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.
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