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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。
Second Round 第二轮
TS-2-1. Find the remainder when 2026 is divided by 2026.
求 2026除以 2026的余数。
TS-2-2. Find the sum of all real roots of the equation
2x2 50x 561 x2 153 25x .
求方程 2x2 50x 561 x2 153 25x的所有实数根的和。
TS-2-3. Given that n is a positive integer not exceeding 2026, and n2 – 1 is a multiple
of 120 , find the number of possible values of n.
已知 n是不超过 2026的正整数，且 n2 – 1是 120的倍数，求 n的个数。
1
TS-2-4. In the Cartesian coordinate plane xOy, let P be a point on the line l: y =
x+m(m>0). From P, draw the two tangents to the circle O : x2 y2 1 , with points
of tangency A and B, respectively. If the area of△OAB is equal to the area of
△PAB, find the maximum possible value of m.
在直角坐标系 xOy中，过直线 l: y = x+m(m>0)上的点 P作圆O : x2 y2 1的
两条切线，切点分别为 A，B。若△OAB的面积与△PAB的面积相等，求 m
的最大值。
TS-2-5. Let x1, x2, and x3 be the three real roots of the equation x3 – 3x + 1 = 0. Find
the value of x12 + x22 + x32.
设 x1，x2，x3是方程 x3 – 3x + 1 = 0的三个实根，求 x12 + x22 + x32的值。
TS-2-6. In the right triangle ABC, where ∠ BAC=90 ° , a square BCDE is
constructed externally on the hypotenuse BC as its side length. As shown in the
figure, lines AD and AE intersect BC at F and G, respectively. Given that BG=9,
CF=4, find the value of FG.
在 Rt△ABC中，∠BAC=90°，以斜边 BC为边长向外作正方形 BCDE，如
图，连接 AD，AE分别交 BC于 F，G。若 BG=9，CF=4，求 FG的值。
2
Answer（答案）
Question
TS-2-1 TS-2-2 TS-2-3 TS-2-4 TS-2-5 TS-2-6
题目
Answer
1548 25 270 2 6 6
答案
3

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