解题方法
1 . 在平行四边形
中,
,
,点
在边
上,满足
,则向量
在向量
上的投影向量为________ (请用
表示);若
,点
,
分别为线段
,
上的动点,满足
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4814565292192e40bd86a10ee7b661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5dc30c658a62dbd19edf9e0bc10e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304a7f07db2ec637baadf8f0ab91c85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304a7f07db2ec637baadf8f0ab91c85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dae942a35d9c35f196959a35dc608e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12529b9d6f852fa8ff21ea95e0591c0c.png)
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2 . 已知函数
的最大值为2,其部分图象如图所示,则下列判断错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3080cc97928ed7cef5bd7edbb5bbeb.png)
A.![]() |
B.函数![]() |
C.若函数![]() ![]() ![]() |
D.![]() ![]() |
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2024高三下·天津·专题练习
解题方法
3 . 关于函数
有下述四个结论:
①
是偶函数;②
在区间
上单调递增;③
的最大值为2;④
在
有4个零点.
其中所有正确结论的编号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10276e1f4d5b7c84bb1633f2f76478f4.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe386ad25a4c1cce633ed4e129127047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af46e7742b81527867de26c973c67b00.png)
其中所有正确结论的编号是( )
A.①②④ | B.②④ | C.①④ | D.①③ |
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解题方法
4 . 点O是平面
上一定点,A,B,C是平面
上
的三个顶点,
,
分别是边AC,AB的对角.有以下四个命题:
①动点P满足
,则
的外心一定在满足条件的P点集合中;
②动点P满足
,则
的内心一定在满足条件的P点集合中;
③动点P满足
,则
的重心一定在满足条件的P点集合中;
④动点P满足
,则
的垂心一定在满足条件的P点集合中.其中正确命题的个数为______ .
![](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/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
①动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194928662ef5170ec329fa0839e96810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
②动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f06ef8a11b1b7e4977bd57fbf89aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
③动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34459872490d5f5a616999415532470a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
④动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b31a28180fdba611bcaedadbddd67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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5 . 将函数
的图象横坐标伸长为原来的2倍,再向左平移
单位,得到函数
的部分图象(如图所示).对于
,
,且
,若
,都有
成立,则下列结论中不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb97f92552ed6f2c56ae60823fb0c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60d9bb0e2917a4991d602b3d36feb0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933b194cf207714e3981addfd8a9d339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01e507e0f1beca672efcab23dcc76c0.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.函数![]() ![]() ![]() ![]() |
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6 . 设函数
,若函数
恰有三个不同的零点,分别为
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a214e6e3def115dcaa9844866865e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9c82c1ec9a0ff6eec86178962285f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcee20976de0e0e8c1ccd7a951674691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd43286b58600b12e973f4c7b2b7e3f8.png)
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7 . 已知函数
是定义在
上的奇函数.
(1)求实数
的值;
(2)根据函数单调性定义证明
在
上单调递减;
(3)如果对任意
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a309da175b45f60cdbbc3b7b2f689cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)根据函数单调性定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(3)如果对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55ded3d8a770d25d6d83bb5779f7462f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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8 . 已知函数
的对称中心到对称轴的最小距离为
,将
的图象向右平移
个单位长度后所得图象关于y轴对称,且
关于函数
有下列四种说法:
①
是
的一个对称轴;②
是
的一个对称中心;
③
在
上单调递增;④若
,则
,
.
以上四个说法中,正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb6861bab7a36655b00bcb024939cb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c63dc335623c17b99b4c8cb60d7988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c6cb0cc172657611e286e7fa669584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689116c47f780e85fdfea834a2a164df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8459cf94469082b06b06f26e1b24cd83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e71b7cc594da8081cc8599f6e2c529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/062cd1cf62c63f969693f85a62960c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de7a464af3174c4edc0e908eab4409d.png)
以上四个说法中,正确的个数为( )
A.1 | B.2 | C.3 | D.4 |
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5卷引用:天津市八校联考2023-2024学年高三上学期期末质量调查数学试卷
天津市八校联考2023-2024学年高三上学期期末质量调查数学试卷(已下线)考点6 三角函数的奇偶性、对称性、零点 --2024届高考数学考点总动员【讲】福建省福州市平潭县岚华中学2023-2024学年高一上学期期末模拟数学试题上海市建平中学2023-2024学年高一下学期期中教学质量检测数学试题(已下线)专题02 三角函数-期末考点大串讲(沪教版2020必修二)
9 . 已知函数
.
(1)求函数
的最小正周期;
(2)求函数
在
上的单调递减区间;
(3)已知函数
在
上存在零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2801ad38b8ca4ff832d80e3c33ee152e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50a80865f6c9a3b2a9f196826663808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb935734bfd51c3338f223934a668e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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|
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3卷引用:天津市滨海新区2023-2024学年高一上学期期末检测卷数学试题
天津市滨海新区2023-2024学年高一上学期期末检测卷数学试题(已下线)第八章:向量的数量积与三角恒等变换章末重点题型复习(2)-同步精品课堂(人教B版2019必修第三册)四川省成都市石室蜀都中学2023-2024学年高一下学期3月月考数学试题
10 . 若函数
(
,
)的最小正周期为
,且
.给出下列判断:
①若
,则函数
的图象关于直线
对称
②若
在区间
上单调递增,则
的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2e40d1e4d047249453f36ce4e60377.png)
③若
在区间
内没有零点,则
的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3189ba678499e528de7574e5adbf33.png)
④若
的图象与直线
在
上有且仅有1个交点,则
的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35af404cb8618c09a8040fff9fb1e9c.png)
其中,判断正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306bc38c05e863481825f5639cea9ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c9e46448bc791c441ca02d8f4508eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb6e52d1733c6ce9f78ba2bfe142355.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c404ebac6d321a29190c57b1c9c55ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e1c64c42b7f3b7fdc396d4756cab.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/620709ed747abad41e3a58a0c64dd875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2e40d1e4d047249453f36ce4e60377.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9bbf6e7847f96706b54f079716bf23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3189ba678499e528de7574e5adbf33.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bccd6a6e85bdf500218a3e75b31f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35af404cb8618c09a8040fff9fb1e9c.png)
其中,判断正确的个数为( )
A.1 | B.2 | C.3 | D.4 |
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|
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