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1 . 已知函数
的图像关于点
中心对称,关于直线
对称(直线
是与点
距离最近的一条对称轴),过函数
的图像上的任意一点
作点
、直线
的对称点分别为
、
,且
,当
时,
,记函数
的导函数为
,则当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425699baed2affe966d1cd73e4272840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44782a2577a8a7740b92d317a849567d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be03641c9e23456c63a8eb57a3540f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb57bb18755127be041d346444a4743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042f6277c98e108cab95992342e4bfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09490514476657414d8991d633c9d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c854ab19c3db3e3d94cb43d1be4e8b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177ff3b46044219ba2c486c1a0208239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4ad8ea3f4ad0dc599a3c0e3c429baf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7994bbcf39f4dda34e877b21af71f103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce83ef34471fb2f65c789e0f82eb8142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ebaa6a0467bd309efdb9be0b37a75f1.png)
A.-2 | B.-1 | C.![]() | D.![]() |
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【市级联考】福建省南平市2019届普通高中毕业班第二次(5月)综合质量检查数学(理)试题广东省深圳市南山区华侨城中学2020届高三下学期线上测试(一)理科数学试题(已下线)专题01 两大策略应对三角函数综合问题(第二篇)-2020高考数学压轴题命题区间探究与突破(已下线)专题03 三角(第一篇)-备战2020高考数学黄金30题系列之压轴题(新课标版)
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解题方法
2 . (1)已知函数
是
上的增函数,求实数
的取值范围;
(2)试比较两数
与
的大小,并证明你得出的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b903a8ed7b0ad14e57dd14567aca541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe3414b32bbd1190b41ed8307f905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)试比较两数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f2aa0a262124d743c7766e5a223dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b289cdc5360048aaeeb734512f630e.png)
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3 . 如图,直角三角形的两直角边长分别为6和8,三角形内的阴影部分是三个半径为3的扇形,向该三角形内随机掷一点,则该点落在阴影部分的概率为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/82a79593-4604-4b65-9268-82215731e185.png?resizew=145)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/82a79593-4604-4b65-9268-82215731e185.png?resizew=145)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 选修4-4:坐标系与参数方程
在平面直角坐标系
中,以坐标原点
为极点,以
轴正半轴为极轴,建立极坐标系,曲线
的极坐标方程为
,射线
交曲线
于点
,倾斜角为
的直线
过线段
的中点
且与曲线
交于
、
两点.
(1)求曲线
的直角坐标方程及直线
的参数方程;
(2)当直线
倾斜角
为何值时,
取最小值,并求出
最小值.
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4824c0712c60735b486cffb7d8a316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe8471560900ca428a33fe7134d586b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc40c1f606f4af6bdb6b70069c674cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc40c1f606f4af6bdb6b70069c674cf.png)
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5 . 如图,在四棱锥
中,底面
是梯形,
,
,
是正三角形,
为
的中点,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/5311ca4b-249b-4359-bb07-b575c9b4df2c.png?resizew=214)
(1)求证:
平面
;
(2)在棱
上是否存在点
,使得二面角
的余弦值为
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380a2da962a97e1d3f5f14a55393d00e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9552e8165f4609eee6785ddfc2b6e483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9068f29d671d76d1e95ba3a4eaff5b96.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/5311ca4b-249b-4359-bb07-b575c9b4df2c.png?resizew=214)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4cf4e5c97ecf44aa5201d912e6abaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5437bb969e417c1c12f03326c14e0457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa0fe5da877bd3d3e406957d58a2679.png)
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|
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6 . 已知数列
的的前
项和为
,且1,
,
成等差数列.
(1)求数列
的通项公式;
(2)数列
满足
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4b93113913cfcf9e5a0cc1e9d6f9f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d1e0ec9b10d3b74ebffecd4513bbe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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7 . 在
中,角
的对边分别是
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
,则
的面积为.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6129fbf40a950fc8c516f0abaab21957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20949a6d77175b586ee777d23afc0ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 若复数
满足
,则
=.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba949c2b18ad199baccf0f7cc6ed48ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a678436954052ad6011b9e102a8c5f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知
,
,
,平面区域
是由所有满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5503bcfacb52ae8536b6bc42aec0dc5a.png)
的点
组成的区域,则区域
的面积是.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b931faee548175c7895ac9eeca6fed83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7291b3d921f595f28960abcdce6dfbed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647c97da671781944dcbac93af7cadcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5503bcfacb52ae8536b6bc42aec0dc5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6b610f646652e7187f3c82f2693955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51b617659e04083178dd7fa4e848f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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【市级联考】福建省南平市2019届普通高中毕业班第二次(5月)综合质量检查数学(理)试题广东省深圳市南山区华侨城中学2020届高三下学期线上测试(一)理科数学试题(已下线)专题7.2 二元一次不等式(组) 与简单的线性规划问题(精练)-2021年高考数学(文)一轮复习讲练测江西省宁冈中学2022届高三9月份开学考数学(理)试题(已下线)专题7-1 线性规划归类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)
名校
10 . 若实数
,
满足不等式组
,则
的最小值为________ .
![](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/9896c3483b7146249817c61d613050fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b911fd13d0ffb7b38c4f8b4dac19db8.png)
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