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篇一:《高考数学试题与》

高考数学试题与《数学教学与测试》

宁夏固原市一中 田彦武 马占山 756000

2003年高考已结束。从整个试卷来看，今年的数学试题与现在高二年级正在学习的新

教材联系较紧，它充分体现了课改的观念。从难易程度上来说，较2002年文、理科难。选择题的试题面孔不新，但加大了运算量的考查；填空题除第（13）题为基础题外，后面的三道试题加大了能力考查；六道大解答题突破容易，但是得分难，要做完整几乎很难，有几道题确有竞赛味道。考生普遍反映不良，纷纷表示今年的数学试题“杀伤力太强”，尤其是解答题，有些考生一下考场就掉眼泪。事实也真是如此。但仍有部分题目却在某些资料中找到。 笔者翻阅了一下2002年版由苏州大学出版社出版，《中学数学月刊》编辑部主编的《高

三数学教学与测试》（上册）（旧教材）教师用书(以下简称为教书)，发现这次高考数学试卷上竟然有50多分的题目与这本书上的部分题目相近或完全一样。这种情况在前几年的高考中也是如此，不过分值没有这么大，足见这套书的价值和权威性。

下面笔者就全国高考数学（理工类）题与原书中的题目加以对照并做以分析。为方便读

者，高考题按原题序号编排，其中前面为高考题。

4，则tan2x（ ） 25

772424(A) (B)  (C) (D) 242477

11/．(P71)一、1．若cos，则tan2 21．已知x(,0),cosx

评析：考题给出了x的范围，答案唯一，而教书上的题没有给出变量的范围，答案有二，

但二者形式和本质完全一样。

2．圆锥曲线8sin的准线方程是（ ） 2cos

(A)cos2 (B) cos2 (C) sin2 (D) sin2

2/．(P296)四、2．抛物线8cos上有一点M，它的极径等于点M到准线的距离，2sin

求点M的极坐标。

评析：考题中的抛物线开口方向向右，而教书上题中的抛物线开口方向向上，并且考题

较简单。

4．函数y2sinx(sinxcosx)的最大值为（ ） (A) 12 (B) 21 (C)2 (D)2

4/．(P64)三、7．已知f(x)sinx(sinxcosx)，求f(x)的单调区间。

评析：二者形式和问法虽然不同，但化简方法完全一样，都要用到降次公式、二倍角公

式与和差化积公式。

225．已知圆C:(xa)(y2)4(a0)及直线l:xy30，当直线l被C截得的弦长为23时，则a（ ）

1

(A) 2 (B) 22 (C)21 (D)21

5/． (P239)三、1．过点P(6,4)且被圆x2y220截得长为62的弦所在直线方

程是 。

评析：考题主要考查了直线和圆的位置关系及弦长公式，属基本题型，和教书上的题目

大同小异。另外P238的典型例题2和P239的测试题第6题也属此种类型。

6．已知圆锥的底面半径为R，高为3R，在它的所有内接圆柱中，全面积的最大值是

（ ）

(A) 2R (B) 29285R (C)R2 (D)R2 432

6/．(P218)四、3．圆锥底面半径为5cm，高为12cm，为了使它的内接圆柱的全面积

最大，求内接圆柱的高。

评析：二者本质完全一样。

9．函数f(x)sinx,x[3

2,2]的反函数f1(x)（ ）

(A) arcsinx,x[1,1] (B) arcsinx,x[1,1]

(C) arcsinx,x[1,1] (D) arcsinx,x[1,1]

9/．(P273)三、1．ysinx,x[

评析：这两题完全一样。

222C2C32C4Cn11．lim（ ） nn(C1C1C1C1)234n32,2]的反函数是

(A) 3 (B)

/11 (C) (D)6 36n123nCnCnCnCn 11．(P的值。 122)二、2．已知an1242，求limnan

评析：教书上的题目为高考题提供了模版。事实上，考题中的两个组合数的求和都要用

mmm1到组合数的性质：Cn，这在2002年版《高二数学教学与测试》（新教材）1CnCn

教师用书P242例1中有：计算C3C4C5C10，紧接着P244备用题第5题又给出了

一般性结论：证明CnCn1Cn2CnpCnp1。

13．(xnnnnn1333319)展开式中x9的系数是。 2x

1n2(x)的展开式中，第四项与第七项的二项式系数相13/．(P二、1．（1）如果)1643x2

2

等，求展开式的中间项；

（2）求(x1

2x)8的展开式中的所有有理项。

评析：教书上的题远远难于考题，但形式相差无几。另外，象这种考题（属基本题型）

在前几年的高考中已出现过很多次，这里不再赘述，请读者自行查阅。

15．如图，一个地区分为5个行政区域，现给地图着色， 2 要求相邻区域不得使用同一颜色。现有4种颜色可供选择， 1 5 则不同的着色方法共有 种。（以数字作答） 3 4

15/．(P160)四、4．用五种不同的颜色给图中4个区域涂色，

如果每一区域涂一种颜色，相邻区域不能同色，那么共有

种涂色方法。

评析：考题和教书上的题仅调换了颜色数和区域数，本质一样。另外，P157 的 例1和

P162的测试题第3题属同种类型，在此不一一列出，望读者自行翻阅查看。 北

20．在某海滨城市附近海面有一台风。据监测，当前 南

台风中心位于城市O（如图）的东偏南(2)方 10

0向300km的海面P处，并以20km/h的速度向西偏北45方

向移动。台风侵袭的范围为圆形区域，当前半径为60km，并

以10km/h的速度不断增大，问几小时后该城市开始受到台风 的侵袭？

20/．(P236)二、3．据气象台预报，在C城正东300km的

海面上生成了一股台风，并且该台风中心正以每小时40km的

速度向西北方向移动。在距台风中心250km以内的地区将受其影响，问从现在起，经过多

长时间台风将影响C城，持续时间多久？（时间以小时计，最后结果保留小数点后一位有

效数字）。

评析：二者的背景完全一样，只是教书上的题目中，台风移动时范围不变，而考题中台

风在移动时范围在逐渐变化，增加了难度。另外，这个题在2001年版《高二数学教学与测

试》（旧教材）教师用书P207中就出现过。

顺便指出，在《高一数学教学与测试》和《高二数学教学与测试》中的同步训练题中，

也能找到与高考题完全类似甚至完全一样的题，请读者认真研究。

注：苏州大学《中学数学月刊》编辑部主编的这套《数学教学与测试》（高一、高二、

高三），我校已连用七年，效果非常好。这套书的特点笔者认为有以下几个特点：

1、作者阵容大，是全国千万个老师的智慧结晶；

2、知识内容细腻，与教材同步，难度适中，题型多样，适合不同层次的学生用；

3、错误极少，无论是印刷还是题目本身。 3

篇二:《高考模拟题》

高考模拟卷

考试时间120分钟 第I卷 （共105分）

（做在答题卡上,其中听力17-24题做在答题纸上，答题卡上17-24题空着不涂点）

I. Listening comprehension (30%)

Part A Short Conversations

Directions: In Part A, you will hear ten short conversations between two speakers. At the end of each

conversation, a question will be asked about what was said. The conversations and the questions will

be spoken only once. After you hear a conversation and the question about it, read the four possible

answers in your paper, and decide which one is the best answer to the question you have heard.

1. A. On Sunday B. On Monday C. On Saturday D. On Friday

2. A. In a classroom. B. In a stationery shop

C. At a supermarket. D. At a restaurant.

3. A. He can go bowling on Sunday night. B. He can go bowling on Tuesday.

C. He has to prepare for a text on Sunday. D. He has to study for a test on Tuesday.

4. A. Both Bill and Tom went to York. B. Both Bill and Tom went to London.

C. Bill went to York, and Tom went to London. D. Bill went to London, and Tom went to York.

5. A. Teacher and student. B. Doctor and patient.

C. Employer and applicant. D. Boss and clerk

6. A. The woman is satisfied with the food here. B. The man is satisfied with the steak here.

C. The man agrees with the woman. D. The woman‟s steak is overcooked.

7. A. The man will restart the computer first. B. The man will save the document first.

C. The woman will restart the computer first. D. The woman will save the document first t.

8. A. Location of some stores. B. Prices of some shoes.

C. Quality of some clothes. D. Storage of goods.

9. A. Jonathon used to be a popular child actor.

B. Jonathon was popular with young child actors.

C. Jonathon wrote some stories about popular actors.

D. Jonathon was popular because of his unusual childhood.

10. A. The new apartment is cheaper. B. He likes to listen to the radio.

C. He needs a quieter place. D. The present one is too expensive软件下载高考试题

Part B Passages软件下载高考试题

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 once. When you

hear a question, read the four possible answers in 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. Pizza B. Thai food. C. Local food.. D. Vegetables.

12. A. Going to the beach. B. Going overseas.

C. Enjoying local sights. D. Relaxing with the family.

13. A. Alternative music. B. 1980s rock music

C. 1970s rock music. D. Japanese music. 第 1 页

Questions 14 through 16 are based on the following passage.

14. A. It is listed in the teaching program. B. It is important to English teaching.

C. Effective listening results in good grades. D. It‟s more taught than any other subject.

15. A. Listening helps to send plain message. B. Listening develops personal relationship.

C. Listening has little to do with personal relationship.

D. Good listening helps to deliver an important speech.

16. A. Good listening means a good job. B. Listening requires understanding.

C. With good listening, you can receive message.

D. Listening is an important means of communication.

Part C Longer Conversations

Directions: In Part C, you will hear two longer conversations. The conversations will be read

twice. After you hear the conversations, you are asked to fill in the numbered blanks with the

information you have heard.

II. Grammar and Vocabulary

Section A ( 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. Let‟s go to the cinema. That‟ll take your mind _____ the problem for a while.

A. on B. away C. from D. off

26. Early children education is important in that the percentage of working mothers of children under 6

is growing faster than _____ of any other group of working mothers.

A. one B. those C. that D. the one

27. --- What‟s happened to Smith? He seems to be working hard for his exams.

--- I don‟t know. It‟s unbelievable that he _____ so hard.

A. shall work B. shall be working

C. should work D. should be working

28. The widening gap between the rich and the poor would become ______.

A. the most explosive the dynasty‟s problem B. the dynasty most explosive problem

C. the dynasty‟s most explosive problem 第 2页

D. the dynasty‟s the most explosive problem

29. I sense that there‟s a change in the way people celebrate the Spring Festival though the change _____ rather quietly.

A. has been taking place B. takes place

C. will be taking place D. had taken place

30. It was very kind of you to buy me the nice watch. As a matter of fact, you needn‟t have taken all

the trouble to do so, ______ you?

A. did B. need C. have D. do

31. --- May I go and play with Dick this afternoon, Mum?

--- No, you can‟t go out _________ your work is being done.

A. before B. until C. as D. the moment

32. His article deals with the life of a rare animal ______.

A. and most people didn‟t know existed B. that most people didn‟t know it existed

C. most people didn‟t know existed D. that most people didn‟t know existed

33. The court hears about 120 cases a year; visitors are welcome to see a case _________.

A. argued B. to be argued C. to be arguing D. being argued

34. On Sundays there were a lot of children playing in the park, _________ parents seated together

joking.

A. their B. whose C. which D. that

35. ______ people in western countries think we Muslim women are oppressed and controlled by men

is wrong and it makes me sad _____ people won‟t learn the truth by asking us how we feel.

A. That…why B. /…why C. /…what D. That…that

36. ______ to radioactive matter very often, the scientist was almost blind in the rest of her life.

A. Exposing B. Having exposed C. Exposed D. To expose herself

37. ---- Tom wasn‟t in the house when I telephoned him last night.

---- ______.

A. Nor he was B. So he was C. No, he wasn‟t D. So was he

38. Some sections of the coast are shaped in such a way _____ much higher tides than are experienced

in other areas.

A. as causing B. to cause C. only to cause D. as to cause

39. Sir Denis, who is 78, has made it known that much of his collection _____ to the nation.

A. has left B. is to leave C. leaves D. is to be left

40. ________, Dr. Baker is invited to deliver a speech on education and culture sometime in August.

A. Previously arranged B. Having previously been arranged

C. It having previously arranged D. As previously arranged

Section B ( 9%)

Directions : Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.

Sports shoes that work out whether their owner has done enough 第 3 页

exercise to permit time in front of the television have been devised in the UK.

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