数学在线辅导|Stanford大学数学夏令营测试辅导

下面是几道典型的数学竞赛代写测试题目

An equilateral has sides of length $1 \mathrm{~cm}$.
(a) Show that for any configuration of five points on this triangle (on the sides or in the interior), there is at least one pair of from these five points such that the distance between the two points in the pair is less than or equal to $.5 \mathrm{~cm}$.
(b) Show that $.5$ (in part (a)) cannot be replaced by a smaller number even if there are 6 points.
(c) If there are eight points, can $.5$ be replaced by a smaller number? Prove your answer.
Suppose $n$ is a positive integer. The (imaginary) sea of Babab has islands each of which has an $n$-letter name that uses only the letters ” $\mathrm{a}$ ” and “b,” and such that for each $n$-letter name that uses only the letters “a” and ” $\mathrm{b}$,” there is an island. For example, if $n=3$, then Aaa, Aab, Aba, Baa, Abb, Bab, Bba and Bbb are the islands in the sea of Babab. The transportation system for Babab consists of ferries traveling back and forth between each pair of islands that differ in exactly one letter. For example, there is a ferry connecting Bab and Bbb since they differ only in the second letter.
a) How many islands and how many ferry routes are there in terms of $n$ ? Count the ferry route for both directions as a single ferry route, so for example, the ferry from Bab to Bbb is the same ferry route.
Babab does not have much in the way of natural resources or farm land so nearly all food and supplies are provided by the Babab All Bulk Company (BABCO). The people of Babab (Bababians) desire easy access to a BABCO store, where “easy access” means there is a BABCO store on their own island or on one that they can get to with a single ferry ride. However, BABCO finds it uneconomical to give the people on one island easy access to two different BABCO stores, and BABCO is willing to deny some Bababians easy access to a BABCO store in order to meet this restriction.
b) In the cases $n=3, n=4$, and $n=5$, what is the maximum number of stores that $\mathrm{BABCO}$ can build while satisfying the restriction than no one has easy access to more than one BABCO store? Be sure to prove your answer is optimal.
c) Now suppose BABCO changes its strategy and decides it wants to be sure every Bababian has access to a $B A B C O$ store even if it means some Bababians have easy access to two stores. What is the minimum number of stores needed to satisfy this condition in the cases $n=3, n=4$, and $n=5$ ?
d) Can you find optimal solutions to parts b and $\mathrm{c}$ for $n=6$ ?

SUMaC数学竞赛辅导|SUMaC代考|SUMaC保过入学考试

准备申请 SUMaC 和其他暑期课程实际上是大学入学申请的绝佳实践……但规模较小。如果您在SUMaC入学考试方面需要帮助，请查看avatest的数学辅导和数学代写服务。您将在10min内联系到专业数学辅导老师得到联系。

斯坦福大学数学营(SUMaC)可以给你带来什么

当你参加斯坦福大学数学营时，你不仅会参与对数学的深入探索并发展成为一名数学家，而且你将沉浸在一个与你有相同数学天赋和好奇心的人组成的社区中。在三周的时间里，你将参加在线课程，结交新朋友，并接受智力上的挑战。许多参与者说这一经历改变了他们的生活。

Stanford University Mathematics Camp的故事

斯坦福大学数学营教给学生的不仅仅是当代数学的抽象概念和数学符号。参与者实际上这个项目中建立联系和友谊，许多人回想起来SUMaC的往事都说这是一次改变人生的经历。Mykel Kochenderfer是斯坦福大学航空和工程系副教授。Kochenderfer教授在高中时代参加了SUMaC，然后作为学生来到斯坦福大学，并最终加入了斯坦福大学成为了一名教授。

如何成为一个有竞争力的SUMaC候选人？

大量的高级数学课程有助于增加你的录取机会。如果一个对数学感兴趣的高中学生正在为未来的申请制定策略，我建议如果可能的话，尝试从学校的基础数学课程中考出来，而选择更多的高级数学课程。许多参加SUMaC的同学（10年级和11年级的学生）已经完成了微积分，有些人甚至对更高级的数学课题有经验，如三角学。

PSAT高分也有助于你的申请。与所有标准化考试一样，实践出真知。确保在你的PSAT考试日期之前进行几次模拟测试。

任何能证明你对数学的热情的额外课外活动也会帮助你脱颖而出；无论是参加数学竞赛，还是你以前参加过其他数学营，一定要强调你对数学活动感兴趣的所有证据。

申请还涉及到一个书面测试，主要是基于写证明。

一个有竞争力的SUMaC申请人应该有

• 高的GPA，包括但不限于数学课程的高成绩
• 高标准的分数，特别是数学部分的分数
• 通过数学竞赛等课外活动表现出对数学的热情
• 参加过以前的数学训练营
• 特别是：在SUMaC基于证明的入学考试中表现优异！

数学在线辅导|Stanford大学数学夏令营测试辅导 请认准avatest™. avatest™为您的留学生涯保驾护航。