03年英国数学奥林匹克第2轮试题及解答(高一、高二、高三)

一、试题原文1. For each integer n > 1, let p(n) denote the largest prime factor of n. Determine all triples x,y,z of distinct positive integers satisfying(i) x,y,z are in arithmetic progression and(ii) p(xyz)≤3.2. Let ABC be a triangle and let D be a point on AB such that 4AD = AB. The half - line l is drawn on the same side of AB as C, starting from D and making an angle of θwith DA where θ=∠ACB. If the     

France Team Selection Test 2006

Dayl 1 .Let ABCD be a square and let厂be theeireumeirele of ABCD.M 15 a Point of厂belonging tothe are CD whieh doesn,t eontain A.P and R areresPeetively the interseetion Points of(AM)with〔BD〕and[eD〕,Q and 5 are respeetively theinterseetion points of(BM     

生活在2002年的标志

1 You just tried to enter your password on the microwave (微波炉) 2. You have a list of 15 phone numbers to reach your family of three. 3. You call your son s beeper (BP机) to let him know it's time to eat, he emails you back from his bedroom. 4. Your daughter sells Girl     

体会重点，走进高考——Unit 18 Inventions

1.课本原文:If you use our inflatable bike,you can simply let the air out and put your bike in a bag.(P.57)透视:1)let out可以表示"放……出去,(无意中)泄密,放大(衣服)";2)let alone更不用说;3)let sb.be听任/不管某人等。     

短文填空专练(英文)

A S c h o o l F r i e n d o f E n g l i s h (A) Most Americans don1t like to get advice __1__ members of their family. They get advice from “__2__ (strange)”. When they need advice, they don1t usually go to people they know. __3__ many of them write let…     

Units 1-10重点句型错解析

一、重点句型解析1.否定倒装形式【课文原句】Nor did he let the disease stop him from living the kind of life he had always dreamed of.(Unit1)     

疑难解析（Units21-24）

1.The same is true for these verbs:hit,hurt,let,cut.(L.84)动词hit,hurt,let和cut也存在同样的情形。句型“The same is true of/for…”意思是“同样的情形也适用于…;对…情况同样如此。”例如: A lot of trees are being cut down in theU.S.A.. The same is true of the trees in China.在美国大量的树木正在被砍伐,在中国情况同样如此。     

Hollow dimension of modules

In this paper, we are interested in the following general question: Given a module Mwhich has finite hollow dimension and which has a finite collection of submodules Ki (1≤i≤n) such that M=K1 ... Kn, can we find an expression for the hollow dimension of Min terms of hollow dimensions of modules built up in some way from K1 Kn? We prove the following theorem:Let Mbe an amply supplemented module having finite hollow dimension and let Ki (1≤i≤n) be a finite collection of submodules of Msuch that M=K1 ... Kn. Then the hollow dimension h(M) of Mis the sum of the hollow dimensions of Ki (1≤i≤n) ifand only if Ki is a supplement of K1 ... Ki-1 Ki 1 ... Kn in Mfor each 1≤i≤n.     

CONVERSATIONS

(A) A: It's really very kind of you to do this for me. Thanks alot. B: It's my pleasure. Please let me know when you need myhelp.     

Who Was the Boss?

1.Peter tom one of his fi'iemlsthat he was out of work. “Whv didn’t the boss(老饭)let you work there?”said his friendin sm33rise(惊奇). 2.“Oh.”answerelj Peter.“t{【)you know what he usuall.y dot,∥He just stands there with his hanf i、in his pockets and only wat(、hes hi-men working.”Who Was the Boss?@姜红伟 @刘碧群…     

你问我答

问：有这样一道题： His funny stories___us laugh. A．allowed B．put C．let D．made     

剖析分词作状语的几种情况

高三语数外先请大家思考下面几道高考题目:1.We all know that,,the situation willget worse.(2007全国)A.not if dealt carefully withB.if not carefully dealt withC.if dealt not carefully withD.not if carefully dealt with2.The glass doors have taken the place of thewooden ones at the entrance,in the naturallight in the day.(2007天津)A.to let B.lettingC.let D.having let3.that she didn t do a good job,I don tthink I amabler than her.(2007陕西)A.To have said B.Having saidC.To say D.Saying4.As the …     

英语秃头不定式的用法

英语中的动词不定式有两种,一种是带小品词(particle)to的不定式,另一种是不带to的不定式,即秃头不定式(bare infinitive)。秃头不定式除用于情态动词之后外,还用于下列情况: 1.用于使役动词make, have, let之后作宾语补足语。例如: She made him sit down and have a cup of     

FUNNY STORIES

A Snake in Class One of my third-grade students brought in a snake for show. I am afraid of snakes, but since the boy was responsible (负责的), I decided to let him go ahead. Another teacher had come in to help that day and,not being fearful of snakes, picked the snake up with the stem (柄) of her glasses so everyone could see it.     

FUNNY STORIES

A Snake in Class One of my third-grade students brought in a snake for show.I amafraid of snakes,but since the boy was responsible(负责的),I decidedto let him go ahead.Another teacher had come in to help that day and,not being fearful of snakes,picked the snake up with the stem(柄)ofher glasses so everyone could see it.     

阅读理解中主旨大意题的解题技巧

所谓主旨大意就是文章或段落所表达的中心思想或主要内容,主旨大意题主要考查考生对文章主旨大意的概括和归纳能力,这类试题在高考阅读理解题中所占比例较大。一、命题形式主旨大意题多有main idea,topic,title等字眼,可细分为主题型和标题型两类。常见的题干形式有:1.主题型主旨大意题(1)The main/general/central idea of the massageis______.(2)Which of the following statements can best sum-marize/sum up/express the main idea of the passage?(3)What does the passage mainly discuss?(4)The passage mainly discuss______.(5…     

专题五 其他题型

任务型阅读(1)(江苏省南菁高级中学2012~2013学年度第二学期高三第一次考试)Guiding students through open-ended discussions can help students develop their understanding of the nature of science.One useful practice in classroom discussions involves developing a discussion map.A discussion map is a graphic timeline created by the teacher on which a discussion is recorded-who initially states the idea and who adds to or refuses the idea.Discussion maps let teachers gain a deep understanding of students’level of participation,the     

完形填空精练(英文)

LETTING GO OF SUCCESS I want to make the most of every day.And,like most people,I’ve 1 that the best way to do it is to let go of past     

上海版《牛津英语》3B Module2 Unit1 Animals I like

Step1.Warm-up(略)Step2.Presentation 1.Teach"lion"Boys and girls,I like dogs.I like animals.They are my friends.Today I take my friends here.Now let’s watch a videotogether.Then answer my question:What animals can you see in the video?(Play the video of Madagascar)T:What animals can you see?S1:狮子T:Good!Please look here.(出示狮子     

哭出来就好了

I remembered losing my father to a sudden car accident a number of years ago.I tried to remain strong through it all.One day,when a song came on the radio that reminded me of my dad,I completely 1)lost it.It was the first time since the 2)funeral that I just 3)let go and cried.It felt good to not 4)hold back anymore.