名校
解题方法
1 . 如图,在棱长为2的正方体
中,点E,F分别是
和
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
A.![]() |
B.![]() |
C.点F到平面EAC的距离为![]() |
D.过E作平面![]() ![]() ![]() |
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2024-05-17更新
|
534次组卷
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4卷引用:福建省厦门市2024届高中毕业班第二次质量检查基础巩固练习数学试题
福建省厦门市2024届高中毕业班第二次质量检查基础巩固练习数学试题(已下线)专题3 立体几何中的范围、最值问题【讲】(已下线)专题5 空间向量的应用问题【讲】广东省广州市广雅中学2024届高三下学期教学情况检测(一)数学试题
名校
解题方法
2 . 如图,
的半径等于2,弦BC平行于x轴,将劣弧BC沿弦BC对称,恰好经过原点O,此时直线
与这两段弧有4个交点,则m的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b74381f68eb1e33d412a7a3d62313f.png)
A.![]() | B.![]() | C.![]() | D.1 |
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2024-05-17更新
|
367次组卷
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3卷引用:福建省厦门市2024届高中毕业班第二次质量检查基础巩固练习数学试题
3 . 已知函数
,
.
(1)当
时,求函数
的极值;
(2)已知实数
.
①求证:函数
有且仅有一个零点;
②设该零点为
,若
图象上有且只有一对点
,
关于点
成中心对称,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fe84ecdcafb66c2e3a4dd702503729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068eeacfc105bcd3cb3e547a9cc3f39c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38ada7012b4fd07e9d345c87f346157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)已知实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0c40f94da9ef7dc21e296235b2326a.png)
①求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②设该零点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad9a4881ebe1a4a566d0fab96d71baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9938230f82e91cf09f8157b532baaba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
4 . 已知函数
,
.
(1)求函数
的值域;
(2)设函数
,证明:
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d770179a24541b9d811da5d944cdfa5.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4f3c214da1a20a9ccd33b224531829.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5066adf9157eb0385dc86a44479d91af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112d3c32a1a43115e1f57a7c910a7840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823a11fc7541e66fb15b95884ce476ee.png)
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5 . 已知A,B分别为椭圆
的上下顶点,P为直线
上的动点,且P不在椭圆上,
与椭圆E的另一交点为C,
与椭圆E的另一交点为D,(C,D均不与椭圆E上下顶点重合).
(1)证明:直线
过定点;
(2)设(1)问中定点为Q,过点C,D分别作直线
的垂线,垂足分别为M,N,记
,
,
的面积分别为
,
,
,试问:是否存在常数t,使得
,
,
总为等比数列?若存在,求出t的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4574be1104de2f44eca29d8787fff20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020d714d62aacf77f1f89f575931659f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)设(1)问中定点为Q,过点C,D分别作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020d714d62aacf77f1f89f575931659f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51496e5f2d2f91c5c4aade9bc504ecfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589554d1c4a022cf782658a7856f8f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d0e5912f14c7c91801387a2e93684b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
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6 . 设
,有如下两个命题:
①函数
的图象与圆
有且只有两个公共点;
②存在唯一的正方形
,其四个顶点都在函数
的图象上.
则下列说法正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b636844dddba5c8e2a96f34e03c7eddb.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
②存在唯一的正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
则下列说法正确的是( ).
A.①正确,②正确 | B.①正确,②不正确 |
C.①不正确,②正确 | D.①不正确,②不正确 |
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7 . 已知函数
的图象关于点
中心对称,也关于点
中心对称,则
的中位数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef66a0582e95fb5c57a405acdea9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a8fd4c249b86cec67292b178957c00.png)
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解题方法
8 . 已知集合
且
,若
中的点均在直线
的同一侧,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8892c70febbbced59d19e9c2eeaeba83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435f47f6e6b75ebcab948d15889e5d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66719cddfed0197a80bdfbe48cdb3cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-05-16更新
|
1286次组卷
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3卷引用:浙江省宁波市2023-2024学年高三下学期高考模拟考试数学试题
浙江省宁波市2023-2024学年高三下学期高考模拟考试数学试题安徽省六安第一中学2023-2024学年高三下学期期末质量检测卷(二)数学试题(已下线)压轴题01集合新定义、函数与导数13题型汇总-2
解题方法
9 . 我们知道,二维空间(平面)向量可用二元有序数组
表示;三维空间向盘可用三元有序数组
表示.一般地,
维空间向量用
元有序数组
表示,其中
称为空间向量的第
个分量,
为这个分量的下标.对于
维空间向量
,定义集合
.记
的元素的个数为
(约定空集的元素个数为0).
(1)若空间向量
,求
及
;
(2)对于空间向量
.若
,求证:
,若
,则
;
(3)若空间向量
的坐标满足
,当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1acd1459dd96e861e6e04abccb2a3817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c2a29087dbd2e7635da13f7d288c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a3c6c6fe94124d76957d9a8c837701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4e5fb9e41d1310778b0dda692066dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afad70ea217c830631639e8508ad410b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0196cb738ee760339a9e15c8e6d9a41.png)
(1)若空间向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4517944d03f267b87ee1c184f463dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a0d7cdd1e3a38753d1290d9de9f9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc51f796615bfd474cee9d4d80e1eae.png)
(2)对于空间向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09611387d4de23004d388c9a8dde3438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daee8af73118698c77e022651f69ef22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
(3)若空间向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd074bea5f4eb8f60729b75e970afda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3894099d6bf29b73086842a48da10174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1653bed33a88140f16d494e8454f5225.png)
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解题方法
10 . 阿波罗尼斯是古希腊著名数学家,他的主要研究成果集中在他的代表作《圆锥曲线》一书中.阿波罗尼斯圆是他的研究成果之一,阿波罗尼斯圆指的是已知动点
与两定点
的距离之比
且
是一个常数,那么动点
的轨迹就是阿波罗尼斯圆,圆心在直线
上.已知动点
的轨迹是阿波罗尼斯圆,其方程为
,定点分别为椭圆
的上顶点与右顶点,且椭圆
的离心率为
.
(1)求椭圆
的标准方程;
(2)已知点
,过点
斜率分别为
的直线与椭圆
的另一个交点分别为
,且满足
,试探究
面积是否存在最大值,若存在,求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d639ec461b081a514298195ecd287a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d25d2cb4e60dd4acec4b2df4ea698a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa54ac815e53ee67c18f42407d0f30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51a37d31d19715a50d6e5f3c3d007fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78eba6f91d97cea1dfd73bae53e7b689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f90eb172dbd2ff7ae6f705801c0737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d200a411fbc2f50ad72f1fd729a7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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