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It outlines AMC 10 contest format, scoring, and calculator restrictions, then provides practical qualifying strategies for AIME, including an answer-skipping approach. 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Students have 75 minutes, no calculators, earn 6 points per correct answer, 1.5 points for unanswered problems, and 0 points for incorrect answers.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What strategy is recommended for maximizing chances of qualifying for AIME?",{"text":117,"@type":113},"The document recommends answering 21 questions on AMC 10. It notes that even with two mistakes, a qualifying score of 120 is still achievable, allowing time to spend about 3.5 minutes per answered question and skip the four most difficult ones.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the document suggest solving certain number theory problems about factor sums?",{"text":121,"@type":113},"It demonstrates prime factorization first, then uses a distribution idea: distributing the sum of powers across primes captures every factor. It provides worked examples for the sum of factors of 20 and for 5!.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},444293,1790766400,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},13056703020460,"https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923","AMC 10 Contest Problems  \nInstructor: Natalya St . Clair  \nToday's session is dedicated to exploring a variety of AMC 10 contest problems you might 􀀌nd. So, if you get bored, wait a few minutes, and you might encounter something new and inspiring!  \nRemark. Some AMC 10 contest guidelines:  \n􀀏 The AMC 10 is a twenty-􀀌ve question, multiple choice test. You have choices A, B, C, D, and E. Only one is correct. You have 75 MINUTES working time to complete the test. No calculators are allowed.  \n􀀏 SCORING: You will receive 6 points for each correct answer, 1 .5 points for each problem left unanswered, and 0 points for each incorrect answer.  \n􀀏 How many questions should you answer on AMC 10 and AMC 12 to get the best chances of qualifying for AIME? The optimal strategy is to answer 21 questions on AMC 10 (if you make two mistakes, you still qualify with a score of 120) . You can a􀀋ord to make two mistakes and still achieve a qualifying score of 120 (19 􀀂 6 + 4 􀀂 1:5 = 120) . This strategy allows you to spend about 3.5 minutes on each of the 21 questions you will answer and skip the four most di􀀎cult questions (usually questions \\#22{\\#25) .  \n1 Warm-Up Exercises  \n1. (AMC 10A 2013) Central High School is competing against Northern High School in a backgammon match. Each school has three players, and the contest rules require that each player play two games against each of the other school's players. The match takes place in six rounds, with three games played simultaneously in each round. In how many di􀀋erent ways can the match be scheduled?  \n2. (AMC 10 2001) The median of the list n; n + 3; n + 4; n + 5; n + 6; n + 8; n + 10; n + 12; n + 15 is 10 . What is the mean?  \n3. (AMC 10 2001) What is the maximum number for the possible points of intersection of a circle and a triangle?  \n4. (AMC 10 2007) A circle of radius 1 is surrounded by 4 circles of radius r as shown. What is r?  \n5. (AMC 10 2007) All sides of the convex pentagon ABCDE are of equal length, and \\A = \\B = 90􀀎 . What is the degree measure of \\E?  \n6. A pyramid with a square base is cut by a plane that is parallel to its base and is  \n2 units from the base. The surface area of the smaller pyramid that is cut from the top is half the surface area of the original pyramid. What is the altitude of the original pyramid?  \n2 General Contest Strategies  \n􀀏 Take advantage of symmetry.  \n􀀏 Know what kind of problem you're looking at (Algebra, Number Theory, Geometry, Counting & Probability, General Logic / Problem-Solving) .  \n􀀏 Practice. All past AMC 10 contests are available online.  \n2.1 Number Theory Example. Sum of the Factors:  \nWhat is the sum of the factors of 20? Find the prime factorization:  \n20 = 22 􀀁 5  \nNotice what happens when we distribute the sum of the powers of 2 to the sum of the powers of 5:  \n(20 +2 1 +22 )(50 +5 1 ) = (1+2+4)(1+5) = 1(1+5)+2(1+5)+4(1+5) = (1+2+4)(1+5) = 42 : Distribution gives us every factor!  \nExample. Find the sum of the factors of (5!) . Solution: Begin with the prime factorization of (5!):  \n5! = 5 􀀁 4 􀀁 3 􀀁 2 􀀁 1 = 23 􀀁 3 􀀁 5 :  \nThe sum of the factors is (1 + 2 + 4 + 8)(1 + 3)(1 + 5) = 360 :  \n2.2 Exercises  \n1. Product of the Factors. Now that you can count the number of factors quickly, let's 􀀌nd a quick way to 􀀌nd the product of these factors. Make a list of all factors of 96 and 196 . Be sure to list all the factors as pairs! How many factors does 96 have? How many pairs is this? Try to come up with a general formula for the product of the factors.  \n2. (2003 AIME) Two positive integers di􀀋er by 60 . The sum of their square roots is the square root of an integer that is not a perfect square. What is the maximum possible sum of the two integers?  \n3. There are 9 divisors for number A and 10 divisors for number B . The least common multiple of A and B is 2800 . What are these two numbers?  \n4. (2007 AMC 10) How many pairs of positive integers (a; b) are there such that a and b have no common factors greater than 1 and  \na  14b  \n+ ","cbCaidg4nJPCwfHD","https://ap.wps.com/l/cbCaidg4nJPCwfHD","pdf",122452,"English","# Remark: AMC 10 Guidelines\n# Warm-Up Exercises\n# General Contest Strategies\n## Number Theory Example: Sum of the Factors\n## Exercises\n# Counting and Probability\n## Exercises\n# Geometry\n## Exercises\n# Algebra","[{\"question\":\"What are the AMC 10 guidelines and scoring rules mentioned in the document?\",\"answer\":\"AMC 10 is a 25-question, multiple-choice test with choices A–E and one correct answer. Students have 75 minutes, no calculators, earn 6 points per correct answer, 1.5 points for unanswered problems, and 0 points for incorrect answers.\"},{\"question\":\"What strategy is recommended for maximizing chances of qualifying for AIME?\",\"answer\":\"The document recommends answering 21 questions on AMC 10. It notes that even with two mistakes, a qualifying score of 120 is still achievable, allowing time to spend about 3.5 minutes per answered question and skip the four most difficult ones.\"},{\"question\":\"How does the document suggest solving certain number theory problems about factor sums?\",\"answer\":\"It demonstrates prime factorization first, then uses a distribution idea: distributing the sum of powers across primes captures every factor. It provides worked examples for the sum of factors of 20 and for 5!.\"}]","AMC 10 Contest Problems - Instructor Natalya St. Clair - Warm-Up Exercises - General Contest Strategies | PDF",1790707473]