名校
解题方法
1 . 设函数
.
(1)讨论
的单调性;
(2)证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19918216dccbc84a439e750f76916bb.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481adcf2f35f31e5e661b2541c0f44b5.png)
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2 . 已知
,则m的值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8f64a9c2cabbe8342936189918f793.png)
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解题方法
3 . 已知曲线
的参数方程为
(
为参数),曲线
极坐标方程为
.
(1)将曲线
的参数方程化为普通方程,曲线
极坐标方程化为直角坐标方程;
(2)以坐标原点
为极点,以
轴的非负半轴为极轴,建立极坐标系.若射线
与曲线
分别交于
两点(异于极点),点
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fb818b89d897ca5a9079897c7358257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b34a1e7a48f450d883f9a0197e5c9.png)
(1)将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)以坐标原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2adf4a5e4715309d2c7b04af4e9cc81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96499747e4aea990f4b878eea8d73ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703b40a6293ed9e33001e2919379b168.png)
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4 . 如图,在四棱锥
中,底面
是等腰梯形,
,侧面
平面
,
,
,
为
的中点.
(1)证明:
平面
;
(2)点
在棱
上,直线
与平面
所成的角的正弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70e550fa3c5aaf1b9c28f36fd5ed5d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77c16357eabed95d85bbd4e3dada92e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/f371ba93-80ea-4449-aaea-b02b100c3d14.png?resizew=140)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44cd09d9ad46264de4620c60370d49d.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44cd09d9ad46264de4620c60370d49d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241a37fb1eff68a7133822b1b52d627e.png)
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解题方法
5 . 设实数x,y满足约束条件
,则
的最大值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fc6d9585f23e3cb7e310416299b95c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1995404eb114809bc18fbdb4f1388b2.png)
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6 . 已知抛物线C:
的焦点为F,过点F的直线l交抛物线C于A、B两点,且
,
(O为坐标原点),则抛物线C的方程为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b34061bab79590585e525c0912d8c12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce50eb3d71e81613c4dac1e8ecae6db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6b06b01d1bc1cf1b0c1f23e8529cdd.png)
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7 . 在等比数列
中,
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40ed131350af1c6506327df7bd44f007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27d520a002d3eebd1758e2c05c15c3f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 对于函数
,以下结论错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ace8056cabe476149f7b9398783d9c.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() |
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9 . 正方体ABCD—A1B1C1D1的棱长为2,点E、F是平面A1B1C1D1内的动点,若
,AC⊥DF,现有以下四个命题:p:点E的轨迹是一个圆;q:点F的轨迹是一个圆;r:三棱锥F—A1BD的体积是定值;s:
.则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600c2b2a205cc72c31bdda134bc60501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33793be9405b184ada8d98b0b1ef78a2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 在平面直角坐标系xOy中,曲线
的参数方程为
(
为参数). 以坐标原点O为极点,x轴的正半轴为极轴,取相同的长度单位,建立极坐标系,曲线
的极坐标方程为
.
(1)求曲线
的极坐标方程和曲线
的直角坐标方程;
(2)若直线l:
与曲线
交于O,A两点,与曲线
交于O,B两点,当
取得最大值时,求直线l的直角坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f23bb05e586ec0a3d42bdf95399ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a9318b83a0a52e7307812a2916ee8c.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61dd74028f4132cf2765da5ba5ec3b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba36a367738b4452e3b6190940284fe7.png)
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