名校
1 . 为了调查疫情期间数学网课学习情况,某校组织了高一年级学生进行了数学测试.根据测试成绩(总分100分),将所得数据按照
分成6组,其频率分布直方图如图所示.
(2)试估计本次数学测试成绩的平均分;(同一组中的数据用该组区间的中点值作代表);
(3)该校准备对本次数学测试成绩优异(将成绩从高到低排列,排在前
的为优异)的学生进行嘉奖,则受嘉奖的学生分数不低于多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093679ff08f32c98b109918bbecd0a88.png)
(2)试估计本次数学测试成绩的平均分;(同一组中的数据用该组区间的中点值作代表);
(3)该校准备对本次数学测试成绩优异(将成绩从高到低排列,排在前
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe75950eecc2343e47cc594b0ac011d.png)
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名校
解题方法
2 . 如图,三棱柱
中,E为
中点,F为
中点.
平面ABC;
(2)若
,平面
平面ABC,
,求证:
平面ABC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073a88b42836fb88433679932b48ad03.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72bf47c909082e035c91146b1293426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9bdbbdfabc737323692c796e41930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25e8fc3dda4f8b45491514b6e22a962.png)
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名校
3 . 在
中,AD是
的角平分线,AE是边BC上的中线,点D、E在边BC上.
(1)用正弦定理证明
;
(2)若
,求DE的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3322a2ad9a95bdc9fc576a7a158d4d.png)
(1)用正弦定理证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c6ba1dce1e32a78ea2f3a85a3c8962.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95d54823e4a9895941d5b88b802670c.png)
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解题方法
4 . 已知集合,
,全集
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
5 . 求值
(1)已知
是第三象限角,且
,求
的值;
(2)已知
,求
的值.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07a22d487e54ec1f2719b7a50a82965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d74c74c3c6890362d623a44fcc6e41f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82dabe724194628c06966777a914e961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f35152720e43c6403d43bef47c0377d.png)
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解题方法
6 . 已知等差数列
的前
项和为
,
,
;数列
的前
项和
.
(1)求数列
与
的通项公式;
(2)若
,求数列
的前
项和
.
![](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/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2243888a494faf3e899eaff6e8fc123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f6ba63d37f1597a15c3f2f7f86263d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac07953530e3c248b3438fb200fb1661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9445875e1d2f78a79c38a04897435418.png)
您最近一年使用:0次
2024-02-23更新
|
454次组卷
|
2卷引用:江苏省连云港市2023-2024学年高二上学期期末调研考试数学试题
名校
解题方法
7 . 已知椭圆
:
(
)经过点
,
.
(1)求椭圆
的标准方程;
(2)已知点
,
,
为椭圆
上异于A的两点,且
,证明:直线
过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cda9ce6d633bc1f3a249fb0fc458a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303e6de91a36b8ca92ae42c952cad8af.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2024-02-23更新
|
359次组卷
|
2卷引用:江苏省连云港市2023-2024学年高二上学期期末调研考试数学试题
8 . 如图1,有一块半径为2(单位:
)的半圆形钢板,计划裁剪成等腰梯形
的形状,它的下底
是半圆的直径,上底
的端点在圆周上.为了求出等腰梯形
的周长
(单位:
)的最大值,小明和小亮两位同学分别给出了如下两种方案:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/1e9d5c2f-889f-4d20-8c53-9da34bed8576.png?resizew=338)
(1)小明的方案:设梯形的腰长为
(单位:
),请你帮他求
与
之间的函数关系式,并求出梯形周长的最大值;
(2)小亮的方案:如图2,连接
,设
,请你帮他求
与
之间的函数关系式,并求出梯形周长的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/1e9d5c2f-889f-4d20-8c53-9da34bed8576.png?resizew=338)
(1)小明的方案:设梯形的腰长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)小亮的方案:如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ed15020c1c669e06a3a3b1557242e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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9 . 已知函数
(
).
(1)记
,讨论
的单调性;
(2)若对任意的
,都有
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8521eff2f145b88056f337e335b606ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2259e91a333ecf7900f6289f1fc22759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
10 . 已知圆
经过两点
,
,且圆心
在直线
上.
(1)求圆
的标准方程;
(2)求过点
且与圆
相切的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30ca15af0d5cbd9c45b2453a733810b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f12f12b6e78f741846da2d56089631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953b0e963195605a67975c6f8f3caa0c.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947bca78fd2d7a7436dd9dedbba3baa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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