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1 . 在直角坐标系
中,直线
的参数方程为
(
为参数),在以坐标原点
为极点,
轴的正半轴为极轴的极坐标系中,曲线
的极坐标方程为
.
(1)写出直线
的普通方程与曲线
的直角坐标方程;
(2)设点
.若直线
与曲线
相交于不同的两点
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a1d4dd7d5b84dc481454eb729813066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f58ce08dfb6311605cb0d4b6d8a183.png)
(1)写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a29ba49963134a7232fa8574105fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de13b1ae79166a207c174dab94cdae6e.png)
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2 . 已知函数
.
(1)讨论
的单调性;
(2)当时
,
,求实
数的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862c6f588e676ff92ef8f4fd99bd9a5b.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当时
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bef2bc7a558debc5f4f3d0bd7af4edd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 在四棱锥
中,侧面
底面ABCD,底面ABCD为直角梯形,
,
,
,
,E,F分别为AD,PC的中点.
![](https://img.xkw.com/dksih/QBM/2019/2/17/2142824740323328/2144979324903424/STEM/b3e8f545ccda4f2eb0d15c55b0ac5ab9.png?resizew=187)
Ⅰ
求证:
平面BEF;
Ⅱ
若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebbb79892c8cb8871a08437acc09bc80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58bafdd3bb54ba3491b49ab60b172f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb655dcddebb50942249461aa852fba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96897a3650133b139bb8216967008f3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b90fe3657d4dbe1ac0839572866037e.png)
![](https://img.xkw.com/dksih/QBM/2019/2/17/2142824740323328/2144979324903424/STEM/b3e8f545ccda4f2eb0d15c55b0ac5ab9.png?resizew=187)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1666b45ed176d648dd1764f4a2dbd73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56982f8cf241b04a9885681626bd4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ca211f5091244d59a9380111f2e5ca3.png)
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4 . 若变量
、
满足约束条件
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/185ac945ce0ef36d89b66f12e56ac54d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7c99486743e17633d086d868f0680c.png)
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解题方法
5 . 在三棱锥中
,
,
,
两两相互垂直,
,则此三棱锥内切球的半径为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50094bfee564d9c1b03088ac2ece28c3.png)
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6 . 已知向量
,
,若
与
垂直,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47deef0274b0ab2da8ec7c1e22bf50a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb0b6f8071090e4893c9a63e10e0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4a4b7619661850b2f3d62aed3b8d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
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7 . 已知
为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b66b2a7b3f06c2ba231fec57b858f91.png)
的一个对称中心,则
的对称轴可能为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9d99886d87e26805639038e73e3dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b66b2a7b3f06c2ba231fec57b858f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbc54062e597874ebeb3f3d9d878ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 已知随机变量
服从正态分布
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e21bf43e150fea77df06acecb439586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a27d24d68285a6f132880a398f98f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知
的三边满足条件
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2a8bf5e05a07c93a7104839fc21849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6886ce81752c2a15f6559982fddf21f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2a8bf5e05a07c93a7104839fc21849.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 函数
的图象可能是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada55f3c74f0d568441f3d211cbdc62d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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