名校
解题方法
1 . 已知
的内角
,
,
所对的边分别为
,
,
,且
.
(1)求角
;
(2)若
,
,求边
及
的面积;
(3)在(2)的条件下,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/0a6936d370d6a238a608ca56f87198de.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/aeac01cbfca4071ff96f9192df7754e5.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783d6adfa8fb1352679c5185258d842a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)在(2)的条件下,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc90eb7e72622d0665504a09286fa26.png)
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解题方法
2 . 如图,四棱锥
的底面是矩形,
底面
,
,
为
的中点,且
.
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffddeafce03aae663bc823e2d5127c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186e5e7efe51fd25b9e38dc0fa23de9d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b312de408dda638ca3e9c687549d46.png)
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3 . 在极坐标系中,圆
的极坐标方程为
.以极点为坐标原点,以极轴为
轴的非负半轴,建立平面直角坐标系.
(1)写出圆
的直角坐标方程;
(2)已知圆
的极坐标方程为
,求圆
与圆
的公共弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)写出圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094ab3a9f3a40f6fc88a4184371dc745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2卷引用:甘肃省平凉市静宁县两校2022-2023学年高三上学期第一次质检考试数学(理科)试题
解题方法
4 . 已知函数
(
).
(1)若
恒成立,求实数
的取值范围;
(2)当
时,解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f4ec4938c540a4a11dff445b94a932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940adbf54e96ecb2bb2637e5f976a3b0.png)
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5 . 已知一扇形的圆心角为
(
为正角),周长为
,面积为
,所在圆的半径为
.
(1)若
,
,求扇形的弧长;
(2)若
,求
的最大值及此时扇形的半径和圆心角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa57d7c189fcfd360247063053fc2f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210e4cc913c2b111e67f1e033b69824a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786cb3b718223d49726e1ad5cbd12b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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6 . 在
的展开式中,把
,
,
,…,
叫做三项式的
次系数列.
(1)求
的值;
(2)将一个量用两种方法分别算一次,由结果相同得到等式,这是一种非常有用的思想方法,叫做“算两次”.对此,我们并不陌生,如列方程时就要从不同的侧面列出表示同一个量的代数式,几何中常用的等积法也是“算两次”的典范.根据二项式定理,将等式
的两边分别展开可得左右两边的系数对应相等,如考察左右两边展开式中
的系数可得
.利用上述思想方法,请计算
的值(可用组合数作答).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa1c8db5d9615fcd93f27c51f2cebbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7de8b609e254729c979ed2d78de9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80af4d1f81cd067cf2d6a96f314479c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e4bded23ed1500d9368d6cb117149e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50738c74cc3b9a0f7739ee511803dbd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca593eda84c841a7172cd7e4bf4e90b.png)
(2)将一个量用两种方法分别算一次,由结果相同得到等式,这是一种非常有用的思想方法,叫做“算两次”.对此,我们并不陌生,如列方程时就要从不同的侧面列出表示同一个量的代数式,几何中常用的等积法也是“算两次”的典范.根据二项式定理,将等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b624491c6cb586836d591bf8fa3fce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e26f2235031a8d214d82a5e405db676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65383aa7a73843bd22eac3dc3262dbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ac6d04e7725a6d18d36052fc772b14.png)
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7 . 已知函数
.
(1)若
,求实数x的取值范围;
(2)求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11e0836c170e289223b650976f83b17.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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名校
解题方法
8 . 已知椭圆
的左、右焦点分别为
,经过左焦点
的直线与椭圆交于
两点(异于左、右顶点).
(1)求
的周长;
(2)求椭圆
上的点到直线
距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2c2c7a8f822a339a40fb724c3be2b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
(2)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f524ac41ac7f7ee26b566bc145b082.png)
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9 . 已知
或
.
(1)若
是
的充分条件,求实数
的取值范围;
(2)若
是
的必要不充分条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558723a72857184db7c8ba0d2c2fa840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87492cf46ac0260bef61414c8035134.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e26b38e357c7d985656ba7bb3c794a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
10 . 已知集合
.
(1)若
,求实数
的值;
(2)若命题
为真命题,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f19ed48c4b65f777695d5d25031f22.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed961de27af72b7d11887ccfb6f15071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c712af17f519beff6c8fe6ba648e6d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4卷引用:云南省曲靖市马龙区第一中学校2023-2024学年高一上学期期中考试数学试题
云南省曲靖市马龙区第一中学校2023-2024学年高一上学期期中考试数学试题云南省曲靖市沾益区第一中学2023-2024学年高一上学期第一次月考数学试题河北省辛集市第三中学2023-2024学年高一上学期10月月考数学试题(已下线)周测1 集合与常用逻辑用语 一轮周测卷(基础卷)