“咚呛”通过精心收集，向本站投稿了8篇高一数学必修一第一单元提纲，以下是小编整理后的高一数学必修一第一单元提纲，欢迎阅读与收藏。
篇1：高一数学必修一第一单元提纲
高一数学必修一第一单元提纲
一.知识归纳：
1.集合的有关概念。
1)集合(集)：某些指定的对象集在一起就成为一个集合(集).其中每一个对象叫元素
注意：①集合与集合的元素是两个不同的概念，教科书中是通过描述给出的，这与平面几何中的点与直线的概念类似。
②集合中的元素具有确定性(a?A和a?A，二者必居其一)、互异性(若a?A，b?A，则a≠b)和无序性({a,b}与{b,a}表示同一个集合)。
③集合具有两方面的意义，即：凡是符合条件的对象都是它的元素;只要是它的元素就必须符号条件
2)集合的表示方法：常用的有列举法、描述法和图文法
3)集合的分类：有限集，无限集，空集。
4)常用数集：N，Z，Q，R，N
x
.子集、交集、并集、补集、空集、全集等概念。
1)子集：若对x∈A都有x∈B，则AB(或AB);
2)真子集：AB且存在x0∈B但x0A;记为AB(或，且)
3)交集：A∩B={x|x∈A且x∈B}
4)并集：A∪B={x|x∈A或x∈B}
5)补集：CUA={x|xA但x∈U}
注意：①?A，若A≠?，则?A;
②若，，则;
③若且，则A=B(等集)
3.弄清集合与元素、集合与集合的关系，掌握有关的术语和符号，特别要注意以下的符号：(1)与、?的区别;(2)与的区别;(3)与的区别。
4.有关子集的几个等价关系
①A∩B=AAB;②A∪B=BAB;③ABCuACuB;
④A∩CuB=空集CuAB;⑤CuA∪B=IAB。
5.交、并集运算的性质
①A∩A=A，A∩?=?，A∩B=B∩A;②A∪A=A，A∪?=A，A∪B=B∪A;
③Cu(A∪B)=CuA∩CuB，Cu(A∩B)=CuA∪CuB;
6.有限子集的个数：设集合A的元素个数是n，则A有2n个子集，2n-1个非空子集，2n-2个非空真子集。
二.例题讲解：
【例1】已知集合M={x|x=m+,m∈Z},N={x|x=,n∈Z},P={x|x=,p∈Z}，则M,N,P满足关系
A)M=NPB)MN=PC)MNPD)NPM
分析一：从判断元素的共性与区别入手。
解答一：对于集合M：{x|x=,m∈Z};对于集合N：{x|x=,n∈Z}
对于集合P：{x|x=,p∈Z}，由于3(n-1)+1和3p+1都表示被3除余1的数，而6m+1表示被6除余1的数，所以MN=P，故选B。
分析二：简单列举集合中的元素。
解答二：M={…，，…}，N={…，,,，…}，P={…，,，…}，这时不要急于判断三个集合间的关系，应分析各集合中不同的元素。
=∈N，∈N，∴MN，又=M，∴MN，
=P，∴NP又∈N，∴PN，故P=N，所以选B。
点评：由于思路二只是停留在最初的归纳假设，没有从理论上解决问题，因此提倡思路一，但思路二易人手。
变式：设集合，，则(B)
A.M=NB.MNC.NMD.
解：
当时，2k+1是奇数，k+2是整数，选B
【例2】定义集合Ax={x|x∈A且xB}，若A={1,3,5,7},B={2,3,5}，则Ax的子集个数为
A)1B)2C)3D)4
分析：确定集合Ax子集的个数，首先要确定元素的个数，然后再利用公式：集合A={a1，a2，…，an}有子集2n个来求解。
解答：∵Ax={x|x∈A且xB}，∴Ax={1,7}，有两个元素，故Ax的子集共有22个。选D。
变式1：已知非空集合M{1,2,3,4,5}，且若a∈M，则6?a∈M，那么集合M的个数为
A)5个B)6个C)7个D)8个
变式2：已知{a,b}A{a,b,c,d,e},求集合A.
解：由已知，集合中必须含有元素a,b.
集合A可能是{a,b},{a,b,c},{a,b,d},{a,b,e},{a,b,c,d},{a,b,c,e},{a,b,d,e}.
评析本题集合A的个数实为集合{c,d,e}的真子集的个数，所以共有个.
【例3】已知集合A={x|x2+px+q=0},B={x|x2?4x+r=0},且A∩B={1},A∪B={?2,1,3},求实数p,q,r的值。
解答：∵A∩B={1}∴1∈B∴12?4×1+r=0,r=3.
∴B={x|x2?4x+r=0}={1,3},∵A∪B={?2,1,3},?2B,∴?2∈A
∵A∩B={1}∴1∈A∴方程x2+px+q=0的两根为-2和1，
∴∴
变式：已知集合A={x|x2+bx+c=0},B={x|x2+mx+6=0},且A∩B={2},A∪B=B，求实数b,c,m的值.
解：∵A∩B={2}∴1∈B∴22+m?2+6=0,m=-5
∴B={x|x2-5x+6=0}={2,3}∵A∪B=B∴
又∵A∩B={2}∴A={2}∴b=-(2+2)=4,c=2×2=4
∴b=-4,c=4,m=-5
【例4】已知集合A={x|(x-1)(x+1)(x+2)>0},集合B满足：A∪B={x|x>-2}，且A∩B={x|1
分析：先化简集合A，然后由A∪B和A∩B分别确定数轴上哪些元素属于B，哪些元素不属于B。
解答：A={x|-21}。由A∩B={x|1-2}可知[-1,1]B，而(-∞,-2)∩B=ф。
综合以上各式有B={x|-1≤x≤5}
变式1：若A={x|x3+2x2-8x>0}，B={x|x2+ax+b≤0},已知A∪B={x|x>-4}，A∩B=Φ,求a,b。(答案：a=-2，b=0)
点评：在解有关不等式解集一类集合问题，应注意用数形结合的方法，作出数轴来解之。
变式2：设M={x|x2-2x-3=0},N={x|ax-1=0}，若M∩N=N，求所有满足条件的a的集合。
解答：M={-1,3},∵M∩N=N,∴NM
①当时，ax-1=0无解，∴a=0②
综①②得：所求集合为{-1，0，}
【例5】已知集合，函数y=log2(ax2-2x+2)的定义域为Q，若P∩Q≠Φ，求实数a的取值范围。
分析：先将原问题转化为不等式ax2-2x+2>0在有解，再利用参数分离求解。
解答：(1)若，在内有有解
令当时，
所以a>-4,所以a的取值范围是
变式：若关于x的方程有实根,求实数a的取值范围。
解答：
点评：解决含参数问题的题目，一般要进行分类讨论，但并不是所有的问题都要讨论，怎样可以避免讨论是我们思考此类问题的关键。
提高数学成绩诀窍有哪些
1、态度
在这个科目的学习当中态度是起到非常大的作用的,如果有态度首先就会成功一半,所以有一个认真学习的态度是非常重要的,面对任何的难点.难题,都会尽力去思考,在学习当中有这种态度,就完全可以将这们科目学好.
2、难题
在学习的当中需要养成一些好习惯,比如制定计划、练习、预习等等,这些内容都是在学习当中有非常重要的效果,预习可以让自己更加专注的听课,不会出现走神的情况,练习可以将当天所学的知识运用出来,不会有忘记的问题.
3、错题库
在学习这个科目的时候可能会有一些错题,出现错题之后可以使用小本将其记下来,可以隔几天以后做一遍,并且在复习的时候可以参照一下容易出现错误的题目,这是初中数学怎么学的重点之一.
4、笔记
对于任何的学科来说,记笔记都是非常重要的,它可以将上课所学到的重点记录下来以便于以后复习的时候方便,并且可以随时的拿出来复习一下之前的内容.
5、作业
作业对于很多的学生来说都是不陌生的,一般老师在上完课之后都会布置一些作业,这样使上课所学的内容充分的运用出来,仅仅依靠上课听是不够的,还需要在下课之后进行练习来讲上课所学的知识巩固.
在升到高中的时候,这个阶段马上面临高考,这个阶段一般的科目都讲完了,在这个阶段就开始了复习,这时候之前的笔记以及错题库都会派上用场,可以增加自己的复习效率,可以节省出时间来练习一些其他的科目.
数学学习方法
1、解题训练应立足于中、低档综合题。
⑴中、低档综合题训练价值高，因为它占中考数学试题的70%～80%。
⑵中、低档综合题要讲的深、学的透，教师讲的清楚，学生听得明白。
2、一定要规范解题步骤。
3、习题的来源。来自课本题和历年中考题的改编。
篇2：高一化学必修一第一单元提纲
高一化学必修一第一单元提纲
1.原子定义
原子：化学变化中的最小微粒。
(1)原子也是构成物质的一种微粒。例如少数非金属单质(金刚石、石墨等);金属单质(如铁、汞等);稀有气体等。
(2)原子也不断地运动着;原子虽很小但也有一定质量。对于原子的认识远在公元前5世纪提出了有关“原子”的观念。但没有科学实验作依据，直到19世纪初，化学家道尔顿根据实验事实和严格的逻辑推导，在18提出了科学的原子论。
2.分子是保持物质化学性质的最小粒子。
(1)构成物质的每一个分子与该物质的化学性质是一致的，分子只能保持物质的化学性质，不保持物质的物理性质。因物质的物理性质，如颜色、状态等，都是宏观现象，是该物质的大量分子聚集后所表现的属性，并不是单个分子所能保持的。
(2)最小;不是绝对意义上的最小，而是;保持物质化学性质的最小;
3.分子的性质
(1)分子质量和体积都很小。
(2)分子总是在不断运动着的。温度升高，分子运动速度加快，如阳光下湿衣物干得快。
(3)分子之间有间隔。一般说来，气体的分子之间间隔距离较大，液体和固体的分子之间的距离较小。气体比液体和固体容易压缩，不同液体混合后的总体积小于二者的原体积之和，都说明分子之间有间隔。
(4)同种物质的分子性质相同，不同种物质的分子性质不同。我们都有这样的生活体验：若口渴了，可以喝水解渴，同时吃几块冰块也可以解渴，这就说明：水和冰都具有相同的性质，因为水和冰都是由水分子构成的，同种物质的分子，性质是相同的。
4.原子的构成
质子：1个质子带1个单位正电荷原子核(+)
中子：不带电原子不带电
电子：1个电子带1个单位负电荷
5.原子与分子的异同
分子原子区别在化学反应中可再分，构成分子中的原子重新组合成新物质的分子在化学反应中不可再分，化学反应前后并没有变成其它原子相似点
(1)都是构成物质的基本粒子
(2)质量、体积都非常小，彼此间均有一定间隔，处于永恒的运动中
(3)同种分子(或原子)性质相同，不同种分子(或原子)性质不同
(4)都具有种类和数量的含义
6.核外电子的分层排布规律：第一层不超过2个，第二层不超过8个;;最外层不超过8个。每层最多容纳电子数为2n2个(n代表电子层数)，即第一层不超过2个，第二层不超过8个，第三层不超过18个;最外层电子数不超过8个(只有1个电子层时，最多可容纳2个电子)
高中化学学习要诀
1.基本概念“块”。这一块包括物质组成和分类线，性质变化线，化学用语线，分散系统线，化学量线等五条知识线(或小系统)。
2.基础理论“块”。这块包括结构理论(原子结构，分子即化学键理论，晶体结构理论)和元素周期律，同期表线，电解质溶液(含氧化-还原理论)线，化学反应速度和化学平衡理论线。理论块是化学的灵魂。
3.元素及其化合物知识“块”。这一块是化学的基石，可划分为金属线和非金属线，统一在周期系中。
4.有机物“块”。这一块的核心是烃及其衍生物线，重点是结构和化学性质，而结构又是官能团和与官能团直接相关的化学键。
5.计算“块”。这一块纵贯化学各部分，要掌握基本类型、解题规律和解题技巧。
6.基本实验“块”。这一块充分体现了化学学科的特点。含仪器、基本操作、制备、鉴别(定)、提纯、定量实
化学快速提分方法与技巧
化学科目考试说明只对参考样题进行了局部调整和更换，样题变化带来哪些信号?
希望考生通过样题来理解命题专家在命题思路上的变化。
第一、侧重考查主干知识的基础性和关联性。重视对考生基本能力和基础素养的检测，关注学生基础能力的全面发展。
第二、侧重考查化学知识在实际中的灵活应用，突出学以致用，切身感受化学可以让生活更美好，传递化学正能量。将化学知识与生产、生活实际以及科技发展的学科思想方法融入到试题中，“化学与社会的和谐发展”的学科思想方法正逐渐演化为化学试题的重要特征。
第三、侧重考查实验能力和科学探究能力，体现“以实验为基础”的学科特色，彰显实验方法的实践性、创新性和思想性。考查考生根据实验事实和认知冲突提出假设、运用控制变量等方法设计实验探究事物本质的科学探究能力。
篇3：数学必修五第一单元提纲
数学必修五第一单元提纲
(一)、映射、函数、反函数
1、对应、映射、函数三个概念既有共性又有区别，映射是一种特殊的对应，而函数又是一种特殊的映射.
2、对于函数的概念，应注意如下几点：
(1)掌握构成函数的三要素，会判断两个函数是否为同一函数.
(2)掌握三种表示法——列表法、解析法、图象法，能根实际问题寻求变量间的函数关系式，特别是会求分段函数的解析式.
(3)如果y=f(u)，u=g(x)，那么y=f[g(x)]叫做f和g的复合函数，其中g(x)为内函数，f(u)为外函数.
3、求函数y=f(x)的反函数的一般步骤：
(1)确定原函数的值域，也就是反函数的定义域;
(2)由y=f(x)的解析式求出x=f-1(y);
(3)将x，y对换，得反函数的习惯表达式y=f-1(x)，并注明定义域.
注意①：对于分段函数的反函数，先分别求出在各段上的反函数，然后再合并到一起.
②熟悉的应用，求f-1(x0)的值，合理利用这个结论，可以避免求反函数的过程，从而简化运算.
(二)、函数的解析式与定义域
1、函数及其定义域是不可分割的整体，没有定义域的函数是不存在的，因此，要正确地写出函数的解析式，必须是在求出变量间的对应法则的同时，求出函数的定义域.求函数的定义域一般有三种类型：
(1)有时一个函数来自于一个实际问题，这时自变量x有实际意义，求定义域要结合实际意义考虑;
(2)已知一个函数的解析式求其定义域，只要使解析式有意义即可.如：
①分式的分母不得为零;
②偶次方根的被开方数不小于零;
③对数函数的真数必须大于零;
④指数函数和对数函数的底数必须大于零且不等于1;
⑤三角函数中的正切函数y=tanx(x∈R，且k∈Z)，余切函数y=cotx(x∈R，x≠kπ，k∈Z)等.
应注意，一个函数的解析式由几部分组成时，定义域为各部分有意义的自变量取值的公共部分(即交集).
(3)已知一个函数的定义域，求另一个函数的定义域，主要考虑定义域的深刻含义即可.
已知f(x)的定义域是[a，b]，求f[g(x)]的定义域是指满足a≤g(x)≤b的x的取值范围，而已知f[g(x)]的定义域[a，b]指的是x∈[a，b]，此时f(x)的定义域，即g(x)的值域.
2、求函数的解析式一般有四种情况
(1)根据某实际问题需建立一种函数关系时，必须引入合适的变量，根据数学的有关知识寻求函数的解析式.
(2)有时题设给出函数特征，求函数的解析式，可采用待定系数法.比如函数是一次函数，可设f(x)=ax+b(a≠0)，其中a，b为待定系数，根据题设条件，列出方程组，求出a，b即可.
(3)若题设给出复合函数f[g(x)]的表达式时，可用换元法求函数f(x)的表达式，这时必须求出g(x)的值域，这相当于求函数的定义域.
(4)若已知f(x)满足某个等式，这个等式除f(x)是未知量外，还出现其他未知量(如f(-x)，等)，必须根据已知等式，再构造其他等式组成方程组，利用解方程组法求出f(x)的表达式.
(三)、函数的值域与最值
1、函数的值域取决于定义域和对应法则，不论采用何种方法求函数值域都应先考虑其定义域，求函数值域常用方法如下：
(1)直接法：亦称观察法，对于结构较为简单的函数，可由函数的解析式应用不等式的性质，直接观察得出函数的值域.
(2)换元法：运用代数式或三角换元将所给的复杂函数转化成另一种简单函数再求值域，若函数解析式中含有根式，当根式里一次式时用代数换元，当根式里是二次式时，用三角换元.
(3)反函数法：利用函数f(x)与其反函数f-1(x)的定义域和值域间的关系，通过求反函数的定义域而得到原函数的值域，形如(a≠0)的函数值域可采用此法求得.
(4)配方法：对于二次函数或二次函数有关的函数的值域问题可考虑用配方法.
(5)不等式法求值域：利用基本不等式a+b≥[a，b∈(0，+∞)]可以求某些函数的值域，不过应注意条件“一正二定三相等”有时需用到平方等技巧.
(6)判别式法：把y=f(x)变形为关于x的一元二次方程，利用“△≥0”求值域.其题型特征是解析式中含有根式或分式.
(7)利用函数的单调性求值域：当能确定函数在其定义域上(或某个定义域的子集上)的单调性，可采用单调性法求出函数的值域.
(8)数形结合法求函数的值域：利用函数所表示的几何意义，借助于几何方法或图象，求出函数的值域，即以数形结合求函数的值域.
2、求函数的最值与值域的区别和联系
求函数最值的常用方法和求函数值域的方法基本上是相同的，事实上，如果在函数的值域中存在一个最小(大)数，这个数就是函数的最小(大)值.因此求函数的最值与值域，其实质是相同的，只是提问的角度不同，因而答题的方式就有所相异.
如函数的值域是(0，16]，值是16，无最小值.再如函数的值域是(-∞，-2]∪[2，+∞)，但此函数无值和最小值，只有在改变函数定义域后，如x>0时，函数的最小值为2.可见定义域对函数的值域或最值的影响.
3、函数的最值在实际问题中的应用
函数的最值的应用主要体现在用函数知识求解实际问题上，从文字表述上常常表现为“工程造价最低”，“利润”或“面积(体积)(最小)”等诸多现实问题上，求解时要特别关注实际意义对自变量的制约，以便能正确求得最值.
(四)、函数的奇偶性
1、函数的奇偶性的定义：对于函数f(x)，如果对于函数定义域内的任意一个x，都有f(-x)=-f(x)(或f(-x)=f(x))，那么函数f(x)就叫做奇函数(或偶函数).
正确理解奇函数和偶函数的定义，要注意两点：(1)定义域在数轴上关于原点对称是函数f(x)为奇函数或偶函数的必要不充分条件;(2)f(x)=-f(x)或f(-x)=f(x)是定义域上的恒等式.(奇偶性是函数定义域上的整体性质).
2、奇偶函数的定义是判断函数奇偶性的主要依据。为了便于判断函数的奇偶性，有时需要将函数化简或应用定义的等价形式：
注意如下结论的运用：
(1)不论f(x)是奇函数还是偶函数，f(|x|)总是偶函数;
(2)f(x)、g(x)分别是定义域D1、D2上的奇函数，那么在D1∩D2上，f(x)+g(x)是奇函数，f(x)·g(x)是偶函数，类似地有“奇±奇=奇”“奇×奇=偶”，“偶±偶=偶”“偶×偶=偶”“奇×偶=奇”;
(3)奇偶函数的复合函数的奇偶性通常是偶函数;
(4)奇函数的导函数是偶函数，偶函数的导函数是奇函数。
3、有关奇偶性的几个性质及结论
(1)一个函数为奇函数的充要条件是它的图象关于原点对称;一个函数为偶函数的充要条件是它的图象关于y轴对称.
(2)如要函数的定义域关于原点对称且函数值恒为零，那么它既是奇函数又是偶函数.
(3)若奇函数f(x)在x=0处有意义，则f(0)=0成立.
(4)若f(x)是具有奇偶性的区间单调函数，则奇(偶)函数在正负对称区间上的单调性是相同(反)的。
(5)若f(x)的定义域关于原点对称，则F(x)=f(x)+f(-x)是偶函数，G(x)=f(x)-f(-x)是奇函数.
(6)奇偶性的推广
函数y=f(x)对定义域内的任一x都有f(a+x)=f(a-x)，则y=f(x)的图象关于直线x=a对称，即y=f(a+x)为偶函数.函数y=f(x)对定义域内的任-x都有f(a+x)=-f(a-x)，则y=f(x)的图象关于点(a，0)成中心对称图形，即y=f(a+x)为奇函数。
高中学好数学的方法是什么
1.学数学要善于思考，自己想出来的答案远比别人讲出来的答案印象深刻。
2.课前要做好预习，这样上数学课时才能把不会的知识点更好的消化吸收掉。
3.数学公式一定要记熟，并且还要会推导，能举一反三。
4.学好数学最基础的就是把课本知识点及课后习题都掌握好。
5.数学80%的分数来源于基础知识，20%的分数属于难点，所以考120分并不难。
6.数学需要沉下心去做，浮躁的人很难学好数学，踏踏实实做题才是硬道理。
7.数学要想学好，不琢磨是行不通的，遇到难题不能躲，研究明白了才能罢休。
8.数学最主要的就是解题过程，懂得数学思维很关键，思路通了，数学自然就会了。
9.数学不是用来看的，而是用来算的，或许这一秒没思路，当你拿起笔开始计算的那一秒，就豁然开朗了。
10.数学题目不会做，原因之一就是例题没研究明白，所以数学书上的例题绝对不要放过。
高中学数学的技巧
1.重视课堂的学习效率
新知识的接受和数学能力的培养，主要是在课堂上进行，所以要特别重视课堂的学习效率，上课时要紧跟老师的思路，积极开展思维，预测下面的步骤，比较自己的解题思路与老师所讲的有哪些不同。课后要及时复习，不留疑点，对不懂的地方要及时请教老师或同学，切忌不懂将懂，或将不懂的地方跳过。课后还要注重基础知识的学习和基本技能的培养，要多记公式、定理，因为它们是学好数学的关键和必备条件。
2.多做习题，养成良好的解题习惯
要想学好数学，多做题是不可避免的。当然，多做题并不等于搞题海战术。做的题目要有代表性，不能胡子眉毛一把抓，碰到哪道题就做哪道题。有些题适合我们做，而有些题却超出了我们的能力范围，做这些题目只能是浪费我们宝贵的时间，不会达到任何效果。做的题要难易适中，通过做些有代表的题目，要力争能举一反三。数学是一门逻辑性很强的学科，需要缜密的思维，解题要有条理，在做题的过程中学会熟练运用正确的解题方法，掌握一些基本题型的解题规律。只有平时大量的训练，见多了、做多了，自然就熟能生巧，考试的时候就会应付自如，不至于乱了阵脚。
3.调整好心态，正确对待平时的考试
大家都知道，数学是个逻辑性极强的学科，要求有清醒的头脑，数学运算过程中的每个解题步骤都很重要，漏掉了哪个步骤都是不行的。因此，在做数学题的时候，保持一个平静的心态是很重要。这就要求我们平时要学会善于把握自己的情绪，要能及时地调整好自己的心态，戒骄戒躁，千万不能一遇到解不出来的题目就焦躁不安。焦躁是学习数学的大忌。
篇4：高中必修四第一单元数学提纲
高中必修四第一单元数学提纲
立体几何初步
(1)棱柱：
定义：有两个面互相平行，其余各面都是四边形，且每相邻两个四边形的公共边都互相平行，由这些面所围成的几何体。
分类：以底面多边形的边数作为分类的标准分为三棱柱、四棱柱、五棱柱等。
表示：用各顶点字母，如五棱柱或用对角线的端点字母，如五棱柱
几何特征：两底面是对应边平行的全等多边形;侧面、对角面都是平行四边形;侧棱平行且相等;平行于底面的截面是与底面全等的多边形。
(2)棱锥
定义：有一个面是多边形，其余各面都是有一个公共顶点的三角形，由这些面所围成的几何体
分类：以底面多边形的边数作为分类的标准分为三棱锥、四棱锥、五棱锥等
表示：用各顶点字母，如五棱锥
几何特征：侧面、对角面都是三角形;平行于底面的截面与底面相似，其相似比等于顶点到截面距离与高的比的平方。
(3)棱台：
定义：用一个平行于棱锥底面的平面去截棱锥，截面和底面之间的部分
分类：以底面多边形的边数作为分类的标准分为三棱态、四棱台、五棱台等
表示：用各顶点字母，如五棱台
几何特征：①上下底面是相似的平行多边形②侧面是梯形③侧棱交于原棱锥的顶点
(4)圆柱：
定义：以矩形的一边所在的直线为轴旋转，其余三边旋转所成的曲面所围成的几何体
几何特征：①底面是全等的圆;②母线与轴平行;③轴与底面圆的半径垂直;④侧面展开图是一个矩形。
(5)圆锥：
定义：以直角三角形的一条直角边为旋转轴，旋转一周所成的曲面所围成的几何体
几何特征：①底面是一个圆;②母线交于圆锥的顶点;③侧面展开图是一个扇形。
(6)圆台：
定义：用一个平行于圆锥底面的平面去截圆锥，截面和底面之间的部分
几何特征：①上下底面是两个圆;②侧面母线交于原圆锥的顶点;③侧面展开图是一个弓形。
(7)球体：
定义：以半圆的直径所在直线为旋转轴，半圆面旋转一周形成的几何体
几何特征：①球的截面是圆;②球面上任意一点到球心的距离等于半径。
向量的向量积
定义：两个向量a和b的向量积(外积、叉积)是一个向量，记作a×b。若a、b不共线，则a×b的模是：∣a×b∣=|a|?|b|?sin〈a，b〉;a×b的方向是：垂直于a和b，且a、b和a×b按这个次序构成右手系。若a、b共线，则a×b=0。
向量的向量积性质：
∣a×b∣是以a和b为边的平行四边形面积。
a×a=0。
a‖b〈=〉a×b=0。
向量的向量积运算律
a×b=-b×a;
(λa)×b=λ(a×b)=a×(λb);
(a+b)×c=a×c+b×c.
注：向量没有除法，“向量AB/向量CD”是没有意义的。
如何提高数学成绩
一、课内重视听讲，课后及时复习
接受一种新的知识，主要实在课堂上进行的，所以要重视课堂上的学习效率，找到适合自己的学习方法，上课时要跟住老师的思路，积极思考。下课之后要及时复习，遇到不懂的地方要及时去问，在做作业的时候，先把老师课堂上讲解的内容回想一遍，还要牢牢的掌握公式及推理过程，尽量不要去翻书。尽量自己思考，不要急于翻看答案。还要经常性的总结和复习，把知识点结合起来，变成自己的知识体系。
二、多做题，养成良好的解题习惯
要想学好数学，大量做题是必可避免的，熟练地掌握各种题型，这样才能有效的提高数学成绩。刚开始做题的时候先以书上习题为主，答好基础，然后逐渐增加难度，开拓思路，练习各种类型的解题思路，对于容易出现错误的题型，应该记录下来，反复加以联系。在做题的时候应该养成良好的解题习惯，集中注意力，这样才能进入最佳的状态，形成习惯，这样在考试的时候才能运用自如。
三、调整心态，正确对待考试
考试的时候，大部分的题都是基础题，只有少数几道题时比较难的题，所以我们要调整好心态，鼓励自己，在做题的时候认真思考，不要浮躁，在考试之前做好准备，做一做常规的题型，不要为了赶时间而增加做题速度，要有条不紊的进行。
数学速算技巧
一、充分利用五大定律
教师要扎实开展好现行教材四年级数学下册中计算的五大运算定律的教学(加法交换律、加法结合律、乘法交换律、乘法结合律、乘法分配律)，引导学生弄清来龙去脉，不让一个学生掉队，训练每个学生能自觉运用简便办法，能针对不同题型灵活选择简便方法正确而快捷地进行计算。
二、巧妙运用首同末合十
利用首同末合十的方法来训练。首同末合十法是两个两位数，它们的十位数相同，而个位数相加的和是10。利用首同末合十的两个两位数相乘，积的右边的两位数正好是个位数的乘积，积的左面的数正好是十位上的数乘以比它大1的积，合并起来就是它们的乘积。例如，54x56=3024，81x89=7209。
三、留心左右两数合并法
任意的两位数乘上99或任意的三位数乘上999的速算法叫做左右两数合并法。
1.任意两位数乘上99的巧算方法是，将这个任意的两位数减去1，作为积的左面的两位数字，再将100减去这个任意两位数的差作为积的右边两位数，合并起来就是它们的积。例如，62x99=6138，48x99=4752。
2.任意三位数乘上999的巧算方法，就是将这个任意的三位数减去1，作为积的左面的三位数字，再将1000减去这个任意三位数的差作为积的右边的三位数字，合并起来就是它们的积。例如，781x999=780219，396x999=395604。
四、利用分数与除法的关系来巧算
在一个只有二级运算的题里，按顺序计算需要多步计算，利用乘除法的关系进行计算就会简便。比如，
24/18x36/12=(24/18)x(36/12)=24/18x36/12=4。
五、利用扩大缩小的规律进行简算
有些除法计算题直接计算比较繁琐，而且容易算错，利用扩缩规律进行合理的变形可以找到简便的解决方法。比如，
7/25=(7x4)/(25x4)=28/100=0.28，
24/125=(24x8)/(125x8)=192/1000=0.192。
六、数字颠倒的两、三位数减法巧算
形如73与37、185与581等的数称为数字颠倒的两、三位数，巧算方法为：
1.数字颠倒的两位数减法，可用两位数字中的大数减去小数，再乘以9，积就是它们的差。如73-37=(7-3)x9=36，82-28=(8-2)x9=54。
2.数字颠倒的三位数减法，可用三位数中最大数减去最小数，再乘以9，乘积分两边，中间填上9，就是它们的差。比如，581-158=(8-1)x9=63，所以851-158=693。
七、用添零加半的方法巧算
一个数乘上15的速算方法叫做添零加半。比如，26x15将26后面添0得260，再加上260的一半130，即260+130=390，所以26x15=360。
八、利用拆和法进行巧算
有些计算题，乍看起来都与运算定律没有关系，但经过变形后，直接地应用运算定律来进行计算。
九、用两边拉中间加的方法速算
任何数同11相乘，只要把原数的个位移到积的个位的位置，最高位移到积的最高位的位置，中间的数分别是个位上的数加十位上的数的和就是十位，十位上的数加百位上的和就是百位。如果相加的数的和满十要向前一位数进1。比如，124x11=1364，568x11=6248。
十、用十加个减法速算
十加个减法就是任何两位数加上9的和，可以把这个两位数变成十位加1个位减1的数，即36+9=45，17+9=26。这种计算技巧适合低年级的小学生。
很多学生计算结果不正确是由于马虎、粗心等不良习惯造成的。培养学生良好计算习惯时，教师要讲究训练形式，激发学生计算兴趣，寓教于乐，采用多样化形式训练。如用游戏、竞赛、卡片、小黑板视算、听算、限时口算、自编计算题、小故事等多种形式训练，教师要有耐心，有恒心，要统一办法与要求，要坚持不懈，抓到底。教师要引导学生养成良好的审题习惯、书写习惯和检验习惯。
篇5：高一英语必修一第一单元说课稿
高一英语必修一第一单元说课稿
大家好！今天我说课的内容是高一英语新课程实验教科书必修1 Unit One， The first perid。下面我就从教材分析、教法分析、学法分析、教学过程、教学评价五个方面进行说明。
一、教材分析
（一）教材的地位和作用
本节课是本单元以及本教材的第一节课，本课谈论的是：朋友是不是仅限于人类、朋友的真正含义、如何与人相处的问题等关于朋友的话题。本课涉及的有陈述句和疑问句的直接引语和间接引语的掌握和运用等语法要点。学生从初中到高中，来到一个新的学校，同学彼此陌生，不免想起老同学，老朋友。这样的话题正好能引起学生的兴趣。而且本课的内容和语法的启发性和实用性都很强，能使学生在学中用，在用中学，对综合提高学生的听说读写能力有较好的促进作用。
（二）教学目标
英语教学大纲规定，通过听说读写的训练，使学生获得英语基础知识和运用英语的能力，激发学生的学习兴趣，为进一步学习打下良好的基础。因此，我制定以下教学目标：
知识目标：1、掌握和使用陈述句和疑问句的直接引语和间接引语。
2、讨论朋友和友谊。
3、学习掌握本课的重点词汇。
技能目标：1、学会阅读的技能——scanningand siing 。
2、通过谈论朋友和友谊，既锻炼学生的语言运用能力，又培养了学生发现问题、思考问题、解决问题的能力。
3、理解阅读文段，复述故事。
情感态度：1、患难之交才是真朋友。
2、知音难得。
3、海内存知己，天涯若比邻。
文化意识：认识德国纳粹党。让学生了解那段德国法西斯残害犹太人的历史，使学生在感受外国历史文化的同时自然而然的习得语言。
（三）重点与难点
重点：1、训练scanningand siing等阅读技能。
2、认识朋友的真正含义以及与人相处的问题。
难点：1、阅读技能的训练。
2、陈述句和疑问句的直接引语和间接引语的互相转换(人称的变化、时态的变化、指示代词、时间状语、地点状语和动词的变化)。
（四）教具
本课利用录音机、投影仪等辅助设备，激发学生的学习兴趣，调动他们的积极性，为展开话题提供丰富的材料，使教学收到事半功倍的效果。
二、教法分析
在新课程背景下，教师要成为学生学习的促进者、组织者和合作者。本课采用讨论法，主要采用小组合作讨论的方式。在读前阶段我就提出问题，让学生思考讨论是不是只有人与人之间才可以交朋友，然后在阅读中通过安妮的日记向学生说明我们也可以与动物及无生命的日记交朋友。在深刻理解、充分训练的基础上，我再引导学生深入讨论几个与本课有关的话题，展开教师为主导、学生为主体的师生双边活动。通过创设真实自然的语言环境，使学生在语言实践中把语言知识和技能主动转化为交流能力，变苦学为乐学，从而培养学生大胆用英语进行交际的能力。
三、学法分析
教务于学。传统教育的弊端是教师“满堂灌”，只重视怎么教而忽视怎样学，结果高分低能的现象十分严重。为了改变教师牵着学生鼻子走的被动状态，我通过创设话题，寓教于乐，引导学生自学、自做、自助、自悟，让学生学会自己动手，收集信息、处理信息，用所学语言去实践和解决问题，使学生在运用语言的过程中感悟体验所学语言的规律，培养语言意识，积累语言经验，形成语言感觉，达到语言运用的目的。从而使学生真正成为学习的主人。
四、教学过程
新课程改革的核心理念是“一切为了学生的发展”。学生的英语学习不仅仅是掌握几个单词和句型，更重要的是学会运用语言来交流思想，办实事。因此我精心设计了以下教学环节：
（一）激趣导入，务于新知
一节课的良好开始，对于整节课教学的顺利进行起着至关重要的作用。在Waring up 部分我分四步进行：
1、用问问题的形式导入(屏幕显示)。同时板书Unit 1 Friendship。
D u have an friends? Are u gd t ur friends?
Which ind f friend d u thin is the best friend?
2、做调查：在Waring up部分有5个问题，我让学生独立完成。然后在屏幕上显示下列表格。
3、调查结果：显示各得分情况所对应的调查结果，让学生自行对照。
Grade 1 (5分以下) 直截了当，做事果断，没考虑不良后果。
Grade 2 (10分以下) 能用更合理的方法处理问题，又不伤朋友之间的感情，但自己的利益有时会受损。
Grade 3 (10分以上) 不伤感情，又能保全自己利益。
通过调查问卷的形式，引导学生了解日常生活中朋友之间发生的真实问题以及解决这些问题的方法，最后的'问卷调查结果让学生兴趣和热情倍增，这样能促使学生很快进入语言学习和探究活动中去，愉快的进入学习状态。
4、学习三句谚语，使学生明确对待朋友和友谊的态度。
A friend in need is a friend indeed. 患难之交才是真朋友。
Real friends are few and far between. 知音难得。
Lng distance separates n bs friends. 海内存知己，天涯若比邻。
（二）创设话题，教学新知
新课程指出，教师不再是居高临下的管理者，而是学生学习的促进者、组织者、合作者。
1、我布置Pre-reading部分的几个问题启发学生对“朋友”和“友谊”进行思考，使学生明确不仅人与人之间可以做朋友，日记也可以成为人们的朋友。接着让学生就问题进行小组讨论。然后让个别学生回答问题。
接着屏幕显示我补充的问题：
Wh d u need friends?
What d u thin a gd friend shuld be lie?
Des a friend alwas have t be a persn?
让学生讨论后回答。引出课文的主题 Anne’s best friend –DIAR.
2、介绍故事背景：这是一个真实的故事。1933年－1945年，纳粹党对德国人民进行法西斯统治。只要他们一发现任何犹太人，就会把他们送到东欧波兰的集中营区。为了避免被抓，安妮和她的家人选择了躲藏，藏在了一栋房子的阁楼里，在躲藏的日子里，她只能和日记交朋友，她把心里一切的感受都告诉了日记，后来《安妮日记》出版后，很快成为全世界广为流传的一本书。
3、教学新的语言项目和句子结构。我在教学语言项目的时候，一是培养学生根据语篇、语境来猜词，一是用举例的方式来说明词的用法。
（三）阅读文段，强化新知
1、Scanning（查读）:学生们在了解了当时的历史背景后，以及理解了安妮当时的心境和为什么将日记视为自己的朋友，这样才能深刻理解安妮日记的内涵。在此基础上，我设计了几个问题，让学生带着问题听录音。这样做能使学生更加集中注意力，抓住重点。（屏幕显示）。
Wh did Anne ae her diar her best friend ?
When did this str happen?
Hw lng did the hide befre the were discvered?
Anne’s best friend：
When was the diar written?
Wh didn’t she g dwnstairs until the windw had t be shut?
Saple diar:
2、Siing(略读)：在学生对课文进行了探究之后，学生已经将课文的大部分内容融会贯通，消化理解了。这时让他们通过讨论来解决问题，可以使学生的学习潜能得以挖掘。（屏幕显示谈论的主题）
Mae a free discussin.（Ex3 in cprehensin）
* What wuld u iss st if u went int hiding lie Anne and her fail? Explain wh.
* Hw wuld u describe Anne’s feelings as she was ling ut int the night s?
（四）难点再现，深化新知
在一节课结束前几分钟将重难点知识进行总结和归纳，是提高课堂教学效率的有力措施。我在屏幕上又显示了下列的句子，让学生明确什么地方需要加强，学习策略要做怎样的调整。
Explanatin ：
* She said, “I dn’t want t set dwn a series f facts in a diar as st peple d, but ……” (Change Direct Speech int Indirect Speech)
* I wnder if it’s because I haven’t been able t be utdrs fr s lng that I’ve grwn s craz abut everthing t d with nature. (it’s because ……that )
* It was the first tie in a ear and a half that I’d seen the night face t face ……(Understanding Anne’s inside thughts.)
（五）布置作业，巩固新知
为了巩固今天所学的内容，我要求学生课后用100字左右来复述故事，完成Cprehending里的关于直接引语和间接引语的练习。
最后，我说一下我的板书设计。为了浓缩教学内容，使学生对新课内容能一目了然，印象深刻，我采用纲目式设计板书，左侧列出课文中出现的重要的单词和词组，右侧列出重点句型。
Unit 1 Friendship
1、Useful wrds and expressins 2、Iprtant structures
五、教学评价
这一节课我主要采取任务型的教学形式，从任务呈现到任务准备（也就是知识与技能的教学），学生们在完成任务的驱使下，得到了语言交际和思想交流的机会，在讨论问题的过程中把知识和技能转化为交流能力。我以与学生平等的身份参与到学生的交际和交流中去，这充分体现了师生互动、生生互动的教学思想，从而达到预期的目的。
由于本人经验不足和能力有限，因此在备课和说课的过程中存在着一些不足之处，恳请各位领导、老师提出宝贵意见。谢谢！
篇6：高一必修一英语作文第一单元
Ladies and gentlemen，
It's my honor to stand here and say something about friendship.
First, I think everyone needs friends and is eager to get friendship.When you are happy, you can share your happiness with your friends and when you are sad, you can complain to your friends.If you are arrogant, your friends can persuade you and they can make you confident and brave when you are discouraged.
Second, as we all know, friendship is valuable.It can touch your heart and give you hope.Many people are proud of having a good friend.We must cherish our friends when we are happy with our friends.We should try our best to protect the friendship from being hurt.
We will meet a lot of friends in our life.We should find the people who can understand us and share not only happiness but also sadness.When you lose it, both you and your friend will feel very sorrowful.So you can't give up those friends, please don't forget to keep in touch with your old friends, because staying with old friends is cherishable.
Finally, just as an old saying goes, love comes and goes but friendship stays.It's sweet and poetic, full of tears, hopes and happiness.So let's cherish friendship!
That's all.Thank you for listening.
篇7：高一必修一英语作文第一单元
Military Training
When September comes, it is the time for students to go to school, for the freshmen, they need to join the military training at the beginning of the semester. It will be a hard time for them, because they are princes and princess at home, now they need to be burned in the hot sun, how terrible it is. But the military training is good for the new students, they will learn to be a strong person, they have to bear the hot sun, listen to the order. Comparing at home, most students will give orders to their parents, they are spoiled by their parents. But when they come to the school, they need to live alone, so they must learn to get along with others.
When they meet troubles, sometimes they need to get over them, military training teaches students to be a strong person, no matter what difficulty they have met.
篇8：高一英语试卷必修一第一单元试卷
一、基础测试(每小题1分，满分20分)
A. 单词拼写
1. Something is wrong with the e__________ of the car. It can’t start.
2. Marie Curie was the discoverer of r_________.
3. According to the t________ of relativity (相对论), nothing can travel faster than light.
4. After all his mathematical calculations, Copernicus drew a c__________ that the earth was not the center of the solar system.
5. I__________ she’d gone, I remembered her name.
6. In the Anti-Japanese War, the Chinese ___________ (打败) the Japanese invaders.
7. Shall he ________ (参加) the meeting to be held tomorrow?
8. Work on the new railway will be ___________ (完成) at the end of next year.
9. Our new offices are still under ____________ (建设).
10. They have found some evidences that are __________ (联系) to this murder.
B. 句型转换
11. A: From the facts John Snow concluded that polluted water carried the disease.
B: From the facts John Snow ________ _______ _______ that polluted water carried the disease.
12. A: He determined to find out why.
B: He __________ his __________ to find out why.
13. A: We will begin the work immediately.
B: We will begin the work ______ _______.
14. A: How will you deal with these letters?
B: What will you _____ _______these letters?
15. A: The movements of the other planets in the sky made sense only if you put the sun there.
B: Only if you put the sun there _______the movements of the other planets in the sky _______ sense.
C. 完成句子
16. He suggested that the machine ________ ________ (检查) carefully before we used it.
17. She ______ _______ _______ (全神贯注于) reading, so she didn’t notice what was happening.
18. We ______ _______ (下决心) that this should never be allowed to happen again.
19. ______ _______ ________ (除…之外) Wang Hai, who will go there?
20. The teacher is popular with the students because he _______ ______ ______ ______ (对他们要求严格).
二、单项填空 (每小题1分，满分15分)
21.Our team was ahead during the first half, but we _____ in the last ten minutes.
A. were won B. were lost
C. were beaten D. won
22. Usually children are allowed to ___________ when they are six years old.
A. attend school
B. attend the school
C. join school
D. join the school
23. Professor Hawking stepped into the office I knew that there was no hope.
A. Unless B. Now that
C. Although D. The moment
24. His failure in the experiment suggested that he ________ his teacher’s proper instructions.
A. should not have followed
B. should not follow
C. mustn’t have followed
D. hadn’t followed
25. I suggested that he _____ telephone the manager before he decided.
A. telephoned B. would telephone
C. telephone D. had to telephone
26. —I'm terribly sorry that I failed to win the game.
—You are not ________ for all you could do.
A. to blame B. pleased
C. right D. satisfied
27. Yang Liwei was surrounded by the audience ________ he stepped off the stage.
A. until B. through
C. now that D. immediately
28. Gathering clouds the coming storm.
A. declared B. turned out
C. connected D. announced
29. Seeing their son playing computer games all day, the parents don’t know ______ it.
A. how to do
B. what to do
C. how to deal with
D. how to do with
30. — So hard ______ in the past few months that he has made great progress in English.
— I can see that; only a few mistakes ______ in the exam.
A. has he worked; did he make
B. he has worked; did he made
C. he has worked; he made
D. has he worked; he made
31. Enough of it! Nobody here thinks what you are saying should make any ________.
A. value B. sense
C. fun D. use
32. Only by shouting at the top of his voice .
A. he was able to make himself hear
B. he was able to make himself heard
C. was he able to make himself hear
D. was he able to make himself heard
33. Only after the second tower of the World Trade Centre did people know it was not an accident, but an attack of some kind.
A. had hit B. did fall
C. was hit D. was fallen
34. Last summer holiday, I went back to my hometown, ________ the neighbors and the house ________ I used to be familiar with were gone.
A. only finding; which
B. only to find; that
C. only to find; whom
D. found; that
35. It’s quite strange that the man sleeps with his mouth ____ and his eyes _____.
A. closing; open B. closed; opened
C. closing; opening D. closed; open
三、完形填空 (每小题1分，满分20分)
阅读下面短文，掌握大意，然后从36-55各题所给的四个选项(A、B、C和D)中，选出最佳答案。
A person may have an idea about himself that will prevent him from doing good work.
He may have the 36 that he is not capable (有能力的) of it. A child may think he is stupid because he does not understand how to make the 37 of his mental faculties(官能). Older people may be mistaken that they are incapable of 38 anything new because of their age.
A person who believes that he is incapable will not make a real 39 , because he feels that it 40 be useless. He won’t go at a job with the confidence(信心) necessary for success, and he won’t work his hardest, even though he may 41 he is doing so. He is 42 likely to fail, and the failure will 43 his belief in his incompetence(无能).
Alfred Adler, a famous doctor, had 44 like this. When he was a small boy, he had a poor 45 in maths. His teacher told his 46 he had no ability in maths in order that they would not 47 too much of him. In this way, they too 48 the idea. He accepted 49 mistaken thinking of his ability, felt that it was useless to 50 , and was very poor at maths, 51 as they expected.
One day he worked out a problem which 52 of the other students had been able to solve.
Adler succeeded in solving the problem. This gave him confidence. He now 53 with interest, determination and purpose, and he soon became especially good at 54 . He not only proved that he could learn maths well, but luckily he learned early in his life from his own experience that if a person goes at a job with determination and purpose, he may 55 himself as well as others by his ability.
36. A. belief B. way
C. fact D. condition
37. A. biggest B. most
C. higher D. deepest
38. A. teaching B. learning
C. accepting D. using
39. A. decision B. success
C. effort D. trouble
40. A. would B. should
C. must D. could
41. A. forget B. think
C. guess D. understand
42. A. truly B. really
C. however D. therefore
43. A. lead to B. strengthen
C. increase D. add to
44. A. an experience B. an expert
C. a thought D. a story
45. A. state B. mind
C. start D. ending
46. A. classmates B. friends
C. neighbours D. parents
47. A. blame B. expect
C. get D. win
48. A. developed B. organized
C. discovered D. found
49. A. a B. one
C. its D. the
50. A. manage B. succeed
C. try D. act
51. A. only B. almost
C. just D. then
52. A. none B. all
C. many D. most
53. A. lived B. worked
C. played D. graduated
54. A. lesson B. medicine
C. subjects D. maths
55. A. encourage B. love
C. astonish D. disappoint
四、阅读理解 (每小题1.5分，满分30分)
阅读下列短文，从每题所给的四个选项(A、B、C或D)中，选出最佳选项
A
Albert Einstein was probably the most famous scientist of the twentieth century. He changed scientific thinking in the modern world. He is generally considered as the greatest physicist who ever lived. What’s more, he devoted a lot of his time and energy to working for human rights and progress.
In 1933, while Einstein was visiting England and the United States, the Nazi government of Germany took all his things away, including his position and his citizenship. Einstein then settled down in the United States. In 1939, Einstein, who loved peace—afraid of a world in which only Hitler would had an atomic bomb(原子弹)—tried hard to persuade President Franklin D. Roosevelt in a famous letter to have the United States start uranium research. That Germany, after all, had no bomb, and that the first bomb would fall on Japan, could not have been expected. After the war, Einstein never stopped working for peace and reducing the number of soldiers in the world.
Although he wasn’t connected with any accepted religion(宗教), Einstein felt that trust in a personal God was too special an idea to be suitable to the God at work in this universe, but he never believed that the universe was one of chance or disorder. The universe to him was one of pure law and order. He once said, “God may know everything, but he is not hateful.”
56. From the passage we know that .
A. no scientist is as great as Albert Einstein during this century
B. Albert Einstein was likely to be the greatest scientist of his time
C. Albert Einstein made the first atomic bomb for the United States of America
D. Albert Einstein gave up his German citizenship for political reasons
57. If Einstein had known that Hitler had no atomic bomb and that the first atomic bomb would fall on Japan, he would .
A. have continued his scientific research
B. have won another Nobel Prize for physics
C. not have advised starting uranium research in the U. S. A.
D. not have moved to the U. S. A.
58. Einstein in 1933.
A. visited England and the U. S. A.
B. lost everything
C. became a man without a country
D. both A and C
59. Einstein believed that everything in the universe .
A. was kept in order by its own law
B. had nothing to do with each other
C. happened in an irregular way
D. was made by the personal God
B
“That’s funny! These fellows in the middle of the plate have died.” Dr Alexander Fleming was talking to another doctor in a laboratory in London. He had been studying some germs(细菌)that he was growing on a plate. They were very dangerous germs because they caused different kinds of illnesses that could kill people. Dr Fleming found that a mould(霉菌)had floated in through the window landing on the plate. It had killed some of the germs it had touched.
“This certainly looks promising.” Fleming said. “We must grow some of this mould to see if it will kill other germs.”
He named the strange mould “penicillin”. It proved to be a killer of many germs. Fifty mice were given deadly germs and then half of them were injected(注射)with penicillin. The twenty-five untreated mice died, but twenty-four of those lived that had been treated with penicillin. Dr Fleming wrote a report about what he had found out. Hardly anybody took any notice of it.
In 1938 Dr Howard Florey, an Australian working in London, read Dr Fleming’s report and was very interested. He found that penicillin was effective in treating blood poisoning in human beings.
When World War II broke out, it was not possible to make enough penicillin in England. Dr Florey went to America where he helped to have enormous amounts of this wonderful drug made. It saved the lives of thousands of soldiers, sailors and airmen who would have died from their wounds if the hospitals had not had penicillin.
60. Dr Alexander Fleming .
A. had been studying a mould which was very dangerous and could kill people
B. had been studying some of the germs on a plate which could cure illnesses
C. had been making experiments on some germs that he was growing on a plate
D. had been making experiments on different germs that could help sick people to get better
61. Some of the germs on the plate .
A. had been killed by a mould floating in through the window
B. had been killing one another, which was a surprise to Fleming
C. had been killed by a mould that had been grown by Dr Alexander Fleming
D. had been killed by a mould found by another doctor
62. The reason why the twenty-five mice died was that .
A. they had been given deadly germs and had been injected with penicillin
B. they were almost dead ahead of the experiment
C. they were easy to die in the experiment
D. they had been given deadly germs and had not been injected with penicillin
63. In 1938, an Australian working in London named Howard Florey read Dr Fleming’s report and .
A. left England for America, making the drug
B. went to America to save the lives of thousands of soldiers, sailors and airmen
C. found penicillin effective in treating blood poisoning in human beings
D. went to America to make this drug for mice
64. The word “enormous” means .
A. 剩余的 B. 恰当的
C. 少许的 D. 巨大的
C
Einstein, a great scientist of the age, was almost as strange as his Theory of Relativity.
Once, while riding a street car in Berlin, he told the conductor that he had not given him the right change. The conductor counted the change again and found it to be correct, so he handed it to Einstein, saying, “The trouble with you is that you don’t know your figures.”
Einstein said that there were only twelve people living who understood his Theory of Relativity although a good many books had been written to explain it.
He had nothing but contempt(藐视)for the things most people set their hearts on—for fame and riches(财富)and luxury(奢华).
He didn’t want money or praise. He made his own happiness out of such simple things as his work and playing the violin and sailing his boat. Einstein’s violin brought him more joy than anything else in life. He said that he often thought in music.
65. The conductor thought Einstein .
A. wasn’t good at maths
B. had good memory
C. was either mad or strange
D. liked to make trouble
66. Einstein meant that many people .
A. knew his Theory of Relativity well because they could explain it
B. had written to have grasped his theory correctly
C. pretended to have grasped his abstract theory
D. admired him very much
67. The underlined part “set…hearts on” means .
A. believe B. have
C. love D. hate
D
Louis Pasteur, the famous French chemist and bacteriologist, invented “pasteurization”. In 1854 Pasteur was made head of the department of science at the University of Lille, and it was there that he made one of his most famous discoveries. Lille was a major center for wine and beer-making, and some of the local wine-makers asked Pasteur if he could help solve the problem of keeping wine fresh. At that time, it was believed that food and drinks go “bad” due to a purely chemical process (变化过程). But during a series of experiments Pasteur proved that tiny living organisms (微生物) caused food and drinks to go bad. In the case of wine and beer the organisms are already present in the form of the various yeasts (酵母) that caused the fermentation (发酵) process. Pasteur discovered that heating the wine gently for a few minutes after it had fermented would kill off the yeast that was left in the wine, with the result that the wine would remain fresh for much longer. He also proved that food and drinks could be turned bad by other organisms that were present in the air, and that they too would keep fresh much longer if they were kept in airtight containers.
The heating process was so successful that it made Pasteur famous. It was named “pasteurization” in his honour, and by about 1900 it had been widely used for processing and bottling cows’ milk. The result was a huge drop in the number of bottle-fed babies dying from infant diarrhea (婴儿腹泻) and from that time on it has been a standard treatment for milk and many other food products. This simple process has saved thousands, possibly millions, of lives worldwide.
68. Pasteur became in 1854.
A. the chairperson of the science department at the University of Lille
B. the director of a chemical laboratory at the University of Lille
C. the general manager of a large beer-making company
D. the president of the University of Lille
69. According to the passage, Lille was a major center for in the mid-19th century.
A. growing grain crops
B. making beer and wine
C. doing chemical research
D. producing various kinds of yeasts
70. In the last sentence of paragraph 1, the underlined word “they” refers to .
A. wine and beer
B. food and drinks
C. the various yeasts
D. other organisms
71. We can infer from the passage that Pasteur’s discovery .
A. is no longer widely used for treating milk and other food produts
B. did not bring much profit to the wine makers in Lille
C. has done a lot of good to children in the world
D. has greatly reduced the number of wars in the world
E
On the first day of class, Mr Whiteson gave us a lecture about a creature(生物) called cattytiger, a kind of cat-like animal that completely disappeared during the Ice Age. He passed round a skull (头骨) as he talked, and we all felt interested and took notes while listening. Later, we had a test about that.
When he returned my paper, I was very, very surprised. There was a very large cross through each of my answers. And so it was with everyone else’s in our class. What had happened? Everyone was wondering and couldn’t wait to get the answer.
Very simple, Mr Whiteson explained. He had made up all that story about the cattytiger. There had never been such an animal. So why none of us noticed that and how could we expect good marks for the incorrect answers?
Needless to say, we got very angry. What kind of teacher was this?
We should have guessed it out, Mr Whiteson said. After all, at the very moment he was passing around the cattytiger skull (in fact, a cat’s), hadn’t he been telling us that it completely disappeared during the Ice Age? Clearly he was telling a lie. But we just kept busy making notes and none used his head. We should learn something from this. Teachers and textbooks are not always correct.
72. We failed in the test because we didn’t .
A. take notes while listening
B. show interest in what Mr Whiteson said
C. listen to the teacher carefully
D. think carefully
73. We got angry because .
A. Mr Whiteson didn’t tell us the truth about cattytiger
B. we failed in the test
C. we didn’t know why he played the joke on us
D. there was no cattytiger
74. Mr Whiteson gave us a special lesson .
A. to show his special way of teaching
B. to play a joke on us
C. to help us learn our lessons better
D. so that we would no longer believe him
75. Mr Whiteson meant that .
A. teachers couldn’t make any mistakes
B. textbooks might be wrong sometimes
C. we should speak up if we thought our teacher or the textbook was wrong
D. we shouldn’t believe our teachers because sometimes they might tell lies
五、书面表达 (满分15分)
随着人们生活水平的提高，越来越多的人拥有了自己的汽车，你班同学就此展开了一次讨论，提出两种不同的观点和看法。请你根据所提供的信息给报社写一封信，客观介绍这两种看法。
赞同者认为：
1.方便、快捷、舒适的交通工具;
2.反映出国民生活条件提高，国家富强;
3.带动其他行业发展。
反对者认为：
1.废气污染严重;
2.过多则影响交通，导致更多事故;
3.停车问题日益突出。
注意：1.信的开头已给出;
2.词数：100左右;
3.参考词汇：方便的 convenient;交通 transportation
Dear editor，
I'm writing to tell you about the discussion we recently had about whether it is good or not for families to own cars.
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Yours truly,
Li Hua
