Amc8 problems

2015 AMC 8 Results Announced. 2014 AMC 8 Winners for the U.S. Ivy League Education Center. The Hardest Problems on the 2018 AMC 8 are Nearly Identical to Former Problems on the AMC 8, 10, 12, and MathCounts. The Hardest Problems on the 2017 AMC 8 are Extremely Similar to Previous Problems on the AMC 8/10/12 and the …

AMC 12 Problems and Solutions - AoPS Wiki. Art of Problem Solving. AoPS Online. Math texts, online classes, and more. for students in grades 5-12. Visit AoPS Online ‚. Books for Grades 5-12 Online Courses. Beast Academy. Engaging math books and online learning. AMC 8 Practice Questions Example Each of the following four large congruent squares is subdivided into combinations of congruent triangles or rectangles and is partially shaded. What percent of the total area is partially shaded? (A) 12 1 2 (B) 20 (C) 25 (D) 33 1 3 (E) 37 1 2 2011 AMC 8, Problem #7— “Find the shaded portion of each square ... 2008 AMC 8 problems and solutions. The test was held On Tuesday November 18, 2008. The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2008 AMC 8 Problems. 2008 AMC 8 Answer Key. 2008 AMC 8 Problems/Problem 1. 2022 AMC 8 Problems. 2022 AMC 8 Printable versions: Wiki • AoPS Resources • PDF: Instructions. This is a 25-question, multiple choice test. Each question is ... This is the same problem as if we made the spinner A make the tens digit and spinner B make the ones digit. If the tens digit is 5,6,7, or 8, and the ones digit is 1,2,3, or 4, the only possible ways to get a perfect square is 6,4 or 8,1. There are 4x4=16 possible combinations that are equally likely, and 2 of them satisfy the property.2019 AMC 8 Problems Problem 1 Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost each and soft drinks cost 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? Problem 22018 AMC 8 problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2018 AMC 8 Problems; 2018 …

Past AMC 8 and AMC 10 Problems. Welcome to our past problem and solution archive. We've built a smartphone-optimized interface for viewing and working on the past exams on the go. We also have printable PDF versions of each past test. Enjoy these past AMC contests!Resources Aops Wiki 2023 AMC 8 Problems Page. Article Discussion View source History. Toolbox. Recent changes Random page Help What links here Special pages. Search. ONLINE AMC 8 PREP WITH AOPS Top scorers around the country use AoPS. Join training courses for beginners and advanced students.2013 AMC 8 Problems/Problem 22; 2013 AMC 8 Problems/Problem 23; 2013 AMC 8 Problems/Problem 24; 2013 AMC 8 Problems/Problem 25; See also. 2013 AMC 8 : Preceded by 2012 AMC 8: AMC 8: Followed by 2014 AMC 8: Mathematics competitions; Mathematics competition resources; Math books; 2 MAA AMC 8 1. An amusement park has a collection of scale models, with ratio 1:20, of build-ings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its replica at this park, rounded to the nearest whole number? (A) 14 (B) 15 (C) 16 (D) 18 (E) 20 2. What is the value of ... In this comprehensive analysis of the 2024 AMC 8 competition, we'll explore the various modules covered, from Geometry to Probability and Statistics, while also highlighting any changes compared to previous years. Additionally, we'll delve into some intriguing problems from the exam, offering detailed solutions and insights into the key …

2019 AMC 8 problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2019 AMC 8 Problems. 2019 AMC 8 Answer Key. Problem 1.QMAAAMC American Mathematics Competitions . Title: AMC 8 Answer KeyThe best way to prepare for the AMC 8 is to do lots of practice problems either on your own or with a small group and then check your solutions with an answer key. For this reason, we provided 18 sets of past official AMC 8 contests (1999-2016) with answer keys and also developed 20 sets of AMC 8 mock test with detailed solutions to …“master-solution˙final” — 2016/9/13 — 15:30 — page 6 — #5 2016 AMC 8 Solutions 6 20. Answer (A): If b = 1, then a = 12 and c = 15, and the least common multiple of a and c is 60. If b > 1, then any prime factor of b must also be a factor of both 12 and 15, and thus the only possible value is b=3.In this case, a must be a multiple of 4 and a divisor of 12, so a = 4 …2 2019 MAA AMC 8 Solutions 1.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 any remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy?

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The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2001 AMC 8 Problems. 2001 AMC 8 Answer Key. 2001 AMC 8 Problems/Problem 1. 2001 AMC 8 Problems/Problem 2. 2001 AMC 8 Problems/Problem 3. 2001 AMC 8 Problems/Problem 4. 2001 AMC 8 Problems/Problem 5. The AMC 10 and AMC 12 are both 25-question, 75-minute, multiple-choice examinations in high school mathematics designed to promote the development and enhancement of problem-solving skills. The AMC 10 is for students in 10th grade and below and covers the high school curriculum up to 10th grade.2017 AMC 8 problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2017 AMC 8 Problems. 2017 AMC 8 Answer Key. Problem 1. Problem 2. Problem 3. Problem 4.20 20 AMC 8 Problems Problem 1 Luka is making lemonade to sell at a school fundraiser. His recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. He uses 3 cups of lemon juice. How many cups of water does he need? Problem 2 Four friends do yardwork for their neighbors over the weekend, earning $15, $20, $25, and2024 AMC 8 problems and solutions. The test was held from January 18th, 2024 to January 24th, 2024. The first link contains the full set of test problems. The second link contains the answer key. The rest contain each individual problem and its solution. 2024 AMC 8 Problems.

2011 AMC 8 Problems/Problem 22; 2011 AMC 8 Problems/Problem 23; 2011 AMC 8 Problems/Problem 24; 2011 AMC 8 Problems/Problem 25; See also. 2011 AMC 8 : Preceded by 2010 AMC 8: AMC 8: Followed by 2012 AMC 8: Mathematics competitions; Mathematics competition resources; Math books;AMC 8 American Mathematics Contest 8 Tuesday, November 15, 2016 INSTRUCTIONS 1. DO NOT OPEN THIS BOOKLET UNTIL YOUR PROCTOR TELLS YOU. 2. This is a twenty-five question multiple choice test. For each question, only one answer choice is correct. 3. Mark your answer to each problem on the AMC 8 Answer Form with a #2 …3. Mark your answer to each problem on the answer sheet with a #2 pencil. Check the blackened circles for accuracy and erase errors and stray marks completely. Only answers that are properly marked on the answer form will be scored. 4. here is no penalty for guessing. Your score is the number of correct answers.Having a cell phone is great when you need to talk on the go, but if you have a faulty battery, then you may feel like you are chained to your phone's charger. Many things can go w...Resources Aops Wiki 2018 AMC 8 Problems Page. Article Discussion View source History. Toolbox. Recent changes Random page Help What links here Special pages. Search. ONLINE AMC 8 PREP WITH AOPS Top scorers around the country use AoPS. Join training courses for beginners and advanced students.3. Mark your answer to each problem on the answer sheet with a #2 pencil. Check the blackened circles for accuracy and erase errors and stray marks completely. Only answers that are properly marked on the answer form will be scored. 4. here is no penalty for guessing. Your score is the number of correct answers.Problem 7. The integers from to inclusive, can be arranged to form a -by-square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum? Solution. Problem 8. What is the value of Solution. Problem 9Are you prepared for travel problems on your vacation? Check out these tips to help you prevent a vacation nightmare before it starts. Daye Deura When going on a hard-earned vacati...2011 AMC 8 Problems/Problem 22; 2011 AMC 8 Problems/Problem 23; 2011 AMC 8 Problems/Problem 24; 2011 AMC 8 Problems/Problem 25; See also. 2011 AMC 8 : Preceded by 2010 AMC 8: AMC 8: Followed by 2012 AMC 8: Mathematics competitions; Mathematics competition resources; Math books;Aug 16, 2022 · The AMC 8 is part of the American Mathematics Competitions (AMC) series, which includes competitions at both the middle- and high-school levels. It is administered by the Mathematical Association of America. The AMC 8 is the hardest of the three math competitions on this list. Many consider Math Olympiad and Mathcounts to be good preparation ... 2024 AMC 8 problems and solutions. The test was held from January 18th, 2024 to January 24th, 2024. The first link contains the full set of test problems. The second link contains the answer key. The rest contain each individual problem and its solution. 2024 AMC 8 Problems.

AMC 8 connects classroom to unique problem- skills solving challenges in a low -stress, friendly environment. • Over 1 million additional STEM graduates will be needed by 2022 to meet the growing demands of the labor market. The can help AMC 8 your students identify an interest in and prepare them for future

2013 AMC 8 Problems Problem 1 Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way? Problem 2 A sign at the fish market says, "50% off, today only: half-pound packages for just $3 perAMC 8 Mock Test Problems Problem 1 s Ft Eu Fv E® F trtr E trts L (A) Fsrss (B) Fsrsr (C) r (D) srsr (E) srss Problem 2 What is the number halfway between 5 5 : and 5 6 4? (A) 5 5 : 4 (B) 5 < 4 (C) 5 5 < (D) = 5 : 4 (E) 5 = Problem 3 A triangular corner with side length s pn L qn L Ú is cut from equilateral triangle mno of side length 3.2 MAA AMC 8 1. An amusement park has a collection of scale models, with ratio 1:20, of build-ings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its replica at this park, rounded to the nearest whole number? (A) 14 (B) 15 (C) 16 (D) 18 (E) 20 2. What is the value of ...The AMC 8 consists of 25 multiple-choice questions. Students have 40 minutes to complete the exam. The questions cover various math topics, including algebra, geometry, number theory, and probability. The purpose is to assess middle school students’ problem-solving abilities and mathematical knowledge. 2019 AMC 8 Problems. 2019 AMC 8 Printable versions: Wiki • AoPS Resources • PDF: Instructions. This is a 25-question, multiple choice test. Each question is ... The AMC 8 consists of 25 multiple-choice questions. Students have 40 minutes to complete the exam. The questions cover various math topics, including algebra, geometry, number theory, and probability. The purpose is to assess middle school students’ problem-solving abilities and mathematical knowledge.AMC 10 Problems and Solutions - AoPS Wiki. Art of Problem Solving. AoPS Online. Math texts, online classes, and more. for students in grades 5-12. Visit AoPS Online ‚. Books for Grades 5-12 Online Courses. Beast Academy. Engaging math books and online learning.2013 AMC 8 Problems/Problem 24; 2013 AMC 8 Problems/Problem 25; See also. 2013 AMC 8 : Preceded by 2012 AMC 8: AMC 8: Followed by 2014 AMC 8: Mathematics competitions;The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2001 AMC 8 Problems. 2001 AMC 8 Answer Key. 2001 AMC 8 Problems/Problem 1. 2001 AMC 8 Problems/Problem 2. 2001 AMC 8 Problems/Problem 3. 2001 AMC 8 Problems/Problem 4. 2001 AMC 8 …

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If school is canceled on the day that the AMC 8 was scheduled, the competition manager can administer the AMC 8 on a different day as long as it falls within the AMC 8 competition period, Jan. 17-23, 2023. The AMC 8 cannot be administered after the final day of the competition period. During the last two cycles, we temporarily allowed remote ...Two Problems on the 2020 AMC 8 are Exactly the Same as Two Problems on Our Sample AMC 8 Mock Test in 2017. 20 Sets of AMC 8 Mock Test with Detailed …Resources Aops Wiki 2023 AMC 8 Problems Page. Article Discussion View source History. Toolbox. Recent changes Random page Help What links here Special pages. Search. ONLINE AMC 8 PREP WITH AOPS Top scorers around the country use AoPS. Join training courses for beginners and advanced students.AMC 8 connects classroom to unique problem- skills solving challenges in a low -stress, friendly environment. • Over 1 million additional STEM graduates will be needed by 2022 to meet the growing demands of the labor market. The can help AMC 8 your students identify an interest in and prepare them for futureThe basic economic problem is scarcity, which is the idea that human beings want more things than are available to them. The economic problem, also known as the central economic pr...2019 AMC 8 problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2019 AMC 8 Problems. 2019 AMC 8 Answer Key. Problem 1.According to the AMC policy, students, teachers, and coaches are not allowed to discuss the contest questions and solutions until after the end of the competition window, as emphasized in 2020 AMC 8 Teacher’s Manual. We posted the 2020 AMC 8 Problems and Answers below at 11:59PM on Monday, November 16, 2020 Eastern Standard Time. If school is canceled on the day that the AMC 8 was scheduled, the competition manager can administer the AMC 8 on a different day as long as it falls within the AMC 8 competition period, Jan. 17-23, 2023. The AMC 8 cannot be administered after the final day of the competition period. During the last two cycles, we temporarily allowed remote ... ….

AMC 8 Problems and Solutions. AMC 8 / AJHSME problems and solutions. 2024 AMC 8. 2023 AMC 8. 2022 AMC 8. 2020 AMC 8. 2019 AMC 8. 2018 AMC 8. 2017 AMC 8.3. Mark your answer to each problem on the AMC 8 Answer Form with a #2 pencil. Check the blackened circles for accuracy and erase errors and stray marks completely. Only answers properly marked on the answer form will be graded. 4. There is no penalty for guessing. Your score on this test is the number of correct answers. 5.Click here to download. The Mastering AMC 8 book covers the most important concepts on the AMC 8 exam (and MATHCOUNTS) and includes 100s of examples and practice problems with detailed video solutions. This book covers the following topics: Combinatorics. Algebra. Number Theory.Problem 1. Rachelle uses pounds of meat to make hamburgers for her family. How many pounds of meat does she need to make hamburgers for a neighborhood picnic?. Solution. Problem 2. In the country of East Westmore, statisticians estimate there is a baby born every hours and a death every day. To the nearest hundred, how many people are …2015 AMC 8. 2015 AMC 8 problems and solutions. The test was held on Tuesday, November 17, 2015. 2015 AMC 8 Problems. 2015 AMC 8 Answer Key. 2015 AMC 8 Problems/Problem 1. 2015 AMC 8 Problems/Problem 2. 2015 AMC 8 Problems/Problem 3. 2015 AMC 8 Problems/Problem 4.The original problem and choices from the 2011 AMC 8 contest (A) 12 1 2 (B) 20 (C) 25 (D) 33 1 3 (E) 37 1 2 2011 AMC 8, Problem #7— “Find the shaded portion of each square separately. ” Problem number Hint Solution Answer (C): The upper left and the lower right squares are each one-fourth shaded, for a total of one-half square.Solution. Problem 23. A or is placed in each of the nine squares in a -by-grid. Shown below is a sample configuration with three s in a line. How many configurations will have three s in a line and three s in a line?. …Problem 1. What is the value of . Solution. Problem 2. Mike cycled laps in minutes. Assume he cycled at a constant speed throughout. Approximately how many laps did he complete in the first minutes? Solution. Problem 3. The sum of three numbers is The first number is times the third number, and the third number is less than the second number ... Amc8 problems, Click here to download. The Mastering AMC 8 book covers the most important concepts on the AMC 8 exam (and MATHCOUNTS) and includes 100s of examples and practice problems with detailed video solutions. This book covers the following topics: Combinatorics. Algebra. Number Theory., 2019 AMC 8 Problems Problem 1 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 any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy? Problem 2, AMC 12 Problems and Solutions - AoPS Wiki. Art of Problem Solving. AoPS Online. Math texts, online classes, and more. for students in grades 5-12. Visit AoPS Online ‚. Books for Grades 5-12 Online Courses. Beast Academy. Engaging math books and online learning., 2014 AMC 8. 2014 AMC 8 problems and solutions. The test was held ON TUESDAY NOVEMBER 18, 2014. 2014 AMC 8 Problems. 2014 AMC 8 Answer Key. 2014 AMC 8 Problems/Problem 1. 2014 AMC 8 Problems/Problem 2. 2014 AMC 8 Problems/Problem 3. 2014 AMC 8 Problems/Problem 4. , It is hard when your baby is sick, many problems are not serious. Learn about how to help your baby, and warning signs for more serious issues. It is hard when your baby is sick. C..., 2011 AMC 8, Problem #7— “Find the shaded portion of each square separately.” Solution Answer (C): The upper left and the lower right squares are each one-fourth shaded, fora total of one-half square. The shaded portions of the upper right and lower left squares makeu p one-half square.S o the total shaded area is, AMC hasn't renewed Interview with the Vampire for a third season yet, possibly due to audience decline. Season 3 might explore Anne Rice's sequel books like The Vampire …, Problem 7. The integers from to inclusive, can be arranged to form a -by-square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum? Solution. Problem 8. What is the value of Solution. Problem 9, 2020 AMC8 Problems (A) 35 (B) 37 (c) 39 (D) 43 (E) 49 Problem 3 Carrie has a rectangular garden that measures 6 feet by 8 feet. She plants the entire garden with strawberry plants. Carrie is able to plant 4 strawberry plants per …, 2019 AMC 8 Problems Problem 1 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 any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy? Problem 2 , The first link contains the full set of test problems. The rest contain each individual problem and its solution. 2001 AMC 8 Problems. 2001 AMC 8 Answer Key. 2001 AMC 8 Problems/Problem 1. 2001 AMC 8 Problems/Problem 2. 2001 AMC 8 Problems/Problem 3. 2001 AMC 8 Problems/Problem 4. 2001 AMC 8 …, Problem 1. What is the value of . Solution. Problem 2. Mike cycled laps in minutes. Assume he cycled at a constant speed throughout. Approximately how many laps did he complete in the first minutes? Solution. Problem 3. The sum of three numbers is The first number is times the third number, and the third number is less than the second number ..., On the 2020 AMC 8, there are 8 counting problems, 15 arithmetic and algebra problems, 1 geometry problem and 1 number theory problem. Surprisingly, there are no probability problems. This year's AMC 8 was harder than ever before. All the problems are word problems, and require critical thinking along with advanced math skills., 2022 AMC 8 Problems/Problem 25. Contents. 1 Problem; 2 Solution 1 (Casework) 3 Solution 2 (Casework) 4 Solution 3 (Complement) 5 Solution 4 (Recursion) 6 Solution 5 (Dynamic Programming) 7 Solution 6 …, “master-solution˙final” — 2016/9/13 — 15:30 — page 6 — #5 2016 AMC 8 Solutions 6 20. Answer (A): If b = 1, then a = 12 and c = 15, and the least common multiple of a and c is 60. If b > 1, then any prime factor of b must also be a factor of both 12 and 15, and thus the only possible value is b=3.In this case, a must be a multiple of 4 and a divisor of 12, so a = 4 …, The AMC 8 is part of the American Mathematics Competitions (AMC) series, which includes competitions at both the middle- and high-school levels. It is administered by the Mathematical Association of America. The AMC 8 is the hardest of the three math competitions on this list. Many consider Math Olympiad and Mathcounts to be good preparation ..., Jan 19, 2024 ... Sadly, the questions and the solutions to the AMC 8 2024 test have leaked even though the test is still in progress., 2016 AMC 8 Problems/Problem 22; 2016 AMC 8 Problems/Problem 23; 2016 AMC 8 Problems/Problem 24; 2016 AMC 8 Problems/Problem 25; See also. 2016 AMC 8 : Preceded by 2015 AMC 8: AMC 8: Followed by 2017 AMC 8: Mathematics competitions; Mathematics competition resources; Math books;, If school is canceled on the day that the AMC 8 was scheduled, the competition manager can administer the AMC 8 on a different day as long as it falls within the AMC 8 competition period, Jan. 17-23, 2023. The AMC 8 cannot be administered after the final day of the competition period. During the last two cycles, we temporarily allowed remote ..., Solution 2. If a rectangle has area then the area of the quadrilateral formed by its midpoints is. Define points and as Solution 1 does. Since and are the midpoints of the rectangle, the rectangle's area is Now, note that is a parallelogram since and As the parallelogram's height from to is and its area is Therefore, the area of the rectangle ..., 2024 AMC 8 Problems. 2024 AMC 8 ( Answer Key) Printable versions: Wiki • AoPS Resources • PDF. Instructions. This is a 25-question, multiple choice test. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct., 2013 AMC 8 Problems/Problem 22; 2013 AMC 8 Problems/Problem 23; 2013 AMC 8 Problems/Problem 24; 2013 AMC 8 Problems/Problem 25; See also. 2013 AMC 8 : Preceded by 2012 AMC 8: AMC 8: Followed by 2014 AMC 8: Mathematics competitions; Mathematics competition resources; Math books;, Problem 1. Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost each and soft drinks cost each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks., 2014 AMC 8. 2014 AMC 8 problems and solutions. The test was held ON TUESDAY NOVEMBER 18, 2014. 2014 AMC 8 Problems. 2014 AMC 8 Answer Key. 2014 AMC 8 Problems/Problem 1. 2014 AMC 8 Problems/Problem 2. 2014 AMC 8 Problems/Problem 3. 2014 AMC 8 Problems/Problem 4., 2016 AMC 8 Problems. 2016 AMC 8 Printable versions: Wiki • AoPS Resources • PDF: Instructions. This is a 25-question, multiple choice test. Each question is ... , Jan 25, 2022 ... My review of the 2022 Winter AMC8 problems & solutions. You can find the problems at ..., upcoming AMC8 competition too with the idea of just dwelling on the first 10 problems there and see which ones make you think and wonder. Most people don’t realize that making progress on the first 10 problems is actually a …, The AMC 8 is a math contest organized by the Mathematical Association of America (MAA). The AMC 8 contest contains 25 multiple choice questions that must be completed within 40 minutes. There is no negative marking on the test, so remember to put an answer for every problem (even if you have to guess). Who can take the AMC 8., Answer: E. The ratio of water to sugar to lemon juice, in general, is 8:2:1. So if 3 cups of lemon juice is used, 8×3=24 cups of water would be needed. AMC 8 Problem 2. Four friends do yardwork for their neighbors over the weekend, earning 15 dollars, 20 dollars, 25 dollars, and 40 dollars, respectively., Hello everybody! I've been receiving a lot of requests to write more competition-related articles, especially because the AMC is approaching pretty quickly: the exams will be hosted on February 4 and February 10, 2021. Today, I thought I'd take the opportunity to curate a set of my 40 favorite problems to serve as a resource for your AMC prep, grouped by category. I aimed this compilation at ..., Advertisement In theory, rail guns are the perfect solution for short- and long-range firepower. In reality, they present several serious problems: Advertisement A coil gun (or Gau..., Resources Aops Wiki 2023 AMC 8 Problems Page. Article Discussion View source History. Toolbox. Recent changes Random page Help What links here Special pages. Search. ONLINE AMC 8 PREP WITH AOPS Top scorers around the country use AoPS. Join training courses for beginners and advanced students., Problem 1. Luka is making lemonade to sell at a school fundraiser. His recipe requires times as much water as sugar and twice as much sugar as lemon juice. He uses cups of lemon juice. How many cups of water does he need? Solution. Problem 2