2022 AMC 8 Problems
IMPORTANT: When copied a problem, replace the X's for answer choices.
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
Problem 1
The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches?
usepackage("mathptmx"); defaultpen(linewidth(0.5)); size(5cm); defaultpen(fontsize(14pt)); label("$\textbf{Math}$", (2.1,3.7)--(3.9,3.7)); label("$\textbf{Team}$", (2.1,3)--(3.9,3)); filldraw((1,2)--(2,1)--(3,2)--(4,1)--(5,2)--(4,3)--(5,4)--(4,5)--(3,4)--(2,5)--(1,4)--(2,3)--(1,2)--cycle, mediumgray*0.5 + lightgray*0.5); draw((0,0)--(6,0), gray); draw((0,1)--(6,1), gray); draw((0,2)--(6,2), gray); draw((0,3)--(6,3), gray); draw((0,4)--(6,4), gray); draw((0,5)--(6,5), gray); draw((0,6)--(6,6), gray); draw((0,0)--(0,6), gray); draw((1,0)--(1,6), gray); draw((2,0)--(2,6), gray); draw((3,0)--(3,6), gray); draw((4,0)--(4,6), gray); draw((5,0)--(5,6), gray); draw((6,0)--(6,6), gray); (Error making remote request. Unexpected URL sent back)
Problem 2
Consider these two operations:
What is the value of
Problem 3
When three positive integers ,
, and
are multiplied together, their product is
. Suppose
. In how many ways can the numbers be chosen?
Problem 4
The letter M in the figure below is first reflected over the line and then reflected over the line
. What is the resulting image?
Problem 5
Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is
years. How many years older than Bella is Anna?
Problem 6
Three positive integers are equally spaced on a number line. The middle number is and the largest number is
times the smallest number. What is the smallest of these three numbers?
Problem 7
When the World Wide Web first became popular in the s, download speeds reached a maximum of about
kilobits per second. Approximately how many minutes would the download of a
-megabyte song have taken at that speed? (Note that there are
kilobits in a megabyte.)
Problem 8
What is the value of
Problem 9
A cup of boiling water () is placed to cool in a room whose temperature remains constant at
. Suppose the difference between the water temperature and the room temperature is halved every
minutes. What is the water temperature, in degrees Fahrenheit, after
minutes?
Problem 10
One sunny day, Ling decided to take a hike in the mountains. She left her house at , drove at a constant speed of
miles per hour, and arrived at the hiking trail at
. After hiking for
hours, Ling drove home at a constant speed of
miles per hour. Which of the following graphs best illustrates the distance between Ling’s car and her house over the course of her trip?
Problem 11
Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating inches of pasta from the middle of one piece. In the end, he has
pieces of pasta whose total length is
inches. How long, in inches, was the piece of pasta he started with?
Problem 12
How many positive integers can fill the blank in the sentence below?
“One positive integer is _____ more than twice another, and the sum of the two numbers is .”
Problem 13
Problem 14
In how many ways can the letters in be rearranged so that two or more
s do not appear together?
Problem 15
Problem 16
Four numbers are written in a row. The average of the first two is the average of the middle two is
and the average of the last two is
What is the average of the first and last of the numbers?
Problem 17
If is an even positive integer, the double factorial notation
represents the product of all the even integers from
to
. For example,
. What is the units digit of the following sum?
Problem 18
The midpoints of the four sides of a rectangle are and
What is the
area of the rectangle?
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25