2023 AMC 10B Problems
2023 AMC 10B (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 |
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely but runs out of juice when the fourth glass is only full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into the fourth glass so that all four glasses will have the same amount of juice?
Problem 2
Carlos went to a sports store to buy running shoes. Running shoes were on sale, with prices reduced by on every pair of shoes. Carlos also knew that he had to pay a
sales tax on the discounted price. He had
dollars. What is the original (before discount) price of the most expensive shoes he could afford to buy?
Problem 3
A right triangle is inscribed in circle
, and a
right triangle is inscribed in circle
. What is the ratio of the area of circle
to the area of circle
?
Problem 4
Jackson's paintbrush makes a narrow strip with a width of 6.5 millimeters. Jackson has enough paint to make a strip 25 meters long. How many square centimeters of paper could Jackson cover with paint?
Problem 5
Maddy and Lara see a list of numbers written on a blackboard. Maddy adds to each number in the list and finds that the sum of her new numbers is
. Lara multiplies each number in the list by
and finds that the sum of her new numbers is also
. How many numbers are written on the blackboard?
Problem 6
Problem 7
Square ABCD is rotated 20 degrees clockwise about its center to obtain square EFGH, as shown below. What is the degree measure of <EAB?
Problem 8
What is the units digit of ?
Problem 9
The numbers 16 and 25 are a pair of consecutive postive squares whose difference is 9. How many pairs of consecutive positive perfect squares have a difference of less than or equal to 2023?
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
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 sum of the areas of all 6 faces of 𝒫 is , and the volume of 𝒫 is
. What is the length of the longest interior diagonal connecting two vertices of 𝒫 ?
Problem 18
Problem 19
Problem 20
Four congruent semicircles are drawn on the surface of a sphere with radius 2, as
shown, creating a close curve that divides the surface into two congruent regions.
The length of the curve is . What is 𝑛?
Problem 21
Each of 2023 balls is randomly placed into one of 3 bins. Which of the following is closest to the probability that each of the bins will contain an odd number of balls?
Problem 22
Problem 23
Problem 24
What is the perimeter of the boundary of the region consisting of all points which can be expressed as with
,
and
?
Problem 25
A regular pentagon with area is printed on paper and cut out. All five vertices are folded to the center of the pentagon, creating a smaller pentagon. What is the area of the new pentagon?
See also
2023 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by 2022 AMC 10A Problems |
Followed by 2024 AMC 10A Problems | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.