[小学丨中学] 新西兰高一的一些数学problem solving题- chapter 4 28.05.2012 [复制链接]

cindyppz

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电梯直达

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发表于 2012-5-20 22:17:07 |只看该作者 |倒序浏览 微信分享

本帖最后由 cindyppz 于 2012-5-28 21:00 编辑

老妈说我闲着不如对社会做点贡献~~ 大家说，我咋就这么听我妈的话呢？？

那先借此贴再给自己打个小小广告：各位阿姨们姐姐们，九月-十月份我要再three kings开一个kumon centre啦~~~ 啦啦啦~~~~ 主要是针对5-15岁左右的学生，数学和英语阅读

注意是9-10月，不是7月啦，因为想拖到生完宝宝嘿嘿

刚刚翻出高一(form 3)当初类似于maths extension给的两个小册子，名为gauss enrichment series: mathematics challenge for young australians.

http://www.amt.edu.au/mcya.html

其中一个小册子是很多试题，还有解答，做完之后可以做第二个小册子的problem (如果没记错，第二个小册子的答案是要上缴的~）

大家娱乐一下，算是我抛砖引玉。新西兰最讨厌的就是题库太少了~ 多做做这种题没啥坏处.

还有啊，这些题有的简单，初中学生也可以算，有一些涉及到几何，三角，函数等可能就稍微难一点咯~ （全部插图都是我尽量模仿的，如果有误，一概不负责嘿嘿）

（如果侵犯了版权。。。嘘。。。。。。。小点声。。。。。。）

一共11个chapter, 我每周更新一次，为了小小尊重一下版权，更新后只会保留最新的题，旧的全部删除~

上周给了chapter 1, 今天给chapter 4，因为2-3都是几何图，我有点懒的画。。。。。

chapter 4

1a) list all the arrangements of the letters A, B, C eg BAC
b) each of these arrangements is written on a tile. the tile is then arranged in a circle so that adjacent letters are different. show with an illustration how this may be done.

2. mr smith wants to stop smoking after he finishes his remaining 9 cigarettes. he can make a new cigarette by wrapping 3 buttes in a piece of cigarette paper. if he uses this technique as many times as he can, how many cigarettes can he smoke before he finally quits?

3. find the sum when all the three digit numbers which can be made up from the digits 2, 3 and 7 are added up, eg 733, 222, 327

4. a rectangular lawn is 10m by 24m. in mowing it a man starts by going right round the perimeter and then continues in the same direction spiralling into the centre. find the dimentions of the rectangle left when exactly half the area has been cut. assuming for simplicity that this occurs exactly as a circuit is completed.

5. find a number divisible by 41 whose digits are all nines. whiout doing the division find the remainder when
90 000 800 007 000 060 000 500 004 000 030 000 200 001 is divided by 41

6. if x, y and z represent different non zero digits, what is the smallest possible value of the fraction xyz/(x+y+z), where xyz=x.100+y.10+z

7. if the product of a woman's present age (W) and wedding age (w) is subtracted from the product of her husband's present age (M) and wedding age (m) and the result of this is added to (Wm-Mw) the result is 553. Find the present ages.

8. For two digit numbers
a) what number is twice the product of its digits?
b) what number is 3 times the sum of its digits?
c) what number is the square of its units digit?
d) what number exceeds its reversal by 20% (the reversal of ab is ba)
e) what numbers when added to their reversals result in a perfect square?

9. a) find the area of a regular hexagon circumscribed around a circle of radius 1.
b) the area of a circle circumscribed about a hexacgon is (2 pi) square units. find the area of the hexagon

10. the addition below is not quite correct, but if you cross out 9 of the digits (replacing with zeros if necessary), the remaining numbers will add up to 111. what digits must be removed? find five solutions and show that these are the only moves

111
333
555
777
999
1111

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