名校
解题方法
1 . 已知A,B,C为
的三个内角,
,
,M,N分别为边AB,AC上的动点(不包括端点),点A关于直线MN的对称点D在边BC上.
(1)记
时,求θ的取值范围;
(2)当AN长度取得最小值时,求MN的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0977a829ae6577586e01637ce9d9ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e83ac5efc4c142c43c5e7a3e156c407.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e31cf7ea7942bbc0fe4680878e5dd2f.png)
(2)当AN长度取得最小值时,求MN的长度.
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2卷引用:江西省赣州市兴国县联考2023届高三下学期5月月考理科数学试题
2 . 瑞士数学家雅各布·伯努利在1694年类比椭圆的定义,发现了双纽线.双纽线的图形如图所示,它的形状像个横着的“8”,也像是无穷符号“∞”.定义在平面直角坐标系
中,把到定点
距离之积等于
的点的轨迹称为双纽线
.以
为极点,
轴的正半轴为极轴建立极坐标系.
(1)求双纽线
的极坐标方程;
(2)双纽线
与极轴交于点P,点M为C上一点,求
面积的最大值(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1aa1a5565eef09e163e2b3487beaa6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd0f31afe865a63682ccd4a18a0e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/26/5dede47c-56c9-4ba0-b918-1a0fc4f70c20.png?resizew=179)
(1)求双纽线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)双纽线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a51268fce97426487c3338d6ec3d571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
3 . 下列命题中,下列命题正确的个数是( )
①已知随机变量
,若
,则
.
②已知随机变量
,且函数
为偶函数,则
.
③函数
的图象的对称中心为
,
.
④已知函数
在
上单调递增,则k的取值范围是
.
⑤已知函数
的定义域为
,若
为偶函数,则函数
的图象关于点
对称.
①已知随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5950bc13f4fad98d672d4ce14d64f54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba870165217330510153bb352721047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
②已知随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6814d3993a9ff7100ccb592db3253e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad334fd27fd3fa5aa096135344cb836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad6f1c0e0c0d5c6bc5913caf162ef87.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da4d29868ebe81762d4785dc3737d429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dccef15d4974f07a0014f70bd584c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a173784888adf2946382fa093ba53a.png)
④已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09821b0756650c349730c8b9b0cd8181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ec5e0de82f13e711b23f9ae37cdac3.png)
⑤已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7126322cb41f98ec7d0c22fc8c31e086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334ae8e253052af92df5d83c65a6bf62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
A.1 | B.2 | C.3 | D.4 |
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名校
4 . 角
的始边与x轴的非负半轴重合,终边与单位圆交于点P.已知
.则点P可能位于如图所示单位圆的哪一段圆弧上( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76d152939baacebf7efe2fc69d54efd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:江西省南昌市第十九中学2023届高三下学期第三次模拟考试理科数学试卷
5 . 特值法就是选取一个恰当的特殊值代替一般的情况,将复杂或抽象的问题简单化具体化的方法,例如:若
是定义域为R的奇函数,且
是偶函数,
,则可以选择
,由此计算出结果.已知函数
是定义域为R的偶函数,且
,
是奇函数,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1093125b6aed397eaf9b517ff39227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d273cad03d1a0e2ce863630b66e85451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447c83efc857176a1789233af052ecc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25bacb5a64d4ae725bfcce99f0496dfb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:江西省南昌市新建区第二中学2024届高三上学期8月份学业水平考核数学试题
江西省南昌市新建区第二中学2024届高三上学期8月份学业水平考核数学试题广西示范性高中2022-2023学年高一下学期联合调研测试数学试题湖南省长沙市浏阳市2022-2023学年高二下学期期末数学试题(已下线)专题08 三角函数图象与性质1-期末复习重难培优与单元检测(人教A版2019)【人教A版(2019)】专题18(一轮复习)函数概念与基本初等函数(第一部分)-高二下学期名校期末好题汇编
6 . 如图,在扇形
中,C是弦
的中点,D在
上,
.其中
,
长为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
.则
的长度约为(提示:
时,
)( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a70c3643ec1b266fcb976cc081b012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7577fa22dadc7abcc56b3439d9ba6be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1df2a8b51ea0efaaec4d6f96742e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694e2317b8815f878ed322e2c8630917.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 相传我国古代有这样一个故事:一个身处他乡的小伙子得知父亲病重的消息,便连夜赶回家,他父亲弥留之际不停念叨“胡不归?胡不归?”,这就是流传千百年的“胡不归问题”.如图,假设小伙子处于
地,家在
地,
是驿道,其他地方均为沙地,
,小伙子在驿道,沙地上行走的速度分别为
,若小伙子为了更快回到家中,从
沿
走到
(
在
上),再从
走沙地直线回家,设
,则此方案所用时间为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/30/b67064f3-21c7-429c-af99-d8c6f9f24be8.png?resizew=192)
![](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/e675a92cad72c65aa4071b9d9e226090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a1000f594a66dde1954f797c8c07ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d535de796f6072f1d007d886d353272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f1a5615a04e8002ad7957db5e712f3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/30/b67064f3-21c7-429c-af99-d8c6f9f24be8.png?resizew=192)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 已知点
是角
终边上一点,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590e5b8636baa2cef22526c823325c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155862db7d8b167e5a833c2e08f2c114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:江西省赣抚吉十一校联盟体2023届高三下学期4月联考数学(文)试题
江西省赣抚吉十一校联盟体2023届高三下学期4月联考数学(文)试题(已下线)北京市丰台区2023届高三下学期3月一模数学试题变式题1-5(已下线)第01讲 三角函数的概念与诱导公式(八大题型)(讲义)河南省南阳市桐柏县2022-2023学年高一下学期期中数学试题
9 . 如图所示,在等腰梯形
中,
,现将梯形
依次绕着
各点顺时针翻转,则在第一次绕着点
翻转的过程中,对角线
扫过的平面区域面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/e748e22a-cc92-41c8-b835-8383704dd89f.png?resizew=231)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304d140bf689c07b057d922648da3dbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28855a0db693584aabac1df99dfade3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/e748e22a-cc92-41c8-b835-8383704dd89f.png?resizew=231)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知函数
的最小正周期
,
,且
在
处取得最大值.现有下列四个结论:①
;②
的最小值为
;③若函数
在
上存在零点,则
的最小值为
;④函数
在
上一定存在零点.其中结论正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114eef9b222c5481d2e53e4efd77d067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c3998d58abf7be810d3fc31e0fae52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e3129378e15392b3d3078bbc0147f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3204d98fd0532edb9a010693b835716b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b9889e0cbe3df77335191563ca41b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7163395f9aaa29be7f6b3106ba48b744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f985e053aa34c664db8457ada68d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/490dab77e2976fd4ae7535cb0ff54ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1e89691838b95288ece44d97e445a6.png)
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