美国数学竞赛试题-部分.pdfVIP

2000 AMC 12 Problems Problem 1 In the year , the United States will host the International Mathematical Olympiad. Let and bedistinctpositive integerssuchthattheproduct .What is the largest possible value of the sum ? Problem 2 Problem 3 Each day, Jenny ate of the jellybeans that were in her jar at the beginning of that day. At the end of the second day, remained. How many jellybeans were in the jar originally? Problem 4 The Fibonacci sequence startswith two 1s, and each term afterwards isthe sumof itstwopredecessors. Which one of the ten digits isthe lastto appear intheunits position of a number in the Fibonacci sequence? Problem 5 If where then Problem 6 Twodifferentprimenumbersbetween and arechosen.When theirsum issubtractedfromtheir product, which of the following numbers could be obtained? Problem 7 How many positive integers have the property that is a positive integer? Problem 8 Figures , , , and consist of , , , and non-overlapping squares. If the pattern continued, how many non-overlapping squares would there be in figure ? Problem 9 Mrs.Walter gavean exam inamathematics classof five students.She enteredthe scores inrandom order intoa spreadsheet,which recalculated theclassaverage after each scorewas entered.Mrs. Walter noticed that after each score was entered, the average was always an integer.The scores (listedinascendingorder)were71,76,80,82,and91.Whatwas thelastscoreMrs.Walters entered? Problem 10 The point is reflected in the -plane, then its image is rotated by about the -axis to produce , and finally, is translated by 5 units in the positive- direction to produce . What are the coordinates of ? Problem 11 Two non-zero real numbers, and satisfy . Which of the following is a possible value of ? Problem 12 LetA,M, andCbenonnegative integerssuc