河南焦作市2018年中考第一次质量抽测试卷(含答案)
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（ ） A ．﹣3 B ．﹣1
2
C ．0
D ．1
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
1032.41? B ． 7
10132.4? C ． 6
10132.4? D ．7
1032.41? 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 ．a 3b ÷2ab ＝a 2
D ．（－2ab 2）3＝－6a 3b 5 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 ．x 2＋1＝0 B ．x 2＋x ﹣1＝0 C ．x 2＋2x ﹣3＝0 D ．4x 2﹣4x ＋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
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+
π B ．π125 C ．2
3
127-
π D ．π32
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 ．
C
B
三、解答题（本大题共8小题，满分75分） 16.（8分）化简并求值：
22211y 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：
sin
22°≈，cos 22°≈，tan 22°≈）
D
A
20.（9分）如图，一次函数y ＝－12x ＋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．
x
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.
A B
B
C
图1 图
2
A
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北京市海淀区2018届初三一模英语word版
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