry: parabolas and distances

21

A

algebra and geometry: complex numbers, ellipses, and eccentricity

22

D

algebra: trigonometric identities and Vieta’s theorem

23

D

combinatorics: cases and total probability

24

D

geometry: circles, tangents, and triangles

25

E

number theory: prime factorizations and the divisor function

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

AMC 10A

AMC 12A

3

3

7

4

8

5

9

7

10

9

12

10

14

12

16

16

17

17

18

18

23

23

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 and 12A 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.