名校
解题方法
1 . 已知函数
在
上为奇函数,
,
.
(1)求实数
的值;
(2)指出函数
的单调性(说明理由,不需要证明);
(3)设对任意
,都有
成立;请问是否存在
的值,使
最小值为
,若存在求出
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8932f7d6ef4d9e276fdfd582d9fd9934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)指出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1fd4b6d54199a7ef857ecd2359c0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1359b9d7aac57284a7886ab2a7b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459c84c9addfbd1cdd0a877ba7c584e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-09-29更新
|
804次组卷
|
3卷引用:浙江省杭州第四中学吴山校区2021-2022学年高一上学期期末数学试题
浙江省杭州第四中学吴山校区2021-2022学年高一上学期期末数学试题(已下线)第5章 三角函数(基础、典型、易错、压轴)分类专项训练(2)福建省龙岩市长汀县第一中学分校2023-2024学年高一上学期第三次月考数学试题
名校
2 . 利用拉格朗日(法国数学家,1736-1813)插值公式,可以把二次函数
表示成
的形式.
(1)若
,
,
,
,
,把
的二次项系数表示成关于f的函数
,并求
的值域(此处视e为给定的常数,答案用e表示);
(2)若
,
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5457d763fd9698e27fbcc1ef6d53f00a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5bac75f36bb1dc5c8190d4dbe681d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf94d263ea1e5ddad405ccbc1eb2a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f6db131eb532855af41d5e84ad22cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d0667df710a11c9f9f073babe66e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d0667df710a11c9f9f073babe66e7a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27763d65ec630511141303dad69545b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0e86caa2ab1bd37b67efe864815c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68982e0dd0bb3d87b344d23df4c2213.png)
您最近一年使用:0次
名校
3 . 设
的定义域是
,在区间
上是严格减函数;且对任意
,
,若
,则
.
(1)求证:函数
是一个偶函数;
(2)求证:对于任意的
,
.
(3)若
,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff565afbddafe8625ef376d7eb3fa649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc2435121b2b68da22ba4662e5734c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333cf846facfab1283527ebe48961a95.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)求证:对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5967cc62862986840af4dd29df4bcc41.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f8b235e47a99a065a102c259b81db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3059047431efe07f36b3fb319f709a78.png)
您最近一年使用:0次
2021-11-26更新
|
1211次组卷
|
5卷引用:专题03 函数的概念与性质(练习)-2
(已下线)专题03 函数的概念与性质(练习)-2(已下线)上海高一上学期期中【压轴42题专练】(2)重庆市南开中学2022-2023学年高一上学期12月月考数学试题上海市复旦大学附属中学2021-2022学年高一上学期期中数学试题(已下线)专题3-6 抽象函数性质综合归类(2) - 【巅峰课堂】题型归纳与培优练
名校
解题方法
4 . 有一正方形景区
,
所在直线是一条公路,该景区的垃圾可送到位于
点的垃圾回收站或公路
上的流动垃圾回收车,于是,景区分为两个区域
和
,其中
中的垃圾送到流动垃圾回收车较近,
中的垃圾送到垃圾回收站较近,景区内
和
的分界线为曲线
,现如图所示建立平面直角坐标系,其中原点
为
的中点,点
的坐标为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/f2081f60-dda2-4d2b-bbf3-8173e9952f7c.png?resizew=150)
(1)求景区内的分界线
的方程;
(2)为了证明
与
的面积之差大于1,两位同学分别给出了如下思路,思路①:求分界线
在点
处的切线方程,借助于切线与坐标轴及景区边界所围成的封闭图形面积来证明;思路②:设直线
:
,分界线
恒在直线
的下方(可以接触),求
的最小值,借助于直线
与坐标轴及景区边界所围成的封闭图形面积来证明.请选择一个思路,证明上述结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/f2081f60-dda2-4d2b-bbf3-8173e9952f7c.png?resizew=150)
(1)求景区内的分界线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)为了证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07565f10847840e0fb07b05218ad17fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
您最近一年使用:0次
名校
解题方法
5 . 正四棱锥
的展开图如图所示,侧棱
长为1,记
,其表面积记为
,体积记为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/e2bf084b-f7e5-47d8-add0-6ed4bfada543.png?resizew=202)
(1)求
的解析式,并直接写出
的取值范围;
(2)求
,并将其化简为
的形式,其中
为常数;
(3)试判断
是否存在最大值,最小值?(写出结论即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c55c1c441f921d874702a4f19ed17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9d76fb48eb30e7946cb96047e08206.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/e2bf084b-f7e5-47d8-add0-6ed4bfada543.png?resizew=202)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d0adafeb8e5d088e974f1246880055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a296bb758c36b50b102a4ceb2dea42bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
(3)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d0adafeb8e5d088e974f1246880055.png)
您最近一年使用:0次
2022-07-05更新
|
813次组卷
|
7卷引用:北京一零一中学2021-2022 学年高一下学期期末考试数学模拟试题(一)
北京一零一中学2021-2022 学年高一下学期期末考试数学模拟试题(一)上海市洋泾中学2022-2023学年高二上学期期中数学试题湖北省郧阳中学、恩施高中、沙市中学、随州二中、襄阳三中2022-2023学年高二上学期10月联考数学试题湖北省五校(郧阳中学、恩施高中、沙市中学、随州二中、襄阳三中)2022-2023学年高二上学期10月月考数学试题湖北省黄石市第二中学2023-2024学年高二上学期9月月考数学试题(已下线)湖南省长沙市雅礼中学2024届高三上学期月考(二)数学试题变式题19-22(已下线)期中测试卷01(测试范围:第10-11章)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)
名校
6 . 如图所示,等腰梯形
中,
,
,已知E,F分别为线段
,
上的动点(E,F可与线段的端点重合),且满足
,
.
关于x,y的关系式并确定x,y的取值范围;
(2)若
,判断是否存在恰当的x和y使得
取得最大值?若存在,求出该最大值及对应的x和y;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c3f33f58f50ec2d5f038e620c3294f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1578eb173c8b9a7a124c988f77a690bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c37cb57db83fb57e6a0d3a0afa1127.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a5df115177284576970a912b09ba7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916bb2cc1b29574ff95b47567c59ee0c.png)
您最近一年使用:0次
2022-04-03更新
|
1179次组卷
|
8卷引用:重庆市开州中学2021-2022学年高一下学期第一次阶段性考试数学试题
2022高一·全国·专题练习
7 . 抛物线
与
轴交于(0,3)点.
(1)求出
的值并画出这条抛物线;
(2)求它与
轴的交点和抛物线顶点的坐标;
(3)
取什么值时,抛物线在
轴上方?
(4)
取什么值时,
的值随
值的增大而减小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1be7c1888168829b95f01a02b65ae13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求它与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
8 . 已知函数
(e为自然对数的底数).
(1)求证:
时,
;
(2)设
的解为
(
,2,…),
.
①当
时,求
的取值范围;
②判断是否存在
,使得
成立,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2abd52a21627a3233cd377aa1a257189.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a90f71a22daa4df7bd75c1e3e66fcb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8a82d291105594bb2f97fb81b165d0.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2e727ac09acdaafb6c97e4f5c50aa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803092f422dcd99c23e821770b923188.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2daf2bf93c9c6fceee6b8068ee19d111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9727721cbac7d8d47c511fe934f9215d.png)
②判断是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2498a2158280a2502d58ccfc84e5bc69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2bed16e997a85f5d6d1a4d2d89a83f.png)
您最近一年使用:0次
名校
解题方法
9 . 已知实数
,且函数
,
,
,
,
,当
时,
的最小值记为
.
(1)若
,求函数
的单调递减区间;
(2)
,
,
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380067a20c25338eb0312e8df6c2760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7051b8cbec548d942b62fd290db4460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383330e8699c6ce53da6c5aaa70097d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/442a82cb501aeda22a086a2fe7ef7cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e9ac469995de3fcccf9300fbe8c68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edb160b3d56fdc5cb2123cbcac44c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7341e9d43f8456a913620d9938205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6dd3fa42436802a270cd2ff46ba51d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be555d216bf07f824f3164f05e1cb72.png)
您最近一年使用:0次
2022-11-11更新
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704次组卷
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3卷引用:福建省龙岩市一级校联盟(九校)联考2022-2023学年高一上学期期中考数学试题
名校
10 . 同时定义在D上的函数
,如果满足对任意
恒成立,且
具有相同的单调性,则乘积函数
也是D上的单调函数.已知函数
.
(1)试判断函数
在区间
上的单调性,并求出其值域;
(2)若函数
在
上满足不等式
恒成立,求实数a的取值范围;
(3)已知
是关于x的方程
的实数根,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0ed188d083966baaae94e6b86064f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c7798fa55adfb47a0bcd52095086b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0ed188d083966baaae94e6b86064f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d532291921aa03a5fa5418fe664f9598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd843b397888a9d670b267a1b3cd7a89.png)
(1)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d532291921aa03a5fa5418fe664f9598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8fcad7338ba22445542a2acaccc4479.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c728f94b77941ae0962f6cc9f72da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36bccfa0a1e8fd98384e6912803f32e1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e62c65265f8fccd7a5df4a15ac4595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e51720e989624573d41c81c5fb8eff4.png)
您最近一年使用:0次
2022-03-19更新
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781次组卷
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3卷引用:湖北省宜昌一中、龙泉中学、荆州中学三校2021-2022学年高一下学期3月阶段性检测数学试题