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 2024 AMC 10B and 2024 AMC 12B held on November 12th, 2024.
2024 AMC 10B Answers
1
B
arithmetic and spatial reasoning
2
B
algebra: factorials and factoring
3
E
arithmetic: inequalities and estimation
4
D
algebra: sum of positive integers, patterns, and estimation
5
B
algebra: arithmetic series, inequalities, and estimation
6
B
number theory: prime factorization, factors, and minimizing perimeter
7
A
number theory: factoring and remainders
8
D
number theory: factors, number of factors, pairing, and units digit
9
A
algebra: means, sums, and factoring
10
A
geometry: parallelograms, similar triangles, and area ratios
11
C
geometry: areas, Pythagorean theorem, and equations
12
A
combinatorics: counting subsets and careful thinking
13
B
number theory: Diophantine equations, factoring, perfect squares, and quadratic equations
14
B
combinatorics: geometric probability and areas and equations of circles and diamonds
15
C
algebra: statistics (means, medians, and range), equations, and cases
16
A
number theory: parity (mod 2) and careful thinking
17
D
combinatorics: counting, permutations, and grouping
18
B
number theory: modular arithmetic and Euler’s Totient Function
19
C
algebra: lines, slopes, lattice points, and rational and irrational numbers
20
A
combinatorics: counting, pairing, cases, and careful thinking
21
C
geometry: tangent circles, tangent lines, and the Pythagorean theorem
22
A
combinatorics and number theory: choosing groups and prime factorizations
23
B
combinatorics: Fibonacci sequence, patterns, and sums
24
E
number theory: polynomials and modular arithmetic
25
E
algebra: systems of equations
2024 AMC 12B Answers
1
B
arithmetic and spatial reasoning
2
B
algebra: factorials and factoring
3
E
arithmetic: inequalities and estimation
4
D
algebra: sum of positive integers, patterns, and estimation
5
B
algebra: arithmetic series, inequalities, and estimation
6
B
algebra and number theory: number bases, logarithms, and estimation
7
C
geometry: areas, Pythagorean theorem, and equations
8
C
algebra: logarithms, change of base, and equations
9
B
combinatorics: geometric probability and areas and equations of circles and diamonds
10
C
algebra: statistics (means, medians, and range), equations, and cases
11
E
algebra: averages, trig. identities, and pairing
12
D
algebra: complex numbers, polar form, and areas of triangles
13
C
algebra and geometry: completing the square, equations of circles, tangent circles, and inequalities
14
B
number theory: modular arithmetic and Euler’s Totient Function
15
B
geometry: areas of triangles or Shoelace theorem and logarithms
16
A
combinatorics and number theory: choosing groups and prime factorizations
17
C
algebra and combinatorics: probability, integer roots, and Vieta’s theorem
18
B
combinatorics: Fibonacci sequence, patterns, and sums
19
B
geometry: rotations, areas, trigonometry, and trig. identities
20
C
geometry: triangles, medians, areas, inequalities, and careful thinking
21
C
geometry and algebra: Pythagorean triples and trig. Identities
22
C
geometry: circumcircles and cyclic quadrilaterals, Ptolemy’s theorem, and Diophantine equations
23
B
geometry: pyramids, volume, octagons, and trig. identities
24
B
geometry: triangles, incircles, equations, and the triangle inequality
25
A
combinatorics: probability, independence, and casework
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
5
5
11
7
14
9
15
10
18
14
22
16
23
18
Want to see the problems? The 2024 AMC 10B and 12B problems will 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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