2nd exam done! Yesterday, thousands of middle school and high school students participated in this year’s AMC 10B and 12B Competition.
The problems can now be discussed! See below for answer keys and concepts tested for every problem on the 2023 AMC 10B and AMC 12B held on November 14th, 2023.
2023 AMC 10B Answers
1
C
arithmetic: word problems and fractions
2
B
arithmetic: percentages, discounts, and taxes
3
D
geometry: circles, inscribed triangles, and Pythagorean triples
4
C
arithmetic: units, conversions, and areas
5
A
algebra: sums, logic, and systems of equations
6
E
number theory: sequences, patterns, and parity
7
B
geometry: squares, triangles, angles, and rotations
8
A
number theory: powers, units digits, and patterns
9
B
algebra: difference of squares and inequalities
10
C
careful thinking, logic, and games
11
B
algebra and number theory: Diophantine equations and patterns
12
C
algebra: polynomials, end behavior, and patterns
13
B
algebra and geometry: areas, absolute values, and symmetry
14
C
algebra and number theory: Diophantine equations, factoring, and squares
15
C
number theory: perfect squares, prime factorization, and grouping
16
E
combinatorics: counting, careful thinking, and subsets
17
D
geometry and algebra: distances in 3D, edges, surfaces areas, volumes, and Vieta’s formulas
18
E
number theory: Diophantine equations, careful thinking, and GCDs
19
B
combinatorics: geometry probability, law of total probability, and cases
20
A
geometry: spheres, circles, squares, and perimeter
21
E
combinatorics: probability, states, and patterns
22
B
algebra: equations and the floor function
23
B
algebra and number theory: arithmetic series and modular arithmetic
24
E
algebra and geometry: vectors, transformations, and perimeter
25
B
geometry: similar polygons, area ratios, and the Golden ratio
2023 AMC 12B Answers
1
C
arithmetic: word problems and fractions
2
B
arithmetic: percentages, discounts, and taxes
3
D
geometry: circles, inscribed triangles, and Pythagorean triples
4
C
arithmetic: units, conversions, and areas
5
C
careful thinking, logic, and games
6
C
algebra: polynomials, end behavior, and patterns
7
E
algebra: logarithms, domains, and inequalities
8
D
combinatorics: subsets, patterns, and the Fibonacci sequence
9
B
algebra and geometry: areas, absolute values, and symmetry
10
E
geometry: circles, equations, and lines
11
D
geometry: trapezoids, area formulas, maximization, and AM-GM
12
E
algebra: complex numbers, modulii, and equations
13
D
geometry and algebra: distances in 3D, edges, surfaces areas, volumes, and Vieta’s formulas
14
A
algebra: polynomials, factors, and Vieta’s formula
15
E
number theory: Diophantine equations, careful thinking, and GCDs
16
D
number theory: GCDs and Bezout’s identity
17
E
geometry: triangles, law of cosines, and areas
18
A
algebra: averages vs totals, careful thinking, and Simpson’s paradox
19
E
combinatorics: probability, states, and patterns
20
E
combinatorics and geometry: geometric probability, angles, and trigonometry
21
E
geometry: cones, frustrums, similar triangles, and tangents
22
E
algebra: functional equations, logic, and factoring
23
A
combinatorics: careful thinking, cases, and stars and bars
24
C
number theory: prime factorizations, GCDs, and LCMs
25
B
geometry: similar polygons, area ratios, and the Golden ratio
In total, 11 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
3
3
4
4
10
5
12
6
13
9
17
13
18
15
21
19
25
25
Want to see the problems? The 2023 AMC 10B and 12B 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.
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