Competition · AMC preparation · step 4 of 4

AMC 8 2022: 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 2022 #1 grade 6+ geometry-2d
The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the…
AMC 8 2022 #2 grade 6+ arithmetic
Consider these two operations: a ◆ b = a² - b² a ★ b = (a - b)² What is the output of (5 ◆ 3) ★ 6?
AMC 8 2022 #3 grade 4+ number-theory, counting
When three positive integers a, b, and c are multiplied together, their product is 100. Suppose a < b < c. In how many w…
AMC 8 2022 #4 grade 8+ geometry-2d
The letter M in the figure below is first reflected over the line q and then reflected over the line p. What is the resu…
AMC 8 2022 #5 grade 2+ arithmetic, algebra
Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned 6 years old, she received a n…
AMC 8 2022 #6 grade 3+ arithmetic, algebra
Three positive integers are equally spaced on a number line. The middle number is 15, and the largest number is 4 times…
AMC 8 2022 #7 grade 6+ rate-ratio
When the World Wide Web first became popular in the 1990s, download speeds reached a maximum of about 56 kilobits per se…
AMC 8 2022 #8 grade 5+ arithmetic
What is the value of 1/3·2/4·3/5…18/20·19/21·20/22?
AMC 8 2022 #9 grade 4+ arithmetic, algebra
A cup of boiling water (212°F) is placed to cool in a room whose temperature remains constant at 68°F. Suppose the diffe…
AMC 8 2022 #10 grade 6+ rate-ratio
One sunny day, Ling decided to take a hike in the mountains. She left her house at 8 textscam, drove at a constant speed…
AMC 8 2022 #11 grade 4+ arithmetic, logic
Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating 3 inches of pasta…
AMC 8 2022 #12 grade 7+ probability, counting
The arrows on the two spinners shown below are spun. Let the number N equal 10 times the number on Spinner A, added to t…
AMC 8 2022 #13 grade 4+ algebra, number-theory
How many positive integers can fill the blank in the sentence below? “One positive integer is _____ more than twice anot…
AMC 8 2022 #14 grade 3+ counting
In how many ways can the letters in BEEKEEPER be rearranged so that two or more Es do not appear together?
AMC 8 2022 #15 grade 6+ rate-ratio
Laszlo went online to shop for black pepper and found thirty different black pepper options varying in weight and price,…
AMC 8 2022 #16 grade 4+ arithmetic, algebra
Four numbers are written in a row. The average of the first two is 21, the average of the middle two is 26, and the aver…
AMC 8 2022 #17 grade 4+ arithmetic, number-theory
If n is an even positive integer, the double factorial notation n!! represents the product of all the even integers from…
AMC 8 2022 #18 grade 6+ geometry-2d
The midpoints of the four sides of a rectangle are (-3,0), (2,0), (5,4), and (0,4). What is the area of the rectangle?
AMC 8 2022 #19 grade 6+ arithmetic
Mr. Ramos gave a test to his class of 20 students. The dot plot below shows the distribution of test scores. Later Mr. R…
AMC 8 2022 #20 grade 8+ arithmetic, algebra
The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the nu…
AMC 8 2022 #21 grade 7+ algebra, rate-ratio
Steph scored 15 baskets out of 20 attempts in the first half of a game, and 10 baskets out of 10 attempts in the second…
AMC 8 2022 #22 grade 5+ rate-ratio, logic
A bus takes 2 minutes to drive from one stop to the next, and waits 1 minute at each stop to let passengers board. Zia t…
AMC 8 2022 #23 grade 7+ counting
A △ or bigcirc is placed in each of the nine squares in a 3-by-3 grid. Shown below is a sample configuration with three…
AMC 8 2022 #24 grade 7+ geometry-3d
The figure below shows a polygon ABCDEFGH, consisting of rectangles and right triangles. When cut out and folded on the…
AMC 8 2022 #25 grade 7+ probability, counting
A cricket randomly hops between 4 leaves, on each turn hopping to one of the other 3 leaves with equal probability. Afte…

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