解题方法
1 . 如图,在矩形
中,过边
上的点
分别作
的垂线,分别交
于
,过
边上点
作
的垂线,分别交
于
,
,则集合
中的元素个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6029062c6a3c9b36225574d393489db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb45ab3ba0ec44779c85e32719f5d60d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4386d82eb8d40b0080aea374ecf6962c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9baa6286e8d3fee65fa15af683a227ac.png)
A.2 | B.4 | C.6 | D.8 |
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2 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39d4e199031b74357e9fbd723916fbc.png)
A.![]() |
B.![]() ![]() |
C.方程![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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名校
解题方法
3 . 已知两个非零向量
与
的夹角为
,我们把数量
叫作向量
与
的叉乘
的模,记作
,即
.若向量
,
,则
( )
![](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/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4dda6a0ba7fbe7bacf15a5e63d8b9c.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/6b4e6bae1b67a0a1eeafdd1114a792df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997d8a3acf19e132587e8115cd1384fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54eb5317665c796a0853517b7e9be9e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa27c09a5c955e423743bda656d0b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c759dbf3a4250335fbc1d24f9c9be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6a462c248f46fdbc9a7f8a5a4cf816.png)
A.![]() | B.10 | C.![]() | D.2 |
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4 . 在直角坐标系
中,已知质点
从点
处出发以
沿着单位圆逆时针方向运动,
后质点
也从点
处出发以
沿着单位圆顺时针运动.设在
运动
后,质点
分别位于
处,若第二次出现
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2362096fa475a1051827bddcdcac22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e10255bb77fcab3b44ef6a054f16384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0513d14384fa76fd284f63ff4d8f08bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1a48b92c61d209d0556e4cd8fdb70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d24a48ccfd55f1ef484556341eb78c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854a9165ac4c4163449f590d4408e8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 已知点
,
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb9e88d3e58141dba299dcd8edc4e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02af485e17e7628fd5a3ace6e0a32ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a56e5ddc6dc057aa4076130cc6ce19.png)
A.![]() |
B.若点![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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解题方法
6 . 如图,
分别是等腰梯形
的边
上的动点,
,其中
为定值,
,设
,其中
.
,求出
的表达式;
(2)证明:
的余弦值与
的取值无关;
(3)求
的取值范围.
![](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/596d41b6556f383445536d1c534ac182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f07948e9258b482a2164ac871f90f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a18fec3e4a4fbc7b3e0e037ce650023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d91513d2e546a5a0b5fd42379db8df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e72cf7374a65ced433b6fa113ef57d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e2be3e9225c71609248299caa49432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192c2f1059f6e05d44df048f5fdca04b.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db625151987f893816de66b15d9e699.png)
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7 . 如图,某商场内有一家半圆形时装店,其平面图如图所示,
是圆心,直径
为24米,
是弧
的中点.一个时装塑料模特
在
上,
.计划在弧
上设置一个收银台
,记
,其中
.
表示
;
(2)当
时,求
的大小;
(3)当
越大时,该店店长在收银台
处的视线范围越大,试问当店长在收银台
处的视线范围最大时,
的长度为多少米?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae728c7be0f0cf78711f3fa5ccccf30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7b628bd4ac303c86e30508eb81ff60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa33d0f23b18d580b8b2afb0dfd0c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e595083e5fd6282c93a636c66680ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7223bf3fdadd6f44abce82899bc1ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a6e3d819ca9f73eeb0f872b33c9e5f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3416881a6f67d05fe6b67787047fc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2bc29145f6e7557711c34b443bd5e84.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2bc29145f6e7557711c34b443bd5e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
8 . 下列说法正确的是( )
A.设![]() ![]() ![]() ![]() |
B.设![]() ![]() ![]() ![]() ![]() |
C.设![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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解题方法
9 . 如图,在直角梯形
中,
与
交于点
,点
在线段
上.
和
表示
;
(2)设
,求
的值;
(3)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d3106f047d529703433b6dbad96fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083a20abb668d4c26fe5039bd108b40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf8f16f66227c7c9897bf5d5a863f78.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015756e8dd84a004652163864e639d61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e785769901eda9d2f346462e228444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92bee4bf1aa98667dd4fe6d9bf18b3b5.png)
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10 . 如图1,这是一幅扇形装饰挂画,可将其视为如图2所示的扇形环面(由扇形
挖去扇形
后构成的),
米.该扇形环面的周长为4米,则该扇形环面的面积是__________ 平方米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5b1c21ed3fc6413bbaa9762e0a4bd1.png)
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