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山西省中考试卷及答案

山西省中考试卷及答案
山西省中考试卷及答案

2008年山西省高中阶段教育教育招生统一考试

数 学

一、填空题(每小题2分,共20分)

1.-5的相反数是 。 2.在“2008北京”奥运会国家体育场“鸟巢”钢结构工程施工建设中,首先使用了我国科研人员自主研制的强度为460 000 000帕的钢材,这个数据用科学计数法表示为 帕。

3.计算:()=-?2

332x x 。 4.如图,直线a ∥b ,直线AC 分别交a 、b 于点B 、C ,直线

AD 交a 于点D 。若∠1=20 o , ∠2=65 o ,则∠3= 。

5.某校开展为地震灾区捐款活动,九年级(2)班第1 组8名

学生捐款如下(单位:元)

100 50 20 20 30 10 20 15

则这组数据的众数是 。

6.不等组?

??+<+≥-71403x x x 的解集是 。 7.计算:()=??? ??+---10212328 。

8.在方格纸上建立如图所示的平面直角坐标系,将△

ABO 绕点O 按顺时针方向旋转90 o ,得△A’B’O ,则点A

的对应点A’的坐标为 。

9.二次函数322-+=x x y 的图象的对称轴是直

线 。

10.如图所示的图案是由正六边形密铺而成,黑色正六边形周围第

一层有六个白色正六边形,则第n 层有 白色正六边形。

二、选择题(在下列各小题中,均给出四个备选答案,其中只有一

个是正确答案,请将正确答案的字母代号填入下表相应的空格内。

每小题3分,共24分)

题号

11 12 13 14 15 16 17 18 答案

11.一元二次方程032=+x x 的解是

A .3-=x

B .3,021==x x

C .3,021-==x x

D .3=x

12.下列运算正确的是

A .a

b a b 11+-=+- B .()2222b ab a b a ++=--

C

.12316+=+a a D .()222-=-

13.如图所示的图形是由7个完全相同的小立方体组成的立体图形,这个立体图形的主视力是

14.在平面直角坐标系中,点()12,7+--m 在第三象限,则m 的取值范围是

A .21

B .21->m

C .21-

D .2

1>m 15.抛物线5422---=x x y 经过平移得到22x y -=,平移方法是

A .向左平移1个单位,再向下平移3个单位

B .向左平移1个单位,再向上平移3个单位

C .向右平移1个单位,再向下平移3个单位

D .向右平移1个单位,再向上平移3个单位

16.王师傅在楼顶上的点A 处测得楼前一棵树CD 的顶端C 的俯角为60 o , 又知水平距离BD=10m ,楼高AB=24 m ,则树高CD 为

A .()31024-m

B .???? ??

-331024m C .()

3524-m D .9m 17.如图,第四象限的角平分线OM 与反比例函数()0≠=

k x

k y 的图象交于点A ,已知OA=23,则该函数的解析式为 A .x y 3=

B .x

y 3-= C .x y 9= D .x y 9-= 18.如图,有一圆心角为120 o 、半径长为6cm 的扇形,若将OA 、OB 重合后围成一圆锥侧面,那么圆锥的高是

A .24cm

B .35cm

C .62cm

D .32cm

三、解答题(本题共76分)

19.(本题8分)求代数式的值:212244632--+-÷+++x x x x x x ,其中6-=x 。

20.(本题6分)如图,在4× 3的网格上,由个数相同的白色方

块与黑色方块组成一幅图案,请仿照此图案,在下列网格中分别

设计出符合要求的图案(注:①不得与原图案相同;②黑、白方

块的个数要相同)。

21.(本题10分)“安全教育,警钟长鸣”,为此某校从14000名学生中随机抽取了200名学生就安全知识的了解情况进行问卷调查,然后按“很好”、“较好”、“一般”、“较差”四类汇总分析,并绘制了扇形统计图(如图)。

(1)补全扇形统计图,并计算这200名学生中对安全知识了解“较好”、“很好”的总人数。

(2)在图(2)中,绘制样本频数的条形统计图。

(3)根据以上信息,请提出一条合理化建议。

22.(本题10分)甲、乙两人在玩转盘游戏时,把转盘A 、B 分成3等份、4等份,并在每一份内标有数字(如图)。

游戏规则:同时转动两个转盘,当转盘停止后,指针所在区域的数字之积为奇数时,甲胜;

指针所在区域的数字之积为偶数时,乙胜。如果指针恰好在分割线上,则需重新转动转盘。

(1)用树状图或列表的方法,求甲获胜的概率。

(2)这个游戏规则对甲、乙双方公平吗?请判断并说明理由。

23.(本题8分)如图,已知CD 是△ABC 中AB 边上的高,以CD 为直径的⊙O 分别交CA 、CB 于点E 、F ,点G 是AD 的中点。求证:GE 是⊙O 的切线。

24.(本题8分)某文化用品商店用200元购进一批学生书包,面市后发现供不应求,商店又购进第二批同样的书包,所购数量是第一批购进数量的3倍,但单价贵了4元,结果第二批用了6300元。

(1)求第一批购进书包的单价是多少元?

(2)若商店销售这两批书包时,每个售价都是120元,全部售

出后,商店共盈利多少元?

25.(本题12分)如图,已知△ABC 是等边三角形,D 、E 分别

在边BC 、AC 上,且CD=CE ,连结DE 并延长至点F ,使EF=AE ,

连结AF 、BE 和CF 。

(1)请在图中找出一对全等三角形,用符号“≌”表示,并加

以证明。

(2)判断四边形ABDF 是怎样的四边形,并说明理由。

(3)若AB=6,BD=2DC ,求四边形ABEF 的面积。

26.(本题14分)如图,已知直线1l 的解析式为

63+=x y ,直线1l 与x 轴、y 轴分别相交于A 、B 两

点,直线2l 经过B 、C 两点,点C 的坐标为(8,0),

又已知点P 在x 轴上从点A 向点C 移动,点Q 在直

线2l 从点C 向点B 移动。点P 、Q 同时出发,且移动

的速度都为每秒1个单位长度,设移动时间为t 秒(101<

(1)求直线2l 的解析式。

(2)设△PCQ 的面积为S ,请求出S 关于t 的函数关系式。

(3)试探究:当t 为何值时,△PCQ 为等腰三角形?

2008山西省高中阶段教育教育招生统一考试数学答案 一、

1.5

2.8106.4?

3.518x

4.45 o

5.20元

6.2

7.22+

8.(2,3)

9.1-=x

10.6n

二、

题号

11 12 13 14 15 16 17 18 答案 C B C D D A D A

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