Competition · AMC preparation · step 4 of 4

AMC 10 2023B: 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 2023B #1 grade 5+ rate-ratio
Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses comp…
AMC 10 2023B #2 grade 6+ arithmetic
Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by 20% on every pair…
AMC 10 2023B #3 grade 7+ geometry-2d
A 3-4-5 right triangle is inscribed in circle A, and a 5-12-13 right triangle is inscribed in circle B. What is the rati…
AMC 10 2023B #4 grade 5+ geometry-2d
Jackson's paintbrush makes a narrow strip with a width of 6.5 millimeters. Jackson has enough paint to make a strip 25 m…
AMC 10 2023B #5 grade 6+ arithmetic
Maddy and Lara see a list of numbers written on a blackboard. Maddy adds 3 to each number in the list and finds that the…
AMC 10 2023B #6 grade 4+ arithmetic
Let L₁=1, L₂=3, and L_(n+2)=L_(n+1)+L_n for n≥ 1. How many terms in the sequence L₁, L₂, L₃,...,L₂₀₂₃ are even?
AMC 10 2023B #7 grade 7+ geometry-2d
Square ABCD is rotated 20° clockwise about its center to obtain square EFGH, as shown below. What is the degree measure…
AMC 10 2023B #8 grade 4+ arithmetic
What is the units digit of 2022²⁰²³ + 2023²⁰²²?
AMC 10 2023B #9 grade 6+ arithmetic
The numbers 16 and 25 are a pair of consecutive positive squares whose difference is 9. How many pairs of consecutive po…
AMC 10 2023B #10 grade 4+ geometry-2d
You are playing a game. A 2 × 1 rectangle covers two adjacent squares (oriented either horizontally or vertically) of a…
AMC 10 2023B #11 grade 6+ arithmetic
Suzanne went to the bank and withdrew $800. The teller gave her this amount using $20 bills, $50 bills, and $100 bills,…
AMC 10 2023B #12 grade 8+ algebra
When the roots of the polynomial P(x) = (x-1)¹ (x-2)² (x-3)³ · · · · (x-10)¹⁰ are removed from the number line, what rem…
AMC 10 2023B #13 grade 8+ geometry-2d
What is the area of the region in the coordinate plane defined by | | x | - 1 | + | | y | - 1 | ≤ 1?
AMC 10 2023B #14 grade 8+ algebra
How many ordered pairs of integers (m, n) satisfy the equation m²+mn+n² = m²n²?
AMC 10 2023B #15 grade 8+ arithmetic
What is the least positive integer m such that m·2!·3!·4!·5!...16! is a perfect square?
AMC 10 2023B #16 grade 8+ arithmetic
Define an upno to be a positive integer of 2 or more digits where the digits are strictly increasing moving left to righ…
AMC 10 2023B #17 grade 8+ geometry-3d
A rectangular box P has distinct edge lengths a, b, and c. The sum of the lengths of all 12 edges of P is 13, the areas…
AMC 10 2023B #18 grade 8+ number-theory
Suppose a, b, and c are positive integers such thata/14+b/15=c/210.Which of the following statements are necessarily tru…
AMC 10 2023B #19 grade 7+ geometry-2d
Sonya the frog chooses a point uniformly at random lying within the square [0, 6] × [0, 6] in the coordinate plane and h…
AMC 10 2023B #20 grade 8+ geometry-3d
Four congruent semicircles are drawn on the surface of a sphere with radius 2, as shown, creating a close curve that div…
AMC 10 2023B #21 grade 8+ probability
Each of 2023 balls is randomly placed into one of 3 bins. Which of the following is closest to the probability that each…
AMC 10 2023B #22 grade 6+ arithmetic
How many distinct values of x satisfy ⌊x⌋²-3x+2=0, where ⌊x⌋ denotes the largest integer less than or equal to x?
AMC 10 2023B #23 grade 8+ arithmetic
An arithmetic sequence of positive integers has n ≥ 3 terms, initial term a, and common difference d > 1. Carl wrote dow…
AMC 10 2023B #24 grade 8+ geometry-2d
What is the perimeter of the boundary of the region consisting of all points which can be expressed as (2u-3w, v+4w) wit…
AMC 10 2023B #25 grade 8+ geometry-2d
A regular pentagon with area √5+1 is printed on paper and cut out. The five vertices of the pentagon are folded into the…

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