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2026 Global Peak Challenge (IHC A)
2026 希望杯国际数学邀请赛巅峰对决（IHC A）
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. Find the minimum value of |sinx|+|sin2x|+|cosx|+|cos2x|.
求|sinx|+|sin2x|+|cosx|+|cos2x|的最小值。
TS-1-2. Given the function f(x)=a0+a1x+a2x2+a3x3+a4x4+x5. If f(n)=n2(n=1,2,3,4,5),
find the value of a0.
已知函数 f(x)=a0+a1x+a2x2+a3x3+a4x4+x5。若 f(n)=n2(n=1，2，3，4，5），
求 a0的值。
TS-1-3. In a cube with side length 1, four vertices that are pairwise non-adjacent are
selected to form a tetrahedron. Find the volume of this tetrahedron.
在棱长为 1的正方体中，取四个两两不相邻的顶点构成四面体，求该四面
体的体积。
1
TS-1-4. Definition: [x] represents the greatest integer less than or equal to x. Find the
number of real roots of the equation x2 – 11[x] + 9 = 0.
定义：[x]表示不超过 x的最大整数。求方程 x2 – 11[x] + 9 = 0的实数根的个
数。
TS-1-5. Given an acute triangle ABC, let its circumcenter and orthocenter be O and
, respectively. If the four points B, C, O, and H are concyclic, find the value of
∠A.
已知锐角△ABC的外心和垂心分别是 O，H。若 B，C，O，H四点共圆，则
∠A等于多少度？
TS-1-6. Let a, b, and c be three positive real numbers satisfying a+b+c=6. Find the
maximum value of ab2c3.
已知三个正实数 a，b，c的和为 6，求 ab2c3的最大值。
2
Answer（答案）
Question
TS-1-1 TS-1-2 TS-1-3 TS-1-4 TS-1-5 TS-1-6
题目
Answer 1
2 -120 4 60 108
答案 3
3

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