2026年希望杯国际数学邀请赛巅峰对决个人思考赛IHC8-I八年级数学试题

Mathematics invitational 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) nternationa Individual Thinking Round个人思考赛 Total of 10 questions,each worth 10 points,for a total of 100 points Time limit:30 minutes No discussion allowed.Each person answers one exam paper and submits one answer sheet. 共10道题，每题10分，共100分。 限时：30分钟。 不允许讨论，每人答一份试卷，各提交一份答题卡。 I-1.Given that a and b satisfy 1+a-(b-11-b=0,find the value of a2026- b2027. 已知，b满足V1+a-(b-1)1-b=0,求2026-b2027的值。 I-2.As shown in the figure,in right triangle ABC,the right-angled side AC=30 and BC=40.A circle is drawn with the altitude CD of the hypotenuse as its diameter, and a semicircle is drawn with the right-angled side AC as its diameter.Find the area of the shaded region in the figure.(Take n as 3) 如图，在Rt△ABC中，直角边AC=30,BC-40。以斜边的高CD为直径作圆， 以直角边AC为直径作半圆，求图中阴影部分的面积。（π取3） tional Hope Cup Mathematics Invitational International Hope Cup I-3.In a Cartesian coordinate system,each vertex of a rectangle is an integer (i.e., both its x and y coordinates are integers),and its four sides are parallel to the coordinate axes.If the x-coordinates of all four vertices of a rectangle satisfy 2< x<7,and the y-coordinates satisfy 2<y<6,how many rectangles satisfy these conditions? 在平面直角坐标系中，长方形各顶点均为整点（即横、纵坐标均为整数）， 且长方形四边分别平行于坐标轴。若长方形四个顶点的横坐标均满足2<x< 7,纵坐标均满足2<y<6,则符合条件的长方形共有多少个？ I-4.In parallelogram ABCD,square ABEF is constructed outwards with AB as a side, and square ADGH is constructed outwards with AD as a side.The area of square ABEF is 4,and the area of square ADGH is 8.Connect CE,DH,and FH.Given that points C,D,and H are collinear,find the area of trapezoid FECH 在平行四边形ABCD中，以AB为边向外作正方形ABEF,以AD为边向外作 正方形ADGH,其中正方形ABEF面积为4，正方形ADGH面积为8。连接 CE,DH,FH,已知C,D,H三点共线，求梯形FECH的面积。 B Hope Cup H I-5.Alice,Bill,and Charlie solved a total of 108 math problems,with each of them solving 77.Problems that only one person could solve are called difficult problems,and problems that all three could solve are called easy problems.How many more easy problems were there than difficult problems? Alice、Bill和Charlie三人合计解出l08道不同的数学题，每人各解出77道。 仅一人解出的题目称为难题，三人都解出的题目称为容易题，则容易题比难 题多几道？ Mathematics invitational International Hope Cup I-6.In the group stage of the World Cup,each group consists of four teams playing a round-robin tournament.Each team plays three matches.A win earns 3 points,a draw earns 1 point,and a loss eamns 0 points.The top two teams in each group advance to the next round.If teams have the same total points,their rankings are determined according to additional tiebreaker rules,and the top two teams still qualify.What is the highest number of points a team can earn while still having the possibility of failing to advance? 在世界杯小组赛中，每个小组有4支球队进行单循环比赛，每支球队各踢3 场，胜一场积3分，平一场积1分，负一场积0分，小组排名前两名可以出 线；总积分相同时依据后续附加规则确定名次，依旧取前两名出线。那么一 支球队最高拿到多少分，仍然有无法出线的可能。 I-7.How many pairs of positive integers (x,y)satisfy the Diophantine equation 1,11 2 xy2026 不定方程 1+1-1 xy2026 有多少组正整数解？ I-8.When Michael goes up the stairs,he can take 1,2 or 3 steps at a time.How many different ways can he go to the 10th step? Michael上台阶时，每步可跨1级、2级或3级台阶，他登上第10级台阶一 共有多少种不同走法？ I-9.Five points are marked on a circle with a circumference of 20cm.The arc length between any two points is an integer centimeter.The circumference is defined as the longest arc.What is the maximum number of different arc lengths that can occur? 周长为20cm的圆周上标有5个点，任意两点间的弧长均为整数厘米，规定 圆周为最长的弧，那么最多能出现多少种互不相等的弧长？ I-10.How many of the positive divisors of 26!have a units digit of 9? 在26！的所有正因数中，个位为9的正因数有多少个？ Mathematics invitatisnal International Hope Cup Answer(答案) Question 题目 I-1 I-2 1-3 I-4 I-5 Answer 答案 0 337.5 18 16 15 Question 题目 I-6 I-7 I-8 I-9 I-10 Answer 答案 6 9 274 19 792 International Hope Cup International Hope Cup Hope Cup International Hope Cup International Hope Cu nternational Hope Cup International Hope Cup