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1 . 如图,已知圆O的面积为
,AB为直径,弧AC的度数(劣弧AC所对圆心角的度数)为
,弧BD的度数为
,点P为直径AB上任一点,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c055a02fba0827ffcaa92f73ce7720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391479c151307826c9765a47a5f10503.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aee6e4e9350a2665df8597ff8045bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186dee1a1cf68677d143172a2a50709c.png)
![](https://img.xkw.com/dksih/QBM/2021/9/22/2813365822922752/2814982063136768/STEM/671374264e384426aca60ee9990eecb5.png?resizew=215)
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3卷引用:新疆疏附县第二中学2021-2022学年高一上学期开学考试数学试题
新疆疏附县第二中学2021-2022学年高一上学期开学考试数学试题上海交通大学附属中学2021-2022学年高一上学期开学摸底数学试题(已下线)高一数学上学期开学分班考试卷(沪教版2020)-2022-2023学年高一数学考试满分全攻略(沪教版2020必修第一册)
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2 . 如图,点C是线段AB上的一点,分别以AC、BC为边在AB的同侧作正方形ACDE和正方形CBFG,连接EG、BG、BE,当
时,
的面积记为
;当
时,
的面积记为
,……,以此类推,当
时,
的面积记为
,则
的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20227c155003de7163d407daf0a5e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20227c155003de7163d407daf0a5e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/890aea25780f7ba34adb23e799808462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20227c155003de7163d407daf0a5e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe3373f7bcdfcd1223ffd12700c5285.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/89abe346-f89d-4657-a4b0-de567129e6d7.png?resizew=175)
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2卷引用:新疆疏附县第二中学2021-2022学年高一上学期开学考试数学试题
3 . 如图,在四边形
中,
,
,动点
从
开始沿
边向
点以
的速度运动,动点
从点
开始沿
向
点以
的速度运动,
,
分别从点
,
同时出发,当其中一点到达终点时,另一点也随之停止运动,运动的时间为
秒.
![](https://img.xkw.com/dksih/QBM/2021/9/15/2808765401153536/2810832115703808/STEM/5342823a55174dc788246509316798a3.png?resizew=230)
(1)
为何值时,四边形
为矩形?
(2)
为何值时,四边形
为平行四边形?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21e0f88eb08617a47678fee9f70ba70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfb8fd7ceba575602e6cdaacf2b5713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9174c3b1324cf81098e42e0480bcc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79789686104cab147c239d152271e076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/2021/9/15/2808765401153536/2810832115703808/STEM/5342823a55174dc788246509316798a3.png?resizew=230)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dd74d529f994ca8e67630f774a639b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c203fa789096869f098e7b024dae26.png)
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4 . 已知关于
的一元二次方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559299f59b89b7f033dc95f56c1a0b70.png)
(1)
时,求证:方程一定有两个实数根.
(2)有甲、乙两个不透明的布袋,甲袋中装有3个除数字外完全相同的小球,分别标有数字1,2,3,乙袋中装有4个除数字外完全相同的小球,分别标有数字
,从甲袋中随机抽取一个小球,记录标有的数字为
,从乙袋中随机抽取一个小球,记录标有的数字为
,利用列表法或者树状图,求
的值使方程
两个相等的实数根的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559299f59b89b7f033dc95f56c1a0b70.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2371f9a64360a759b658db846aa166.png)
(2)有甲、乙两个不透明的布袋,甲袋中装有3个除数字外完全相同的小球,分别标有数字1,2,3,乙袋中装有4个除数字外完全相同的小球,分别标有数字
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14db37344529d273e36d835241d0d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c61bd0e9c2313936d4c4cdc1c8f1eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559299f59b89b7f033dc95f56c1a0b70.png)
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2卷引用:新疆疏附县第二中学2021-2022学年高一上学期开学考试数学试题
5 . 在平面直角坐标系
中,我们称横从坐标都是整数的点为整点,若坐标系内两个整点
、
满足关于
的多项式
能够因式分解为
,则称点
是
的分解点.例如
、
满足
,所以
是
的分解点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/d56a6936-b6bc-4402-92ac-caf32b2b0b84.png?resizew=607)
(1)在点
、
、
中,请找出不存在分解点的点__________;
(2)点
、
在纵轴上(
在
的上方),点
在横轴上,且点
、
、
都存在分解点,若
面积为
,请直接写出满足条件的
的个数及每个三角形的顶点坐标;
(3)已知点
在第一象限内,
是
的分解点,请探究
是否可能是等腰三角形?若可能请求出所有满足条件的点
的坐标;若不可能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/690f909c735031cb2ef82b845f73edd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e9b5ee7caf49d2a02b52dacb78d51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c114f3cc1fd54e5fa3e32fc8a15389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77683a3043e8da4c5e53ea6b8abc7718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643b31966f52a03f001f2e613cd701dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266504a4bd910b292c74765dc9772f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fe84f8c9667d04d9ce4877a2fa41c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/d56a6936-b6bc-4402-92ac-caf32b2b0b84.png?resizew=607)
(1)在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f0711cb9435f4c250674c4fe017e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8fb54d753ec8758925e5605b307867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f7517a7716dee9534c93f77431ce87.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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