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四川省资阳市2008―2009学年度高中三年级第二次高考模拟考试

数学(理)

本试卷分为第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分. 第Ⅰ卷1至2页,第Ⅱ卷3至8页.全卷共150分,考试时间为120分钟. (考试时间3月28日

第Ⅰ卷(选择题 共60分)

注意事项:

1.答第Ⅰ卷前,考生务必将自己的姓名、考号、考试科目用铅笔涂写在答题卡上.

2.每小题选出答案后,用铅笔把答题卡上对应题目的答案标号涂黑.如需改动,用橡皮擦干净后,再选涂其它答案,不能答在试题卷上.

3.考试结束时,将本试卷和答题卡一并收回.

参考公式:

如果事件A、B互斥,那么.

如果事件A、B相互独立,那么.

如果事件A在一次试验中发生的概率是P,那么n次独立重复试验中恰好发生k次的概率.

球的表面积,其中R表示球的半径.

球的体积,其中R表示球的半径.

试题详情

四川省资阳市2008―2009学年度高中三年级第二次高考模拟考试

数 学(文史财经类)

 

本试卷分为第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分. 第Ⅰ卷1至2页,第Ⅱ卷3至8页.全卷共150分,考试时间为120分钟. (考试时间3月28日

第Ⅰ卷(选择题 共60分)

注意事项:

1.答第Ⅰ卷前,考生务必将自己的姓名、考号、考试科目用铅笔涂写在答题卡上.

2.每小题选出答案后,用铅笔把答题卡上对应题目的答案标号涂黑.如需改动,用橡皮擦干净后,再选涂其它答案,不能答在试题卷上.

3.考试结束时,将本试卷和答题卡一并收回.

参考公式:

如果事件A、B互斥,那么.

如果事件A、B相互独立,那么.

如果事件A在一次试验中发生的概率是P,那么n次独立重复试验中恰好发生k次的概率.

球的表面积,其中R表示球的半径.

球的体积,其中R表示球的半径.

试题详情

成都市2009届高中毕业班第二次诊断性检测

理科综合能力测试

(物理部分)

试题详情

2009年高考数学难点突破专题辅导三十四

难点34  导数的运算法则及基本公式应用

导数是中学限选内容中较为重要的知识,本节内容主要是在导数的定义,常用求等公式.四则运算求导法则和复合函数求导法则等问题上对考生进行训练与指导.

●难点磁场

(★★★★★)已知曲线Cy=x3-3x2+2x,直线l:y=kx,且lC切于点(x0,y0)(x0≠0),求直线l的方程及切点坐标.

●案例探究

[例1]求函数的导数:

6ec8aac122bd4f6e

命题意图:本题3个小题分别考查了导数的四则运算法则,复合函数求导的方法,以及抽象函数求导的思想方法.这是导数中比较典型的求导类型,属于★★★★级题目.

知识依托:解答本题的闪光点是要分析函数的结构和特征,挖掘量的隐含条件,将问题转化为基本函数的导数.

错解分析:本题难点在求导过程中符号判断不清,复合函数的结构分解为基本函数出差错.

技巧与方法:先分析函数式结构,找准复合函数的式子特征,按照求导法则进行求导.

6ec8aac122bd4f6e

 

(2)解:y=μ3,μ=axbsin2ωx,μ=avby

v=x,y=sinγ  γx

y′=(μ3)′=3μ2?μ′=3μ2(avby)′

=3μ2(av′-by′)=3μ2(av′-byγ′)

=3(axbsin2ωx)2(abωsin2ωx)

(3)解法一:设y=f(μ),μ=6ec8aac122bd4f6e,v=x2+1,则

yx=yμμv?vx=f′(μ)?6ec8aac122bd4f6ev6ec8aac122bd4f6e?2x

=f′(6ec8aac122bd4f6e)?6ec8aac122bd4f6e6ec8aac122bd4f6e?2x

=6ec8aac122bd4f6e

解法二:y′=[f(6ec8aac122bd4f6e)]′=f′(6ec8aac122bd4f6e)?(6ec8aac122bd4f6e)′

=f′(6ec8aac122bd4f6e)?6ec8aac122bd4f6e(x2+1)6ec8aac122bd4f6e?(x2+1)′

=f′(6ec8aac122bd4f6e)?6ec8aac122bd4f6e(x2+1) 6ec8aac122bd4f6e?2x

=6ec8aac122bd4f6ef′(6ec8aac122bd4f6e)

[例2]利用导数求和

(1)Sn=1+2x+3x2+…+nxn1(x≠0,nN*)

(2)Sn=C6ec8aac122bd4f6e+2C6ec8aac122bd4f6e+3C6ec8aac122bd4f6e+…+nC6ec8aac122bd4f6e,(nN*)

命题意图:培养考生的思维的灵活性以及在建立知识体系中知识点灵活融合的能力.属

★★★★级题目.

知识依托:通过对数列的通项进行联想,合理运用逆向思维.由求导公式(xn)′=nxn1,可联想到它们是另外一个和式的导数.关键要抓住数列通项的形式结构.

错解分析:本题难点是考生易犯思维定势的错误,受此影响而不善于联想.

技巧与方法:第(1)题要分x=1和x≠1讨论,等式两边都求导.

解:(1)当x=1时

Sn=1+2+3+…+n=6ec8aac122bd4f6en(n+1);

x≠1时,

x+x2+x3+…+xn=6ec8aac122bd4f6e,

两边都是关于x的函数,求导得

(x+x2+x3+…+xn)′=(6ec8aac122bd4f6e)′

Sn=1+2x+3x2+…+nxn1=6ec8aac122bd4f6e

(2)∵(1+x)n=1+C6ec8aac122bd4f6ex+C6ec8aac122bd4f6ex2+…+C6ec8aac122bd4f6exn,

两边都是关于x的可导函数,求导得

n(1+x)n1=C6ec8aac122bd4f6e+2C6ec8aac122bd4f6ex+3C6ec8aac122bd4f6ex2+…+nC6ec8aac122bd4f6exn1,

x=1得,n?2n1=C6ec8aac122bd4f6e+2C6ec8aac122bd4f6e+3C6ec8aac122bd4f6e+…+nC6ec8aac122bd4f6e,

Sn=C6ec8aac122bd4f6e+2C6ec8aac122bd4f6e+…+nC6ec8aac122bd4f6e=n?2n1?

●锦囊妙计

1.深刻理解导数的概念,了解用定义求简单的导数.

6ec8aac122bd4f6e表示函数的平均改变量,它是Δx的函数,而f′(x0)表示一个数值,即f′(x)=6ec8aac122bd4f6e,知道导数的等价形式:6ec8aac122bd4f6e.?

2.求导其本质是求极限,在求极限的过程中,力求使所求极限的结构形式转化为已知极限的形式,即导数的定义,这是顺利求导的关键.

3.对于函数求导,一般要遵循先化简,再求导的基本原则,求导时,不但要重视求导法则的应用,而且要特别注意求导法则对求导的制约作用,在实施化简时,首先必须注意变换的等价性,避免不必要的运算失误.

4.复合函数求导法则,像链条一样,必须一环一环套下去,而不能丢掉其中的一环.必须正确分析复合函数是由哪些基本函数经过怎样的顺序复合而成的,分清其间的复合关系.

●歼灭难点训练

试题详情

圆锥曲线专题精选

近三年广东高考圆锥曲线考题(解答题)特点:

1.题目位置前移,难度降低,己成为中档题;

2.都在知识交汇处设计试题,常有两个圆锥曲线作载体;

3.突出考查方程和方程组的方法。

2009年高考展望预测:坚持这几年成功的命题方向,主要是难度和风格,

但要强化圆的地位,弱化双曲线,关注函数与圆锥曲线交汇处的试题。

                     (1)

解答题:解答须写出文字说明.证明过程和演算步骤.

1.过抛物线的焦点作直线交抛物线两点,过点分别作抛物线的切线

(1) 证明:

(2)设切线轴于,当直线转动时,

求四边形面积的最小值.

2.设点,点轴上移动,点轴正半轴上移动,动点满足:①;②

(1)求点的轨迹方程;

(2)若;经过中点的直线轴于,且,设; ①求数列的通项公式;②试比较的大小.

3.已知函数的图像关于点(1,2)对称,且

(Ⅰ)求函数的解析式;

(Ⅱ)把的图像绕它的顶点逆时针方向旋转,并把图像按向量=(1,1)(向左和向上分别移1个单位)平移得到新的曲线C。

(1)       写出曲线C的方程及焦点坐标;

(2)       过焦点作直线交C于A、B,交轴于D,若=1∶2,求直线OA、OB的斜率。

4. 已知在平面直角坐标系中,若在曲线的方程中以为正实数)代替得到曲线的方程,则称曲线关于原点“伸缩”,变换称为“伸缩变换”,称为伸缩比.

(1) 已知曲线的方程为,伸缩比,求关于原点“伸缩变换”后所得曲线的标准方程;

(2) 射线的方程,如果椭圆经“伸缩变换”后得到椭圆,若射线与椭圆分别交于两点,且,求椭圆的标准方程;

(3) 对抛物线,作变换,得抛物线;对作变换得抛物线,如此进行下去,对抛物线作变换,得抛物线.若,求数列的通项公式

                                 (2)

解答题:解答须写出文字说明.证明过程和演算步骤.

1.已知AB分别是椭圆的左右两个焦点,O为坐标原点,点P)在椭圆上,线段PBy轴的交点M为线段PB的中点。

   (1)求椭圆的标准方程;

   (2)点C是椭圆上异于长轴端点的任意一点,对于△ABC,求的值。

2.椭圆的两个焦点F1、F2,点P在椭圆C上,且P F1⊥PF2, | P F1|=, | P F2|=.

(I)求椭圆C的方程;

(II)若直线L过圆的圆心M交椭圆于A、B两点,且A、B关于点M对称,求直线L的方程。

3.已知直线1:mx-y=0, 2:x+my-m-2=0.

(1)求证:12

(2)求证:对m的任意实数值,12的交点P在一定圆上;

(3)若1与定圆另一交点为P12与定圆另一交点为P2,求当ΔPP1P2的面积取得最大值时1的方程。

4 已知抛物线y2=2px(p>0),过动点M(a,0)且斜率为1的直线l与该抛物线交于不同的两点AB,且|AB|≤2p 

(1)求a的取值范围 

(2)若线段AB的垂直平分线交x轴于点N,求△NAB面积的最大值

5、有一张长为8,宽为4的矩形纸片ABCD,按图示方法进行折叠,使每次折叠后点B都落在AD边上,此时将B记为(注:图中EF为折痕,点F也可落在边CD上)。过交EF于T点,求T点的轨迹方程。

6..设,椭圆方程为,抛物线方程为如图6所示,过点轴的平行线,与抛物线在第一象限的交点为G,已知抛物线在点G的切线经过椭圆的右焦点

(1)求满足条件的椭圆方程和抛物线方程;

(2)设A,B分别是椭圆长轴的左、右端点,试探究在抛物线上是否存在点P,使得为直角三角形?若存在,请指出共有几个这样的点?并说明理由(不必具体求出这些点的坐标)

                                (3)

解答题:解答须写出文字说明.证明过程和演算步骤.

1. 在平面直角坐标系中,设二次函数的图象与两坐标轴有三个交点,经过这三个交点的圆记为C.

   (Ⅰ)求圆C的方程;

   (Ⅱ)设定点A是圆C经过的某定点(其坐标与无关),问是否存在常数使直线与圆交于点,且.若存在,求的值;若不存在,请说明理由.

2.设x1、x2ÎR,常数m>0,定义运算“*”:.

(1)  若x≥0,,求动点P(x,y)的轨迹C的方程并说明轨迹C的形状;

(2)  设A(x,y)是坐标平面上任一点,定义d1(A)=,

d2(A)=,计算d1(A)、d2(A),并说明d1(A)和d2(A)的

几何意义;

(3)  在(1)中的轨迹C上,是否存在不同两点A1(x1,y1)、A2(x2,y2),使之满足d1(Ai)=?d2(Ai)(i=1,2),若存在,求出m的取值范围;若不存在,请说明理由.

3.设F1、F2分别为椭圆C: (a>b>0)的左、右焦点.(1)设椭圆C上的点 到F1、F2两点距离之和等于4,写出椭圆C的方程和焦点坐标. (2)设点K是(1)中所得椭圆上的动点,求线段的中点的轨迹方程.

4、半径为1的圆柱体与地平面切于B点,在离地平面距离为3的上方放一个与地平面平行的平面镜,在圆柱体的左侧地面上有一点光源A,AB=5,如图,求地面上圆柱体右侧被光照射的长度MN。

 

 

 

 

 

 

5. 在平面内,已知定点A定到直线L的距离为,动点M到A点的距离等于它到直线L的距离.

(1)建立适当的坐标系,求动点M的轨迹方程;

(2)设点 , 在(1) 中的轨迹上,若

证明: 、A三点共线.

(4)    在(2) 条件下求∆(O是坐标原点)的最小面积.

                        

 (4)

  解答题:解答须写出文字说明.证明过程和演算步骤.

1. 已知圆内接于此圆,点的坐标为坐标原点.

   (Ⅰ)若的重心是,求直线的方程;(三角形重心是三角形三条中线的交点,并且重心到顶点的距离是它到对边中点距离的两倍)

   (Ⅱ)若直线与直线的倾斜角互补,求证:直线的斜率为定值.

2.如图直线相交于点,点,以为端点的曲线上的任意一点到的距离与到点的距离相等,若是锐角三角形,建立适当的坐标系,求曲线的方程。

3.已知双曲线的两个焦点分别为.又双曲线C上的任意一点E满足

   (1)求双曲线C的方程;

   (2)若双曲线C上的点P满足的值;

(3)若直线与双曲线C交于不同两点MN,且线段MN的垂直平分线过点A(0,-1),求实数m的取值范围.

4.有一幅椭圆型彗星轨道图,长4cm,高,如下图,已知O为椭圆中心,A1,A2是长轴两端点,太阳位于椭圆的左焦点F处.

   (Ⅰ)建立适当的坐标系,写出椭圆方程,并求出当彗星运行到太阳正上方时二者在图上的距离;

 

 

 

 

 

 

 

 

 

                                   (5)

解答题:解答须写出文字说明.证明过程和演算步骤.

1.已知m∈R,直线l:和圆C:

(1)求直线l斜率的取值范围;

(2)直线l能否将圆C分割成弧长的比值为的两段圆弧?为什么?

2.过点T(2,0)的直线交抛物线y2=4xAB两点.

(1)若直线l交y轴于点M,且m变化时,求的值;

(2)设AB在直线上的射影为DE,连结AEBD相交于一点N,则当m变化时,点N为定点的充要条件是n=-2.

3.在平面直角坐标系,已知圆心在第二象限、半径为的圆与直线相切于坐标原点.椭圆与圆的一个交点到椭圆两焦点的距离之和为

(1)求圆的方程;

(2)试探究圆上是否存在异于原点的点,使到椭圆右焦点的距离等于线段的长,若存在,请求出点的坐标;若不存在,请说明理由.

4.设函数分别在处取得极小值、极大值.平面上点的坐标分别为,该平面上动点满足,点是点关于直线的对称点.求

(I)求点的坐标;

(II)求动点的轨迹方程.

5、设直线与椭圆相交于A、B两点。

    (1) 线段AB中点M的坐标及线段AB的长;

(2) 已知椭圆具有性质:设A、B是椭圆上的任意两点,M是线段AB的中点,若直线AB、OM的斜率都存在,并记为kAB,kOM,则kAB×kOM为定值。试对双曲线写出具有类似特性的性质,并加以证明。

 

 

 

 

试题详情

2009年安徽高考高中数学基础知识归纳

第一部分   集合

1.理解集合中元素的意义是解决集合问题的关键:元素是函数关系中自变量的取值?还是因变量的取值?还是曲线上的点?…

2 .数形结合是解集合问题的常用方法:解题时要尽可能地借助数轴、直角坐标系或韦恩图等工具,将抽象的代数问题具体化、形象化、直观化,然后利用数形结合的思想方法解决

3.(1) 元素与集合的关系:,.

(2)德摩根公式: .

(3)       注意:讨论的时候不要遗忘了的情况.

(4)集合的子集个数共有 个;真子集有?1个;非空子集有 ?1个;

非空真子集有?2个.

4.是任何集合的子集,是任何非空集合的真子集.

第二部分  函数与导数

1.映射:注意: ①第一个集合中的元素必须有象;②一对一或多对一.

2.函数值域的求法:①分析法 ;②配方法 ;③判别式法 ;④利用函数单调性 ;⑤换元法 ;

⑥利用均值不等式 ; ⑦利用数形结合或几何意义(斜率、距离、

绝对值的意义等);⑧利用函数有界性(等);⑨平方法;⑩ 导数法

3.复合函数的有关问题:

(1)复合函数定义域求法:

① 若f(x)的定义域为[a,b],则复合函数f[g(x)]的定义域由不等式a ≤  g(x) ≤  b解出

② 若f[g(x)]的定义域为[a,b],求 f(x)的定义域,相当于x∈[a,b]时,求g(x)的值域.

(2)复合函数单调性的判定:

①首先将原函数分解为基本函数:内函数与外函数

②分别研究内、外函数在各自定义域内的单调性

③根据“同性则增,异性则减”来判断原函数在其定义域内的单调性.

4.分段函数:值域(最值)、单调性、图象等问题,先分段解决,再下结论。

5.函数的奇偶性:

⑴函数的定义域关于原点对称是函数具有奇偶性的必要条件

是奇函数是偶函数.

⑶奇函数在0处有定义,则

⑷在关于原点对称的单调区间内:奇函数有相同的单调性,偶函数有相反的单调性

⑸若所给函数的解析式较为复杂,应先等价变形,再判断其奇偶性

6.函数的单调性:

⑴单调性的定义:

在区间上是增函数时有

在区间上是减函数时有

⑵单调性的判定:①定义法:一般要将式子化为几个因式作积或作商的形式,以利于判断符号;②导数法(见导数部分);③复合函数法;④图像法

注:证明单调性主要用定义法和导数法。

7.函数的周期性:

(1)周期性的定义:对定义域内的任意,若有 (其中为非零常数),则称函数为周期函数,为它的一个周期。所有正周期中最小的称为函数的最小正周期。如没有特别说明,遇到的周期都指最小正周期。

(2)三角函数的周期:① ;② ;③

;⑤

(3)与周期有关的结论:

的周期为

8.基本初等函数的图像与性质:

㈠.⑴指数函数:;⑵对数函数:

⑶幂函数: ;⑷正弦函数:;⑸余弦函数:

(6)正切函数:;⑺一元二次函数:(a≠0);⑻其它常用函数:

①     正比例函数:;②反比例函数:;③函数

㈡.⑴分数指数幂:(以上,且).

⑵.①;       ②

;  ④.

⑶.对数的换底公式:.对数恒等式:.

9.二次函数:

⑴解析式:①一般式:;②顶点式:为顶点;

③零点式: (a≠0).

⑵二次函数问题解决需考虑的因素:

①开口方向;②对称轴;③端点值;④与坐标轴交点;⑤判别式;⑥两根符号。

二次函数的图象的对称轴方程是,顶点坐标是

10.函数图象:

⑴图象作法 :①描点法 (特别注意三角函数的五点作图)②图象变换法 ③导数法

⑵图象变换:

①     平移变换:?)―――左“+”右“-”;

              ?) ―――上“+”下“-”;

②     对称变换:?);?)

?) ; ?)

③     翻折变换:

?)―――(去左翻右)y轴右不动,右向左翻(左侧图象去掉);

?)―――(留上翻下)x轴上不动,下向上翻(||在下面无图象);

11.函数图象(曲线)对称性的证明:

(1)证明函数图像的对称性,即证明图像上任意点关于对称中心(对称轴)的对称点仍在图像上;

(2)证明函数图象的对称性,即证明图象上任意点关于对称中心(对称轴)的对称点在的图象上,反之亦然。

注:①曲线C1:f(x,y)=0关于原点(0,0)的对称曲线C2方程为:f(-x,-y)=0;

曲线C1:f(x,y)=0关于直线x=0的对称曲线C2方程为:f(-x, y)=0;

曲线C1:f(x,y)=0关于直线y=0的对称曲线C2方程为:f(x, -y)=0;

曲线C1:f(x,y)=0关于直线y=x的对称曲线C2方程为:f(y, x)=0

②f(a+x)=f(b-x) (x∈R)y=f(x)图像关于直线x=对称;

特别地:f(a+x)=f(a-x) (x∈R)y=f(x)图像关于直线x=a对称.

的图象关于点对称.

特别地:的图象关于点对称.

④函数与函数的图象关于直线对称;

      函数与函数的图象关于直线对称。

12.函数零点的求法:

⑴直接法(求的根);⑵图象法;⑶二分法.

(4)零点定理:若y=f(x)在[a,b]上满足f(a)?f(b)<0 , 则y=f(x)在(a,b)内至少有一个零点。

13.导数:

⑴导数定义:f(x)在点x0处的导数记作

⑵常见函数的导数公式: ①;②;③;④;⑤;⑥;⑦;⑧

⑶导数的四则运算法则:

⑷(理科)复合函数的导数:

⑸导数的应用:                                                      

①利用导数求切线:注意:?)所给点是切点吗??)所求的是“在”还是“过”该点的切线?

②利用导数判断函数单调性:i)是增函数;ii)为减函数;iii)为常数;

③利用导数求极值:?)求导数;?)求方程的根;?)列表得极值。

④利用导数求最大值与最小值:?)求极值;?)求区间端点值(如果有);?)比较得最值。

第三部分  三角函数、三角恒等变换与解三角形

1.⑴角度制与弧度制的互化:弧度弧度,弧度

⑵弧长公式:;扇形面积公式:

2.三角函数定义:角终边上任一点(非原点)P,设 则:

3.三角函数符号规律:一全正,二正弦,三正切,四余弦;(简记为“全s t c”)

4.诱导公式记忆规律:“奇变偶不变,符号看象限”

5.⑴ 对称轴:令,得  对称中心:

对称轴:令,得;对称中心:

⑶周期公式:①函数的周期 (A、ω、为常数,

且A≠0).②函数的周期 (A、ω、为常数,且A≠0).

6.同角三角函数的基本关系:

7.三角函数的单调区间及对称性:

  ⑴的单调递增区间为,单调递减区间为

,对称轴为,对称中心为.

的单调递增区间为,单调递减区间为

对称轴为,对称中心为.

的单调递增区间为,对称中心为.

8.两角和与差的正弦、余弦、正切公式:

.

.

=(其中,辅助角所在象限由点所在的象限

决定, ).

9.二倍角公式:①.

(升幂公式).

(降幂公式).

10.正、余弦定理:

⑴正弦定理:  (外接圆直径 )

注:①;②;③

⑵余弦定理:等三个; 等三个。

11.几个公式:⑴三角形面积公式:①分别表示a、b、c边上的高);②.③

⑵内切圆半径r=; 外接圆直径2R=

第四部分   立体几何

1.三视图与直观图:⑴画三视图要求:正视图与俯视图长对正;正视图与侧视图高平齐;侧视图与俯视图宽相等。 ⑵斜二测画法画水平放置几何体的直观图的要领。

2.表(侧)面积与体积公式:

⑴柱体:①表面积:S=S+2S;②侧面积:S=;③体积:V=Sh

⑵锥体:①表面积:S=S+S;②侧面积:S=;③体积:V=Sh:

⑶台体:①表面积:S=S+S下底;②侧面积:S=;③体积:V=(S+)h;

⑷球体:①表面积:S=;②体积:V=  .

3.位置关系的证明(主要方法):

⑴直线与直线平行:①公理4;②线面平行的性质定理;③面面平行的性质定理。

⑵直线与平面平行:①线面平行的判定定理;②面面平行线面平行。

⑶平面与平面平行:①面面平行的判定定理及推论;②垂直于同一直线的两平面平行。

⑷直线与平面垂直:①直线与平面垂直的判定定理;②面面垂直的性质定理。

⑸平面与平面垂直:①定义----两平面所成二面角为直角;②面面垂直的判定定理。

注:以上理科还可用向量法。

4.求角:(步骤-------Ⅰ.找或作角;Ⅱ.求角)

⑴异面直线所成角的求法:

①平移法:平移直线,构造三角形;②用向量法

⑵直线与平面所成的角:

①直接法(利用线面角定义);②用向量法

5.求距离:(步骤-------Ⅰ.找或作垂线段;Ⅱ.求距离)

点到平面的距离:①等体积法;②向量法

6.结论:

⑴棱锥的平行截面的性质如果棱锥被平行于底面的平面所截,那么所得的截面与底面相似,截面面积与底面面积的比等于顶点到截面距离与棱锥高的平方比(对应角相等,对应边对应成比例的多边形是相似多边形,相似多边形面积的比等于对应边的比的平方);相应小棱锥与小棱锥的侧面积的比等于顶点到截面距离与棱锥高的平方比.

⑵长方体从一个顶点出发的三条棱长分别为a,b,c,则体对角线长为,全面积为2ab+2bc+2ca,体积V=abc。

⑶正方体的棱长为a,则体对角线长为,全面积为,体积V=

⑷球与长方体的组合体: 长方体的外接球的直径是长方体的体对角线长.

  球与正方体的组合体:正方体的内切球的直径是正方体的棱长, 正方体的棱切球的直径是正方体的面对角线长, 正方体的外接球的直径是正方体的体对角线长.

⑷正四面体的性质:设棱长为,则正四面体的:

①     高:;②对棱间距离:;③内切球半径:;④外接球半径:

第五部分   直线与圆

1.斜率公式:,其中.

直线的方向向量,则直线的斜率为=.

2.直线方程的五种形式:

(1)点斜式: (直线过点,且斜率为).

(2)斜截式:Paris                   D. When he is returning

4. A. Yes, because he has plenty of money           B. No, because it’s not for sale

  C. Yes, if he borrows money from the woman  D. No, he wants to wait until it goes on sale

5. A. It’s boring                                               B. The subject is hard

  C. It is hard to understand teacher’s speech      D. It is hard to pronounce some words

6. A. The man was waiting to do something        B. The man was asking for directions

  C. The man was making a trip                        D. The man was asking for help

7. A. Take the bus with him                               B. Drive him home from the station

  C. Drive him to work                                    D. Drive him to the station

8. A. He is tired of using his new computer        

B. He has just assembled the computer

  C. He has used his new computer for waiting his report

  D. He has found something wrong with the new computer

9. A. Shopping for new clothes                          B. Having a party

  C. Looking for her black dress                       D. Getting dressed

10. A. She does not like the apartment.

   B. She is concerned about the rent for the apartment.

   C. She wants to live in the apartment

   D. She agrees with the man.

 

Part B Passages

Directions: In Part B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.

Questions 11 through 13 are based on the following passage.

11. A. Right decisions                                B. Wrong decisions

   C. Experience                                      D. Opportunity

12. A. She was lucky to have many marvelous opportunities.

   B. She was afraid of taking risks.

   C. She made wrong decisions in her work.

   D. She felt bad when she made a mistake.

13. A. Forget it and move on,

   B. Don’t make the same mistake repeatedly.

   C. Mistakes are a necessary part of learning

   D. The more mistakes you make, the better you will become.

 

Questions 14 through 16 are based on the following news.

14. A. The third            B. The fourth                C. The fifth           D. The sixth

15. A. He could not see their eyes                      B. He thought they were useless

   C. He could see no willingness to help           D. He thought they were in a hurry

16. A. He was grateful   B. He was curious         C. He was happy    D. He was excited

 

Part C Longer Conversations

Directions: In Part C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with information you have heard. Write your answers on your answer sheet.

 

Questions 17 through 20 are based on the following conversation.

 

Complete the following table using NO MORE THAN TWO WORDS for each question.

 

Linda’s Dairy

                                                  Dec.28th.,2002

Today’s the second day of our camping holiday.

Got up    At (17) _____________

Problem   (18) ________________

Solution   Put (19) ______________on our camping car to attract (20) _______.

          The noise they made woke us up.

It did work. What a brilliant idea!

 

Questions 21 through 24 are based on the following conversation.

Complete the following table using NO MORE THAN THREE WORDS for each question.

BIKES FOR HIRE

Kinds of bikes                      Push bikes and (21)_________.

Minimum age                      Must be (22) _____________.

Minimum days                     At least (23) ______________.

Can take kids on the back?           Yes.

Necessity for booking                (24)_____________________.

 

II. Grammar and Vocabulary 16%

Directions: Beneath each of the following sentences there are four choices marked A, B. C and D.   Choose the one answer that best completes the sentence.

25. The company had about 20 notebook computers but only one-third ____ used regularly. Now we have 60 working all day long.

A. is                            B. are                           C. was                          D. were

26. I have just finished a book about a piano player ____ sole ambition in life was to perform for the pope.

A. whose               B. which                      C. who                         D. whom

27. _____ well prepared you are, you still need a lot of luck in mountain climbing.

A. No mater          B. Whatever                 C. However                  D. Although

28. We are aware that, ____, the situation will get worse.

A. if not dealing with carefully                   B. if dealt not carefully with

C. if not carefully dealt with                       D. if not carefully dealing with

29. _______ snacks and drinks, but they also brought cards for entertainment when they had a picnic in the forest.

A. Not only they brought                           B. Not only did they bring

C. Not only brought they                           D. Not only they did bring

30. ---English has a large vocabulary, hasn’t it?

   ---Yes. ____ more words and expressions and you will find it easier to read and communicate.

A. Know               B. Knowing                  C. To know                   D. Known

31. It was the university ___ he was studying ____ sent him abroad.

A. which, that        B. where, that               C. that, which               D. that, had

32. ___ electricity, you should turn off the lights when you leave a room.

A. Saving              B. Having saved            C. Being saved              D. To save

33. Wolves will soon be extinct everywhere ____ we stop killing them.

A. because             B. if               C. unless               D. when

34. Go and get your coat. It’s ___ you left it.

A. there                 B. where               C. there where                     D. where there

35. Many thousands of people were walking along the Bund on the evening of our National Day, ____ the magnificent night scene.

A. to enjoy            B. enjoying            C. to watch                   D. noticing

36. ____ he made an important speech at yesterday’s meeting was true.

A. That                 B. Why                 C. It was said                D. When

37. I would appreciate ___ it a secret.

A. your keeping     B. that you keep     C. you to keep                     D. that you will keep

38. It is reported that 82% of women ___ 50% or more of their income on clothing were aged between 25 to 35.

A. spent                B. to spend            C. spend                       D. spending

39. She had never spent a ___ day.

A. more worry              B. most worrying          C. more worrying          D. most worried

40. With time going on, the method she has stuck ___ very effective and it was worthy of ___.

A. proves, adopting                                   B. to proving, being adopted

C. to proved, being adopted                 D. to prove, adopting

 

III. Vocabulary 9%

Directions: Complete the passage with the words in the box. There is one extra word.

文本框: A. threatens    B. killers    C. cases    D. victims    E. suffering    F. target   	 G. because     H. population   I. affects  	J. effect

The new figures are the result of detailed research that gives the most accurate assessment of the disease that kills at least a million people a year. Scientists now believe there are about 515 million _1__ of malaria (疟疾) out of 2.2 billion people who are at risk ----- about a third of the world’s _2__.

Malaria has never captured the public imagination as AIDS has done, even though children are its chief _3___. Malaria is old and AIDS is new. Most important, malaria is not a disease that __4__ the West ---- except for those fortunate enough to holiday in the tropics ---- while AIDS _5__ us all.

Six years ago the WHO set a _6__ to halve the number of deaths by the year 2010, but instead the number has risen by at least a quarter, and in some areas by as much as 50 percent, _7__ victims have not had the right drugs. Hundreds of thousands of children have died needlessly and the disease has gone virtually unnoticed in the West. Malaria has been a cause of great _8__ for humanity since ancient times and although it is largely preventable with the use of mosquito nets and insecticides, it remains one of the biggest __9_ of children under five.

 

IV. Cloze (15%)

Directions: For each blank in the following passages there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.

Crime has its own cycle, a magazine reported some years ago. Police records that were studied for five years from over 2,400 cities and towns show a surprising _41_ between changes in the season and crime patterns.

The pattern of crime has varied very little over a long period of years. Murder _42_ its high during July and August, as do rape and other __43__ attacks. Murder, __44__, is more than seasonal: it is a weekend crime. It is also a high time crime: 62 percent of murders are __45__ between 6 pm and 6 am.

Unlike the summer high in crimes of bodily harm, burglary has a(n) __46__ cycle. You are most __47__ to be robbed between 6 p.m. and 2 a.m. __48__ a Saturday night in December, January or February. May is the most non-criminal month of all except for one strange statistics.   __49__ dog bites are reported in this month than in any other month of the year.

Apparently our intellectual seasonal cycles are __50__ different from our criminal tendencies. Professor Huntington, of the Foundation for the Study of Cycles, made extensive __51__ to discover the seasons when people read serious books, attend scientific meetings, make __52__ scores on examinations and propose the most changes to parents. In all instances, he found a spring peak and an autumn peak __53__ by a summer low. On the other hand, Professor Huntington’s studies indicated that June is the __54__ month for suicides and __55__ to mental hospitals. June is also a peak month for marriages!

41.A.difference        B.link                 C.coincidence      D.similarity

42.A.reaches            B.increases          C.kills                D.falls

1,3,5

44.A.while                     B.therefore          C.otherwise         D.however

45.A.admitted          B.committed              C.accused            D.connected

46.A.strange            B.unexpected       C.different          D.serious

47.A.likely                     B.unlucky           C.ready               D.possible

48.A.in                   B.on                   C.at                    D.for

49.A.Easier             B.Fewer              C.More               D.No

50.A.slightly            B.typically          C.specially          D.completely

51.A.experiment      B.test                  C.studies             D.requests

52.A.average           B.high                C.poor                D.unsatisfactory

53.A.divided            B.separated         C.dropped           D.shortened

54.A.only                B.common          C.peak                D.rare

55.A.management    B.admissions       C.explosion         D.explanations

 

V.Reading Comprehension (35%)

Directions: Read passage A, B, C and D. Each passage is followed by several questions or unfinished statements. For each of them there are four choices. Choose the one that fits best according to the information given in the passage you have just read.

(A)

Life is difficult

It is a great truth because once we truly understand and accept it, then life is no longer difficult.

      Most do not fully see this truth. Instead they are always blaming their problems and difficulties as if life should be easy. It seems to them that their difficulties represent a special kind of suffering especially forced upon them or else upon their families, their class, their race, or even their nation.

What makes life difficult is that the process of facing and solving problems is a painful one. Problems, depending on their nature, cause in us sadness or loneliness or regret or anger or fear. These are uncomfortable feelings, often as painful as any kind of physical pain. And since life causes an endless series of problems, life is always difficult and is full of pain as well as joy.

Yet it is this whole process of meeting and solving problems that life has its meaning.

Problems are the serious test that tells success from failure. When we desire to encourage the growth of the human spirit, we challenge and encourage the human ability to solve problems, just as in school we purposely set problems for our children to solve. It is through the pain of confronting and resolving problems that we learn. As Benjamin Franklin said, “Those things that hurt, instruct.” It is for this reason that wise people learn not to fear but actually to welcome problems and actually to welcome the pain of problems.                                           

 

56. From the passage, it can be inferred that ____.

A. people like to complain about their problems

B. we become stronger by facing and solving the problems of life

C. life is difficult because our problem bring us pain

D. everybody has problems

57. The writer probably used just one short sentence in the first paragraph ________.

A. make readers laugh                        B. persuade readers   

C. save space                                     D. get readers' attention

58. According to the passage, we give school children difficult problems to solve in order to ______.

A. teach them how to respect for problems

B. help them learn to deal with pain

C. encourage them to learn

D. teach them to fear the pain of solving problems

59. The saying from Benjamin Franklin “Those things that hurt, instruct” suggests that _______.

A. pain teaches us important lessons     B. we do not learn when we are in pain

C. pain cannot be avoided                   D. we do not learn from experience

 

(B)

Ambassador Hotel
Welcome to the Ambassador Hotel. To make your stay as enjoyable as possible, we hope you will use our facilities to the full.

Dining Room
Breakfast is served in the dining mom from 8 a. m. to 9: 30 a.m. Alternatively, the room staff will bring a breakfast tray to your room at any time after 7 a.m. In this case, please fill out a card and hang it outside your door when you go to bed.
Lunch: 12:00a.m. to2:30p.m.
Dinner: 7:30 p.m. to 9:00 p.m.
Room Service
This operates 24 hours a day; phone the Reception desk, and your message will be passed on to the room staff.
Telephones
To make a phone call, dial 0 for Reception and ask to be connected. We apologize for delays in putting calls through when the staff are very busy. There are also public telephone booths near the Reception Desk.

Shop

The hotel shop is open for small things, gifts and cosmetics from 9 a.m. to 5:30 p.m.
Laundry
We have a laundry here and will wash, iron and return your clothes within 24 hours. Ask the room staff to collect them
Bar
The hotel bar is open from 12 a.m. to 2 p.m. and 7 p.m. to 1 a.m.

Banking

The Reception staff will cash cheques and exchange money in many foreign currencies (货币).

 

60. You have arrived to stay at the hotel at 2 a.m. and want a snack ( a light meal). What should you do?

A. Go to the hotel shop                                     B. Go to the hotel bar

C. Hang a message outside your door                 D. Phone the Reception desk

61. You have come back to the hotel just in time to make a very important phone call. As you come in, you notice a lot of people around the Reception desk. Judging from the notice, it would be quickest to ____.

A. go to your room and phone from there.

B. ask at the Reception desk

C. use one of the telephones in the entrance-hall

D. go out again and look for a public phone box.

62. Imagine you are one of the room staff on night duty. What do you think your last job is before you go off duty at 6 a.m.?

A. Lay the tables in the dining room

B. Check the bedroom doors

C. Start preparing the breakfast

D. Wake any of the guests who have asked for early calls.

 

(C )

A is for always getting to work on time.

B is for being extremely busy.

C is for the conscientious(勤勤恳恳的)way you do your job.

You may be all these things at the office, and more. But when it comes to getting ahead, experts say, the ABCs of business should include a P, for politics, as in office politics. Dale Carnegie suggested as much more than 90 years ago: Hard work alone doesn't ensure career advancement. You have to be able to sell yourself and your ideas, both publicly and behind the scenes. Yet, despite the obvious rewards of engaging in office politics - a better job, a raise, praise- many people are still unable or unwilling - to "play the game."

"People assume that office politics involves some manipulative(工于心计的)behavior," says Deborah Comer, an assistant professor of management at Hofstra University. "But politics derives from the word 'polite'. It can mean lobbying(疏通)and forming associations. It can mean being kind and helpful, or even trying to please your superior, and then expecting something in return."

In fact, today, experts define office politics as proper behavior used to pursue one's own self-interest in the workplace. In many cases, this involves some form of socializing within the office environment - not just in large companies, but in small workplaces as well.

"The first thing people are usually judged on is their ability to perform well on a consistent basis," says Neil P. Lewis, a management psychologist. "But if two or three candidates are up for a promotion, each of whom has reasonably similar ability, a manager is going to promote the person he or she likes best. It's simple human nature."

Yet, psychologists say, many employees and employers have trouble with the concept of politics in the office. Some people, they say, have an idealistic vision of work and what it takes to succeed. Still others associate politics with flattery, fearful that, if they speak up for themselves, they may appear to be flattering their boss for favors.

Experts suggest altering this negative picture by recognizing the need for some self-promotion.

63. To get promoted, one must not only be competent but  ___.

A. give his boss a good impression

B. honest and loyal to his company

C. get along well with his colleagues

D. avoid being too outstanding

64. Why are many people unwilling to "play the game"?

A. They believe that doing so is impractical.

B. They feel that such behavior is unprincipled.

C. They are not good at manipulating colleagues.

D. They think the effort will get them nowhere.

65. The author considers office politics to be ____.

A. unwelcome at the workplace

B. bad for interpersonal relationships

C. essential to the development of company culture

D. an important factor for personal advancement

66. It is the author's view that ____.

A. speaking up for oneself is part of human nature

B. self-promotion does not necessarily mean flattery

C. hard work contributes very little to one's promotion

D. many employees fail to recognize the need of flattery

 

(D)

Students create online university store

Want to buy brand-name cosmetics? In need of a GRE preparation book? Plan to order a bunch of flowers for your girlfriend?

No need to rush to different stores. Students at Tsinghua University can go shopping with a click of the mouse.

Liuxingxiaozhan.com, an e-commerce company set up by Tsinghua students last year, promises to give students the most convenient shopping experiences. And while most dotcom companies off-campus are struggling to make ends meet, the owners of the student company are proudly declaring a profit.

Each month, more than 1,000 transactions are done at Liuxingxiaozhan.com. The monthly sales volume has reached 30,000 yuan, according to Tang Yang, head of the campus e-commerce web.

At Tsinghua University, nearly every dormitory has computer and Internet access, making it likely that e-commerce will prosper.

Just like the name implies, Tang said friendly services and demand-oriented supply explained the profits. The pinyin--- Liuxing, frequently used in the students’ verses--- means shooting star.

“ An old story says that when a shooting star flashes across the sky, your dreams will come true if you pray to it. So if you log on Liuxingxiaozhan, your dreams will be realized,” the 23-year-old CEO said.

He really means it.

At Liuxingxiaozhan, you can propose a new item if you want it. The webmaster may supply this commodity for you. People can comment on this proposition, saying whether the online shop should offer it or not.

“In this way, we can supply according to the demand,” Tang said.

Sending flowers to your “mm” is one new item proposed by the users. “mm” are the initials for meime, the way boys address girls at Tsinghua’s BBS.

Starting just with VCD rentals in October, 1999, Liuxingxiaozhan now covers nearly all student needs, including cosmetics, books and second-hand items.

Xiang Jie, who ordered an Avon facial mask at the virtual shop, said she was satisfied with the service.

“It is quite convenient and the service is nice. I got the mark in two days,” Xiang said. Most of her classmates use these services.

The webmasters promise that every item ordered will be sent to the destination within three days. And they pay by cash only when they have received the goods. Part-time workers will distribute the ordered goods.

But the current success does not mean they have been without failure.

“In the beginning, we suffered losses because the goods we offered did not sell,” Tang said. “This is also one of the reasons we buy information about consumer demand from our members.’

Money is another problem. Students don’t have a lot of money to invest in the business. Things improved when they received an initial venture capital investment of 1 million yuan.

However, Tang was faced with other problems. His parents, who expected the electronic engineering major to be an excellent engineer, did not know their son had been working in e-commerce until they saw a CCTV report about him.

Working day and night, like most Internet talents do, Tang said his academic performance was greatly affected by the business.

Even so, the young entrepreneur is still thinking of expanding his business.

“So far, the business is only confirmed to the Tsinghua community. Some universities are copying our model of e-commerce,” Tang said.

“We are thinking of co-operating with other universities in Beijing, Shanghai and Xi’an,” Tang added, in an effort to solve the distribution bottleneck of e-commerce with a kind of a community e-distribution box.

 

67. Which of the following statements is Not true?

A. Liuxingxiaozhan e-company is making profits

B. The yearly sales volume of Liuxingxiaozhan has reached 30,000 yuan

C. At Tsinghua University, nearly every dorm has computer and Internet access

D. Most off-campus e-companies can only make ends meet.

68. At The very beginning, Liuxingxiaozhan started with ___.

A. renting VCDs                         B. selling many kinds of goods

C. sending flowers                       D. developing software

69. Each year, Liuxingxiaozhan can do more than ____ transactions.

A. 10,000                     B. 3,000                C. 12,000                     D. 2,000

70. According to the article, Tang’s major in university is ____.

A. computer application               B. financial engineering

C. electronic engineering              D. e-commerce

 

Directions: Read the following text and choose the most suitable heading from A ? F for each paragraph. There is one extra heading which you do not need.

 

文本框: A. Great leaders’ messages are always simplified
B. What must a leader be able to do with his power?
C. Timing is one of the most important aspects of leadership
D. We produce our leaders.
E. What an image should a leader have?
F. Leaders are sure to use power.

 

 

 

 

 

 

 

文本框: 71.

 

Leadership is as much a question of timing as anything else. The leader must appear on the scene at a moment when people are looking for leadership, as Churchill did in 1940, as Roosevelt did in 1933, as Lenin did in 1917. And when he comes, he must offer a simple, eloquent message.

文本框: 72.

 

 

Great leaders are almost always great simplifiers, who cut through argument, debate and doubt to offer a solution everybody can understand and remember. Churchill warned the British to expect “blood, toil, tears and sweat”; Roosevelt told the Americans that “the only thing we have to fear is fear itself”; Lenin promised the war-weary Russians peace, land and bread. Straightforward but effective messages

文本框: 73.

 

 

We have an image of what a leader ought to be. We even recognize the physical signs; leaders may not necessarily be tall, but they must have bigger-than-life, commanding features -- Lyndon Baines Johnson’s nose and ear lobes, Ike’s broad grin. A trade-mark also comes in handy; Lincoln’s stovepipe hat, Kennedy’s rocking chair. We expect our leaders to stand out a little, not to be like an ordinary man. Half of President Ford’s trouble lay on the fact that, if you closed your eyes for a moment, you couldn’t remember his face, figure of clothes. A leader should have an unforgettable identity, instantly and permanently fixed in people’s minds.

 

文本框: 74.

 

A leader must know how to use power (that’s what leadership is about), but he also has to have the way of showing that he does. He has to be able to project firmness -- no physical clumsiness (笨拙) (like Ford), no rapid eye movements (like Carter).He won’t come until we’re ready for him, for the leader is like a mirror, reflecting back to us our own sense of purpose, putting into words our own dreams and hopes, transforming our needs and fears into coherent (连贯的) policies and programs.

 

文本框: 75.

 

Our strength makes him strong; our determination makes him determined; our courage makes him a hero; he is, in the final analysis, the symbol of the best in us, shaped by our own spirit and will. And when these qualities are lacking in us, we can’t produce him; and even with all our skill at image-building, we can’t fake him. He is, after all, merely the sum of us.

 

 

 

 

1,3,5

I.Translation (20%)

Directions: Translate the following sentences into English, using the words given in the brackets.

1.       正是在英特网上他找到了他所需要的东西。(what )

2.       我感觉我们无法在三小时内到达那里。 (it)

3.       只有全力以赴,我们才能按时完成这项任务。(unless)

4.       外国游客印象最深的是中国人民对未来很有信心。 (impress)

5.       如果不采取适当的措施,同样的事故有可能再度发生。 (possibility)

6.       预计,不久中国在很多领域将赶上了许多世界上的发达国家。(expect)

 

 

 

II.Guided Writing (25%)

Directions: Write an English composition in 120 ? 150 words according to the instructions given below in Chinese.

目前,高中生零用钱(pocket money)主要消费在饮食、买书、游戏等方面,谈谈你对高中生应该如何合理使用零用钱的看法和理由。

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer Sheet

I.Listening Comprehension

17.________           18._________19.________20.____________

21._________    22.________23._________24.____________

Ⅱ. Grammar and Vocabulary

1.___2.___3.___4.___5.___6.___7.___8.___9.___

II. Reading Comprehension

71.___72.___73.___74.___75.___

III.Translation

1.__________________________________________________

 

2.__________________________________________________

 

3.__________________________________________________

 

4.__________________________________________________

 

5.__________________________________________________

 

6.__________________________________________________

 

 

Guided Writing:  (25%)

 

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江苏省苏北四市2009届高三第三次调研考试

物  理  试  题

注意:本试卷?分120分,考试时间100分钟.请将答案填写在答题卡上,直接写在试卷上不得分.

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