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2010年杭州文澜中学中考模拟卷

2010年杭州文澜中学中考模拟卷
2010年杭州文澜中学中考模拟卷

2010年杭州文澜中学中考模拟卷

数 学

考生须知:

1. 本试卷分试题卷和答题卷两部分,满分120分,考试时间120分钟.

2. 答题时,应该在答题卷指定位置内写明校名,姓名和准考证号.

3. 所有答案都必须做在答题卷标定的位置上,请务必注意试题序号和答题序号相对应.

4. 考试结束后,上交试题卷和答题卷.

试 题 卷

一. 仔细选一选(本题有10个小题,每小题3分,共30分)

下面每小题给出的四个选项中,只有一个是正确的。注意可以用多种不同的方法来选取正确答案。 1. 如果b a c >+,那么a b c ,,三个实数必定( )

A .b a c >+

B .b a c <-+

C .22

b a

c >+()

D .不能确定

2. 为了解我杭州市参加中考的15 000名学生的视力情况,抽查了1 000名学生的视力进行统计分析.下面四个

判断正确的是( )

A .15 000名学生是总体

B .1 000名学生的视力是总体的一个样本

C .每名学生是总体的一个个体

D .以上调查是普查

3. 如图所示,正方形ABCD 中,点E 是CD 边上一点,连结AE ,交对角线BD 与F ,

连结CF ,则图中全等三角形共有 A .1对

B .2对

C .3对

D .4对

4. 有以下四个说法:①两边和其中一边上的中线(或第三边上的中线)对应相等的两个三角形全等;②两角和

其中一角的角平分线(或第三角的角平分线)对应相等的两个三角形全等;③两边和其中一边上的高(或第三边上的高)对应相等的两个三角形全等;④刘徽计算过π的值,认为其为10 .其中正确的有 A .1个

B .2个

C .3个

D .4个

5. 反比例函数与二次函数在同一平面直角坐标系中的大致图象如图所示,它们的解析式可能分别是( ).

A .y =k

x

,y =kx 2-x

B .y =k

x

,y =kx 2+x

C .y =-k

x ,y =kx 2+x

D .y =-k

x

,y =-kx 2-x

6. 在数轴上,点A 所表示的实数为3,点B 所表示的实数为a ,⊙A 的半径为2.下列说法中不正确...

的是( ) A .当5a <时,点B 在⊙A 内 B .当15a <<时,点B 在⊙A 内

C .当1a <时,点B 在⊙A 外

D .当5a >时,点B 在⊙A 外

7. 如图,P 是Rt △ABC 斜边AB 一点(A 、B 点除外),过P 点作一直线,使截得的三角形与Rt △ABC 相似,这

样的直线可以作( ) A .1条

B .2条

C .3条

D .4条

8. 如图,线段AB =CD ,AB 与CD 相交于点O ,且∠AOC =60°,则AC +BD 与AB

的大小关系是

A .AC +BD <A

B B .A

C +B

D >AB

C .AC +B

D =AB D .AC +BD ≥AB

9. 如图,点E 、F 是以线段BC 为公共弦的两条圆弧的中点,BC =6.点A 、D 分别为线段EF 、BC 上的动点.连结

AB 、AD ,设BD =x ,AB 2-AD 2=y ,下列图像中,能表示y 与x 的函数关系的图象是

10.

D

C E B

(第3题)

(第8题)

(第5题)

P n 的“绝对坐标”为 A

.(

2

n n --或()20n ,

B .()20n

或()

02n , C .(

)20n

或(

2n n --

D

.(

2

n n --或()20n

或()02n

二. 认真填一填(本题有6个小题,每小题4分,共24分)

要注意认真看清楚题目的条件和要填写的内容,尽量完整地填写答案

11. 抛物线2

5289y x =++()的顶点坐标为______________.

12. 因式分解:322363x x y xy -+=__________________

13. 从1到10这十个自然数中,任意取出两个数,它们的积大于10的概率是 .

14. 平面上A 、B 两点到直线l 的距离分别是5与3,则线段AB 的中点C 到直线l 的距离为___________. 15. 在平面直角坐标系中,我们称边长为1、且顶点的横、纵坐标均为整数的正方形为单位格点正方形.若菱形

A n

B n

C n

D n 的四个顶点坐标分别为(-2n ,0),(0, n ),(2n ,0),(0,-n )(n 为正整数),则菱形A n B n C n D

n 能覆盖的单位格点正方形的个数为 (用含有

n 的式子表示).

16. 在△AOB 中,AB =OB =2,△COD 中,CD =OC =3,∠ABO =∠DCO .连

结AD 、BC ,点M 、N 、P 分别为OA 、OD 、BC 的中点.①若A 、O 、C 三点在同一直线上,且∠ABO =2α,则AD BC =_____________(用含有α

的式子表示);②固定△AOB ,将△COD 绕点O 旋转,PM 最大值为____________.

三. 全面答一答(本题有8个小题,共66分)

解答应写出文字说明、证明过程或推演步骤。如果觉得有的题目有点困难,那么把自己能写出的解答写出一部分也可以。

17. (本小题满分6分)

如图为一个棱长为10cm 的木制立方体和一个直径为12cm 的球,能否在立方体上挖一个洞,使球通过?若能,请简单说明或画图示意;若不能,请说明理由.

18. (本小题满分6分)

如图,⊙O 中,弦AB 、CD 相交于AB 的中点E ,连接AD 并延长至

点F ,使DF =AD ,连接BC 、BF .

(1)求证:△CBE ∽△AFB ; (2)当58BE FB =时,求CB AD 的值.

19. (本小题满分6分)

在△ABC 中, BC =a ,BC 边上的高h =a 2,沿图中线段DE 、CF 将△ABC 剪开,分成的三块图形恰能拼成正方形CFHG ,如图1所示. 请你解决如下问题:

已知:如图2、图3,在△A ′B ′C ′中, B ′C ′=a ,B ′C ′边上的高h =

a 2

1

.请你设计两种不同的分割方法,将△A ′B ′C ′沿分割线剪开后,所得的三块图形恰能拼成一个正方形,请在图2、图3中,画出分割线及拼接后的图形.

20. (本小题满分8分)

如图,已知边长为a 的正方形ABCD .

(1)只用直尺(没有刻度)和圆规,求作该正方形绕点A 逆旋转30°后的正方形AB 1C 1D 1; (2)求两正方形不重合部分的面积.

(第15题)

B

A

P

C

O

M N

D

F

B

A ′

B ′

C ′

图2 A ′

B ′

C ′

图3

D

C

(第19题)

(第18题)

图1

21. (本小题满分8分)

文澜中学学生会为了解该校学生喜欢球类活动的情况,采取抽样调查的方法,从足球、乒乓球、篮球、排球等四个方面调查了若干名学生的兴趣爱好,并将调查的结果绘制成如下的两幅不完整的统计图(如图1,图2要求每位同学只能选择一种自己喜欢的球类;图中用乒乓球、足球、排球、篮球代表喜欢这四种球类中的某一种球类的学生人数),请你根据图中提供的信息解答下列问题: (1)在这次研究中,一共调查了多少名学生?

(2)喜欢排球的人数在扇形统计图中所占的圆心角是多少度? (3)补全频数分布折线统计图.

22. (本小题满分10分)

随着人民生活水平的不断提高,我市家庭轿车的拥有量逐年增加.据统计,某小区2006年底拥有家庭轿车64辆,2008年底家庭轿车的拥有量达到100辆.

(1)若该小区2006年底到2009年底家庭轿车拥有量的年平均增长率都相同,求该小区到2009年底家庭轿

车将达到多少辆?

(2)为了缓解停车矛盾,该小区决定投资15万元再建造若干个停车位.据测算,建造费用分别为室内车位

5000元/个,露天车位1000元/个,考虑到实际因素,计划露天车位的数量不少于室内车位的2倍,但不超过室内车位的2.5倍,求该小区最多可建两种车位各多少个?试写出所有可能的方案.

23. (本小题满分10分)

已知:反比例函数2y x =和8y x = 在平面直角坐标系xOy 第一象限中的图象如图所示,点A 在8

y x =的图象上,AB ∥y 轴,与2y x =

的图象交于点B ,AC 、BD 与x 轴平行,分别与2y x =、8

y x

=的图象交于点C 、D . (1)若点A 的横坐标为2,求梯形ACBD 的对角线的交点F 的坐标;

(2)若点A 的横坐标为m ,比较△OBC 与△ABC 的面积的大小,并说明理由; (3)若△ABC 与以A 、B 、D 为顶点的三角形相似,请直接写出点A 的坐标.

24. (本小题满分12分)

如图,在平面直角坐标系xOy 中,一次函数333+=x y 的图象与x 轴交于点A ,与y 轴交于点B ,点C 的坐标为(3,0),连结BC . (1)求证:△ABC 是等边三角形;

(2)点P 在线段BC 的延长线上,连结AP ,作AP 的垂直平分线,垂足为点D ,并与y 轴交于点E ,分别

连结EA 、EP .

①若CP =6,直接写出∠AEP 的度数;

②若点P 在线段BC 的延长线上运动(P 不与点C 重合),∠AEP 的度数是否变化?若变化,请说明理由;若不变,求出∠AEP 的度数;

(3)在(2)的条件下,若点P 从C 点出发在BC 的延长线上

匀速运动,速度为每秒1个单位长度. EC 与AP 于点F ,设△AEF 的面积为S 1,△CFP 的面积为S 2,y =S 1-S 2,运动时间为t (t >0)秒时,求y 关于t 的函数关系式.

图2

乒乓球 20%

足球

排球

篮球

40%

图1

(第24题) (第23题)

2019年杭州文澜中学中考模拟卷

2019年杭州文澜中学中考模拟卷 数 学 考生须知: 1. 本试卷分试题卷和答题卷两部分,满分120分,考试时间120分钟. 2. 答题时,应该在答题卷指定位置内写明校名,姓名和准考证号. 3. 所有答案都必须做在答题卷标定的位置上,请务必注意试题序号和答题序号相对应. 4. 考试结束后,上交试题卷和答题卷. 试 题 卷 一. 仔细选一选(本题有10个小题,每小题3分,共30分) 下面每小题给出的四个选项中,只有一个是正确的。注意可以用多种不同的方法来选取正确答案。 1. 如果b a c >+,那么a b c ,,三个实数必定( ) A .b a c >+ B .b a c <-+ C .22 b a c >+() D .不能确定 2. 为了解我杭州市参加中考的15 000名学生的视力情况,抽查了1 000名学生的视力进行统计分析.下面四个 判断正确的是( ) A .15 000名学生是总体 B .1 000名学生的视力是总体的一个样本 C .每名学生是总体的一个个体 D .以上调查是普查 3. 如图所示,正方形ABCD 中,点E 是CD 边上一点,连结AE ,交对角线BD 与F , 连结CF ,则图中全等三角形共有 A .1对 B .2对 C .3对 D .4对 4. 有以下四个说法:①两边和其中一边上的中线(或第三边上的中线)对应相等的两个三角形全等;②两角和 其中一角的角平分线(或第三角的角平分线)对应相等的两个三角形全等;③两边和其中一边上的高(或第三边上的高)对应相等的两个三角形全等;④刘徽计算过π的值,认为其为10 .其中正确的有 A .2个 B .3个 C .4个 D .5个 5. 反比例函数与二次函数在同一平面直角坐标系中的大致图象如图所示,它们的解析式可能分别是( ). A .y =k x ,y =kx 2-x B .y =k x ,y =kx 2+x C .y =-k x ,y =kx 2+x D .y =-k x ,y =-kx 2-x 6. 在数轴上,点A 所表示的实数为3,点B 所表示的实数为a ,⊙A 的半径为2.下列说法中不正确... 的是( ) A .当5a <时,点B 在⊙A 内 B .当15a <<时,点B 在⊙A 内 C .当1a <时,点B 在⊙A 外 D .当5a >时,点B 在⊙A 外 7. 如图,P 是Rt △ABC 斜边AB 一点(A 、B 点除外),过P 点作一直线,使截得的三角形与Rt △ABC 相似,这 样的直线可以作( ) A .1条 B .2条 C .3条 D .4条 8. 如图,线段AB =CD ,AB 与CD 相交于点O ,且∠AOC =60°,CE 是由AB 平移 所得,则AC +BD 与AB 的大小关系是 A .AC +BD <A B B .A C +B D >AB C .AC +B D =AB D .AC +BD ≥AB 9. 如图,点E 、F 是以线段BC 为公共弦的两条圆弧的中点,BC =6.点A 、D 分别为线段EF 、BC 上的动点.连结 AB 、AD ,设BD =x ,AB 2-AD 2=y ,下列图像中,能表示y 与x 的函数关系的图象是 10. D C E B (第3题) (第8题) (第5题)

杭州市文澜中学七年级上学期英语真题试卷【1.10周末练习】

Weekend Exercise (2017-1-10) 单项选择: ---I like biology and history. ---Why do you like_______? A. they B. it C. their D. them Ann ________ English at 9:00 o’clock. A.have B. has C. takes D. bring ________ is the first day of a week. A.Sunday B. Monday C. Tuesday D. Wednesday ---______ does she like music? ---Because it’s relaxing. A.Why B. What C. Which D. How ---_______? ---It’s Monday. A.What’s the time B. What day is it today C. Is it Monday D. What’s the date _______ is your English teacher? A.Where B. What C. How D. Who ---When do you have math? ---I have it _______ Monday, Tuesday and Thursday. A.on B. at C. on D. of It is time ______ go home. A.for B. and C. to D. about I have history ______ the afternoon of Monday. A. in B. at C. on D. for Mr. Zhang teaches _______ Chinese. We like ______ class very much. A.me, her B. me, his C. us, his D. us, her Do you have ______ today? A.Chinese B. a Chinese C. the Chinese D. an Chinese Mr. Wang and Mrs. Li are both _______. A.English teachers B. Englishes teachers C. Englishes teacher D. Englishs teachers This is ______ Li. He has three children.

《含中考21套》浙江省杭州市文澜中学2019-2020学年中考英语模拟试卷含解析

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