2026年希望杯国际数学邀请赛巅峰对决IHC8-TS1团队速度赛第一轮八年级数学试题

Mathematics invtational International Hope Cup 2026 Global Peak Challenge(IHC 8) 2026希望杯国际数学邀请赛巅峰对决(HC8) Team Speed Rounds团队速度赛 There are a total of 12 questions,divided into two rounds with 6 questions each.Each question is worth 10 points,for a total of 120 points. Time limit:Round 1-10 minutes;Round 2-10 minutes. Discussion is allowed.Each team will answer one set of question papers and submit only one answer sheet. 共12道题，分两轮进行，每轮6题，每题10分，共120分。 限时：第1轮，10分钟；第2轮，10分钟。 允许讨论，每个队答一份试卷，只提交一份答题卡。 First Round第一轮 TS-1-1.In a convex quadrilateral,the lengths of two of its sides and its two diagonals are all equal to 2026.What is the measure,in degrees,of the largest possible interior angle of the quadrilateral? 在一个凸四边形中，两条边的长与两条对角线的长均为2026，该四边形的最 大内角为多少度？ TS-1-2.There are 16 stones in a pile.Allen and Bob take turns removing stones, with Allen going first.On each turn,a player may remove only a prime number of stones.If there are 0 or 1 stones remaining at the start of a player's turn,that player has no legal move and loses.How many stones should Allen remove on his first move to guarantee a win? 共有16颗石子，Allen和Bob两人轮流取石子，每次只能取质数颗石子；剩 余石子为0颗或1颗时，轮到的人无法取石子则判定为输。若由Allen先取 石子，Allen第一次应取多少颗石子能保证必胜？ International Hope Cup Mathematics Invitational TS-1-3.Fill the circles in the diagram with the numbers 1 through 8,using each number only once.Let d,be the distance between the centers of the circles containing the numbers n and n+1 (where n is 1 through 7),and d be the distance between the centers of the circles containing the numbers 2 and 3.If the filling order satisfies di<d<d3<d4<ds<de<d7,which number should be filled in the circle marked with a "?" 将数字18分别填入图中各个圆圈，每个数字仅使用一次。规定d为数字n 和数字叶1所在圆的圆心距离(n为1~7)，如d为数字2和3所在圆的圆心 距离。若填法满足d<d<d<d4d<d6<h,则图中标注“？”的圆内应填入 哪个数字？ TS-1-4.Given that n is a positive integer,and n!+76 is a perfect square.Find the maximum value of n. 已知n是正整数，nl+76是完全平方数，求n的最大值。 TS-1-5.As shown in the figure,right trapezoid ABCD is formed by joining two isosceles right triangles ABC and ACD.Points E and F lie on line segments AB and BC respectively,and CELDF.Given CF-20 and AE-26,find the area of right trapezoid ABCD. 如图，直角梯形ABCD由两个等腰直角三角形ABC和ACD拼接而成，点E, F分别在线段AB,BC上，且CE⊥DF。已知CF=20,AE=26,求直角梯形 ABCD的面积。 TS-1-6.In how many different ways can a 2x10 board be completely tiled with 1x2 dominoes,without overlaps or gaps? 使用1×2的多米诺骨牌无重叠、无空隙铺满2×10的棋盘，共有多少种不同 的铺设方法？ International Hope Cup Mathematics Invitational Answer(答案) Question 题目 TS-1-1 TS-1-2 TS-1-3 TS-1-4 TS-1-5 TS-1-6 Answer 150 7 5 答案 1944 89 International Hope Cup International Hope Cup Hope Cup International Hope Cup International Hope Cu nternational Hope Cup International Hope Cup