剑已出鞘,谁与争锋

字体 -

博客“数学第一剑”近来小有名气。我去CIBC谈贷款,吃惊地发现那个贷款专家竟然知道我的博客,说我在华人社区也算是个“名人”了。上周,又有一位开地产公司的李先生近日开起了补习学校;他访遍大多地区的这个校那个院,想找人合作;直到有一天,朋友提醒他:搞数学辅导,不看“数学第一剑”怎么行?看后过于感慨,便找到真人搞起了合作。

李先生说,在多伦多,在奥数及大中小学数学教育界,敢称数学第一剑的,非我莫属。“数学第一剑”是谁?中科院数学研究所数学博士,硕士导师,数学建模竞赛导师,北京市高等数学竞赛导师,加拿大Carleton University高级访问学者,数学数论专家。2003年起,在多伦多地区开办各种数学班,涵盖大学,中小学,及奥数竞赛各个方面,一周7,每天至少授课6小时,10多年如一日,对加拿大的中小学数学教育,可谓了如指掌。结合高深的数学造诣和在加拿大丰富的教学经验,创建了一套从小学五年级到大学年级(涵盖IMO)的系统数学教材和针对加拿大本地学生的创新的教学方法. 经不断使用完善, 效果显著10多年来,有很多教授的学生进入美加名校,在各种数学竞赛上不断拿奖。

难得有人赏识本人的才华,我便答应了他的合作建议。我们的第一个目标是:把有才有志的高中生(911年级)送进数学奥林匹克国家队。只要做做后面的几道测试题,写清你的思路,我便能看出你是不是英雄好汉;再加上你愿意学习的决心,我保证让你成为数学高手,受益终生。现在,我的剑已经出鞘,你敢接招吗?!

  1. Solve the equation x2 + x2/(x + 1)2 = 8.

  2. Let A be the sum of the digits of 44444444, and B is the sum of the digits of A. Find the sum of the digits of B.

  3. Find the last digit of [(sqrt(3) + sqrt(2))^2015], where [x] is the integer part of x.

  4. Prove that logx is not a rational function of x.

  5. Solve (2cos8x – 1)(2cos4x – 1)(2cos2x – 1)(2cosx – 1) = 1.

  6. Determine all functions f : R → R for which f(2f(x) + f(y)) = 2x + y for every x and y.

  7. Sketch the graph of x3 + 3xy + y3 = 1.

  8. The solutions of the equation z6 + 6iz5 – 15z4 – 20iz3 + 15z2 + 6iz = 33 are the vertices of a convex polygon in the complex plane. What is the area of the polygon?

  9. If three points are chosen randomly on the circumferences of a given circle, calculate the probability that the triangle determined by the three points is acute.

  10. The medians of a tetrahedron are the line segments joining a vertex to the centroid of its opposite face. Show that the four medians interest at a single point, and divides each other in the ratio 3:1.

  11. Let f(n, k) be the number of ways of distributing k candies to n children so that each child receives at most 3 candies. Determine the value of f(2016, 1) + f(2016, 4) + f(2016, 7) +…+ f(2016, 1006) + f(2016, 1009).

  12. Two people take turns to withdraw apples from three baskets which contain 3, 4, and 5 apples respectively. On each turn, one must take at least 1 apple from the same basket. The person who gets the last apple wins the game. Who has a certain strategy to win; the one who start first or the other?

解答可以发送到 : [email protected] [email protected].

分享博文至:

    6188 条评论

  1. 71. skäggolja gör skägg mjuk - 2019年9月18日 15:20

    I loved this post! i actually read your blog very often, and you’re constantly coming out with some great stuff. I contributed this on my blog, and my followers really liked it.

    Keep up the great work :)

  2. 72. Jan - 2019年9月18日 15:36

    I really liked this post i actually read your blog very often, and you’re consistently coming out with pretty great stuff. I embedded this on my blog, and my followers adored it. Continue the good work :)

  3. 73. www.smellgood.se/ - 2019年9月18日 15:49

    I loved this post! i read your blog very often, and you’re constantly coming out with pretty great stuff.

    I embedded this on my blog, and my followers really liked it. Keep up the very good work :)

  4. 74. 라스베가스 호텔 추천 - 2019年9月18日 15:50

    I really like it whenever people get together and share ideas.

    Great website, stick with it!

  5. 75. web site - 2019年9月18日 16:23

    Hello colleagues, how is everything, and what you want to say concerning this post, in my view its in fact amazing in support of me.

  6. 76. slot game online malaysia - 2019年9月18日 16:38

    I visited several web pages however the audio feature for audio songs existing at this site is in fact wonderful.

  7. 77. https://smellgood.se/ - 2019年9月18日 17:04

    This post was amazing i try to read your blog fairly often, and you’re always coming out with some great stuff. I contributed this on my blog, and my followers adored it.

    Keep up the good work :)

  8. 78. Margie - 2019年9月18日 18:23

    I really liked this post i actually read your blog very often, and you’re constantly coming out with a lot of great stuff. I contributed this on my blog, and my followers adored it. Continue the great work :)

  9. 79. skäggolja stockholm - 2019年9月18日 18:51

    This post was amazing i try to read your blog fairly often, and you’re always coming out with some great stuff. I shared this on my facebook, and my followers loved it. Keep up the great work :)

  10. 80. skäggolja Sverige - 2019年9月18日 19:11

    This post was amazing i read your blog fairly often, and you’re always coming out with pretty great stuff. I contributed this on my blog, and my followers really liked it. I really admire the great work :)

« 1 …, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, … 619 » - 查看所有评论

发表评论