名校
1 . 已知函数
,点
、
是函数
图象上不同的两个点,设
为坐标原点,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541ec913428703d4cae2476b147ce1a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63711c480473cbc27a06cdb82ddd000.png)
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解题方法
2 . 已知
,
均为锐角,
,则
取得最大值时,
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc394c19712cbbef1c781a6a8286dd59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673f7e66c2a252da4c77c70d90c8cec.png)
A.![]() | B.![]() | C.2 | D.1 |
您最近一年使用:0次
2024-06-11更新
|
604次组卷
|
3卷引用:辽宁省大连育明高级中学2023-2024学年高一下学期期中考试数学试卷
名校
解题方法
3 . 古希腊数学家阿波罗尼奥斯用不同的平面截同一圆锥,得到了圆锥曲线,其中的一种如图所示.用过
点且垂直于圆锥底面的平面截两个全等的对顶圆锥得到双曲线的一部分,已知高
,底面圆的半径为4,
为母线
的中点,平面与底面的交线
,则双曲线的两条渐近线所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab00e0cff0876c4183a47f1272cf9928.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 对于
中角
所对的边分别为
则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832a6ae04b25ef0896bd607cdcda60ca.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
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解题方法
5 . 如图,已知等腰梯形
的外接圆圆心
在底边
上,
,
,
,点
是上半圆上的动点(不包含
,
两点),点
是线段
上的动点,将半圆
所在的平面沿直径
折起,使得平面
平面
.
平面
时,求
的值;
(2)证明:
不可能垂直
;
(3)设
与平面
所成的角为
,二面角
的平面角为
(其中
),求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e01d3d6bd865e16908eb08dec78f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a6241af8eadb720f601ee48f74cb9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745e0525a41fe2e2a7739c75a942290b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b70cef0b79ca64acbb67dc667fc53b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7fdfebdbaddc49e8991ec47d2fb076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9350ccf7500c62835c27f4b946b6db58.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ea10539215794cd76e8b211abd503f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cd47260d190dc5b89e5303879ab164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628560d39eeb0339fa00c9c15ab2c095.png)
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6 . 如图,点
分别是矩形
的边
上的两点,
,
.
、
分别为
、
的中点,求
;
(2)若
,求
的范围;
(3)若
,连接
交
的延长线于点
为
的中点,试探究线段
上是否存在一点
,使得
最大.若存在,求
的长;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ced9844fe2e052c70486af0740afa63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c066b8e15742b2ef57131636e54ca0f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50651ac65f1837e81ce47b71c5f4eeaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5604d3e156df3e7ccca0ccec9c9d45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1697dd04381cd28fece406c739960b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604ed5bece96d5e878aa1c914acc2f9d.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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e3d3a8bb04c4f34676aa6166eac112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
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7 . 如图1,某景区是一个以C为圆心,半径为
的圆形区域,道路
成60°角,且均和景区边界相切,现要修一条与景区相切的观光木栈道
,点
分别在
和
上,修建的木栈道
与道路
,
围成三角地块
.(注:圆的切线长性质:圆外一点引圆的两条切线长相等).
为正三角形时,求修建的木栈道
与道路
围成的三角地块
面积;
(2)若
的面积
,求木栈道
长;
(3)如图2,若景区中心
与木栈道
段连线的
.
①将木栈道
的长度表示为
的函数,并指出定义域;
②求木栈道
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e3dce65f4583f209cc69eed1674341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c63cb79d595e99b19f17ad71de6eae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)如图2,若景区中心
![](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/414ef209e6ce6428bd358eafd74ddaa1.png)
①将木栈道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
②求木栈道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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解题方法
8 . 在锐角三角形
中,已知
,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b473ccb69f1341bd3c084da64d6e55b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6f4e9bb8b453665bfe9b8fa24711cb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 如图,正方形
的边长为
分别为边
上的点,则以下错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850a0ec73c3fba08a6764a7bc2209c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630754333e7043c573d0ecdb64cf1246.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() |
D.![]() ![]() |
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10 . 某大型商场为迎接新年的到来,在自动扶梯
(
米)的
点的上方悬挂竖直高度为5米的广告牌
.如图所示,广告牌底部点
正好为
的中点,电梯
的坡度
.某人在扶梯上点
处(异于点
)观察广告牌的视角
,当人在
点时,观测到视角
的正切值为
.
的长为
米,用
表示
;
(2)求扶梯
的长;
(3)当某人在扶梯上观察广告牌的视角
最大时,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73b83c5c8b32feea33d367096724fd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aabecf66d94e4094f9cc46fd8ee050f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6070f34ccef3dae6e2ff80cf5224c7bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e7106619c08f2bcc1d21f846e8a0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab52a9c7f7b361ad0488f01d714135fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13b2bedd7b3a411b9c4f4efec4fed7d.png)
(2)求扶梯
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(3)当某人在扶梯上观察广告牌的视角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
您最近一年使用:0次
2024-04-18更新
|
624次组卷
|
2卷引用:湖北省武汉市部分重点中学2023-2024学年高一下学期4月期中联考数学试题