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2011-2012年度美国“数学大联盟杯赛”中学组(6 - 9年级)决赛和数学夏令营




美国“数学大联盟”和斯坦福大学联合举办美国“数学大联盟杯赛”中学组(6 - 9年级)决赛和数学夏令营

美国“数学大联盟”(Math League, www.mathleague.com)和斯坦福大学(Stanford University, www.stanford.edu)经过慎重考虑和磋商, 决定由美国“数学大联盟”和斯坦福大学联合举办美国“数学大联盟杯赛”中学组(6 - 9年级)决赛和数学夏令营, 该项目正式命名为 “Stanford Math League Finals & Tournament(www.stanford.edu/dept/spcs/mathleague/) ”, 是美国“数学大联盟”和斯坦福大学永久合作项目,每年举办一次。 (从2012-2013年度起将包括高中学生,即6 - 12年级的学生。)





2011-2012年度美国“数学大联盟杯赛”中学组(6 - 9年级)决赛和数学夏令营将于2012年8月20日至8月25日在斯坦福大学举行。 首先进行决赛,决赛安排如下:

  • 2011-2012年度美国“数学大联盟杯赛”中学组(6 - 9年级)决赛的参赛选手是来自美国、加拿大和中国初赛成绩优异的6 - 9年级的学生。
  • 决赛分为个人决赛和团体决赛。
  • 决赛时间不超过3小时30分钟,将全部采用英文试题,分四轮举行。中国学生可以携带正规出版社出版的纸质简明英汉数学字典。(禁止携带任何电子版的英汉字典、电子词典或计算器等。)
  • 比赛开始前,所有参赛学生将被分成6-7年级组和8-9年级组两个组别, 其中每个组别内又被分成5人的团队若干个。
  • 决赛时间:
    8月22日上午:第一轮 个人决赛
    第二轮 团队决赛
    8月23日上午:第三轮 团队决赛-接力赛
    第四轮 个人决赛-速答
  • 第一轮是个人决赛,参赛学生须独立完成10道填空题,每道题限时5~7分钟不等。参赛学生每次仅获得一道试题,且必须在该题所限定的时间内完成。类似团队决赛的题目设置规则,个人决赛中6-7年级组与8-9年级组也有部分题目相同。
    Individual Round: 10 short-answer questions with variable time limits from 5 minutes to 7 minutes each. Students work on their own to solve these questions. As with the team round, the questions for grades 6 and 7 will be different from the questions for grades 8 and 9 (with some overlap).
  • 第二轮是团队决赛,每个团队将解答10道填空题,需要团队成员在限时1小时内共同完成。其中6-7年级组与8-9年级组将有部分题目相同。
    Team Round (1 Hour Time Limit): 10 short-answer questions that your team works on together. We will divide students into teams when they arrive. There will be one set of questions for 6th and 7th graders and another set of questions (with some overlap) for 8th and 9th graders.
  • 第三轮是团队决赛,以接力赛的形式,每个团队须完成3道接力题,每道接力题又包含5个独立的问题,其中第五题最难。为完成每道接力题,5个团队成员须排成一列(建议将成绩最好的学生安排在第五题的位置),第一个人解答出第一道题后,将答案传递给第二个人,此数据将作为第二个人所获得的第二题中已知条件中缺失的数据,解答完成后,则须将答案传给第三个人,以此类推,最终以第五人提交给监考老师的答案来判定此接力题得分与否。在比赛时限内,若团队成员发现答案有错误,允许其更改答案,并传递给其后面的成员重新计算,但将以最终提交的答案为准。另外,越短的时间内解答出正确答案,团队的得分将越多。
    Relay Questions (3 Relay Questions): A relay question consists of 5 separate problems. Students will be placed in groups of five. In order to solve the relay question, the first student in the group must solve the first problem and pass the answer to the second person. The second person uses the passed answer to fill in some missing data in the 2nd problem, solves the second problem, and passes the answer to the third person. This process continues until the fifth person solves the 5th problem and gives his answer to the proctor. If anyone on the team discovers that the answer that person passed on was incorrect, that person may redo the problem and pass a new answer to the person directly behind, but the final answer submitted is the only answer that counts. The faster the 5 students solve the relay question, the more points the team receives.
  • 接力题(Relay Questions)解释:5个团队成员排成一列,第一个人分配到一道已知条件完整的填空题,解答完成后须将答案传递给第二个人。而第二个人得到的问题中已知条件的某个数值是TNYWR(TNYWR代表The Number You Will Receive),即为第一个人传递来的数值,以此类推,最终根据第五个人提交的答案是否正确判断团队得分与否。其中,第二、三、四道题若没有前一个人传来的数值,根本无法解出,例如题目:What is the largest value of x that satisfies (x - TNYWR)(x + TNYWR) = 2012?而第五道题则与之不同,即使没有第四个人传递的数值,仍可解答出题目的大部分,例如题目:If n is the positive value that satisfies the equation n2 - 2n – 3 = 0, then what is the value of n + TNYWR?很明显,此题中无需第四人的数值即可解出n = 3,当第四人的数值传来后,只须简单的与之相加即可。
  • 接力题的得分判定:以第五人提交的答案为准,第五人提交的答案可以有两个选择:第四人传来的答案或解出第五题后的最终答案,但第五人必须二者择其一。就上例而言,即提交第五题中的TNYWR或n + TNYWR某一个数值。当然,提交五题后的最终正确答案将比仅提交第四人传来的正确答案奖励更多的分数。
    The 5th person on the team will have a choice—that person can either submit the answer received from the 4th person on the team OR the answer that the 5th person obtains after solving the 5th part of the relay. The 5th person may only submit one of these answers. Of course, there will be more points awarded for a correct answer to all 5 parts than a correct answer to only 4 parts.
  • 简单的接力题(Relay Questions)实例:
    a) What is the number of perfect squares greater than 0 and less than 100?
    b) What is the largest possible area of a square with integral sides whose perimeter is less than or equal to TNYWR?
    c) How many different positive integers including 1 and the number itself are divisors of TNYWR?
    d) If n = TNYWR, what is the value of (n + 1)(n - 1)?
    e) If m is the number of integers greater than 0 and less than 100 which is divisible by 9, then what is the value of (m + TNYWR)?
    首先,当第一个人解出第一题的答案,须将所得答案值9传递给第二个人。因为正方形的周长能够被4整除,可得出正方形的边长为2,即面积为4,则第二人须将此答案值传递给第三个人。由第三题,可知4的约数分别为1、2、4,故第三人将答案值3传递给第四个人。解出第四题:(3 + 1)(3 - 1) = 8,则将答案值8传递给第五个人。根据第五题,解出m = 11,加上第四人的数值8,得出最终答案为11 + 8 = 19,此时第五人须决定将8或19的某一个答案提交给监考老师。
    First, person #1 solves the first question, gets an answer of 9, and passes that answer to person #2. Since the perimeter must be divisible by 4, Person #2 finds that the sides of the square have length 2, gets an answer of 4 for the area, and passes that answer to person #3. Person #3 realizes that the divisors of 4 are 1, 2, and 4, so person #3 passes an answer of 3 to person #4. Person #4 multiplies (3 + 1) and (3 - 1) to get 8 and then passes that answer to person #5. Finally, person #5 realizes that there are 11 numbers which satisfy the stated condition, that is m = 11, then 11 + 8 = 19, so person #5 must choose only one answer from 8 or 19 and hand it to the proctor.
  • 第四轮是个人决赛,以速答题的形式,参赛学生必须在45分钟内完成60道填空题。此轮比赛主要考察学生的答题速度与准确度,因此题目相对比较容易,但限时45分钟解答所有的60道题目对学生将是一个挑战。
    Speed Round (60 questions in 45 minutes): This is a test of speed and accuracy. The questions will be relatively easy, but time constraints make solving them all in 45 minutes challenging.
  • 决赛四轮竞赛的分值分布:
    决赛名称 单题分值 题目数 总分值
    个人决赛 9 10 90
    团体决赛 6 10 60
    速答 1 60 60
    接力赛(单题) 5题答案正确 4题答案正确
    答题时间:5分钟 30 20
    答题时间:9分钟 25 15
    答题时间:13分钟 20 10
    注:接力赛图表中所示的是单题分值,而比赛中共有3道题,最终将根据3题的结果合计总分值。
  • 个人在第一轮和第四轮的成绩作为个人决赛的总成绩,个人决赛成绩优异者可获得金、银、铜牌奖。 2011-2012年度美国“数学大联盟杯赛”中学组个人决赛设6年级金、银、铜牌奖各一名, 7年级金、银、铜牌奖各一名, 8年级金、银、铜牌奖各一名,和9年级金、银、铜牌奖各一名。
  • 个人决赛的成绩将带入团体决赛。
  • 团队在所有四轮比赛的成绩作为团体决赛的总成绩,团体决赛第一名将获得当年美国“数学大联盟杯”。 2011-2012年度美国“数学大联盟杯赛”中学组团体决赛设6-7年级组美国“数学大联盟杯”和8-9年级组美国“数学大联盟杯”。
  • 决赛由美国“数学大联盟”和斯坦福大学联合命题,题目新颖、富有趣味性和挑战性, 激发学生解决问题和创造性思维的能力 (fun and creative problems that promote critical-thinking and problem-solving skills), 优异的决赛成绩是申请美国及世界一流大学和高中有效的“敲门砖”。
  • 以上决赛安排作为参考,最终决赛安排可能会有所改动。


决赛后是美国“数学大联盟”和斯坦福大学为同学们精心设计的学习、娱乐项目, 每天的日程安排如下:

Time Mon Tue Wed Thu Fri Sat
8/20/2012 8/21/2012 8/22/2012 8/23/2012 8/24/2012 8/25/2012
8:00 AM Breakfast Breakfast Breakfast Breakfast Breakfast
8:30 AM
9:00 AM Lecture:Rafe Mazzeo Hewlett 101 Math Tournament 160-321, 160-322, 160-323,160-325, 160-326, 160-328 Math Tournament 160-322, 160-323, 160-328 Math Tournament Awards Review of problems Hewlett 101 Depature Day
9:30 AM
10:00 AM
10:30 AM Campus Tour
11:00 AM
11:30 AM
12:00 PM Lunch Lunch Lunch Lunch
12:30 PM
1:00 PM Lecture: The 15-Puzzle and the Rubik's Cube Prof Brian Conrad Hewlett 101 Lecture: Binary Strings,Graphs, and Card Tricks (Dr. Simon-Rubinstein Salzedo) Hewlett 101 Lecture: Cryptography (Prof. Dan Boneh) Hewlett 101 Lecture: Math-Inspired Kinetic Sculptures Prof. John Edmark Hewlett 101
1:30 PM
2:00 PM Breakfast Break
2:30 PM Math Olympiad Problem Solving, Pak Hin Lee Hewlett 101 Visit the Stanford Store
3:00 PM Short recreation period Short recreation period
3:30 PM Arrival at Stanford University Welcome Dinner & Openning Remarks Followed by: Program Orientation Introductions and Ice Breakers Snack Break Snack Break Snack Break Snack Break
4:00 PM Recreational Activities: Sports, Games, Campus Excursions Mathematics and Puzzles Stan Isaacs Treat House Math Activities Bridge Recreational Activities:Sports, Games, Campus Excursions
4:30 PM
5:00 PM
5:30 PM
6:00 PM Dinner Dinner Dinner Dinner
6:30 PM
7:00 PM Recreational Activities: Sports, Games, etc. Recreational Activities: Sports, Games, etc. Recreational Activities: Sports, Games, etc. End-of-Program Activity
7:30 PM
8:00 PM
8:30 PM Reading, Games,Quiet time Reading, Games,Quiet time Reading, Games,Quiet time
9:00 PM
9:30 PM
10:00 PM Lights out Lights out Lights out Lights out
美国“数学大联盟杯赛”中学组(6 - 9年级)决赛和数学夏令营特点总结:
  • 把学习和社会实践完美地结合在学生每天的生活中。
  • 在学习中获得乐趣,在获得乐趣的过程中学习。
  • 结识来自世界各地、不同背景的孩子。
  • 世界一流的教授和助教、世界一流的教学内容、美丽的斯坦福校园一定会使孩子们的这个夏天终身受益和难忘。
  • 学习数学,培养数学的英文第一思维和创新能力。
  • 体验美国开放、启发、趣味性教学。
  • 亲身感受世界一流大学。
  • 亲身体验美国文化和风土人情。
  • 与斯坦福大学教授和学生亲密接触。
  • 获得美国“数学大联盟”和斯坦福大学联合颁发的结业证书。
  • 表现优异的学生可以获得美国“数学大联盟”和斯坦福大学教授写的推荐信。

"We would like to think of this program as providing a way to promote the Stanford mathematics department, and undergraduate program, among mathematically talented middle school and high school students who will eventually be looking at top US universities for undergraduate study."

- Dr. Richard Sommer, Managing Director of Stanford University Education Program for Gifted Youth (Stanford University EPGY)

斯坦福大学和美国"数学大联盟"联合举办美国“数学大联盟杯赛”中学组(6 - 9年级)决赛和数学夏令营的目的就是希望全世界的天才少年能够通过参加此项活动了解斯坦福大学本科教育和斯坦福大学数学系, 并为他们将来申请美国一流大学做好准备。

- 斯坦福大学“天才少年教育计划”执行主管 Richard Sommer博士



报名
  • 报名咨询电话:010-51300753。
  • 决赛报名
  • 有意参加决赛和数学夏令营的学生请尽快办理护照。签证预约需要提供身份证号。