解题方法
1 . 在
中,
是边
的中点,
是边
上的动点(不与
重合),过点
作
的平行线交
于点
,将
沿
折起,点
折起后的位置记为点
,得到四棱锥
,如图所示,给出下列四个结论:正确的是_______ .
不可能为等腰三角形;
②
平面
;
③对任意点
,都有平面
;
④存在点
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e8a02a7f28add9b9f32e836fd8a55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57650963051ccb44a3cfb24f08228405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f9596850884048064a3ec8bd48c4762.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81fa367ec317fe2a30142e1c30cce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
③对任意点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30802944c1ea7d005c392e9a54eabedc.png)
④存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666e81326945f168fc30291f1bb2fc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9986e9390b44ddde72b54779f5825bb6.png)
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2 . 已知函数
,则下面四个结论中:
①函数
在
上单调递减;
②当
或
时,
有一个零点;
③函数
存在最小值;
④当
时,
恒成立.
其中所有正确的结论序号为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b47d4c5d3ddd3ce7f949670d36f974.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75807858b7804a1ad2039c41f323a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63783f2f99cc5d905af8050b34c5e482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a048c77ba546fd52ba4a73db53f092e.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4160810e172570db3367a657605ed7ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c6aeaef586ed4aff1bd3aa93fb728b.png)
其中所有正确的结论序号为
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解题方法
3 . 已知函数
,
,且有
,若关于
的方程
有8个相异实根,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fcf6b8e8c8c88295a6063a83c751d27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24fc566eecaf9d74d0b5a32ec62400bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2855b7a6af3f75a8a2a3270e55cf3259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a644a520b56352a738309ee8592021d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
4 . 已知函数
且
.若存在
,使得不等式
对于任意的
恒成立,求实数
的最小值为_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c5dad340991112758226fd3b5dc1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e30c903d8f8a05332af0b19e7e40df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308c33e7a29c84cbad2252e44f6acb80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd73b03919e2cd703417b4c3c1fe281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ea47220258260d54537f7b5b4be915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
5 . 已知双曲线
的左、右焦点分别为
,过
的直线与双曲线的左、右两支分别相交于
两点,直线
与双曲线的另一交点为
,若
为等腰三角形,且
的面积是
的面积的3倍,则双曲线
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a12a030f853a383a50fd889486c9f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504aada1821b16c69d86752494307d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12bdb8e9f4bd99efe2c4cdb7234b1298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2024-06-11更新
|
235次组卷
|
2卷引用:重庆市第十一中学校2023-2024学年高三第九次质量检测数学试题
名校
解题方法
6 . 在
中,点
,
分别在边
和边
上,且
,
,
交
于点
,设
,
.用
,
表示
为__________ ;若
为
上一动点且
,则
的最小值为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188c4084d1cfff4f1328e24b7621f98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11fbc3a1f1e848cf1349b9327be8607d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20cbdfe479954ba2bc33142bc931c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066bca5c293e81c8579c85cb365c4a34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471ac0f42d01c6d6e094b63628586e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2b40f03244a180953e5c99c929a723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81cef66ee751c4400eda062b694958f.png)
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7 . 如图,在矩形ABCD中,E是AB上一点,连接DE,将
沿DE翻折,恰好使点A落在BC边的中点F处,在DF上取点O,以O为圆心,OF长为半径作半圆与CD相切于点G.若
,则图中阴影部分的面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ace52b64e1e7dfc5211e033255b7d.png)
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8 . 对于任意不为0的实数
定义一种新运算“#”:①
;②
,则关于
的方程
的根为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc9b449710062494286a01537ecdc00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d785aaa5c1be4b5728cf56b4727d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/820023f3de39dffe868be95757ce76d2.png)
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名校
解题方法
9 . 已知点
,动点A在圆M:
上运动,线段AN的垂直平分线交AM于P点,则P的轨迹方程为______ ;若动点Q在圆
上运动,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e258dc5c8b4ea30bca80a56098065402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7087fd4f638a63704624fbec6e67b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d30337ed2f68b73a050688566eac4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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名校
10 . 已知函数
,
,若方程
在区间
内无解,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3474a6bdb7fd647ebbf15ae318c98b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6889205677dfb9a02934c36088b75d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe386ad25a4c1cce633ed4e129127047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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