2026年希望杯国际数学邀请赛巅峰对决IHC8-TS2团队速度赛第二轮八年级数学试题

International Hope Cup Mathematics Invitational 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。 Second Round第二轮 TS-2-1.If two distinct numbers are chosen at random from the eight numbers below, what is the probability that their product is greater than or equal to 0? 从下面的8个数中任选2个不同的数，这2个数的乘积不小于0的概率是多 少？ -1、1、-2、2、-4、4、0、6 TS-2-2.As shown in the figure,the area of the shaded region in the left diagram is 12. Given that a,b,x,and y satisfy ay=bx+20 and ax-by+26,find the area of the shaded region in the right diagram. 如图，已知左图阴影部分的面积为12，且a,b,x,y满足y=bx+20,a=by叶26， 求右图阴影部分的面积。 International Hope Cup Mathematics Invitational TS-2-3.A positive integer n has exactly 2026 positive divisors.What is the maximum possible number of positive divisors ofn2? 设正整数n恰好有2026个正因数，则n最多有多少个正因数？ TS-2-4.There are four distinct prime numbers.The sum of any three of these prime numbers is still a prime number.Find the minimum possible value of the sum of the four prime numbers. 有四个互不相同的质数，其中任意三个质数相加的结果仍为质数，求这四个 质数和的最小值。 TS-2-5.As shown in the figure,rectangle ABCD is divided into 13 identical small rectangles.Given that DE=2 and DF=2.5,find the value of DB 如图，矩形ABCD被分割为13个完全相同的小矩形，已知DE=2,DF=2.5, 求DB的值。 A E B TS-2-6.Three distinct prime numbers less than 50 are selected.The product of these three prime numbers must be divisible by their sum.How many different selections are possible? 选取三个小于50且互不相同的质数，要求这三个质数的乘积能被它们的和 整除，有多少种不同的选法？ national Hope Cup International Hope Cup International Hope Cup Mathematics Invitational Answer(答案) Question 题目 TS-2-1 TS-2-2 TS-2-3 TS-2-4 TS-2-5 TS-2-6 Answer 答案 47 23 6075 48 130 14 International Hope Cup International Hope Cup I Hope Cup International Hope Cup International Hope C nternational Hope Cup International Hope Cup