Competition · AMC preparation · step 4 of 4

AMC 8 2023: all 25 problems

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

AMC 8 2023 #1 grade 5+ arithmetic
What is the value of (8 × 4 + 2) - (8 + 4 × 2)?
AMC 8 2023 #2 grade 4+ geometry-2d
A square piece of paper is folded twice into four equal quarters, as shown below, then cut along the dashed line. When u…
AMC 8 2023 #3 grade 5+ rate-ratio
Wind chill is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be foun…
AMC 8 2023 #4 grade 4+ geometry-2d
The numbers from 1 to 49 are arranged in a spiral pattern on a square grid, beginning at the center. The first few numbe…
AMC 8 2023 #5 grade 4+ rate-ratio
A lake contains 250 trout, along with a variety of other fish. When a marine biologist catches and releases a sample of…
AMC 8 2023 #6 grade 6+ algebra
The digits 2,0,2, and 3 are placed in the expression below, one digit per box. What is the maximum possible value of the…
AMC 8 2023 #7 grade 8+ geometry-2d
A rectangle, with sides parallel to the x-axis and y-axis, has opposite vertices located at (15, 3) and (16, 5). A line…
AMC 8 2023 #8 grade 3+ arithmetic
Lola, Lolo, Tiya, and Tiyo participated in a ping pong tournament. Each player competed against each of the other three…
AMC 8 2023 #9 grade 5+ rate-ratio
Malaika is skiing on a mountain. The graph below shows her elevation, in meters, above the base of the mountain as she s…
AMC 8 2023 #10 grade 5+ arithmetic
Harold made a plum pie to take on a picnic. He was able to eat only 1/4 of the pie, and he left the rest for his friends…
AMC 8 2023 #11 grade 6+ rate-ratio
NASA’s Perseverance Rover was launched on July 30, 2020. After traveling 292,526,838 miles, it landed on Mars in Jezero…
AMC 8 2023 #12 grade 7+ geometry-2d
The figure below shows a large white circle with a number of smaller white and shaded circles in its interior. What frac…
AMC 8 2023 #13 grade 4+ geometry-2d
Along the route of a bicycle race, 7 water stations are evenly spaced between the start and finish lines, as shown in th…
AMC 8 2023 #14 grade 4+ arithmetic
Nicolas is planning to send a package to his friend Anton, who is a stamp collector. To pay for the postage, Nicolas wou…
AMC 8 2023 #15 grade 6+ rate-ratio
Viswam walks half a mile to get to school each day. His route consists of 10 city blocks of equal length and he takes 1…
AMC 8 2023 #16 grade 4+ pattern, counting
The letters P, Q, and R are entered into a 20×20 table according to the pattern shown below. How many Ps, Qs, and Rs wil…
AMC 8 2023 #17 grade 6+ geometry-3d
A regular octahedron has eight equilateral triangle faces with four faces meeting at each vertex. Jun will make the regu…
AMC 8 2023 #18 grade 5+ number-theory, arithmetic
Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump 5 pads to the right or 3…
AMC 8 2023 #19 grade 7+ geometry-2d
An equilateral triangle is placed inside a larger equilateral triangle so that the region between them can be divided in…
AMC 8 2023 #20 grade 6+ arithmetic
Two integers are inserted into the list 3, 3, 8, 11, 28 to double its range. The mode and median remain unchanged. What…
AMC 8 2023 #21 grade 5+ counting
Alina writes the numbers 1, 2, … , 9 on separate cards, one number per card. She wishes to divide the cards into 3 group…
AMC 8 2023 #22 grade 6+ arithmetic
In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term…
AMC 8 2023 #23 grade 7+ geometry-2d
Each square in a 3 × 3 grid is randomly filled with one of the 4 gray and white tiles shown below on the right. What is…
AMC 8 2023 #24 grade 8+ geometry-2d
Isosceles △ ABC has equal side lengths AB and BC. In the figure below, segments are drawn parallel to AC so that the sha…
AMC 8 2023 #25 grade 6+ arithmetic
Fifteen integers a₁, a₂, a₃, …, a₁₅ are arranged in order on a number line. The integers are equally spaced and have the…

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