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1 . 下列导数运算错误的是( )
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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3卷引用:四川省成都市树德中学2023-2024学年高二下学期期末数学试题
四川省成都市树德中学2023-2024学年高二下学期期末数学试题北京市铁路第二中学2023~2024学年高二下学期期中考试数学试卷(已下线)专题08 导数及其应用--高二期末考点大串讲(人教B版2019选择性必修第三册)
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2 . 某植物园种植一种观赏花卉,这种观赏花卉的高度(单位:
)介于
之间,现对植物园部分该种观赏花卉的高度进行测量,所得数据统计如图所示.
的值;
(2)若从高度在
和
中分层抽样抽取5株,在这5株中随机抽取3株,记高度在
内的株数为
,求
的分布列及数学期望
;
(3)以频率估计概率,若在所有花卉中随机抽取3株,记高度在
内的株数为
,求
的数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d592724f330f410956e04e2a47658fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若从高度在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cefc544a6058b597082489e637eb9b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04534be52a9e6a819b6a85b5b281ae89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cefc544a6058b597082489e637eb9b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0919cf56a1b743189a019551b2d5a0.png)
(3)以频率估计概率,若在所有花卉中随机抽取3株,记高度在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cefc544a6058b597082489e637eb9b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
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解题方法
3 . 已知双曲线C:
的左、右焦点分别为
,
,
为原点,若以
为直径的圆与
的渐近线的一个交点为
,且
,则
的离心率为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf120a1c13adc971ba3642b33e9867d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cdfc6a59392d1ac3cd89ddc0308864c.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/e0d08a832eacf576430dc50a8f9e3875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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4 . 在
的展开式中,
项的系数为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e127c0a4938a57988a75dccaec672f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d800f03de80068a1172beac3a2c75587.png)
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5 . 如图,在棱长为2的正方体
中,
为正方体的中心,
为
的中点,
为侧面正方形
内一动点,且满足
平面
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253ffd3fc633d861810ee2e872188b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1df970d8b2fcbb38bfac1dc33da9179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a0a3bb566b5d2404e4bb823abddfa9.png)
A.三棱锥![]() ![]() |
B.动点![]() ![]() |
C.三棱锥![]() |
D.若过![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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6 . 已知椭圆
的左焦点为
,上顶点为
,离心率
,直线FB过点
.
(1)求椭圆
的标准方程;
(2)过点
的直线
与椭圆
相交于M,N两点(M、N都不在坐标轴上),若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbcf0320d94734aedd3d4e2e31b9827.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78957626ea0a503c069eb52ece85635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2卷引用:四川省成都市树德中学2023-2024学年高二下学期期末数学试题
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7 . 如图,在底面
是矩形的四棱锥
中,
,点
在底面
上的射影为点
与
在直线
的两侧
,且
.
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01f7f3bd1c701bf81f4a775136c5443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad2041eace3c1f44542d2afcab2dcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4e813c2b7a248470b1ebef5b8bdcb4.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
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3卷引用:四川省成都市树德中学2023-2024学年高二下学期期末数学试题
8 . 设公差不为
的等差数列
的首项为
,且
成等比数列.
(1)求数列
的通项公式;
(2)已知数列
为正项数列,且
,设数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc54335d4de8adc7c8d5425ba9ee67f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0e24230de5f84e8937dfbd4fb61450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7c561d49be978dafe36601ba26f536.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/8a790ada33239d9fb562525f819a817d.png)
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9 . 某班组织开展知识竞赛,抽取四名同学,分成甲、乙两组:每组两人,进行对战答题.规则如下:每次每名同学回答6道题目,其中有1道是送分题(即每名同学至少答对1题).若每次每组对的题数之和为3的倍数,则原答题组的人再继续答题;若对的题数之和不是3的倍数,就由对方组接着答题,假设每名同学每次答题之间相互独立,且每次答题顺序不作考虑,第一次由甲组开始答题,则第7次由甲组答题的概率为______ .
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2卷引用:四川省成都市树德中学2023-2024学年高二下学期期末数学试题
10 . 已知等比数列
的公比为
,前
项和为
,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.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/552fb73bf6456c14e8890a122fb3f6ff.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2卷引用:四川省成都市树德中学2023-2024学年高二下学期期末数学试题