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.
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