名校
1 . 如图,在长方体
中,
是线段
上异于
的一点,则
的最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18c8850e96a30d05d5f6afede82cf54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffae5dd516ba282003e4ad9ca1b6fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d66a0e246245bcb4f4246bf709ce603.png)
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3卷引用:山东省聊城第一中学等部分学校2023-2024学年高一下学期5月质量监测联合调考数学试题
山东省聊城第一中学等部分学校2023-2024学年高一下学期5月质量监测联合调考数学试题河南省开封市多校2023-2024学年高一下学期第三次月考数学试题(已下线)专题9 立体几何中折叠问题【讲】(高一期末压轴专项)
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解题方法
2 . 已知函数
为偶函数,且在
上为增函数,若
,则x的范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3afeff5ee407c49958d508ade7f2f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e76d9f29753f74d515a34e2f389136.png)
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3 . 已知三个复数
,
,
,且
,
,
,
所对应的向量
,
满足
;则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a67a742d2a43e907fb1c3a1bdf1d6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db439eae71afd7b462a07c61d3861330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb7982e6e8af1887c360ac901143840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30deb1f343048675b9b231620369668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1640d3fff861f45c5eb4019943b000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342546266d9cfe028e7f471b96e92212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17a57d4e598f772b9cbebd54d153289.png)
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3卷引用:山东省潍坊市部分学校2023-2024学年高一下学期第二次月考数学试题
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4 . 三棱锥
的高为
,若三个侧面两两垂直,则
为
的______ 心.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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5 . 在直三棱柱
中,若
,则直线
到平面
的距离为__________ ..
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801678d432f5d93f30045d14960ddcd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
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6 . 已知
,则
在
方向上的投影向量为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0877b43e4934acc7c676273fd8f606f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
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7 . 在三棱锥
中,
平面
,则三棱锥
外接球的表面积为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/514e64d883f9abc0b13326da0559e8b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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8 . 已知函数
,
,
,
.对
,都
,使得
成立,则
的范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92ca3ac04a2bdc12bceee4dfc986054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b7ef89b540c6a358bec1237df699c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3010c07acbe166b98fc886cc846de51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7409b8e4b38636929d90f0ac54b2ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6154e00013d9dee84c0e941f676ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 . 已知正三角形
与正方形
的中心为同一点
,
的边长为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9201e9afbe1a98373191ec7266047b5e.png)
______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9201e9afbe1a98373191ec7266047b5e.png)
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解题方法
10 . 费马点是指位于三角形内且到三角形三个顶点距离之和最小的点.当三角形三个内角都小于
时,费马点与三角形三个顶点的连线构成的三个角都为
.已知点
为
的费马点,角
所对的边分别为
,若
,
,
边上的中线长为
,则
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec3f79448524d6848be51fdd5c7a150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1b5305cb9b5a90c4f13bceaaee4fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734e4bdd3d2a5d489dd863b17687e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec85f29c0860b57a8f0cf8098c13a97e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f352a59a635e3f6570e350ca08de6af5.png)
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