名校
1 . 如图,四面体
中,
是
的中点,
和
均为等边三角形,
.
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e61bb73ed43e922a1ea1e4bc10b110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
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2 . 已知等差数列
满足
,数列
满足
,数列
为等比数列.
(1)求数列
和
的通项公式;
(2)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae793d9bcc66a428a99d71cd8f58a7ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e302fd28e7f8ad835c3cdbdead8ee6ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54786e9cd67005e30a32f61ff97c2a09.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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名校
3 . 已知函数
.
(1)讨论
的单调性;
(2)若
恒成立,求
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0794d168ed670ab3a542c18fc0b26eb.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
4 . 已知函数
,且
的最小值为
.
(1)求
的值;
(2)若
为正数,且满足
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbef3caed2dfc0acbd7ecfab73e4d7d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e6d49738325344bcc6b2015189e194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0be51ec8263c3289ded555b8017c00.png)
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解题方法
5 . 某公司为了确定下季度的前期广告投入计划,收集并整理了近6个月广告投入量x(单位:万元)和收益y(单位:万元)的数据如表(其中有些数据污损不清):
他们分别用两种模型①
,②
进行拟合,得到相应的回归方程并进行残差分析,得到如图所示的残差图及一些统计量的值.
(1)根据残差图,比较模型①,②的拟合效果,应选择哪个模型?
(2)残差绝对值大于2 的数据被认为是异常数据,需要剔除.
(i)剔除异常数据后,求出(1)中所选模型的回归方程;
(ii)若广告投入量x=19,则(1)中所选模型收益的预报值是多少万 元?(精确到0.01)
附:对于一组数据
其回归直线
的斜率和截距的最小二乘估计分别为:
.
月份 | 1 | 2 | 3 | 4 | 5 | 6 |
广告投入量 | 2 | 7 | 8 | 10 | ||
收益 | 20 | 30 | 34 | 37 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b447ac3d1a965572c31b6e4c18d4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dd7bfa66cda5972dde24f1e8f5c590.png)
![]() | ![]() | ![]() | ![]() |
7 | 30 | 1470 | 370 |
(2)残差绝对值大于2 的数据被认为是异常数据,需要剔除.
(i)剔除异常数据后,求出(1)中所选模型的回归方程;
(ii)若广告投入量x=19,则(1)中所选模型收益的预报值是多少
附:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37cf8b64a1856364b5da6f2a31720da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db6103cb0f1d2bd6b19235d53ee7e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2532d1287265fb840f656e652db62dfe.png)
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6 . 已知a、b、c、d均为正数,且
.
(1)证明:若
,则
;
(2)若
,求实数 t 的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd68c14adb3cf12d8f77aec55a053284.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522ea2b031666780e551b93fe8ca4cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94da00cf32ddc7f4ae42deed4674b8c2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a81e75791c51f5723bec31e0bdeea2b.png)
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解题方法
7 . 如图,在三棱柱
中,底面
是等边三角形,
,D为
的中点,过
的平面交棱
于 E,交
于F.
⊥平面
;
(2)若
是等边三角形,
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521e771f98c17242d43c78d511ba7134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb3f0b5d8bf98eeff66f43b7dcbb4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85987061f1bc095faaa296d32f13b316.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16a755e7809e750a33fffd2f361480e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb606548eca84c3b64e1b1f17fd2999.png)
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8 . 在直角坐标系xOy中,曲线C的参数方程为
(t为参数),直线l的方程为
.以坐标原点为极点,x 轴正半轴为极轴建立极坐标系.
(1)求曲线C的普通方程和直线l的极坐标方程;
(2)点 P 的极坐标为
,设直线 l与曲线C的交点为A、B 两点,若线段AB 的中点为D,求线段 PD的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b82caa9ec78e4fe800d40dd32f6ac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baabfd32465e9e50409413d9c1358279.png)
(1)求曲线C的普通方程和直线l的极坐标方程;
(2)点 P 的极坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f806d074c85ab6a28f4d2538c7139ba.png)
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解题方法
9 . 已知
是等差数列,
是等比数列,且
的前n项和为
,在①
,②
这两个条件中任选其中一个,完成下面问题的解答.
(1)求数列
和
的通项公式;
(2)设数列
的前n项和为
,是否存在
,使得
若存在,求出所有满足题意的
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274191cca23e72fa887829f4527e98c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ff8ce3e59c069490084ffc200cfda9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a99b841116f01b845a324da81d786c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2767882820f4ba0defde0e412adb747f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38b6286e5f74b604b9fb639c55d611f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0137430ff7d1753310cf17a5f0e58b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
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名校
解题方法
10 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
(1)若双曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
的一条渐近线方程为
,且与椭圆C有公共焦点,求此双曲线的方程;
(2)过点
的动直线
交椭圆
于
两点,试问在坐标平面上是否存在一个定点
,使得以
为直径的圆恒过定点
?若存在,求出
的坐标,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
(1)若双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d3f9d8344e1c727fbbed5421daaa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920fdf4cd0153c43eb7b9130b86de598.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6831c6674f4bf86df7c8dd730e1c187d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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2024-04-22更新
|
595次组卷
|
4卷引用:四川省德阳市第五中学2023-2024学年高二下学期五月月考数学试卷
四川省德阳市第五中学2023-2024学年高二下学期五月月考数学试卷上海市位育中学2023-2024学年高二下学期期中考试数学试卷(已下线)易错点8 圆锥曲线问题中未讨论直线斜率的特殊情况(已下线)专题02圆锥曲线全章复习攻略--高二期末考点大串讲(沪教版2020选修一)