2023·全国·模拟预测
解题方法
1 . 双曲线
的左、右焦点分别为
,点
是其右支上一点.若
,
,
,则双曲线
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f977940552e09f59ea959965522dfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee4c0cfac5d4c9e2989311400ff7ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7285470bf401f5edaac641234ee6ff6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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名校
解题方法
2 . 在
中,
,若点
为
的中点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c0a6bf0ed3121a4b7ffb045d2ebd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129dac135251933324b0a0d0fefb5cbf.png)
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解题方法
3 . 已知
,
是单位向量,且
.若向量
满足
,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2cc1f1ef9ad32eef62aefa4c3fc3d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d61d76db9af8f375acaa0d6c45ce9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83634e314df24df73ae37d25a44d20e3.png)
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2022高三·全国·专题练习
4 . 在
中,AB=4,AC=3,∠BAC=90°,D在边BC上(与B、C不重合),延长射线AD到P,使得AP=9,若
(m为常数),则DB的长度为 __ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f992e82ed3ba48c20c645719053bdb7.png)
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解题方法
5 . 已知
是圆心为O,半径为R的圆的内接三角形,M是圆O上一点,G是
的重心.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc1aaecdd41b343bc67d6871b1b81e2.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3fa7e8f8cdaebed54846d7c6c9634c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc1aaecdd41b343bc67d6871b1b81e2.png)
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6 . 已知平面内两单位向量
,若
满足
,则
的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4443b73eb57f0f274e87973ae5939cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e2e0fd4322ad7ca917c2df8a00b5a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51ca844e7c16d67f456f56a345ba5cd.png)
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7 . 如图,在
重,点D是线段
上靠近点C的三等分点.若
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2a8bf5e05a07c93a7104839fc21849.png)
___________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d649afbddd907f0dfec1420f02f82fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e768855d77ded4d7566cc9a929171069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2a8bf5e05a07c93a7104839fc21849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/accdcd60-1bfd-43fc-afbc-aca5152b3870.png?resizew=184)
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2022-05-07更新
|
638次组卷
|
2卷引用:浙江省9+1联盟2022届高三下学期5月模拟数学试题
解题方法
8 . 设点
是
的中线
上一个动点,
的最小值是
,则中线
的长是___________ .
![](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/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4375c2e6043d6b700c7f1ca0609d6109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48042bc6f931bc79b03b6faf033547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
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解题方法
9 . 已知
为等边三角形,点G是
的重心.过点G的直线l与线段AB交于点D,与线段AC交于点E.设
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7ef4a3da53511ce0ef1b55b28b990b.png)
__________ ;
与
周长之比的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0d53573554894dbe3b31027d7cdfe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c9ca024d66f87e779fee3922c3b37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7ef4a3da53511ce0ef1b55b28b990b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2022-02-14更新
|
1451次组卷
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4卷引用:全国“星云”大联考2022届高三第三次线上联考数学试题
全国“星云”大联考2022届高三第三次线上联考数学试题(已下线)专题1平面向量线性运算 (提升版)山东省菏泽市2023-2024学年高三上学期11月期中考试数学试题(B)(已下线)专题4-2向量四心及补充定理综合归类-1
10 . 在等腰直角三角形
中,
,点
在三角形内,满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a84b7de4bcbaa36f542b7ac3886bba.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350d9f16e66c2bf7e8e3c7dd6418e639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003d09def07b84a3b85d9a92a9d1c9a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a84b7de4bcbaa36f542b7ac3886bba.png)
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2021-11-05更新
|
1421次组卷
|
3卷引用:浙江省2022届高考模拟卷数学试题(三)
浙江省2022届高考模拟卷数学试题(三)(已下线)专题06 平面向量的模与夹角(练)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(浙江专用)》天津市西青区2021-2022学年高三上学期期末数学试题