Competition · AMC preparation · step 4 of 4

AMC 10 2023A: all 25 problems

Each problem has a solution worked from first principles and the first grade (by CCSS standards) that can solve it.

AMC 10 2023A #1 grade 6+ rate-ratio
Cities A and B are 45 miles apart. Alicia lives in A and Beth lives in B. Alicia bikes towards B at 18 miles per hour. L…
AMC 10 2023A #2 grade 7+ arithmetic
The weight of 1/3 of a large pizza together with 3 1/2 cups of orange slices is the same as the weight of 3/4 of a large…
AMC 10 2023A #3 grade 6+ number-theory
How many positive perfect squares less than 2023 are divisible by 5?
AMC 10 2023A #4 grade 6+ geometry-2d
A quadrilateral has all integer sides lengths, a perimeter of 26, and one side of length 4. What is the greatest possibl…
AMC 10 2023A #5 grade 8+ arithmetic
How many digits are in the base-ten representation of 8⁵ · 5¹⁰ · 15⁵?
AMC 10 2023A #6 grade 4+ geometry-3d
An integer is assigned to each vertex of a cube. The value of an edge is defined to be the sum of the values of the two…
AMC 10 2023A #7 grade 7+ probability
Janet rolls a standard 6-sided die 4 times and keeps a running total of the numbers she rolls. What is the probability t…
AMC 10 2023A #8 grade 6+ algebra
Barb the baker has developed a new temperature scale for her bakery called the Breadus scale, which is a linear function…
AMC 10 2023A #9 grade 4+ arithmetic
A digital display shows the current date as an 8-digit integer consisting of a 4-digit year, followed by a 2-digit month…
AMC 10 2023A #10 grade 6+ arithmetic
Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an 11 on the next quiz, her mea…
AMC 10 2023A #11 grade 8+ geometry-2d
A square of area 2 is inscribed in a square of area 3, creating four congruent triangles, as shown below. What is the ra…
AMC 10 2023A #12 grade 4+ number-theory
How many three-digit positive integers N satisfy the following properties? The number N is divisible by 7. The number fo…
AMC 10 2023A #13 grade 8+ geometry-2d
Abdul and Chiang are standing 48 feet apart in a field. Bharat is standing in the same field as far from Abdul as possib…
AMC 10 2023A #14 grade 7+ probability
A number is chosen at random from among the first 100 positive integers, and a positive integer divisor of that number i…
AMC 10 2023A #15 grade 7+ geometry-2d
An even number of circles are nested, starting with a radius of 1 and increasing by 1 each time, all sharing a common po…
AMC 10 2023A #16 grade 7+ arithmetic
In a table tennis tournament, every participant played every other participant exactly once. Although there were twice a…
AMC 10 2023A #17 grade 8+ geometry-2d
Let ABCD be a rectangle with AB = 30 and BC = 28. Point P and Q lie on BC and CD respectively so that all sides of △ABP,…
AMC 10 2023A #18 grade 8+ geometry-2d
A rhombic dodecahedron is a solid with 12 congruent rhombus faces. At every vertex, 3 or 4 edges meet, depending on the…
AMC 10 2023A #19 grade 8+ arithmetic
The line segment formed by A(1, 2) and B(3, 3) is rotated to the line segment formed by A'(3, 1) and B'(4, 3) about the…
AMC 10 2023A #20 grade 7+ geometry-2d
Each square in a 3×3 grid of squares is colored red, white, blue, or green so that every 2×2 square contains one square…
AMC 10 2023A #21 grade 6+ number-theory
Let P(x) be the unique polynomial of minimal degree with the following properties: P(x) has a leading coefficient 1, 1 i…
AMC 10 2023A #22 grade 8+ geometry-2d
Circle C₁ and C₂ each have radius 1, and the distance between their centers is 1/2. Circle C₃ is the largest circle inte…
AMC 10 2023A #23 grade 8+ arithmetic
If the positive integer n has positive integer divisors a and b with n = ab, then a and b are said to be complementary d…
AMC 10 2023A #24 grade 8+ geometry-2d
Six regular hexagonal blocks of side length 1 unit are arranged inside a regular hexagonal frame. Each block lies along…
AMC 10 2023A #25 grade 7+ probability
If A and B are vertices of a polyhedron, define the distance d(A,B) to be the minimum number of edges of the polyhedron…

A parent dashboard for the family lives at sensimlab.com.