名校
解题方法
1 . 如图所示,在直三棱柱
中,若
,
,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c02338caa8ea2a27a5a37226a8a472.png)
A.三棱锥![]() ![]() |
B.点![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.点![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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2 . 下列命题中正确的是( )
A.梯形的直观图可能是平行四边形 |
B.圆锥的轴截面是所有过顶点的截面中面积最大的一个 |
C.有两个面平行且相似,其他各个面都是梯形的多面体是棱台 |
D.底面是矩形的直平行六面体是长方体 |
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3 . 已知
,
,
与
的夹角为
.
(1)求
;
(2)求
与
夹角的余弦值;
(3)若
,
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ae0d7b3266f32b6a916b6237b6b838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b113dc271cf51b3018bd1de14edf73ad.png)
![](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/d9cbb1eec186a57915e5aced5edce78c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea7e9c354c3e704c6f8ed02de9c2dda.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f0484158c0bb8ef08faf224bba82e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83c5803cc8c05849028a57c4bd4ee72.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f219540d81398b43c1336a8504e857a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5480b4d197235d88c618c52cb8cd01be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8440725e1df5ca0990b572dd84127914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72850427e83ff19a24305783e080b280.png)
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3卷引用:黑龙江省佳木斯市第一中学2023-2024学年高一下学期5月期中考试数学试题
黑龙江省佳木斯市第一中学2023-2024学年高一下学期5月期中考试数学试题(已下线)【高一模块二】类型1 以平面向量为背景的解答题(A卷基础卷)福建省部分优质高中2023-2024学年高一下学期第二次阶段性检测数学试题
名校
解题方法
4 . 三棱柱
中,
、
、
分别是
、
、
中点,则下列直线中与直线
异面的直线为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
A.直线![]() | B.直线![]() | C.直线![]() | D.直线![]() |
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5 . 在棱长为2的正方体
中,P,E,F分别为棱
,
,BC的中点,
为侧面
的中心,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
A.直线![]() | B.直线![]() ![]() |
C.三棱锥![]() ![]() | D.三棱锥![]() ![]() |
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名校
解题方法
6 . 在
中,
,
,
对应的边分别为
,
,
,
.
(1)求
;
(2)若
为
边中点,
,求
的最大值;
(3)奥古斯丁·路易斯·柯西(Augustin Louis Cauchy,1789年-1857年),.法国著名数学家,柯西在数学领域有非常高的造诣,很多数学的定理和公式都以他的名字来命名,如柯西不等式、柯西积分公式.其中柯西不等式在解决不等式证明的有关问题中有着广泛的应用.现在,在(1)的条件下,若
,P是
内一点,过P作AB,BC,AC垂线,垂足分别为D,E,F,借助于三维分式型柯西不等式:
,
,
,
,当且仅当
时等号成立.求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0613b0193c7ca5dcbc9126cb8b6a442e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(3)奥古斯丁·路易斯·柯西(Augustin Louis Cauchy,1789年-1857年),.法国著名数学家,柯西在数学领域有非常高的造诣,很多数学的定理和公式都以他的名字来命名,如柯西不等式、柯西积分公式.其中柯西不等式在解决不等式证明的有关问题中有着广泛的应用.现在,在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0666367a513f4fd1fb3c528e5f3afdd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c1254b9aeec2bbd01d0eecca66d708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5ba135022def1bcc1cddea66496706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebbd1d0e4d44a11d9b0d65e73eef212.png)
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名校
解题方法
7 .
的内角
,
,
的对边分别为
,
,
,已知
.
(1)求
;
(2)若
,
,求
;
(3)若
,
,求
边上的高
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee56e540da5f3a3a19c7e6c8ebf992db.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23725094c363fd158166a8698971694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c8420644d9a31d536e32257e2e7ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d6f212da7915817470bfe8728a8055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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名校
解题方法
8 . 设
,
,则a等于________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf825efc71d548c3e5f23ada63fbcc69.png)
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名校
解题方法
9 . 已知
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd01707e8d32f277b83c007a5b15bd7.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0591b372a58045624f2e57489d4dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac0eba16bb810da7e1da72189a75fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd01707e8d32f277b83c007a5b15bd7.png)
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名校
解题方法
10 . 已知正四棱锥
的所有棱长均为2,点
为正四棱锥
的外接球球面上一动点,
,则动点
的轨迹长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b092934ebc48422434232d474cb7c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次