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2005年全国学科大联考模拟(一)数学试题

2005年全国学科大联考模拟(一)数学试题
2005年全国学科大联考模拟(一)数学试题

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全国学科大联考2005年中考模拟(一)

数 学 试 题

主命题人:黄德轩、政觉清、许伟、李忠武、王永志、艾健 主审核人:邓国伟、苏晗、朱武周 组织者:黄德轩 校对:朱武周、黄德轩 注意事项:

1.答第Ⅰ卷前,考生务必将自己的姓名、考场座位号、考试科目涂写在答题卡上。

2.答卷I 的选择题,选出答案后,将答案写到答题卡上,不能答在试题卷题目上。

3.本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。本试卷满分为120分,考试时间为120分钟.

卷Ⅰ(选择题,共24分)

一、选择题(本大题共12个小题,每小题2分,共24分.) 1.计算12-的结果是( ).

A .-2

B .2

C .2

1-

D .

2

1

2.如果a 与-3互为相反数,那么a 等于( ). A .3 B .-3 C .3

1 D .3

1-

3.计算3

2)(a 的结果是( ).

A .5

a B .6

a C .8

a D .9

a

4.已知?

??1,2==y x 是方程kx -y =3的解,那么k 的值是( ).

A .2

B .-2

C .1

D .-1

5.龟兔赛跑,它们从同一地点同时出发,不久兔子就把乌龟远远地甩在后面,于是兔子便得意洋洋地躺在一棵大树下睡起觉来.乌龟一直在坚持不懈、持之以恒地向终点跑着,兔子一觉醒来,看见乌龟快接近终点了,这才慌忙追赶上去,但最终输给了乌龟.下列图象中能大致反映龟兔行走的路程S 随时间t 变化情况的是( )

6. 某中学新实验楼铺设地面,已有正三角形形状的地砖,现打算购买另一种不同形状的正多边形地砖,与正三角形地砖在同一顶点处作平面镶嵌,则该学校不应该购买的地砖形状是( )

A 、正方形

B 、正六边形

C 、正八边形

D 、正十二边形

7. 在一网格中(如图),每个小网格的长为1的正方形。线段AB 的端点是网格中的两个格点,若网格中有一格点C ,使ABC 的面积为2个正方形的面积,则在图中我们可以确定符合条件的格点C 的个数为( ) A . 2个 B .3个 C .4个 D .5个

8.剪纸是中国的民间艺术.剪纸方法很多,下面是一种剪纸方法的图示(先将纸折叠,然后再剪,展开即得到图案):下面四个图案中,不能用上述方法剪出的是 ( )

9.在日常生活中,你会注意到有一些含有特殊数字规律的车牌号码,

等,这些牌照中的五个数字都是关于中间的一个数字“对称”的,给以对称的美的感受,我们不妨把这样的牌照叫做“数字对称”牌照。如果让你负责制作只以8和9开头且有五个数字的“数字对称”牌照,那么最多可制作

A. 2000个

B.1000

个 C.200个 D.100个

10.一个矩形的面积为3,则这个矩形的一边长y 与它的邻边长x

的函数关系的图象大致是( )

A

D

C

B

11.n 个连续自然数按规律排成右表: 0 3 → 4 7 → 8 11 …

↓ ↑ ↓ ↑ ↓ ↑

1 →

2 5 → 6 9 → 10 根据规律, 从2004到2006,

箭头的方向依次应为( )

A 、 ↑→

B 、↓→

C 、→↑

D 、 →↓

12.一风筝厂准备购进甲、乙两种规格相同但颜色不同的布料生产

一批形状如图所示的风筝,点E ,F ,G ,H 分别是四边形

ABCD 各边的中点.其中阴影部分用甲布料,其余部分用乙布

料(裁剪两种布料时,均不计余料).若生产这批风筝需要甲 布料30匹,那么需要乙布料( )

A .15匹

B .20匹

C .30匹

D .60匹

卷II (非选择题,共96分)

二、填空题:本大题共10个小题;每小题2分,共20分.把答案写在题中横线上.

13.亲爱的同学们,在我们的生活中处处有数学的身影. 请看图,折叠一张三角形纸片,把三角形的三个角拼在 一起,就得到一个著名的几何定理,请你写出这一定理 的结论:“三角形的三个内角和等于_______°.”

14.“世界银行全球扶贫大会”于2004年5月26日在上海开幕.从会上获知,我国国民生产总值达到11.69万亿元,人民生活总体上达到小康水平,其中11.69万亿用科学记数法表示应为 15.点(1,-2)关于原点的对称点的坐标为 ____ 16.设有反比例函数()()11221,,,k y x y x y x

+=

、为其图象上的两点,若120x x <<时,12y y >,则k

的取值范围是__________________

17.写出一个只含字母a 的代数式(要求:(1)要使此代数式有意义,字母a 必须取全体负数;(2)此

代数式的值恒为负数): 。 18.函数y =

x 的取值范围是___________________。

19.一辆客车已晚点6分钟,如将速度每小时增加10千米,那么继续行驶20千米便可正点到达.如果

( 第 题图 ) 11 12题图

设客车提速后的速度为每小时x 千米,那么解决这个问题所列的方程是 . 20.某商场在促销期间规定:商场内所有商品按标价的80%出售,同时,当顾客在该商场内消费满一定金额后,按如下方案获得相应金额的奖券.(奖券购物不再享受优惠)

根据上述促销方法,顾客在该商场购物可获得双重优惠,如果小胡在该商场购标价450元的商品,他获得的优惠额为_________元.

21.△ABC 中,AB =8,AC =6,D 在AC 上,且CD =2,如果要在AB 上找一点E ,使△ADE 与△ABC 相似,则

BE =

22.如果一元二方程x 2

-2x -m =0无实数根,则一次函数y =mx +m -2的图象不经过第 象限. 中学中.考.资.源.网全国学科大联考2005年中考模拟(一)

数 学 试 题 答 题 纸

一、请将选择题正确答案填入下表中:(每题2分,共24分) 考号

----------------------------------------------------------

二、 请将填空题正确答案填入下面的空格内(每小题2分,共20分).

13、 14、 15、

16、 17、 18、

19、 20、

21、 22、

三、本大题共

9个小题;共76分.解答应按要求写出文字说明、或证明过程或演算步骤.

本小题满分8分)

先化简,再选一个你喜欢的x 值代入求值:2

2

2

412(

).

44

2

1

x x x x x x x ---

-+-+ .

本小题满分8分)

如图,下面四个条件中,请你以其中两个为已知条件,另两个中选一个作为结论,给出一个正确命题.(只需写出一种情况)① AE =AD ;② AB =AC ;③OB =OC ④∠B =∠C .

已知: 求证: 证明:

A

D

B

O C

E

22题图

25. (本小题满分8分)

已知:关于x 的方程x 2

-2mx+

4

1n 2

=0,其中m 、n 分别是一个等腰三角形的腰和底边长.

(1)求证:这个方程有两个不相等的实数根;(4分)

(2)若该方程两实数根差的绝对值为8,且等腰三角形的周长为16,求m 、n 的值. (4分)

本小题满分8分)

某职校学生进行打字比赛,每班派5名学生参加,按团体总分多少排列名次,在规定时间内每人打100字以上(含100)为优秀.下表是成绩最好的甲班和乙班5名学生的比赛数据(单位:个):

请你回答下列问题: (1)计算两班的优秀率; (2)求两班比赛数据的中位数; (3)估计两班比赛数据的方差哪一个小?

(4)根据以上三条信息,你认为应该把冠军奖状发给哪一个班级?简述理由.

本小题满分8分)

如图,在湖边高出水面50米的山顶A 处望见一艘飞艇停留在湖面上空某处,观察到飞艇底部标志P 处的仰角为45°,又观其在湖中之像的俯角为60°。试求飞艇离湖面的高度h (观察时湖面处于平静状态)。(结果保留整数)(参考数据:2≈1.414,3≈

1.732),

28

本小题满分8分)

(1)平行四边形是对称图形.能把平行四边形均分为面积相等的两部分的直线有条.(2)如图○1,在一平行四边形木板上有一圆形窟窿.请在图上画一条直线,若沿此线锯开,可将木板分为面积相等的两部分.

实践:如图○2、○3,在一块平行四边形ABCD的荒地内有一块肥沃的矩形菜地,现要将荒地和菜地平均分给两家承包,请设计两种分地方案,分别写出理由,并保留作图痕迹.(每种方案至多用两条线分割)

图○1

A

图○2

A

图○3

29.

本小题满分8分)

如图,R t A B C ?的锐角顶点是直线m x y +=与双曲线x

m y =在第一象限的交点,且S A O B ?=3

(1)求m 的值 (2)求S A B C ?的值

本小题满分8分)

在△ABC 中,BC =6,CA =8,AB =10,∠ABC 的平分线BD 交AC 于点D ,DE ⊥DB 交AB 于点E .

(1)求证:△ABC 是直角三角形;

(2)设⊙O 是△BDE 的外接圆.求证:AC 是⊙O 的切线; (3)设⊙O 交BC 于点F ,连结EF ,求AE 的长和EF ∶AC 的值.

(本题满分12分)

已知:抛物线bx ax y +=2

与x 轴的一个交点为B ,顶点A 在直线y =

上,O 为坐标原点。

(1)证明:△OAB 为等边三角形;

(2)若△OAB 的内切圆半径为1,求出抛物线的解析式;

(3)在抛物线上是否存在点P,使△POB是直角三角形,若存在,请求出点P的坐标;若不存在,请说明理由。

高三四校联考数学试题(理科)

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