全一卷
1.如图,已知四条线段
,
,
,
中的一条与挡板另一侧的线段
在同一直线上,请借助直尺判断该线段是( )
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A.![]() | B.![]() |
C.![]() | D.![]() |
2.不 一定相等的一组是( )
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
3.已知
,则一定有
,“
”中应填的符号是( )
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A.![]() | B.![]() |
C.![]() | D.![]() |
4.与
结果相同的是( ).
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A.![]() | B.![]() |
C.![]() | D.![]() |
5.能与
相加得0的是( )
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A.![]() | B.![]() |
C.![]() | D.![]() |
6.一个骰子相对两面的点数之和为7,它的展开图如图,下列判断正确的是( )
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A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
7.如图1,
中,
,
为锐角.要在对角线
上找点
,
,使四边形
为平行四边形,现有图2中的甲、乙、丙三种方案,则正确的方案( )
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A.甲、乙、丙都是 | B.只有甲、乙才是 |
C.只有甲、丙才是 | D.只有乙、丙才是 |
8.图1是装了液体的高脚杯示意图(数据如图),用去一部分液体后如图2所示,此时液面
( )
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A.![]() | B.![]() |
C.![]() | D.![]() |
9.若
取1.442,计算
的结果是( )
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A.-100 | B.-144.2 |
C.144.2 | D.-0.01442 |
10.如图,点
为正六边形
对角线
上一点,
,
,则
的值是( )
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A.20 | B.30 |
C.40 | D.随点![]() |
11.如图,将数轴上-6与6两点间的线段六等分,这五个等分点所对应数依次为
,
,
,
,
,则下列正确的是( )
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A.![]() | B.![]() |
C.![]() | D.![]() |
12.如图,直线
,
相交于点
.
为这两直线外一点,且
.若点
关于直线
,
的对称点分别是点
,
,则
,
之间的距离可能 是( )
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A.0 | B.5 |
C.6 | D.7 |
13.定理:三角形的一个外角等于与它不相邻的两个内角的和.
已知:如图,
是
的外角.
求证:
.
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下列说法正确的是( )
已知:如图,
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求证:
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下列说法正确的是( )
A.证法1还需证明其他形状的三角形,该定理的证明才完整 |
B.证法1用严谨的推理证明了该定理 |
C.证法2用特殊到一般法证明了该定理 |
D.证法2只要测量够一百个三角形进行验证,就能证明该定理 |
14.小明调查了本班每位同学最喜欢的颜色,并绘制了不完整的扇形图1及条形图2(柱的高度从高到低排列).条形图不小心被撕了一块,图2中 “( )”应填的颜色是( )
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A.蓝 | B.粉 |
C.黄 | D.红 |
15.由
值的正负可以比较
与
的大小,下列正确的是( )
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A.当![]() ![]() | B.当![]() ![]() |
C.当![]() ![]() | D.当![]() ![]() |
16.如图,等腰
中,顶角
,用尺规按①到④的步骤操作:
①以
为圆心,
为半径画圆;
②在
上任取一点
(不与点
,
重合),连接
;
③作
的垂直平分线与
交于
,
;
④作
的垂直平分线与
交于
,
.
结论Ⅰ:顺次连接
,
,
,
四点必能得到矩形;
结论Ⅱ:
上只有唯一的点
,使得
.
对于结论Ⅰ和Ⅱ,下列判断正确的是( )
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①以
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②在
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③作
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④作
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结论Ⅰ:顺次连接
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结论Ⅱ:
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对于结论Ⅰ和Ⅱ,下列判断正确的是( )
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A.Ⅰ和Ⅱ都对 | B.Ⅰ和Ⅱ都不对 |
C.Ⅰ不对Ⅱ对 | D.Ⅰ对Ⅱ不对 |
17.现有甲、乙、丙三种不同的矩形纸片(边长如图).
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(1)取甲、乙纸片各1块,其面积和为___________ ;
(2)嘉嘉要用这三种纸片紧密拼接成一个大正方形,先取甲纸片1块,再取乙纸片4块,还需取丙纸片___________ 块.
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(1)取甲、乙纸片各1块,其面积和为
(2)嘉嘉要用这三种纸片紧密拼接成一个大正方形,先取甲纸片1块,再取乙纸片4块,还需取丙纸片
18.下图是可调躺椅示意图(数据如图),
与
的交点为
,且
,
,
保持不变.为了舒适,需调整
的大小,使
,则图中
应___________ (填“增加”或“减少”)___________ 度.
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19.用绘图软件绘制双曲线
:
与动直线
:
,且交于一点,图1为
时的视窗情形.
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(1)当
时,
与
的交点坐标为__________ ;
(2)视窗的大小不变,但其可视范围可以变化,且变化前后原点
始终在视窗中心.例如,为在视窗中看到(1)中的交点,可将图1中坐标系的单位长度变为原来的
,其可视范围就由
及
变成了
及
(如图2).当
和
时,
与
的交点分别是点A和
,为能看到
在A和
之间的一整段图象,需要将图1中坐标系的单位长度至少变为原来的
,则整数
__________ .
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(1)当
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(2)视窗的大小不变,但其可视范围可以变化,且变化前后原点
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20.某书店新进了一批图书,甲、乙两种书的进价分别为4元/本、10元/本.现购进
本甲种书和
本乙种书,共付款
元.
(1)用含
,
的代数式表示
;
(2)若共购进
本甲种书及
本乙种书,用科学记数法表示
的值.
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(1)用含
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(2)若共购进
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21.已知训练场球筐中有
、
两种品牌的乒乓球共101个,设
品牌乒乓球有
个.
(1)淇淇说:“筐里
品牌球是
品牌球的两倍.”嘉嘉根据她的说法列出了方程:
.请用嘉嘉所列方程分析淇淇的说法是否正确;
(2)据工作人员透露:
品牌球比
品牌球至少多28个,试通过列不等式的方法说明
品牌球最多有几个.
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(1)淇淇说:“筐里
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(2)据工作人员透露:
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22.某博物馆展厅的俯视示意图如图1所示,嘉淇进入展厅后开始自由参观,每走到一个十字道口,她自己可能直行,也可能向左转或向右转,且这三种可能性均相同.
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(1)求嘉淇走到十字道口
向北走的概率;
(2)补全图2的树状图,并分析嘉淇经过两个十字道口后向哪个方向参观的概率较大.
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(1)求嘉淇走到十字道口
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(2)补全图2的树状图,并分析嘉淇经过两个十字道口后向哪个方向参观的概率较大.
23.下图是某机场监控屏显示两飞机的飞行图象,1号指挥机(看成点
)始终以
的速度在离地面
高的上空匀速向右飞行,2号试飞机(看成点
)一直 保持在1号机
的正下方 ,2号机从原点
处沿
仰角爬升,到
高的
处便立刻转为水平飞行,再过
到达
处开始沿直线
降落,要求
后到达
处.
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(1)求
的
关于
的函数解析式,并直接 写出2号机的爬升速度;
(2)求
的
关于
的函数解析式,并预计2号机着陆点的坐标;
(3)通过计算说明两机距离
不超过
的时长是多少.
【注:(1)及(2)中不必写
的取值范围】
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(1)求
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(2)求
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(3)通过计算说明两机距离
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【注:(1)及(2)中不必写
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24.如图,
的半径为6,将该圆周12等分后得到表盘模型,其中整钟点为
(
为1~12的整数),过点
作
的切线交
延长线于点
.
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(1)通过计算比较直径和劣弧
长度哪个更长;
(2)连接
,则
和
有什么特殊位置关系?请简要说明理由;
(3)求切线长
的值.
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(1)通过计算比较直径和劣弧
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(2)连接
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(3)求切线长
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25.下图是某同学正在设计的一动画示意图,
轴上依次有
,
,
三个点,且
,在
上方有五个台阶
(各拐角均为
),每个台阶的高、宽分别是1和1.5,台阶
到
轴距离
.从点
处向右上方沿抛物线
:
发出一个带光的点
.
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(1)求点
的横坐标,且在图中补画出
轴,并直接指出点
会落在哪个台阶上;
(2)当点
落到台阶上后立即弹起,又形成了另一条与
形状相同的抛物线
,且最大高度为11,求
的解析式,并说明其对称轴是否与台阶
有交点;
(3)在
轴上从左到右有两点
,
,且
,从点
向上作
轴,且
.在
沿
轴左右平移时,必须保证(2)中沿抛物线
下落的点
能落在边
(包括端点)上,则点
横坐标的最大值比最小值大多少?
(注:(2)中不必写
的取值范围)
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(1)求点
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(2)当点
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(3)在
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(注:(2)中不必写
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26.在一平面内,线段
,线段
,将这四条线段顺次首尾相接.把
固定,让
绕点
从
开始逆时针旋转角
到某一位置时,
,
将会跟随出现到相应的位置.
(1)论证 如图1,当
时,设
与
交于点
,求证:
;
(2)发现 当旋转角
时,
的度数可能是多少?
(3)尝试 取线段
的中点
,当点
与点
距离最大时,求点
到
的距离;
(4)拓展 ①如图2,设点
与
的距离为
,若
的平分线所在直线交
于点
,直接写出
的长(用含
的式子表示);
②当点
在
下方,且
与
垂直时,直接写出
的余弦值.
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(1)论证 如图1,当
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(2)发现 当旋转角
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(3)尝试 取线段
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(4)拓展 ①如图2,设点
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②当点
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