Yesterday, thousands of middle school and high school students participated in this year’s AMC 10B and 12B 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 2021 AMC 10B and AMC 12B questions as well as the concepts tested on each problem.
AMC 10B Answers
1
D
algebra: absolute values and inequalities
2
D
arithmetic: square roots
3
C
arithmetic: percentages
4
B
arithmetic: careful thinking and calculation
5
B
number theory: factors and multiples
6
C
algebra: ratios and averages
7
D
geometry: circles, areas, and logic
8
A
patterns and sequences
9
D
geometry: coordinates and transformations
10
A
geometry: cones, cylinders, and volumes
11
D
geometry and counting: squares
12
C
number theory: factors and ratios
13
B
number theory: number bases and place values
14
B
geometry: circles, chords and parallel lines
15
B
algebra: factoring, polynomials, and substitution
16
C
combinatorics: counting and divisibility
17
C
logic and careful thinking
18
C
combinatorics: probability and independence
19
D
algebra: sets, averages, and system of equations
20
D
geometry: pentagons, triangles, and symmetry
21
A
geometry: Pythagorean theorem and similar triangles
22
D
combinatorics: probability and inclusion-exclusion
23
C
combinatorics: geometric probability and areas
24
B
games, strategies, and symmetry
25
E
algebra: lattice points, slopes, and patterns
AMC 12B Answers
1
D
algebra: absolute values and inequalities
2
B
arithmetic: careful thinking and calculation
3
A
algebra: fractions and equations
4
C
algebra: ratios and averages
5
D
geometry: coordinates and transformations
6
A
geometry: cones, cylinders, and volumes
7
C
number theory: factors and ratios
8
B
geometry: circles, chords and parallel lines
9
D
arithmetic: rules of logarithms
10
E
algebra: completing the rectangle
11
D
geometry: similar triangles and altitudes
12
D
algebra: sets, averages, and system of equations
13
D
algebra: trigonometry and identities
14
A
geometry: pyramids, distance, and volume
15
D
geometry: pentagons, triangles, and symmetry
16
A
algebra: polynomials and Vieta’s theorem
17
B
geometry: areas, trapezoids, and triangles
18
A
algebra: complex numbers, moduli, conjugates
19
B
probability: dice rolls, cases, and patterns
20
A
algebra: polynomials, roots of unity
21
D
algebra: exponents, logarithms, and equations
22
B
games, strategies, and symmetry
23
A
combinatorics: cases, patterns, and infinite geometric sums
24
A
geometry: projections, parallelograms, and cyclic quadrilaterals
25
E
algebra: lattice points, slopes, and patterns
In total, 11 questions appeared on both the AMC 10B and AMC 12B. They are listed below:
AMC 10B
AMC 12B
1
1
4
2
6
4
9
5
10
6
12
7
14
8
19
12
20
15
24
22
25
25
Want full solutions to all the 2021 AMC 10A & 12A questions? Our full solutions review video has you covered! Click here for registration.
The 2021 AMC 10A, 10B, 12A, and 12B problems are all 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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