名校
解题方法
1 . 在棱长均相等的四面体
中,
为棱
(不含端点)上的动点,过点
的平面
与平面
平行.若平面
与平面
,平面
的交线分别为
,则
所成角的正弦值的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
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2 . 在锐角
中,角
的对边分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
为
的面积,且
,则
的取值范围为__________ .
![](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/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c28d53e229fcea80c26b22d9e1a94ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a6afd3e0a0ed112f0533119fbb35d0.png)
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3 . “杨辉三角”是二项式系数在三角形中的一种几何排列.从第1层开始,第
层从左到右的数字之和记为
,如
,
,…,则
的前9项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4e70b360f988fdbd92300ab22c4613.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7df0430db8db9fc354ffdd038fb432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c996a43ff8843aec0be0a9d0ac0e9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4e70b360f988fdbd92300ab22c4613.png)
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名校
解题方法
4 . 已知数列
的首项
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25960d3812de00a90f060950f4b48197.png)
______ ;满足
的最大整数
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6545b8eca1c4223ed701a199a85683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7643e8b7aa32ebf299048417a94432dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25960d3812de00a90f060950f4b48197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b9587d657211fcc4d689e81ea186c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
解题方法
5 . 在
中,角
,
,
的对边分别为
,
,
,且
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26308ea6d8f321d27acbd7f9b131f9f1.png)
_______ ;若
,
是边
上的高,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705d0cd198f423d1a7d6b9a7999c18ee.png)
________ .
![](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/24b6255489ac5a06717cbe9ff718face.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26308ea6d8f321d27acbd7f9b131f9f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c2831fe21a5f34e06f87de5f8f9a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6655e2fa64a32cd12fe0279afd65d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a4827fe635f4cf5dc9d7d24b357d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705d0cd198f423d1a7d6b9a7999c18ee.png)
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6 . 如图,测量队员在山脚
处测得山顶
的仰角为
,沿着倾斜角为
的斜坡向上走400米到达
处,在
处测得山顶
的仰角为
与
在同一水平面上,
四点在同一铅垂面上,则山的高度OP为_____________ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d57969bf6b59115551b6244ba6f337b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc33e9f6e4fa08e2aa9ad6208241fc.png)
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名校
7 . 一般地,对任意角
,在平面直角坐标系中,设
的终边上异于原点的任意一点P的坐标为
,它与原点的距离是
.我们规定:比值
,
,
分别叫做角
的余切、余割、正割,分别记作
,
,
,即
,
,
,把
,
,
分别叫做余切函数、余割函数、正割函数.
(1)已知
,则
的最大值为_______ ;
(2)设
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7bf9200b351a259ddfc6c0266129d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2d7c084731df9cdabf1f0af121e3e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fee1e0f6c44b3027d0d6f8d9396f209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d494c34104f679bdbea537164f1907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e609ecb22257c1ca2fe78b1dc2e62141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48bd75362790c061d70f80de8febc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b57070a05279ad5e576d13fb9c1bef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851b7eec8ee522611f6b96a60ab9fc63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147f65043356b475c5c2bba102958807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5cac6f59b3e1405a3b64d13c88e8a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175c64c2a2393743bde92b3e46df42cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7688d35e68414fa995babd7437e678b.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1cf8cc0ca8fbbc8863fb416e25730f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bde963bde77dedd5e9859b5a4f5e49e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
名校
解题方法
8 . 古希腊数学家托勒密在他的名著《数学汇编》里给出了托勒密定理,即圆的内接凸四边形的两对对边乘积的和等于两条对角线的乘积.已知
为圆的内接四边形
的两条对角线,
,
,则
面积的最大值为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989c75a3fd02e4971cab421c88de92f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b761b3ceaaa33c9473e3a87d6796f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
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名校
解题方法
9 . 已知
,则
______
.(填“
”,“
”,或“
”)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed04a438788f040f5f45d70ff4d7e2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1d2e5599453f8d4c04369bc8f79962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
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名校
10 . 已知
中,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42acd3ee01d9f843a8579ffb0b7d9d82.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d2eec3b3ef5a2a660315db9f0feb99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42acd3ee01d9f843a8579ffb0b7d9d82.png)
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2024-05-29更新
|
843次组卷
|
2卷引用:广东省江门市新会第一中学2024届高三下学期高考热身考试数学试题