自主招生物理,力学题杆AB水平放置,竖直面内有一个固定圆,半径为R,杆与圆在上顶点相切,杆自由下落,当杆落到距离上顶点R

Dear Max,
Our company is going to buy a set of equipment from China.A lot of specifications and instructions are needed to be translated from Chinese to English within four months.As the time limited,I can't handle this all by myself.Will you please send an advertisement for two experienced translators to help me to complete this job?I need them in a hurry.
Thanks a lot for your help.
Yours,XXX

你题目太多了,应该一题一题分别提问,这么多题目让怎么一口气写完啊,写死了.
我就写个14题吧,设安全间隔为S,速度为V,时间为T
（这个T可以任意取,反正一分钟车流量如果最大,一小时车流量也是最大,一秒也是）,
则S=K0乘以V^2,
在时间T内的车流量为Q=VT/（L+S）=T/(L/v+K0*V) 这步的变化是将分子分母同除以V
接下来应该看出来了吧.是对勾函数,这种打法实在累,我截图吧.如果需要其它答案的话,请联系我吧,打字太累了.

通电直螺线管内部的磁场中间密两边疏,边缘处两边密.分别对应答案B,A（A是大于.不是>>)
第二题根据电流留向分2种情况,其中再根据摩擦因素分2种,列受力平衡方程得B的变化应该为变大和先变小后变大.

解题思路：根据题意，分析可得，原问题可以转化为将7个名额排成一排，在排除两端的6个空位中，插入挡板，将其分为3组，对应3个学校的组合问题，由组合数公式计算可得答案．

根据题意，要求将7个名额分给3给学校，且每个学校至少分到一个名额，
可以转化为将7个名额排成一排，在排除两端的6个空位中，插入挡板，将其分为3组，对应3个学校的组合问题；
则不同的分法有C₆²=15种；
故选B．

点评：
本题考点： 排列、组合及简单计数问题．

考点点评： 本题考查组合数公式的应用，关键是将原问题转化为组合问题，用插空法解题．

解题思路：分类计数原理和分步计数原理区分开，校长推荐的方案中：三校都推；只推二校．

校长推荐三校时，学生只能是1人、1人、2人，共有C₄²•A₃³=36种；
推荐二校时学生只能2人、2人，共有C₃²•C₄²=18种．所以共有36+18=54种．
故选D

点评：
本题考点： 分步乘法计数原理．

考点点评： C42•A33中C42是4人分组，A33是3人全排列；C32•C42中C32是3校选2所，C42是从4人中选2人进一所学校，另2人进另一所．

E=25.
至少得19分的概率也就是至少答对两题的概率，也就是1-P(答对0题)-P(答对1题）.
1 - (1/3)^3*(1/2) - [3*(2/3)*(1/3)*(1/3)+(1/3)^3*(1/2)]=20/27

C
先画出三元环,余下两个碳有以下三种情况：
1、以乙基的形式接在三元环其中一个碳上,1种.
2、以两个甲基的形式接在三元环其中一个碳上,1种.
3、考虑立体异构的地方：
（1）两个碳以两个甲基的形式接在三元环2个碳上,由于三元环上的碳的轨道杂化类型是sp3杂化（接的4根共价键类似正四面体形结构）,所以这两个碳会指向三元环确定平面的上方或者下方.
（2）如果同时指向一个方向,1种.
（3）同时指向2个方向,有两种：
假设三元环上的3个碳分别标为1号,2号,3号,如果1号碳上的甲基指向上方,2号碳接的甲基指向下方和3号碳甲基指向下方是2种不同的情况（镜面异构）.不是很好理解,可以做一个模型试一下,无论如何不可能使2种重合.

华理的自招肯定是没有微积分的,前面是填空,大概是10的空这样,建议带上计算器,会对你的解题有很大的帮助.选择题是5-6个这样,对知识的考察比较灵活,最后是大题,印象中是4道.总的来说试卷的难度不大,考试时间也很宽裕,只要认真考成绩都会很理想.我就是去年考的华理自招,总体来说理科试卷难度不大,但是英语很难,希望会对你有所帮助.

是这样的 我一个舍友就是这么进的北大

之前回答过类似的问题,我复制黏贴了一下.
我举我们10年华师大自主招生的例子吧,一共考语数英三门.
语文是一大一小两篇作文.第一篇写读后感,是龙应台的《十七岁》.第二篇是根据庄子的一句话“桂可食,故伐之；漆可用,故割之.人皆知有用之用,而莫知无用之用也.”写作文.
数学的话题目有点活,有部分能力题,要看个人发挥.
英语的话没有听力,有考词汇量的选择题、阅读理解、中译英和英译中、最后还有作文.
难度的话数学难于高考,英语和高考差不多.
希望对你有所帮助,欢迎报考我们华师大.
翻译的都是句子.其中英译中的句子是阅读里面抽几句出来要求翻译的~

解题思路：（I）设甲，乙，丙三人获得自主招生入选资格的概率分别为P（A）、P（B）、P（C），由题意得P(A)＝

1

2

×

3

5

＝

3

10

，P(B)＝

1

2

×

3

5

＝

3

10

，P(C)＝

2

5

×

3

4

＝

3

10

，由此能求出甲，乙，丙三人中只有一人获得自主招生入选资格的概率．
（Ⅱ）X可能取值为0，1，2，3，分别求出相应的概率，由此能求出X的分布列和期望．

（I）设甲，乙，丙三人获得自主招生入选资格的概率分别为P（A）、P（B）、P（C），
则P(A)＝
1
2×
3
5＝
3
10，P(B)＝
1
2×
3
5＝
3
10，P(C)＝
2
5×
3
4＝
3
10，
所以甲，乙，丙三人中只有一人获得自主招生入选资格的概率：
P＝
C13
3
10(1−
3
10)2＝0.441
（Ⅱ）X可能取值为0，1，2，3，
则P(X＝0)＝(1−
1
2)(1−
3
5)(1−
2
5)＝
3
25，
P(X＝1)＝
1
2×
2
5×
3
5+
1
2×
3
5×
3
5+
1
2×
2
5×
2
5＝
19
50，
P(X＝2)＝
1
2×
3
5×
2
5+
1
2×
2
5×
2
5+
1
2×
3
5×
3
5＝
19
50，
P(X＝3)＝
1
2×
3
5×
2
5＝
3
25，
∴X的分布列为：

X0123
P[3/25][19/50][19/50][3/25]EX＝0×
3
25+1×
19
50+2×
19
50+3×
6
50＝
3
2．

点评：
本题考点： 离散型随机变量的期望与方差；相互独立事件的概率乘法公式．

考点点评： 本题考查概率的求法，考查离散型随机变量的分布列和数学期望的求法，是中档题，解题时要认真审题，在历年高考中都是必考题型．

A中,LiOH可以分解
C中,MgClub晶体焙烧时回水解,故不能得到相应无水盐
D中,纯Al极难溶解,不溶于浓硝酸、浓硫酸等常见强酸.

猫喜欢在冰箱前照镜子

解题思路：利用乘法分布计数原理求出两名同学就读的所有的方法，求出就读于同一所大学的方法，利用古典概型的概率公式求出两名同学录取到同一所大学的概率．

两名同学就读的所有的就读方式有5×5=25，
两名同学录取到同一所大学的方法有5
所以两名同学录取到同一所大学的概率是[5/25＝
1
5]．
故答案为[1/5]．

点评：
本题考点： 相互独立事件的概率乘法公式；等可能事件的概率．

考点点评： 本题考查利用古典概型的概率公式求事件的概率．P（A）=n(A)n(Ω)．

第一小题1.5,第二小题,1.5,用梯形中位线证.

食品生物技术是指食品工业领域里所应用的生物技术,是食品科学技术与生物技术相渗透而形成的一门交叉学科(Food biotechnology)；
广义上讲．食品生物技术包括所有以生产、流通和消费食品为目的的生物技术,其应用范围涵盖了食品从原料的生产制备、加工、储运保藏、流通消费等全部过程,即整个食品工业宏观体系的上中下游.而从目前食品生产过程已经涉及的生物技术内容来看,同样包括了生物技术全部的子技术.
我是一名食品科学与工程专业的本科生,我的学校在这一行能排前三,我们这里食品生物技术只是一门课,自主招生的话你报的学校应该也不差,我们学校貌似新开一专业叫食品生物技术,你报的哪里?兴许我们会成为校友

最后的2篇很短,建议参考下,可以自己修改啊
Good morning,my dear teachers,my dear professors.i am very glad to be here for your interview.my name is song yonghao,i am 22 years old .i come from luoyang,a very beautiful aicent city.my undergratuade period will be accomplished in changan university in july ,2004;and now,i am trying my best for obtaining a key to tongji university.
generally speaking ,i am a hard working student especially do the thing i am interested in. i will try my best to finish it no matter how difficult it is. when i was sophomore, i found web design very interesting, so i learned it very hard . to weaver a homepage for myself, i stayed with my pesonel computer for half a month.,and i am the first one in my class who own his homepage. forthermore,i am a person with great perserverence. during the days preparing for the first examination,i insist on running every day, no matter what the weather was like.and just owning to this,i could concentrate on my study and succeeded in the end.
well ,in my spare time ,i like basketball, tennis and chinese chess. also english is my favorate.i often go to english corner to practise my oral english on every thursday,and write compositions to improve my witten ability .but i know my english is not good enough ,i will continue studying.
ok, that is all,thank you for your attention
英文自我介绍范文2
Good morning, my name is jack, it is really a great honor to have this opportunity for a interview, I would like to answer whatever you may raise, and I hope I can make a good performance today, eventually enroll in this prestigious university in september. now I will introduce myself briefly,I am 21 years old,born in heilongjiang province ,northeast of china,and I am curruently a senior student at beijing XX uni.my major is packaging engineering.and I will receive my bachelor degree after my graduation in june.in the past 4 years,i spend most of my time on study,I have passed CET4/6 with a ease. and I have acquired basic knowledge of packaging and publishing both in theory and in practice. besides, I have attend
several packaging exhibition hold in Beijing, this is our advantage study here, I have taken a tour to some big factory and company. through these I have a deeply understanding of domestic packaging industry. compared to developed countries such as us, unfortunately, although we have made extraordinary progress since 1978,our packaging industry are still underdeveloped, mess, unstable, the situation of employees in this field are awkard. but I have full confidence in a bright future if only our economy can keep the growth pace still. I guess you maybe interested in the reason itch to law, and what is my plan during graduate study life, I would like to tell you that pursue law is one of my lifelong goal,I like my major packaging and I won't give up,if I can pursue my master degree here I will combine law with my former education. I will work hard in thesefields ,patent ,trademark, copyright, on the base of my years study in department of p&p, my character? I cannot describe it well, but I know I am optimistic and confident. sometimes I prefer to stay alone, reading, listening to music, but I am not lonely, I like to chat with my classmates, almost talk everything ,my favorite pastime is valleyball,playing cards or surf online. through college life,I learn how to balance between study and entertainment. by the way, I was a actor of our amazing drama club. I had a few glorious memory on stage. that is my pride.
英文自我介绍范文3
MY BACKGROUND
I was born in a small village of Shan Dong Province on April 4th, 1968. When I was young, my family was very poor, so I had to work to earn money to help my parents after class when I was in the middle school.
In 1986 I was admitted by University of International Business and Economics (or: UIBE) to pursue a bachelor degree in Economics. My major is accounting in Department of International Business Management. The undergraduate education gave me a wide range of vision and taught me how to cooperate with others. I developed several professional interests in Accounting, Finance, and International Trade.
The following eight-year working experience offered me a good chance to give full play to my creativity, intelligence and diligence. In 1990-1993, I worked as an assistant to funding manager in China National Technical Import and Export Corporation. In 1993-present, I was employed by China Kingdom Import and Export Corporation to be the Manger of Financial and Accounting Division.
I do believe that with my hard early life, solid educational background and ample working experience, I would be an excellent student of you MBA program.
MY PERSONAL ACCOMPLISHMENT:
After graduating from UIBE, I was employed as the assistant to the funding manager by China National Technical Import and Export Corporation. After reading a lot of related files, and analyzing the overall funding situation of the corporation, I found that the loan policy was not been put into effect. So we have thousands of millions RMB loan with very high interest rate while a large amount of cash in bank with very low interest rate was idle. I reported this to my supervisor, and then we studied and revised the loan policy. This revision saved the corporation approximately RMB thirty millions yuan. In order to raise the funding effectiveness, after one year’s hard work, I developed the internal banking system within the corporation based on the actual funding supply and need of the different divisions and projects. This internal banking system made full use of the corporation’ funding resources, and due to this, I was highly praised by the president of the corporation.
WHY CHOOSE YOUR MBA PROGRAM?
After I have worked in business area for eight years, I feel that I need to continue my education by pursuing a Master degree in business administration. I have practiced my professional expertise in accounting, demonstrated my leadership abilities and perfected my communication skills. But I have yet to become an entrepreneur in my own right, and to fully master the art of modern business. I want to be trained more vigorously in scientific methods of analysis and synthesis. There are a lot of opportunities and challenges in China that I do not yet fell fully confident to seize. My business career has so far benefited mostly the companies that I worked for, but a good business education in your university will probably become a new era for me.
Your university is well known for its excellence in China’s business education. I am sure that, with my extensive business experience, I can be a worthy student of yours. I am anxious to benefit from your seasoned guidance and take advantage of your research facilities.
原则1．测试的重点考查的是你运用语言的能力,而不是对你的背景的了解.
2．自信
I am working for a XXXXX company as XXXXX（an assistant manager） in the XXXXX section.(我增经在XXXXX公司的XXXXX部门任XXXXX职位,比如经理助理)．
In the company my job is to XXXX(develop new computer software) and I enjoy the job very much, because XXXX(software development is very creative and imaginative work). 在公司里我的工作是XXXX(开发新的电脑软件),我非常喜欢这个工作,因为XXXXX(软件开发是一项非常需要创造性和想象力的工作.：也就是凸现你有创造性和想象力)
The following XXXXX-year working experience offered me a good chance to give full play to my creativity, intelligence and diligence.(接下来的XXX年的工作经验让我得到了很大的发展)
What's more, I have taken a tour to some big company, through these i have a deeply understanding of XXXXX(computer software industry).(我还参观过一些大公司,通过这些,我对XXXXX(电脑软件工业)有了比较深刻的认识)
I choose to come here because I do think that company would XXXXXX(provide me a more challenge work and better develope chance)
(我选择到这里工作因为我认为公司XXXXX（说他的好处,能给我提供一份更具备挑战性的工作和更好的发展机会）)
I do believe that with my solid educational background and ample working experience, I would be an excellent worker in your company.
（我相信以我过硬的教育背景以及工作经验,我会成为公司中出色的一员）
1.Hello, everybody! My name is XXX, and my Chinese name is Xiao Xiao from XX City XXX Province. I am a pleasant and easy-going girl.
For the last year, I engaged in Electric Design. Now I quit my job to study here. Hope I can relax my mind, studay well and make some friends in this beautiful picture-like city. I live in room XXX now. If you like, you can visit my room in you spare time. We can studay together, talk about the life, design our future career and develop together.
Thank you!
2.hello everyone,now let me introduce myself.my name is xxx,24 years old,and my hometown is the city of tai'an. I have a wide range of interest,such as music, reading, movement and so on. I am very gald to train together with everybody,and it makes me to have a great time.Thanks.

因为1和4都接地,所以U13=U43
也就是1和4电势相等

由题意知本题是一个古典概型，
试验发生包含的所有等可能的结果相当于甲、乙、丙、丁四位学生任选四所大学之一，共有4 ⁴ 种，
满足条件的事件是仅有两名学生被录取到同一所大学，
可先把四个同学分成1+1+2三份，有C ₄ ² 种分法，
再选择三所大学就读，即有C ₄ ² A ₄ ³ 种就读方式．
∴所求的概率为

C 24
A 34
4 4 =
9
16 ．
故选B．

正弦成等差数列就是边长成等差数列（正弦定理）
它说了非锐角,a是最小的一个角,如果是钝角三角形,a角应该取不到最大值,因为有一个钝角很大
那么只可能是直角三角形,a2+b2=c2还有2b=a+c
联立就得到最小的角是arcsin3/5
严格证明的话我认为可能比较烦,自招主要讲的就是技巧和猜的功力,如果这是填空题的话

若y=0 则x=1 显然可以验证成立
若y0 则由于x^3-2y^3=1 所以(x^3)/(y^3)-2=1/(y^3)
即(x/y)^3-2=1/(y^3) 从而 (x/y)^3-2=[x/y-2^(1/3)]*[(x/y)^2+(x/y)*2^(1/3)+4^(1/3)]=1/(y^3)
从而|(x/y)-2^(1/3)| * | [(x/y)^2+(x/y)*2^(1/3)+4^(1/3) |=1/|y^3|;
令x/y=t t^2+t*2^(1/3)+4^(1/3)>=(3/4)*4^(1/3) 从而| [(x/y)^2+(x/y)*2^(1/3)+4^(1/3) |>1/4
从而|(x/y)-2^(1/3)|

a b c d我不记得了,但答案好像是6和4.5 我是这么想的
圆锥的圆心角是240 连接扇形的俩个凸出 再双向延长 做他两边的垂线 并相切于圆 剩下的你大概可以猜道了
不过照你来看 你物理写的不错 我最后一题把方程列完就下课了 再给我一分钟就做完了 亏啊!

语文作文50分,英语两篇阅读30分,作文2篇,一篇翻译一篇议论,15分和25分

B

1、P=0.6*（1-0.5）*（1-0.4）+（1-0.6）*0.5*（1-0.4）+(1-0.6）*(1-0.5)*0.4=0.18+0.08+0.12=0.38
2、甲：P=0.6*0.6=0.36
乙：P=0.5*0.5=0.25
丙：P=0.4*0.75=0.3

Impulsive,difficult to control emotions

其实并不是热力学问题,而是局部共振传导障碍问题.患部损伤后会出现异常的离子积累,到一定程度后就出现电子流的移动,出现能量差.这种能量可在波、磁、电等方面表现出来.由于细胞电子的异常作用,细胞通道会引发相关问...

设AB=x,AD=y,AA'=h
x²+h²=8
y²+h²=17
x²+y²+2h²=25
AC²=x²+y²=25-2h²
0

星空天文网,请自己学习

只有大题,难度不大,属于上海高考水平

你这问题提得实在是让人费解,不过还可以勉强看懂
1.苯和甲醇混合后体积增大1%原因
苯是非极性溶剂,减少了甲醇羟基氧与其他羟基氢之间的氢键,使得体积增大.
2.乙醇和水混合体积减小的原因
水是极性溶剂,且偶极矩比乙醇大,分子比乙醇小,能够明显增多溶液中的氢键,使得体积减小.
3.甲醇和乙醇混合体积变化
根据以上分析,可得出如下推论：该类混合溶液的体积变化,与成分的偶极矩及分子大小有关.
对于甲醇和乙醇,它们的偶极矩基本相同,能影响体积的只有分子大小了；而二者分子大小不同,混合体积肯定会变化,但如何变化,单从这靠分析很难确定.

有考文学常识的,英语当然会有选择题和语法题了.这些都是很基本的

底数最小值为1,是大于一的,则指数方程都是恒增的,你会发现式,如果X=0时,左式=2011大于右式,但X趋向于正无穷时则根据指数原理,右式是大于左式的,因为是单调增,又是一正一负,必然有一X满足,但因单调,所以只有一个

(21 + 3)÷2 = 12
12×18 = 216,答案是216.
因为：
(1 + 3)÷2 = 2,2×18 = 36
(5 + 3)÷2 = 4,4×18 = 72
(17 + 3)÷2 = 10,10×18 = 180

设所求式子等于A,1!+2!+3!+.+n!=B.
A+B=2!+3!+4!+.+(n+1)!=B+（n+1）!-1
所以A=（n+1）!-1

过P点分别作直线PE、PF垂直AC、BC于E、F,设PE＝x、PF＝y,则在直角三角形PAE与PBF中,AE=5-y,BF=5-x,利用勾股定理得：x^2+(5-y)^2=5,(5-x)^2+y^2=25,由此解的x=1.y=3(x=2,y=4舍去,因为此时点P在△ABC外）,所以PC=根号（x^2+y^2)=根号10.

解题思路：仅有两名学生被录取到同一所大学，首先从4个大学生中选出2个作为一个元素，同另外两个元素在四个位置排列，写出结果．

∵仅有两名学生被录取到同一所大学，
∴首先从4个大学生中选出2个作为一个元素，同另外两个元素在四个位置排列，
共有C₄²A₄³=144种结果，
故选B．

点评：
本题考点： 排列、组合及简单计数问题．

考点点评： 本题考查排列组合及简单的计数问题，本题解题的关键是首先选出两个元素作为一个元素同其他的元素排列．

设动摩擦因数为K,半球转过的角为θ,无滑动时物体最大距离为X,摩擦力为f,下滑力为F
就有：f=G/8*cosθ*K = F=G/8*sinθ —— K=tgθ
　　　由力矩平衡得：G*3/8R*sinθ= G/8*cosθ*X——X=3R*tgθ
所以：X=3RK
答：求无滑动时物体离球心 O点最大距离是：3RK

由频率分布直方图得合格的频率=（0.035+0.015+0.01）×10=0.6
合格的人数=0.6×1000=600
故答案为：600

这个很难具体讲,估计跟电路的一些动作操作有关系.

v=ωr 小球A速度最大时,系统的角速度最大.而系统一开始有逆时针旋转的力矩,使角速度变大,之后旋转角度大了后,有顺时针旋转的力矩,使角速度变小.所以系统力矩处于平衡状态这个临界点时,角速度最大,小球A速度最大.

冰比较常见,不论南北,不分季节,冰箱里就可以出冰,而雪很难人造,在我国,一般只有北方才可以在冬季看到!
冰可以作为降温材料,比如饮料里加冰,而雪一般不这么使用,没有人在饮料里加雪!
物理上,冰水混合物可以标定零摄氏度,而雪不能!
就自主招生而言,这道题考的是你的反应速度和灵活性以及应变能力,答这种题关键是要选准角度,能反映你的灵敏程度就行!
比如从文学角度,古代文人多出自江南,故而与雪相关的诗词尚有一些（可以念几句）,但由于江南少见壮观冰景,所以于冰相关作品较少!这样也行!

假设结论不真
不妨设1∈A
则3∉A 否则假设不成立
所以3∈B
同样6∈A
10∈B
而15或属于A或属于B
但15若属于A
则因为1∈A 假设不成立
若15∈B
则因为10∈B 假设不成立
因此假设不真
即结论成立

本人算不上翻译高手,对翻译有一些心得.不管是英译汉还是汉译英,原理是相通的：先正确理解原句的意思,然后准确地用另一种语言表达出来.
先回答第5条,句子通顺是一定需要的,就算说汉语,句子通顺也是基础的基础.
让句子通顺的方法：合乎语法.
1,人称的选择——书面翻译,原文什么人称,翻译保持一致就可以.
2,一般情况下,描述事实情况的语句,都用直译.遇到一些俗语、名言、歇后语之类,需要意译（最好能找到英语里意思相近的俗语、名言来译,这个要求高了点）.
还有一些可以意译的情况：符合汉语文化环境的汉语用词,直译反而不符合西方人的理解习惯,那就需要意译.
比如,我们戏称楼主为“楼猪”,如果需要翻译这个称呼,不能直接翻译成floor pig；楼主其实是the founder of the topic “话题的发起人”,那么为了表示戏称,可以利用音近形近单词来译.举个例子,可以翻译成 the founder of the to-pig（这个翻译临时想的,并不算最好,请举一反三）.
3,可以.但尽可能少分.
4,考试评分要求我不清楚,就平常沟通来看,句子结构不适宜太复杂.
个人认为：从英语的角度来看,单句有3个从句是极限了.具备3个从句的句子,不要同时用并列句等其他句式.因为,分句太多,会导致紊乱,而产生误解.
这个板块有很多人丢中文招英文翻译,包括本人也有参与(*^___^*),LZ多看看,比较比较,欢迎来信探讨.

http://m.baidu.com/bd_page_type=1/pu=usm@0,sz@128_160,ta@middle__40_2_2.1/uid=0/t=wap/w=0_10_相交线定理等等之间的转换试题/ssid=0/from=1086k/l=0/

高中的公式,我基本忘了,不知道你们学过导数吗?
y=1-x
另S=x^2n+(1-x)^2n
S'=2n.x^(2n-1)-2n.(1-x)^2n
x=1/2,时,s'=0,有最小值 Smin=1/2^(2n-1)
证得：x^2n+y^2n≥1/2^(2n-1)

第一题用图像法求解 二下面的球可以看成相对运动 3用轨道能量公式4貌似要分类讨论 题目没给磁场方向 5用感应出的等效电荷做6不难 2、5属于竞赛难度大，本人这两没做出，4题忽略了磁场方向，同学说仔细看过题了，没说方向也没有如图所示…………

不用准备太深的东西,找一些高中联赛一试的书看看.最基本的要懂,比如柯西不等式,均值不等式之类的,函数单调性（求导）,排列组合和概率,立体几何和解析几何要熟,数列,向量,三角函数,还有复数,复数几何意义.我也不知道哪些是课内哪些是课外,反正不偏不漏都比较熟练就没问题了,我是搞竞赛的,保送完了.