陕西省10年中考数学试题word版附带详细答案.docx
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陕西省10年中考数学试题word版附带详细答案.docx
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陕西省10年中考数学试题word版附带详细答案
陕西省2010年中考数学试题(word版附带详细答案)
2010年陕西省初中毕业学业考试 一、1.?
13?
选择题 113 B.?
3 C. D.?
3 2.如图,点O在直线AB上,且OC⊥OD.若?
COA?
36°,则?
DOB的大小为° B.54°° D.72°3.计算(?
2a2·)3a的结果是 A.?
6a2 B.?
6a3 4.如图是正方形和圆锥组成的几何体,它的俯视图是 5.一个正比例函数的图象经过点,它的表达式为?
?
?
3232x ?
23x 23x x ?
?
6.中国2010年上海世博会充分体现着“城市,让生活更美好”的主题.据统计:
5月1日到5月7日入园人数分别为,,,,,,这组数据的中位数和平均数分别为 A., B.,C., D., 1?
1?
x≥0,?
7.不等式组?
2的解集是 ?
3x?
2?
?
1?
A.?
1?
x≤2 B.?
2≤x?
1C.x?
?
1或x≥2 D.?
2≤x?
-1 8.若一个菱形的边长为2,则这个菱形两条对角线长的平方和为A.16 B.8 1 C.4 D.1 9.如图,点A、B、P在⊙O上,且?
APB?
50°.若点M是⊙O上的动点,要使 △ABM为等腰三角形,则所有符合条件的点M有 A.1个 B.2个C.3个 D.4个 10.已知抛物线C:
y=x2+3x?
10,将抛物线C平移得到抛物线C?
.若两条抛物线C、C?
关于直线 x?
1对称,则下列平移方法中,正确的是 A.将抛物线C向右平移 52个单位 B.将抛物线C向右平移3个单位 C.将抛物线C向右平移5个单位 D.将抛物线C向右平移6个单位 第二部分 二、填空题 ?
2,?
3,0,π五个数中,最小的数是_______________.11.在1,12.方程x2?
4x?
0的解是______________. 13.如图,在△ABC中,D是AB边上一点,连接CD.要使△ADC与△ABC相似,应添加的条件是______________. 14.如图是一条水平铺设的直径为2米的通水管道横截面,其水面宽为米,则这条管道中此时水最深为_________米. B(x2,y2)都在反比例函数y?
15.已知A(x1,y1), 6x的图象上,若x1x2?
?
3,则y1y2的值为__________. 16.如图,在梯形ABCD中,DC∥AB,?
A?
?
B?
90°.若AB?
10,AD?
4, DC?
5,则梯形ABCD的面积为____________. 三、解答题 2 17.化简:
18. 如图,A、B、C三点在同一条直线上,AB?
2BC.分别以AB、BC为边作正方形ABEF和正方形BCMN,连接FN,EC.求证:
FN?
EC. 19. 某县为了了解“五一”期间该县常住居民的出游情况,有关部分随机调查了1600名常住居民,并根据调查结果绘制了如下统计图:
根据以上信息,解答下列问题:
补全条形统计图.在扇形统计图中,直接填入出游主要目的是采集发展信息人数的百分数;若该县常住居民共24万人,请估计该县常住居民中,利用“五一”期间出游采集发展信息的人数; 综合上述信息,用一句话谈谈你的感想. 3 mm?
n?
nm?
n?
2mnm?
n22. 20. 在一次测量活动中,同学们要测量某公园湖的码头A与它正东方向的亭子B之间的距离,如图.他们选择了与码头A、亭子B在同一水平面上的点P,在点P处测得码头A位于点P北偏西30°方向,亭子B位于点P北偏东43°方向;又测得点P与码头A之间的距离为200米.请你运用以上测得的数据求出码头Atan43°≈)与亭子B之间的距离 某蒜薹生产基地喜获丰收,收获蒜薹200吨.经市场调查,可采用批发、零售、冷库储藏后销售三种方式,并且按这三种方式销售,计划每吨平均的售价及成本如下表:
销售方式售价成本 若经过一段时间,蒜薹按计划全部售出获得的总利润为y,蒜薹零售x,且零售量是批 批发3000700零售45001000储藏后销售550012004 发量的. 31求y与x之间的函数关系式; 于条件上限制,经冷库储藏售出的蒜薹最多80吨,求该生产基地按计划全部售完蒜薹获得的最大利润. 22. 某班毕业联欢会设计了即兴表演节目的摸球游戏.游戏采用了一个不透明的盒子,里面装有五个分别标有数字1、2、3、4、5的乒乓球.这些球除数字外,其它完全相同.游戏规则是:
参加联欢会的50名同学,每人将盒子里的五个乒乓球摇匀后,闭上眼睛从中随机地一次摸出两个球.若两个球上的数字之和为偶数,就给大家即兴表演一个节目;否则,下一个同学接着做摸球游戏,依次进行. 用列表法或画树状图法求参加联欢会的某位同学即兴表演节目的概率;估计本次联欢会上有多少名同学即兴表演节目?
23. 如图,在Rt△ABC中,?
ABC?
90°,斜边AC的垂直平分线交BC于点D,交AC于点E,连接BE.若BE是△DEC外接圆的切线,求?
C的大小;当AB?
1,BC?
2时,求△DEC外接圆的半径.24. 5
如图,在平面直角坐标系中,抛物线经过A(?
1,0),B(3,0),C(0,-1)三点.求该抛物线的表达式; 点Q在y轴上,点P在抛物线上,要使以点Q、P、A、B为顶点的四边形是平行四边形,求所有满足条件的点P的坐标. 25.问题探究 请你在图①中作一条直线,使它将矩形ABCD分成面积相等的两部分;.. 如图②,点M是矩形ABCD内一定点.请你在图②中过点M作一条直线,使它将矩形ABCD分成面积相等的两部分.问题解决 如图③,在平面直角坐标系中,直角梯形OBCD是某市将要筹建的高新技术开发区用地示意图,其中DC∥OB,OB?
6,BC?
4,CD?
4.开发区综合服务管理委员会设在点P(4,,并且使这条路所2)处.为了方便驻区单位,准备过点P修一条笔直的道路在的直线l将直角梯形OBCD分成面积相等的两部分.你认为直线l是否存在?
若存在,求出直线l的表达式;若不存在,请说明理. 2010年陕西省初中毕业学业考试 6 一、选择题 题号A卷答案1C2B3B4D5A6C7A8A9D10C二、填空题11.?
2?
0或x?
413.?
ACD?
?
B(?
ADC?
?
ACB或14.15.?
1216.18 三、解答题17.解:
原式= m(m?
n)(m?
n)(m?
n)2ADAC?
ACAB之一亦可) ?
n(m?
n)(m?
n)(m?
n)2?
2mn(m?
n)(m?
n) = m?
mn?
nm?
n?
2mn(m?
n)(m?
n)m?
2mn?
n22··························································· = (m?
n)(m?
n)(m?
n)2 = = (m?
n)(m?
n)············································································ m?
nm?
n·························································································· 18.证明:
在正方形ABEF和正方形BCMN中, AB?
BE?
EF,BC?
BN,?
FEN?
?
EBC?
90°.········································· 分) .··························································································· 分) ?
FN?
EC.········································································································如图所示.···················································································· 7 24?
161600············································································ ?
该县常住居民利用“五一”期间出游采集发展信息的人数约为万人. 略.·······················20.解:
过点P作PH⊥AB,垂足为H.则?
APH?
30°,?
BPH?
43°.在Rt△APH中, AH?
100,PH?
AP·cos30°?
1003.··············· 在Rt△PBH中, ·············· 答:
码头A与亭子B之间的距离约为262米.·············································21.解:
题意,得批发蒜薹3x吨,储藏后销售吨,···则y?
3x·(3000?
700)?
x·(4500?
1000)?
(200?
4x)·(5500?
1200) =?
6800x?
860000.·················································································题意,得200?
4x≤80.解之,得x≥30.···········································?
y?
?
6800x?
860000,?
6800?
0.?
y的值随x的值增大而减小. 时,y最大值?
?
6800?
30?
860000?
656000. 元.··················· ?
当x?
30?
该生产基地按计划全部售完蒜薹的最大利润为65600022.解:
游戏所有可能出现的结果如下表:
8 ····························································································································从上表可以看出,一次游戏共有20种等可能结果,其中两数和为偶数的共有8种.将参加联欢会的某位同学即兴表演节目记为事件A, ?
P(A)?
P= 820?
25.························································· ?
50?
25?
20. ?
估计本次联欢会上有20名同学即兴表演节目.········································ 23.解:
?
DE垂直平分AC, ?
?
DEC?
90°. ?
DC为△DEC?
DC外接圆的直径. 的中点O即为圆心. ·················································································连接OE. 又知BE是⊙O的切线, ?
?
EBO?
?
BOE?
90°.··················································································· 在Rt△ABC中,E是斜边AC的中点, ?
BE?
EC.?
?
EBC?
?
C. 又?
?
BOE?
2?
C, ?
?
C?
2?
C?
90°. ?
?
C?
30°.······································································································· 在Rt△ABC中,AC?
?
EC?
AB?
BC22?
5.12AC?
52.··························································································· ?
?
ABC?
?
DEC?
90°, ?
△ABC∽△DEC.?
AC?
DC54BC.EC?
DC?
. 58C?
△DE外接圆的半径为.···································································· 24.解:
设该抛物线的表达式为y?
ax2?
bx?
c.根据题意,得 1?
a?
,?
3?
a?
b?
c?
0,?
2?
?
b?
?
,9a?
3b?
c?
0,解之,得·································································?
?
3?
?
c?
?
1.?
?
c?
?
1.?
?
?
所求抛物线的表达式为y?
13x?
223x?
1. ①当AB为边时,只要PQ∥AB,且PQ?
AB?
4即可.又知点Q在y轴上,?
点P的横坐标为4或?
4.这时,符合条件的点P有两个,分别记为P1,P2.而当x?
4时,y?
?
?
5?
3?
53;当x?
?
4时,y?
7. 7).此时P1?
4,?
,P2(?
4,·················································································· ② 当AB为对角线时,只要线段PQ与线段AB互相平分即可. 又知点Q在y轴上,且线段AB中点的横坐标为1, ?
点P的横坐标为2. 这时,符合条件的点P只有一个,记为P3. ?
1).而当x?
2时,y?
?
1.此时P3(2,7),P3(2,.1)综上,满足条件的点P为P1?
4,?
,P2(?
4,······························· ?
?
5?
3?
25.解:
如图①,作直线DB,直线DB即为所求.···················································································· 10 如图②,连接AC、DB交于点P,则点P为矩形ABCD的对称中心.作直线MP,直线MP即为所求.··························································································如图③,存在符合条件的直线l.··························································过点D作DA⊥OB于点A, 则点P(4,·························································2)为矩形ABCD的对称中心.· ?
过点P的直线只要平分△DOA的面积即可. 易知,在OD边上必存在点H,使得直线PH将△DOA面积平分.从而,直线PH平分梯形OBCD的面积. 即直线PH为所求直线l.··················································································设直线PH的表达式为y?
kx?
b,且点P(4,2),?
2?
4k?
b.即b?
2?
4k.?
y?
kx?
2?
4k.?
直线OD的表达式为y?
2x. 2?
4k?
x?
,?
?
y?
kx?
2?
4k,?
2?
k解之,得?
?
?
?
y?
2x.?
y?
4?
8k.?
2?
k?
?
点H的坐标为?
?
2?
4k4?
8,2?
k2?
k?
?
?
.?
?
PH与线段AD的交点F的坐标为(2,2?
2k), 2k?
2.?
?
4?
k?
1.?
0?
?
?
S△DHF?
12?
4?
2?
k4?
?
?
2k·?
2?
2?
?
?
2?
k?
?
?
2114?
?
2.2解之,得k?
8?
b?
?
13?
3?
?
13?
3.k?
不合题意,舍去?
?
?
?
22?
?
?
2.13 ?
直线l的表达式为y?
13?
32x?
8?
213.················································ 11
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