全一卷
1.-4的相反数是( )
A.![]() | B.![]() | C.4 | D.-4 |
2.下列计算结果是
的是( )
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A.![]() | B.![]() | C.![]() | D.![]() |
3.受新冠肺炎疫情影响,自2020年2月起,安徽省对各类企业基本养老保险、失业保险、工伤保险三项社会保险的单位缴费部分,免征或减半征收3~5个月,合计减收约159.7亿元.数据159.7亿用科学记数法表示为( )
A.![]() | B.![]() | C.![]() | D.![]() |
4.一个由圆柱和三棱柱组成的几何体如图水平放置,其主(正)视图是( )
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A.![]() | B.![]() | C.![]() | D.![]() |
5.已知直线
沿
轴向下平移2个单位后与反比例函数
的图象相交于
,
两点,则
的值为( )
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A.0 | B.1 | C.2 | D.3 |
6.如图,在
中,
,
,
,
为
边的中点,则点
到中线
的距离
的长为( )
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A.3 | B.4 | C.![]() | D.![]() |
7.某中学为了解“停课不停学”期间学生在家的学习情况,随机抽查了40名学生每天做家庭作业的时间,并将调查结果统计如下表:
则这40名学生每天做家庭作业的时间的众数和中位数分别为( )
每天做家庭作业的时间(分钟) | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
人数 | 2 | 4 | 5 | 9 | 8 | 7 | 5 |
则这40名学生每天做家庭作业的时间的众数和中位数分别为( )
A.90,95 | B.90,90 | C.100,100 | D.100,95 |
8.2020年是全面建成小康社会目标实现之年,是全面打赢脱贫攻坚战收官之年.根据2月初发布的中央一号文件,我国目前还有近300万农村贫困人口的月平均下降率为
,则4月初我国还未脱贫的农村贫困人口数量约为( )
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A.17万 | B.19万 | C.21万 | D.23万 |
9.将函数
在
轴下方的图像沿
轴向上翻折,在
轴上方的图像保持不变,得到一个新图像.若使得新图像对应的函数最大值与最小值之差最小,则
的值为( )
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A.2.5 | B.3 | C.3.5 | D.4 |
10.如图,在矩形
中,
,
,
为
上一点,
,
为直线
上的动点,以
为斜边作
,交直线
于点
,且满足
,若
为
的中点,连接
,
,则当
最小时,
的值为( )
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A.![]() | B.![]() | C.![]() | D.![]() |
11.不等式
的解集是_________________.
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12.因式分解:
____________________ .
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13.如图,等边
与
相切于点
,
为
上一点,以
为边向
内作等边
,若
的半径为1,
,则
________________
.
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14.已知正方形
的边长为12,
、
分别在边
、
上,将
沿
折叠,使得点
落在正方形内部(不含边界)的点
处,
的延长线交
于点
.若点
在正方形的对称轴上,且满足
,则折痕
的长为______________ .
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15.计算:
.
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16.《算法统宗》中有一首“以碗知僧”的趣味诗,原文如下:巍巍古寺在山中,不知寺内几多僧.三百六十四只碗,恰合用尽不差争.三人共食一碗饭,四人共尝一碗羹.请问先生明算者,算来寺内几多僧?
译文为:寺内有三百六十四只碗,如果三个和尚共吃一碗饭,四个和尚共吃一碗羹,恰好把碗用完,请问寺内共有多少个和尚?请解答上述问题.
译文为:寺内有三百六十四只碗,如果三个和尚共吃一碗饭,四个和尚共吃一碗羹,恰好把碗用完,请问寺内共有多少个和尚?请解答上述问题.
17.如图,在边长为1个单位长度的小正方形网格中建立平面直角坐标系,已知点
,
均为网格线的交点.
(1)请画出点
关于原点
对称的点
;
(2)连接
,将线段
绕点
旋转得到线段
,使得四边形
是以
为对角线的正方形,请画出正方形
.
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(1)请画出点
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(2)连接
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18.观察以下等式:
第1个等式:
,
第2个等式:
,
第3个等式:
,
第4个等式:
,
第5个等式:
,
……
按照以上规律,解决下列问题:
(1)写出第6个等式: ;
(2)写出你猜想的第
个等式 (用含
的等式表示),并证明.
第1个等式:
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第2个等式:
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第3个等式:
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第4个等式:
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第5个等式:
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……
按照以上规律,解决下列问题:
(1)写出第6个等式: ;
(2)写出你猜想的第
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19.某社团在课余时间用无人机为学校航拍宣传片,如图所示的
为无人机某次空中飞行轨迹,
为
延长线上一点,点
,
,
,
在同一平面内,
,
.若
米,求
的长.(结果保留整数,参考数据:
,
,
,
)
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20.如图,在
中,
,
为
上一点,以
为直径的
经过点
,交
于点
,且
,
为
的直径,连接
并延长交
于点
,连接
.
(1)求证:四边形
是平行四边形;
(2)若能
,
,求
的直径.
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(1)求证:四边形
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(2)若能
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21.为了普及垃圾分类知识,倡导低碳生活的理念,更好地推进垃圾分类工作,某市举办了中学生垃圾分类知识竞赛(百分制,评比准则为:60分及以上为及格;80分及以上为良好;90分及以上为优秀).为了解甲、乙两校学生对垃圾分类知识的掌握情况,各随机抽取10名学生的竞赛成绩,抽取的部分数据整理如下:
甲校:90,100,86,89,73,68,54,75,98,
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注:乙校成绩在80分以上的数据是:100,80,88,83,86,94
(1)已知本次抽查的甲校学生成绩的优秀率为
,请判断
对应的成绩是否为优秀,并说明理由;
(2)若乙校共有1000名学生,请你估计乙校学生成绩在85分及以上的人数;
(3)已知本次抽查的甲校学生中有3人成绩为优秀,现从本次抽查的甲、乙两校成绩为优秀的小学生中任选2人作为志愿者普及和宣传垃圾分类知识,求选到的2人成绩都为100分的概率.
甲校:90,100,86,89,73,68,54,75,98,
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注:乙校成绩在80分以上的数据是:100,80,88,83,86,94
(1)已知本次抽查的甲校学生成绩的优秀率为
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(2)若乙校共有1000名学生,请你估计乙校学生成绩在85分及以上的人数;
(3)已知本次抽查的甲校学生中有3人成绩为优秀,现从本次抽查的甲、乙两校成绩为优秀的小学生中任选2人作为志愿者普及和宣传垃圾分类知识,求选到的2人成绩都为100分的概率.
22.2019年10月31日,三大运营商宣布
商用正式启动,
资费套餐上线,
时代大步流星地走来.某电器城准备销售一种型号的
手机,在销售过程中发现,当零售价为4000元时,每天可以售出8台,日销售利润为4000元,当零售价每降低50元,则每天多售出4台.设该型号
手机的零售价降低
(元)时,日销售量为
(台).
(1)求
关于
的函数表达式;
(2)当零售价为多少元时,日销售利润最大,最大利润为多少元?
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(1)求
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(2)当零售价为多少元时,日销售利润最大,最大利润为多少元?
23.已知在
中,
,
,
是边
上一点,
交
于点
,交
于点
.
(1)如图1,若
,
交
于点
,交
于点
,连接
.
①求证:
平分
;
②求
的度数.
(2)如图2,若
,求证:
.
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图1
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图2
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(1)如图1,若
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①求证:
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②求
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(2)如图2,若
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图1
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图2