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 Fall 2021-22 AMC 10A and AMC 12A questions as well as the concepts tested on each problem.
AMC 10A Answers
1
C
arithmetic and factors
2
E
geometry: areas, rectangles, and logic
3
D
geometry: volumes of cubes and spheres and approximations
4
B
algebra: rates and average speeds
5
E
number theory: primes, digits, and divisibility
6
B
algebra: rates, ratios, and careful thinking
7
D
geometry: angles in triangles and squares
8
B
number theory and algebra: digits and sums
9
E
combinatorics: probability
10
B
algebra: averages and weighted averages
11
A
algebra: rates and relative motion
12
D
number theory: number bases and modular arithmetic
13
D
combinatorics: probability and combinations
14
D
algebra: graphing, absolute values, parabolas
15
C
geometry: circles, tangent lines, and circumcircles
16
D
algebra: absolute values, floor functions, and symmetry
17
D
geometry: regular hexagons, planes, and similarity
18
C
combinatorics: cases, careful thinking, and symmetry
19
A
geometry: areas, circular regions, and careful thinking
20
B
algebra: quadratics and discriminants
21
E
combinatorics: arrangements and probability
22
B
geometry: solid geometry, circles, and equilateral triangles
23
D
number theory: prime factorizations, number of factors, and patterns
24
E
combinatorics: cases and careful thinking
25
A
algebra: quadratics, polynomials, and roots
AMC 12A Answers
1
C
arithmetic and factors
2
E
geometry: areas, rectangles, and logic
3
B
algebra: rates and average speeds
4
E
number theory: primes, digits, and divisibility
5
B
algebra: rates, ratios, and careful thinking
6
D
geometry: angles in triangles and squares
7
B
algebra: averages and weighted averages
8
D
number theory: prime factorizations and least common multiples
9
E
algebra and geometry: surface area, prisms, and logarithms
10
D
number theory: number bases and modular arithmetic
11
E
geometry: circles, chords, and power of a point
12
C
combinatorics and algebra: binomial expansion and binomial theorem
13
A
geometry and algebra: slopes, lines, and angle bisector theorem
14
E
geometry: areas, congruent triangles, and Law of Cosines
15
D
algebra: polynomials, complex roots, and Vieta’s theorem
16
B
combinatorics: pigeonhole principle and worst-case scenarios
17
B
algebra: quadratics and discriminants
18
E
combinatorics: arrangements and probability
19
B
geometry: trigonometry, identities, and quadratics
20
D
number theory: prime factorizations, number of factors, and patterns
21
C
geometry: similar triangles, trapezoids, and algebra
22
D
combinatorics: cases and complementary counting
23
A
algebra: quadratics, polynomials, and roots
24
E
geometry and algebra: quadrilaterals, arithmetic sequences, and equations
25
E
number theory and combinatorics: modular arithmetic, residue classes, inclusion-exclusion
In total, 12 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
4
3
5
4
6
5
7
6
10
7
12
10
20
17
21
18
23
20
25
23
Want full solutions to all the 2021 AMC 10A & 12A questions? Our full solutions review video has you covered! Registration and solutions will be available on Friday, November 12th. Click here for registration. The 2021 AMC 10A and 12A 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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