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Questions and Answers
Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy?
Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy?
10
Three identical rectangles are put together to form rectangle ABCD, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle ABCD?
Three identical rectangles are put together to form rectangle ABCD, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle ABCD?
150
Which of the following is the correct order of the fractions 15/11, 19/15, and 17/13, from least to greatest?
Which of the following is the correct order of the fractions 15/11, 19/15, and 17/13, from least to greatest?
Quadrilateral ABCD is a rhombus with perimeter 52 meters. The length of diagonal AC is 24 meters. What is the area in square meters of rhombus ABCD?
Quadrilateral ABCD is a rhombus with perimeter 52 meters. The length of diagonal AC is 24 meters. What is the area in square meters of rhombus ABCD?
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A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance d traveled by the two animals over time t from start to finish?
A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance d traveled by the two animals over time t from start to finish?
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There are 81 grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point P is in the center of the square. Given that Q point is randomly chosen among the other 80 points, what is the probability that the line PQ is a line of symmetry for the square?
There are 81 grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point P is in the center of the square. Given that Q point is randomly chosen among the other 80 points, what is the probability that the line PQ is a line of symmetry for the square?
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Shauna takes five tests, each worth a maximum of 100 points. Her scores on the first three tests are 76, 94, and 87. In order to average 81 for all five tests, what is the lowest score she could earn on one of the other two tests?
Shauna takes five tests, each worth a maximum of 100 points. Her scores on the first three tests are 76, 94, and 87. In order to average 81 for all five tests, what is the lowest score she could earn on one of the other two tests?
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Gilda has a bag of marbles. She gives 20% of them to her friend Pedro. Then Gilda gives 10% of what is left to another friend, Ebony. Finally, Gilda gives 25% of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?
Gilda has a bag of marbles. She gives 20% of them to her friend Pedro. Then Gilda gives 10% of what is left to another friend, Ebony. Finally, Gilda gives 25% of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?
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Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are 6 cm in diameter and 12 cm high. Felicia buys cat food in cylindrical cans that are 12 cm in diameter and 6 cm high. What is the ratio of the volume one of Alex's cans to the volume one of Felicia's cans?
Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are 6 cm in diameter and 12 cm high. Felicia buys cat food in cylindrical cans that are 12 cm in diameter and 6 cm high. What is the ratio of the volume one of Alex's cans to the volume one of Felicia's cans?
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The eighth grade class at Lincoln Middle School has 93 students. Each student takes a math class or a foreign language class or both. There are 70 eighth graders taking a math class, and there are 54 eight graders taking a foreign language class. How many eight graders take only a math class and not a foreign language class?
The eighth grade class at Lincoln Middle School has 93 students. Each student takes a math class or a foreign language class or both. There are 70 eighth graders taking a math class, and there are 54 eight graders taking a foreign language class. How many eight graders take only a math class and not a foreign language class?
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The faces of a cube are painted in six different colors: red (R), white (W), green (G), brown (B), aqua (A), and purple (P). Three views of the cube are shown below. What is the color of the face opposite the aqua face?
The faces of a cube are painted in six different colors: red (R), white (W), green (G), brown (B), aqua (A), and purple (P). Three views of the cube are shown below. What is the color of the face opposite the aqua face?
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A palindrome is a number that has the same value when read from left to right or from right to left. (For example 12321 is a palindrome.) Let N be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of N?
A palindrome is a number that has the same value when read from left to right or from right to left. (For example 12321 is a palindrome.) Let N be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of N?
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Isabella has 6 coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupons last, she decides that she will redeem one every 10 days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the 6 dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?
Isabella has 6 coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupons last, she decides that she will redeem one every 10 days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the 6 dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?
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On a beach, 50 people are wearing sunglasses and 35 people are wearing caps. Some people are wearing both sunglasses and caps. If one of the people wearing a cap is selected at random, the probability that this person is also wearing sunglasses is 2/5. If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?
On a beach, 50 people are wearing sunglasses and 35 people are wearing caps. Some people are wearing both sunglasses and caps. If one of the people wearing a cap is selected at random, the probability that this person is also wearing sunglasses is 2/5. If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?
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Qiang drives 15 miles at an average speed of 30 miles per hour. How many additional miles will he have to drive at 55 miles per hour to average 50 miles per hour for the entire trip?
Qiang drives 15 miles at an average speed of 30 miles per hour. How many additional miles will he have to drive at 55 miles per hour to average 50 miles per hour for the entire trip?
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What is the value of the product?
What is the value of the product?
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The faces of each of two fair dice are numbered 1, 2, 3, 5, 7, and 8. When the two dice are tossed, what is the probability that their sum will be an even number?
The faces of each of two fair dice are numbered 1, 2, 3, 5, 7, and 8. When the two dice are tossed, what is the probability that their sum will be an even number?
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In a tournament there are six teams that play each other twice. A team earns 3 points for a win, 1 point for a draw, and 0 points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams?
In a tournament there are six teams that play each other twice. A team earns 3 points for a win, 1 point for a draw, and 0 points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams?
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What is the area of the triangle formed by the lines y = 5, y = 1 + x and y = 1 - x?
What is the area of the triangle formed by the lines y = 5, y = 1 + x and y = 1 - x?
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A store increased the original price of a shirt by a certain percent and then decreased the new price by the same amount. Given that the resulting price was 84% of the original price, by what percent was the price increased and decreased?
A store increased the original price of a shirt by a certain percent and then decreased the new price by the same amount. Given that the resulting price was 84% of the original price, by what percent was the price increased and decreased?
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After Euclid High School's last basketball game, it was determined that 1/4 of the team's points were scored by Alexa and 2/7 were scored by Brittany. Chelsea scored 15 points. None of the other 7 team members scored more than 2 points. What was the total number of points scored by the other 7 team members?
After Euclid High School's last basketball game, it was determined that 1/4 of the team's points were scored by Alexa and 2/7 were scored by Brittany. Chelsea scored 15 points. None of the other 7 team members scored more than 2 points. What was the total number of points scored by the other 7 team members?
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Alice has 24 apples. In how many ways can she share them with Becky and Chris so that each of the people has at least 2 apples?
Alice has 24 apples. In how many ways can she share them with Becky and Chris so that each of the people has at least 2 apples?
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Study Notes
AMC 8 Flashcards - Study Notes
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Ike and Mike have $30 to spend on sandwiches ($4.50 each) and drinks ($1.00 each). They maximize sandwiches and use the remaining money for drinks. The problem asks for the total number of items they buy.
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Three identical rectangles form rectangle ABCD. The shorter side of each smaller rectangle is 5 feet. Find the area of rectangle ABCD in square feet.
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Order the fractions 15/11, 19/15, and 17/13 from least to greatest.
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Rhombus ABCD has a perimeter of 52 meters and a diagonal AC of 24 meters. Calculate the area of rhombus ABCD in square meters.
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A tortoise and a hare race. The hare initially runs ahead, takes a nap, and then finishes the race. The tortoise walks at a constant speed. The problem asks for the graph depicting the distance traveled by both animals over time.
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An 81-point grid square has point P at the center. A random point Q is selected from the other 80 points. Find the probability that the line PQ is a line of symmetry for the square.
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Shauna took five tests (maximum score of 100 per test). Her scores on the first three tests were 76, 94, and 87. To average 81 for all five tests, what is the lowest score she could earn on one of the remaining two tests?
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Gilda has a bag of marbles. She gives 20% to Pedro, 10% of the remaining to Ebony, and then 25% of the remaining to Jimmy. Find the percentage of marbles left for Gilda.
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Alex and Felicia buy cylindrical cat food cans. Alex's cans have a 6 cm diameter and 12 cm height. Felicia's cans have a 12 cm diameter and 6 cm height. Find the ratio of Alex's can volume to Felicia's can volume.
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Lincoln Middle School has 93 eighth graders. All students take a math class, and 70 take a foreign language class. 54 students take a math class or a foreign language class (or both). Determine the number of eighth graders taking only a math class.
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A cube's faces are colored (red, white, green, brown, aqua, purple). Three views are given. Determine the color opposite the aqua face.
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Find the smallest three-digit integer that is not a palindrome but is the sum of three distinct two-digit palindromes. Calculate the sum of its digits.
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Isabella has 6 ice cream coupons. She redeems one every 10 days. No redemption date is a Sunday. Find the day of the week Isabella redeems her first coupon.
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On a beach, 50 people wear sunglasses and 35 wear caps. Some wear both. If a cap-wearer is randomly selected, the probability of also wearing sunglasses is 2/5. If a sunglasses-wearer is randomly selected, what is the probability of also wearing a cap?
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Qiang drives 15 miles at 30 mph. How many additional miles must he drive at 55 mph to average 50 mph for the entire trip?
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Calculate a given product.
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Two fair dice, each with faces numbered 1, 2, 3, 5, 7, and 8 are tossed. What's the probability that their sum is even?
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A tournament has six teams that play each other twice. The top three teams earned the same number of total points. What is the maximum possible total points for each of the top three teams?
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Determine the area of a triangle formed by lines y = 5, y = 1 + x, and y = 1 - x.
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A shirt's original price is increased by a percentage, then decreased by the same percentage. The resulting price is 84% of the original. Find the percentage increase/decrease.
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At Euclid High, Alexa scored 1/4 of the points, Brittany scored 2/7 points and Chelsea scored 15 points. The other 7 team members scored less than 2 points each. Find the total number of points for the other 7 team members.
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Alice has 24 apples. How many ways can she share them with Becky and Chris so each has at least 2 apples?
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Calculate a given product.
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Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in a circle. They count, and when a number contains 7 or is a multiple of 7, the person leaves the circle. Who is the last person remaining?
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Compute the sum: 1 + 3 + 5 + ... + 2017 + 2019 – 2 – 4 – 6 – ... – 2016 – 2018
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Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove 3 times faster on the highway. He spent 30 minutes on the coastal road. Find the total trip time in minutes.
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The five-digit number 2018U is divisible by 9. Find the remainder when divided by 8.
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Find the harmonic mean of 1, 2, and 4.
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Abby, Bridget, and four classmates are seated in two rows of three for a picture. Find the probability Abby and Bridget are adjacent in the same row or column.
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Sri's car clock gains time at a constant rate. At 12:00 noon, both his watch and car clock show 12:00. At 12:30 and 12:35 on his watch and car clock respectively, Sri loses his watch and sees 7:00 on the car clock. What's the actual time?
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Laila took five math tests with scores between 0 and 100. The first four tests had the same score, and the last test was higher. Her average score was 82. How many values are possible for Laila's score on the 5th test?
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Find the greatest five-digit number whose digits have a product of 120. Calculate the sum of its digits.
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Two smaller circles have a diameter equal to the radius of a larger circle. Their combined area is 1 square unit. Find the area of the shaded region.
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Professor Chang has 9 language books (2 Arabic, 3 German, 4 Spanish) arranged on a bookshelf. How many ways can these be arranged keeping Arabic books together and Spanish books together?
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Bella walks to Ella's house. Ella rides her bicycle at 5 times Bella's walking speed. The distance is 2 miles. How many steps will Bella take to meet Ella?
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How many factors does 23,232 have?
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A sign pyramid with 4 levels. Determine the number of ways to fill the bottom row cells with "+" and "-" to produce a "+" at the top.
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Find three-digit integers that leave remainders of 2, 5, and 7 when divided by 6, 9, and 11, respectively.
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In square ABCD, E is the midpoint of CD. BE meets diagonal AC at F. The area of AFED is 45. Find the area of ABCD.
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From a regular octagon, a triangle is formed by connecting 3 randomly chosen vertices. What is the probability at least one side of the triangle is also a side of the octagon?
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How many perfect cubes are between 2^8 + 1 and 2^18 + 1, inclusive?
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A soccer team attendance graph shows weekday practice attendance. The mean and median are calculated. Wednesday's attendance is corrected to 21 participants. Describe how the mean and median change.
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In a cube ABCDEFGH, J and I are midpoints of FB and HD respectively. R is the ratio of the cross-section EJCI to the area of a face. Find R².
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In triangle ABC, point D divides AC with AD:DC = 1:2. E is the midpoint of BD, and F is the intersection of AE and BC. If the area of ABC is 360, find the area of AEBF.
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In triangle ABC, E is on AB with AE=1, EB=2. D is on AC with DE||BC. F is on BC with EF||AC. Find the ratio of area CDEF to area ABC.
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A bar graph shows exercise days for students in Mr. Garcia's health class. Calculate the mean number of exercise days, rounded to the nearest hundredth.
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Description
Test your understanding of various math concepts featured in the AMC 8 exams. This quiz covers topics such as geometry, probability, and basic arithmetic involving money and distances. Prepare yourself with these key problems to enhance your problem-solving skills.
