2018年河南省焦作市中考第一次质量抽测试卷含答案(PDF版)
焦作市2018年九年级第一次质量抽测试卷
数学
注意事项：
1.本试卷共4页，三个大题，满分120分，考试时间100分钟。
2.本试卷上不要答题，请按答题卡上注意事项的要求直接把答案填写在答题卡上。答在试卷上的答案无效。
一、选择题（每小题3分，共30分）下列各小题均有四个答案，其中只有一个是正确的.
1．在下列各数中，比﹣1小的数是（）
C．0D．1
A．﹣3B．﹣1
2
2.大型纪录电影《厉害了，我的国》3月2日在全国上映，在上映首日收获了4132万人民币的票房。数据“4132万”用科学计数法表示为（）
A．6
132
.4?D．7
32.41?
10
10
10
10
.4?C．6
32.41?B．7
132
3．用8个相同的小正方体搭成一个几何体，从上面看它得到的平面图形如图所示，那么从左面看它得到的平面图形一定不是（）
A．B．C．D．
4．下列计算正确的是（）
A．a＋b＝ab B．
C．a3b÷2ab＝a2D．（－2ab2）3＝－6a3b5
5．下列关于x的一元二次方程中，有两个相等实数根的是（）
A．x2＋1＝0B．x2＋x﹣1＝0
C．x2＋2x﹣3＝0D．4x2﹣4x＋1＝0
6．某中学举行书法比赛，各年龄组的参赛人数如下表所示，则全体参赛选手年龄的平均数和中位数分别为（
）
A ．14.5，14.5
B ．14，15
C ．14.5，14
D ．14，14
7．如图，已知在△ABC ，AB ＝AC ．若以点B 为圆心，BC 长为半径画弧，交腰AC 于点E ，则下列结论一定正确的是（）
A ．AE ＝EC
B ．AE ＝BE
C ．∠EBC ＝∠BAC
D ．∠EBC ＝∠ABE
8．一个不透明的口袋中有四个完全相同的小球，把它们分别标号为1，2，3，4，随机摸出一个小球后不放回，再随机摸出一个小球，则两次摸出的小球标号之和等于5的概率为（）A ．
B ．
C ．
D ．
9．一个寻宝游戏的寻宝通道如图1所示，通道由在同一平面内的AB ，BC ，CA ，OA ，OB ，OC 组成．为记录寻宝者的行进路线，在BC 的中点M 处放置了一台定位仪器．设寻宝者行进的时间为x ，寻宝者与定位仪器之间的距离为y ，若寻宝者匀速行进，且表示y 与x 的函数关系的图象大致如图2所示，则寻宝者的行进路线可能为（
）
A ．A→O→
B B ．B→A→
C C ．B→O→C
D ．C→B→O
年龄组13
岁14岁15岁16岁参赛人数
9
15
3
3
10．如图，AB 为半圆O 的直径，C 为AO 的中点，CD ⊥AB 交半圆于点D ，以C 为圆心，CD 为半径画弧交AB 于E 点，若AB ＝4，则图中阴影部分的面积是（）
A ．
23
127+πB ．
π12
5
C ．
2
3127-πD ．π
3
2二、填空题（每小题3分，共15分）
11．计算：9211
-??
?
??-＝
．
12．不等式组?
??≤-+x x x -8121
2＞的最大整数解是
．
13．已知反比例函数y ＝x
k
（x ≠0）的图象经过（3，﹣1），则当1＜y ＜3时，自变量x 的取值范围是
．
14.如图，在直角坐标系中，正方形ABCO 的点B 坐标（3，3），点A 、C 分别在y 轴、x 轴上，对角线AC 上一动点E ，连接BE ，过E 作DE ⊥BE 交OC 于点D ．若点D 坐标为（2，0），则点E 坐标为
．
15.如图，在Rt △ABC 中，∠A ＝90°,∠B ＝30°，BC ＝3＋1，点E 、F 分别是BC 、AC 边上的动点，沿EF 所在直线折叠∠C ，使点C 的对应点C ′始终落在边AB 上，若△BEC ′是直角三角形时，则BC ′的长为
．
三、解答题（本大题共8小题，满分75分）16.（8分）化简并求值：
22
211y
x y x y x y x --÷???? ?
?+--，其中x ，y 满足|x +2|＋（2x +y ﹣1）2＝0．17.（9分）为了了解学生平均每天“诵读经典”的时间，在全校范围内随机抽查了部分学生进行调查统计，并将调查统计的结果分为：每天诵读时间t ≤20分钟的学生记为A 类，20分钟＜t ≤40分钟的学生记为B 类，40分钟＜t ≤60分钟的学生记为C 类，t ＞60分钟的学生记为D 类四种．将收集的数据绘制成如下两幅不完整的统计图．
请根据图中提供的信息，解答下列问题：（1）这次共抽查了
名学生进行调查统计，m ＝
%，n ＝
%；
（2）请补全上面的条形图；
（3）如果该校共有1200名学生，请你估计该校C 类学生约有多少人.
18.（9分）如图，△ABC内接于⊙O，且AB＝AC.延长BC到点D，使CD＝CA，连接AD交⊙O于点E.
（1）求证：△ABE≌△CDE；
（2）填空：
①当∠ABC的度数为时，四边形AOCE是菱形；
②若AE＝6，BE=8，则EF的长为.
19.（9分）如图，某校教学楼AB的后面有一建筑物CD，在距离CD的正后方30米的观测点P处，以22°的仰角测得建筑物的顶端C恰好挡住教学楼的顶端A，而在建筑物CD上距离地面3米高的E处，测得教学楼的顶端A的仰角为45°，求教学楼AB的高度．（参考数据：sin22°≈，cos22°≈，tan22°≈）
20.（9分）如图，一次函数y＝－1
2
x＋b与反比例函数y＝k
x（x＞0）的图象交于点
A（2，6）和B（m，1）
（1）填空：一次函数的解析式为，反比例函数的解析式为；（2）点E为y轴上一个动点，若S
△AEB
＝5，求点E的坐标．
21.（10分）某文具商店销售功能相同的两种品牌的计算器，购买2个A品牌和1个B品牌的计算器共需122元；购买1个A品牌和2个B品牌的计算器共需124元．
（1）求这两种品牌计算器的单价；
（2）学校开学前夕，该商店举行促销活动，具体办法如下：购买A品牌计算器按原价的九折销售，购买B品牌计算器超出10个以上超出的部分按原价的八折销售，①设购买x个A品牌的计算器需要y1元，购买x个B品牌的计算器需要y2元，分别求出y1、y2关于x的函数关系式；
②小明准备联系一部分同学集体购买同一品牌的计算器，若购买计算器的数量超过10个，问购买哪种品牌的计算器更合算？请说明理由．
22.（10分）如图1：在等边△ABC中，点D，E分别在边AB，AC上，AD＝AE，连结BE，CD，点M、N、P分别是BE、CD、BC的中点.
(1)观察猜想
图1中△PMN的形状是；
(2)探究证明
把△ADE绕点A逆时针方向旋转到图2的位置，△PMN的形状是否发生改变？并说明理由；
(3)拓展延伸
把△ADE绕点A在平面内自由旋转，若AD＝1，AB＝3，请直接写出△PMN的周长的最大值.
图1图2
23.（11分）如图1，已知抛物线y＝﹣x2＋bx＋c交y轴于点A（0,4），交x轴于点B（4,0），点P是抛物线上一动点，过点P作x轴的垂线PQ，过点A作AQ⊥
PQ于点Q，连接AP．
（1）填空：抛物线的解析式为，点C的坐标；（2）点P在抛物线上运动，若△AQP∽△AOC，求点P的坐标；
（3）如图2，当点P位于抛物线,的对称轴的右侧．若将△APQ沿AP对折，点Q
的对应点为点Q’．请直接写出
．．．．当点Q’落在坐标轴上时点P的坐标.
图2
图1
焦作市2018年九年级第一次质量抽测试卷
数学参考答案及评分标准
一、选择题：（每小题3分，共30分）题号12345678910答案
A
B
C
C
D
D
C
B
C
A
二、填空题：（每小题3分，共15分）
题号111213
1415
答案
﹣1
3
﹣3＜x ＜﹣1
（1，2）
3
3
3+或2三、解答题：（本大题共8个小题，满分75分）16.解：（
-）÷
=
()()y x y x y
x y x +-+-+?
………………………………..……….………….4分
=y
x y -22………………………………….……………………..…………….6分
∵|x+2|+（2x+y ﹣1）2=0，
∴??
?=-+=+01202y x x 解得：??
?=-=5
2
y x ………….……………..……..……….....………7分
∴原式=
()9
10
52252-
=--??……………………………………….………8分17.解：（1）50，26，14；
……………………………………..……….…..3分
（2）补全的条形统计图，频数为10，………………….…………………..6分
（3）1200×20%=240（人），即该校C 类学生约有240人．
……………………………………....………..9分
18.（1）证明：∵AB=AC,CD=CA
∴∠ABC=∠ACB,AB=CD…………………………………………….……..….2分
∵四边形ABCE是园内接四边形
∴∠ECD=∠BAE,∠CED=∠ABC
∵∠ABC=∠ACB=∠AEB
∴∠CED=∠AEB……………………………………………………..………....4分∴△ABE≌△CDE…………………………………………..……….…………..5分
（2）①60（填60°不扣分）…………………………………………………7分9………………………………………………………………..……….9分②
2
19.解：如图作EF⊥AB于F，则四边形EFBD是矩形．…………….…1分
∵∠AEF=45°，∠AFE=90°，
∴∠AEF=∠EAF=45°，
∴EF=AF，设EF=AF=x，则BD=EF=x，
在Rt△PAB中，∵AB=x+3，PB=30+x，……………………………………3分
∴tan22°=，
∴=，……………………………………………………………………6分
∴x=15，
经检验：x=15是原方程的根……………………………….……………7分
∴AB=x+3=18m，……………………………………………………………….8分
答：教学楼AB的高度为18m．……………………………………………..9分20.解：（1）y=﹣x+7，y=．…………………………………………..4分（2）如图，直线AB与y轴的交点为P，设点E的坐标为（0，m），连接AE，BE，
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2018年河南省中考作文范文一
2018年河南省中考作文范文一：最懂我的那个人（1）_750字 世上并不是每个人都十分的了解你，而懂你的心的，往往是最爱你的那个人。 ——题记 小时候呀！我总是很贪心，刚买了一个新的玩具，又想要新的玩具，但是最终都玩厌了。这些只不过是十几元的玩具，有什么好玩的，要是有一个“大家伙”那该是多好呀！ 一天，我看到有人在玩摇控飞机，脸上没有流露出感情，可心里却十分的渴慕：要是我也有那样的一架飞机该有多好呀！回到家里也是心不在焉。每当和父母出游，看到别人在玩飞机是，就会莫名其妙的向父亲撒气。有一天母亲对我说：“孩子，妈妈这几天要出差，好好的爸爸待在一起！”“嗯”，我想，又不是给我买玩具，有什么好在意的呢！几天后母亲回来了，对我说：“儿子，你想要什么玩具，妈妈给你买！”我一听，一蹦三尺高，终于有机会向妈妈要飞机了，毫不犹豫的说：“飞机！”“哈，还是我懂你，果然没买错，看，飞机！”母亲像变戏法似的，从包里取出飞机，放在我的手中，我别提有多么高兴了，当天就学会了怎样玩。 步入了初中，每天总是一张张试卷横飞过来，最怕的便是月考，因为考后，在年级里总要排列名次。也许是我后退太多了，或许是别人进步得比我快，反正我就是那个“不幸儿”。 我——落榜了，那天我听到这个消息，很是不爽，真想把成绩单撕毁，但又无奈：已经成为了不能修改的历史！ 回到家中，我想提，也不敢提自己的成绩，因为如果我说出来，母亲的目光是会让我十分难受的。母亲总是喜欢问我成绩，今天却出奇的不问，只是让我好好的休息。 就这样我迷惑的过了一个月，——又迎来了新一轮的月考，与上一次的不同，我这次做好了准备……成绩单下发了，不负所望，我上红榜了，我第一时间把这个消息告诉了母亲，并且问出了我内心的疑惑，没想到母亲只说了一句：“我知道你上次没考好！” 苍天呀！感谢您赠与我一位这么伟大的母亲，她懂我，她知我心，她全心全意爱我。当然，我也不会负了您的希望——成才！ 此文档部分内容来源于网络，如有侵权请告知删除 本文档可自行编辑和修改内容，感谢您的支持