名校
解题方法
1 . 已知正方体
的棱长为1,E是
的中点,则下列选项中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
A.![]() | B.![]() ![]() |
C.三棱锥![]() ![]() | D.异面直线![]() ![]() |
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2024-06-16更新
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418次组卷
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2卷引用:宁夏回族自治区石嘴山市平罗县平罗中学2023-2024学年高一下学期5月期中考试数学试题
名校
解题方法
2 . 《九章算术》是我国古代数学名著,它在几何学中的研究比西方早
多年,在《九章算术》中,将底面为直角三角形且侧棱垂直于底面的三棱柱称为堑堵,将底面为矩形且一侧棱垂直于底面的四棱锥称为阳马,将四个面均为直角三角形的四面体称为鳖臑.如图在堑堵
中,
,
,
,
分别为棱
,
的中点,则下列说法正确的是______ .(只填序号)
①四面体
为鳖臑
②
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
③若
,则
与
所成角的正弦值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
④三棱锥
的外接球的体积为定值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30821635432b069b6c2bf74fa09552f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadc63e6e33743ce590ed968948a5a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30dbd22b0cbb47c914c42a4355e3ca98.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
①四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30821635432b069b6c2bf74fa09552f.png)
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3 . 已知
为直线
的方向向量,
,
分别为平面
,
的法向量(不重合),则正确选项是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95763e154888a080b3b96ff7fb3b39f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e163480714acc9dae5005cac65d217d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 已知向量
,向量
满足
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0ee77aca9d78f2e59940067b1a5ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427fa45527d0ce469bfd060bf6f991f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28fc035c4fbbf0c0faf5a3f81075d36b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d07429c41e8885966a917023f54359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9684cd10a15236bde52b355ac0806975.png)
A.![]() | B.5 | C.![]() | D.25 |
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解题方法
5 . 已知点
,
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb9e88d3e58141dba299dcd8edc4e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02af485e17e7628fd5a3ace6e0a32ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a56e5ddc6dc057aa4076130cc6ce19.png)
A.![]() |
B.若点![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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|
522次组卷
|
6卷引用:宁夏回族自治区石嘴山市平罗县平罗中学2023-2024学年高一下学期5月期中考试数学试题
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解题方法
6 . 已知
的内角A、B、C对的边分别为a,b,c,
,D为边AC上一点,满足
且
,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7bce5b3862e12e5c7d206c35052471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7836f32fe50cc85e092fde49899703b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1ca356addf3fe6a51c33622a57405f.png)
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7 . 为了测量某建筑物的高度AB,可以选与底部
在同一水平面内的两个测量基点
与
.现测得
,
米,并在点
测得塔顶
的仰角为
,则该建筑物的高度![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
______ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c983ccc6be7900aafdab66d34f9d3742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2dcf2debb4c733c88061662bd22a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260200d547998bcac50a4a491382e7f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
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2024-04-03更新
|
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3卷引用:宁夏回族自治区石嘴山市第三中学2023-2024学年高一下学期5月月考数学试题
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解题方法
8 . 如图,正方形ABCD的边长为6,E是AB的中点,F是BC边上靠近点B的三等分点,AF与DE交于点M.
与
所成角的余弦值;
(2)设
,求λ的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c3accb1b8a5479439beff4259660e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa8c53645db602c72b00b599c2c0ff97.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd73c525a69bf64db2867e570933b95.png)
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9 . 已知i是虚数单位,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34a5627935dbaaa0c676610c4a1c934.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34a5627935dbaaa0c676610c4a1c934.png)
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10 . 已知向量
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5618d27a4010782412bc0dbbda61d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec328c735461ce64a92945a7e197c8.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2024-03-29更新
|
880次组卷
|
6卷引用:宁夏回族自治区石嘴山市第三中学2023-2024学年高一下学期期中考试数学试题