数 学 试 题 卷
考生须知:1.本试卷分为试题卷和答题卷两部分.
2.试题卷共4页,满分150分.考试时间120分钟.
3.答题卷共4页,所有答案必须写在答题卷上............,写在试题卷上的无效..........
4.答题前,考生应先在答题卷密封区内认真填写准考证号、姓名、考场号、 座位号、地(州、市、师)、县(市、区、团场)和学校.
5.答题时可以使用科学计算器.......... 一、精心选择(本大题共8小题,每小题5分,共40分.每小题所给四个选项中,只有一个
是正确的.) 1.8-的相反数是
A.8
B.8-
C.18
D.18
- 2.计算23()a -的结果是
A.5a -
B.6a
C.6a -
D.5
a
3.如右图,小明课间把老师的三角板的直角顶点放在黑板的两 条平行线a b 、上,已知155∠=°,则2∠的度数为 A.45° B.35° C.55° D.125°
4.今年我区约有202 000名应届初中毕业生参加学业水平考试, 202 000用科学记数法表示为 A.6
0.20210? B.3
20210? C.4
20.210? D.5
2.0210?
5.如果从小军等10名大学生中任选1名作为“世博会”志愿者,那么小军被选中的概率是
A.1
B.
111 C. 110 D. 1
9
6.如图(1)是一张Rt ABC △纸片,如果用两张相同
的这种纸片恰好能拼成一个正三角形,如图(2),那 么在Rt ABC △中,sin B ∠的值是
A.12
C.1
D.32 7.若点1122()()A x y B x y ,、,在反比例函数3
y x
=-
的图象上,且120x x <<,则12y y 、和0的大小关系是
A.120y y >>
B.120y y <<
C.120y y >>
D.120y y <<
新疆维吾尔自治区 新疆生产建设兵团
2010年初中学业水平考试
第3题图
A
B C
图(1)
图(2)
8.如右图,王大爷家屋后有一块长12m ,宽8m 的矩形空地, 他在以BC 为直径的半圆内种菜,他家养的一只羊平时拴在 A 处,为了不让羊吃到菜,拴羊的绳长可以选用 A.3m B.5m C.7m D.9m
二、合理填空(本大题共6个小题,每小题5分,共30分) 9.
=___________.
10.写出右图中所表示的不等式组的解集:____________. 11.甲、乙两位棉农种植的棉花,连续五年的单位面积产量 (千克/亩)统计如下图,则产量较稳定的是棉农_________.(填甲或乙)
12.利用1个a a ?的正方形,1个b b ?的正方形和2个a b ?的矩形可拼成一个正方形(如图所示),从而可得到因式分解的公式__________. 13.长方体的主视图和左视图如下图所示(单位:cm ),则其俯视图的面积是_________cm 2.
14.抛物线2
y x bx c =-++的部分图象如图所示,若0y >,则x 的取值范围是__________.
三、准确解答(本大题共有10题,共80分) 15.(6分)解方程:2
2760x x -+=
16.(6分)先化简,再求值22111
x x x
x x x ??-÷ ?
---??,
其中1x = A
B
C 8m
12m
D
P
O
(第11题图)
(第12题图) (第13
题图)
(第14题图) O x y 1
-1 3
17.(6分)用四块如下图(1)所示的正方形卡片拼成一个新的正方形,使拼成的图案是一个轴对称图形,请你在图(2)、图(3)、图(4)中各画出一种拼法(要求三种画法各不相同,且其中至少有一个既是轴对称图形,又是中心对称图形)
18.(6分)小王将一黑一白两双相同号码的袜子一只一只地扔进抽屉里,当他随意从抽屉里拿出两只袜子时,恰好成双与不成双的机会是多少?请你用树形图求解.
19.(8分)2010年4月14日我国青海玉树地区发生强烈地震,急需大量赈灾帐篷.某帐篷生产企业接到任务后,加大生产投入,提高生产效率,实际每天生产帐篷比原计划多200顶,现在生产3 000顶帐篷所用的时间与原计划生产2 000顶的时间相同.现在该企业每天能生产多少顶帐篷?
(
(2)补全右面折线统计图;
(3)请你根据下面两个要求对这两种瓜果在去年3月份至8月份的销售情况进行分析:
①根据平均数和方差分析;
②根据折线图上两种瓜果销售量的趋势分析.
21.(8分)圆心角都是90°的扇形AOB与扇形COD如图所示那样叠放在一起,连结AC BD
、.
(1)求证:AOC BOD
△≌△;
(2)若3
AO cm,OC=1cm,求阴影部分的面积.
(第20题图)
A
B
C
D
O
(第21题图)
(2)(3)(4)
(1)
22.(10分)如图(1),某灌溉设备的喷头B 高出地面1.25m ,喷出的抛物线形水流在与喷头底部A 的距离为1m 处达到距地面最大高度2.25m ,试在恰当的直角坐标系中求出与该抛物线水流对应的二次函数关系式.
学生小龙在解答图(1)所示的问题时,具体解答如下:
①以水流的最高点为原点,过原点的水平线为横轴,过原点的铅垂线为纵轴,建立如图(2)所示的平面直角坐标系;
②设抛物线水流对应的二次函数关系式为2y ax =;
③根据题意可得B 点与x 轴的距离为1m ,故B 点的坐标为(1-,1);
④代入2y ax =得11a
-=·,所以1a =-; ⑤所以抛物线水流对应的二次函数关系式为2y x =-.
数学老师看了小龙的解题过程说:“小龙的解答是错误的”.
(1)请指出小龙的解答从第_________步开始出现错误,错误的原因是什么? (2)请你写出完整的正确解答过程. 23.(10分)如图是一个量角器和一个含30°角的直角三角形放置在一起的示意图,其中点B 在半圆O 的直径DE 的延长线上,AB 切半圆O 于点F ,且.BC OE = (1)求证:DE CF ∥;
(2)当2OE =时,若以O B F 、、为顶点的三角形与ABC △相似,求OB 的长.
(3)若2OE =,移动三角板ABC 且使AB 边始终与半圆O 相切,直角顶点B 在直径DE 的延长线上移动,求出点B 移动的最大距离.
24.(12分)张师傅在铺地板时发现,用8块大小一样的长方形瓷砖恰好可以拼成一个大的长方形,如图(1).然后,他用这8块瓷砖又拼出一个正方形,如图(2),中间恰好空出一
图(1)
图(2) A B C O (第23题图) D
F E
个边长为1的小正方形(阴影部分),假设长方形的长为y ,宽为x ,且.y x
(1)请你求出图(1)中y 与x 的函数关系式; (2)求出图(2)中y 与x 的函数关系式;
(3)在图(3)中作出两个函数的图象,写出交点坐标,并解释交点坐标的实际意义;
(4)根据以上讨论完成下表,观察x 与y 的关系,回答:如果给你任意8个相同的长方形,你能否拼出类似图(1)和图(2)的图形?说出你的理由.
图(1) 图(2) 图(3)
数学试卷参考答案及评分标准
(满分150分)
说明:本参考答案供阅卷教师评卷时使用.阅卷中,考生如有其它解法,只要正确、合理,
均可得相应分值.
二、合理填空(本大题共6小题,每小题5分,共30分)
10.32x -<≤ 11.乙 12.2
2
2
2()a ab b a b ++=+ 13.12 14.31x -<<
三、准确解答(本大题共10小题,共80分) 15.(6分)解法不唯一. 例解:2
7
302x x -+= 274949321616x x -+=-+ ····································································2′
271()416x -= ··················································································4′
7144
x -=± ····················································································5′
12x = 232
x = ·········································································6′ 16.(6分)
解:2222111111x x x x x x x x x x x x
????--÷=+ ? ?
-----????· =221
1x x x x x +--· ················································2′ =
(2)1
1x x x x x
+--· ···························
············
·····
····3′ =2x + ····························································4′
当1x =时,原式123+= ·················································6′ 17.(6分)解法不唯一,例解如下:
新疆维吾尔自治区 新疆生产建设兵团
2010年初中学业水平考试
每个图形2′,共6′ 18.(6分)
··············································································································3′
()1
3P =成双 ································································································5′ ()
23
P =不成双 ·····························································································6′ 19.(8)分
例解:设现在该企业每天生产x 顶帐篷,则原计划每天生产(200)x -顶帐篷 ·········1′
由题意得:
3 000 2 000
200
x x =- ·······································································4′ 解得600x = ····························································································6′ 经检验600x =是原方程的解 ·······································································7′
即该企业现在每天生产600顶帐篷 ································································8′ 20.(8分)
··············································································································3′ (2)如图 ················································
··
·············
···············································6′
(1) (2) (3)
24.(12分)解法不唯一
解:(1)由图(1)得:35y x = 5
3
y x =
··················································2′ (2)由图(2)得281(2)xy x y +=+ ····························································3′ 整理得:2(2)1x y -=
21x y -=±
53y x = 5
213
x x ∴-=- 30x =-<
21x y ∴-=-不成立 ·················································································4′
即21y x =- ·····························································································5′ (3)
··············································································································7′ 交点坐标(3,5)······················································································8′ 实际意义解答不唯一
例①:瓷砖的长为5,宽为3时,能围成图(1),图(2)的图形 ························9′ 例②:当瓷砖长为5,宽为3时,围成图(2)的正方形中的小正方形边长为1. (4)
············································································································ 11′ 情况①:不能,长方形的长与宽若不能满足5
3
y x =,则不能 情况②:能,长方形的长与宽只要满足5
3
y x =
即可 情况③:综合上述两种说法 只要符合其中一种情况均给分 ···································································· 12′