全一卷
1.如图,在平面内作已知直线
的垂线,可作垂线的条数有( )
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A.0条 | B.1条 | C.2条 | D.无数条 |
2.墨迹覆盖了等式“
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(
)”中的运算符号,则覆盖的是( )
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A.+ | B.- | C.× | D.÷ |
3.对于①
,②
,从左到右的变形,表述正确的是( )
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A.都是因式分解 | B.都是乘法运算 |
C.①是因式分解,②是乘法运算 | D.①是乘法运算,②是因式分解 |
4.如图的两个几何体分别由7个和6个相同的小正方体搭成,比较两个几何体的三视图,正确的是( )
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A.仅主视图不同 | B.仅俯视图不同 |
C.仅左视图不同 | D.主视图、左视图和俯视图都相同 |
5.如图是小颖前三次购买苹果单价的统计图,第四次又买的苹果单价是
元/千克,发现这四个单价的中位数恰好也是众数,则
( )
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A.9 | B.8 | C.7 | D.6 |
6.如图1,已知
,用尺规作它的角平分线.
如图2,步骤如下,
第一步:以
为圆心,以
为半径画弧,分别交射线
,
于点
,
;
第二步:分别以
,
为圆心,以
为半径画弧,两弧在
内部交于点
;
第三步:画射线
.射线
即为所求.
下列正确的是( )
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如图2,步骤如下,
第一步:以
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第二步:分别以
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第三步:画射线
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下列正确的是( )
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A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
7.若
,则下列分式化简正确的是( )
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A.![]() | B.![]() | C.![]() | D.![]() |
8.在如图所示的网格中,以点
为位似中心,四边形
的位似图形是( )
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A.四边形![]() | B.四边形![]() | C.四边形![]() | D.四边形![]() |
9.若
,则
( )
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A.12 | B.10 | C.8 | D.6 |
10.如图,将
绕边
的中点
顺时针旋转180°.嘉淇发现,旋转后的
与
构成平行四边形,并推理如下:
小明为保证嘉淇的推理更严谨,想在方框中“∵
,”和“∴四边形……”之间作补充.下列正确的是( )
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点![]() ![]() ![]() ![]() 而点 ![]() ![]() ∵ ![]() ∴四边形 ![]() |
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小明为保证嘉淇的推理更严谨,想在方框中“∵
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A.嘉淇推理严谨,不必补充 | B.应补充:且![]() |
C.应补充:且![]() | D.应补充:且![]() |
11.若
为正整数,则
( )
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A.![]() | B.![]() | C.![]() | D.![]() |
12.如图,从笔直的公路
旁一点
出发,向西走
到达
;从
出发向北走
也到达
.下列说法错误 的是( )
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A.从点![]() ![]() ![]() |
B.公路![]() |
C.公路![]() |
D.从点![]() ![]() ![]() ![]() |
13.已知光速为300000千米秒,光经过
秒(
)传播的距离用科学记数法表示为
千米,则
可能为( )
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A.5 | B.6 | C.5或6 | D.5或6或7 |
14.有一题目:“已知;点
为
的外心,
,求
.”嘉嘉的解答为:画
以及它的外接圆
,连接
,
,如图.由
,得
.而淇淇说:“嘉嘉考虑的不周全,
还应有另一个不同的值.”,下列判断正确的是( )
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A.淇淇说的对,且![]() |
B.淇淇说的不对,![]() |
C.嘉嘉求的结果不对,![]() |
D.两人都不对,![]() |
15.如图,现要在抛物线
上找点
,针对
的不同取值,所找点
的个数,三人的说法如下,
甲:若
,则点
的个数为0;
乙:若
,则点
的个数为1;
丙:若
,则点
的个数为1.
下列判断正确的是( )
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甲:若
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乙:若
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丙:若
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下列判断正确的是( )
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A.乙错,丙对 | B.甲和乙都错 |
C.乙对,丙错 | D.甲错,丙对 |
16.如图是用三块正方形纸片以顶点相连的方式设计的“毕达哥拉斯”图案.现有五种正方形纸片,面积分别是1,2,3,4,5,选取其中三块(可重复选取)按图的方式组成图案,使所围成的三角形是面积最大 的直角三角形,则选取的三块纸片的面积分别是( )
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A.1,4,5 | B.2,3,5 | C.3,4,5 | D.2,2,4 |
17.已知:
,则
_________ .
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18.正六边形的一个内角是正
边形一个外角的4倍,则
_________ .
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19.如图是8个台阶的示意图,每个台阶的高和宽分别是1和2,每个台阶凸出的角的顶点记作
(
为1~8的整数).函数
(
)的图象为曲线
.
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(1)若
过点
,则
_________ ;
(2)若
过点
,则它必定还过另一点
,则
_________ ;
(3)若曲线
使得
这些点分布在它的两侧,每侧各4个点,则
的整数值有_________ 个.
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(1)若
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(2)若
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(3)若曲线
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20.已知两个有理数:-9和5.
(1)计算:
;
(2)若再添一个负整数
,且-9,5与
这三个数的平均数仍小于
,求
的值.
(1)计算:
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(2)若再添一个负整数
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21.有一电脑程序:每按一次按键,屏幕的
区就会自动加上
,同时
区就会自动减去
,且均显示化简后的结果.已知
,
两区初始显示的分别是25和-16,如图.
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如,第一次按键后,
,
两区分别显示:
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(1)从初始状态按2次后,分别求
,
两区显示的结果;
(2)从初始状态按4次后,计算
,
两区代数式的和,请判断这个和能为负数吗?说明理由.
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如,第一次按键后,
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(1)从初始状态按2次后,分别求
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(2)从初始状态按4次后,计算
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22.如图,点
为
中点,分别延长
到点
,
到点
,使
.以点
为圆心,分别以
,
为半径在
上方作两个半圆.点
为小半圆上任一点(不与点
,
重合),连接
并延长交大半圆于点
,连接
,
.
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(1)①求证:
;
②写出∠1,∠2和
三者间的数量关系,并说明理由.
(2)若
,当
最大时,直接指出
与小半圆的位置关系,并求此时
(答案保留
).
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(1)①求证:
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②写出∠1,∠2和
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(2)若
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23.用承重指数
衡量水平放置的长方体木板的最大承重量.实验室有一些同材质同长同宽而厚度不一的木板,实验发现:木板承重指数
与木板厚度
(厘米)的平方成正比,当
时,
.
(1)求
与
的函数关系式.
(2)如图,选一块厚度为6厘米的木板,把它分割成与原来同长同宽但薄厚不同的两块板(不计分割损耗).设薄板的厚度为
(厘米),
.
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①求
与
的函数关系式;
②
为何值时,
是
的3倍?
【注:(1)及(2)中的①不必写
的取值范围】
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(1)求
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(2)如图,选一块厚度为6厘米的木板,把它分割成与原来同长同宽但薄厚不同的两块板(不计分割损耗).设薄板的厚度为
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①求
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②
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【注:(1)及(2)中的①不必写
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24.表格中的两组对应值满足一次函数
,现画出了它的图象为直线
,如图.而某同学为观察
,
对图象的影响,将上面函数中的
与
交换位置后得另一个一次函数,设其图象为直线
.
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(1)求直线
的解析式;
(2)请在图上画出 直线
(不要求列表计算),并求直线
被直线
和
轴所截线段的长;
(3)设直线
与直线
,
及
轴有三个不同的交点,且其中两点关于第三点对称,直接 写出
的值.
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![]() | -1 | 0 |
![]() | -2 | 1 |
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(1)求直线
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(2)请在图上
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(3)设直线
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25.如图,甲、乙两人(看成点)分别在数轴-3和5的位置上,沿数轴做移动游戏.每次移动游戏规则:裁判先捂住一枚硬币,再让两人猜向上一面是正是反,而后根据所猜结果进行移动.
①若都对或都错,则甲向东移动1个单位,同时乙向西移动1个单位;
②若甲对乙错,则甲向东移动4个单位,同时乙向东移动2个单位;
③若甲错乙对,则甲向西移动2个单位,同时乙向西移动4个单位.
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(1)经过第一次移动游戏,求甲的位置停留在正半轴上的概率
;
(2)从图的位置开始,若完成了10次移动游戏,发现甲、乙每次所猜结果均为一对一错.设乙猜对
次,且他最终停留的位置对应的数为
,试用含
的代数式表示
,并求该位置距离原点
最近时
的值;
(3)从图的位置开始,若进行了
次移动游戏后,甲与乙的位置相距2个单位,直接写出
的值.
①若都对或都错,则甲向东移动1个单位,同时乙向西移动1个单位;
②若甲对乙错,则甲向东移动4个单位,同时乙向东移动2个单位;
③若甲错乙对,则甲向西移动2个单位,同时乙向西移动4个单位.
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(1)经过第一次移动游戏,求甲的位置停留在正半轴上的概率
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(2)从图的位置开始,若完成了10次移动游戏,发现甲、乙每次所猜结果均为一对一错.设乙猜对
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(3)从图的位置开始,若进行了
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26.如图1和图2,在
中,
,
,
.点
在
边上,点
,
分别在
,
上,且
.点
从点
出发沿折线
匀速移动,到达点
时停止;而点
在
边上随
移动,且始终保持
.
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(1)当点
在
上时,求点
与点
的最短距离;
(2)若点
在
上,且
将
的面积分成上下4:5两部分时,求
的长;
(3)设点
移动的路程为
,当
及
时,分别求点
到直线
的距离(用含
的式子表示);
(4)在点
处设计并安装一扫描器,按定角
扫描
区域(含边界),扫描器随点
从
到
再到
共用时36秒.若
,请直接 写出点
被扫描到的总时长.
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(1)当点
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(2)若点
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(3)设点
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(4)在点
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