1 . 已知函数
,现有如下说法:
①若
,函数
在
上有最小值,无最大值,且
,则
;
②若直线
为函数
图象的一条对称轴,
为函数
图象的一个对称中心,且
在
上单调递减,则
的最大值为
;
③若
在
上至少有2个解,至多有3个解,则
;
则正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973bd09ae9775d390177e5bc07d091c1.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d47dbed3333b180fce58a6d9e440f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3697c286ea301d21ff0dc4305d935883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83d5782f737d37aca7f120d007e0018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a72b38ff26cd0c812d6bcbbeb80ae3b.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e1c64c42b7f3b7fdc396d4756cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc07c41b0edfc14cc49914c02ec6d6b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394a003540c7ddb2086f5dd305cdd159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d4befb403831c40b77b3644020d835.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad56942439368d413f74e0ab7d9fb23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c5feb0608338d11ab9153185e3df98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e14bbcd89836543ba9ffa79a9c41932.png)
则正确的个数为( )
A.0 | B.1 | C.2 | D.3 |
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2 . 调和信号是指频率恒定的一种信号,三角函数性质可以表达调和信号的周期性,指数函数可用来描述信号的衰减.已知一个调和信号的函数为
,它的图象大致为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9d67b5f365195ce28c8d321db0c18a.png)
A.![]() | B.![]() |
C.![]() | D. ![]() |
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2023-12-30更新
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5卷引用:山东2024届高三12月全省大联考数学试题
山东2024届高三12月全省大联考数学试题江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)(已下线)专题05 三角函数1-2024年高一数学寒假作业单元合订本(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】(已下线)高三数学开学摸底考02(新高考专用)
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解题方法
3 . 已知函数
为奇函数,
(a为常数),且
恒成立.设
与
的图象在y轴右侧的交点依次为
,O为坐标原点,若
的面积最小值为
,且
为钝角,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b101c892f1a04c222802624a00254e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/190771756a0c61a95fcf154a3e153b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb6e2f839995ad56cdbc9fa3e4f31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f46494004604bb80f153f3ecfc5cf03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15536798ab47cadce6d4d80f542051f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c28f82fa05741271a0348d8fe970210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7659e29a70d7e17409b91d2aedf5639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5卷引用:2023年高三黑白卷数学试卷(新高考)(黑卷)
2023年高三黑白卷数学试卷(新高考)(黑卷)安徽省2023届4月模拟数学试题(已下线)模块七 第4套 迎接高考之必做基础热身题( 数列与立几)(已下线)模块六 专题9 易错题目重组卷(安徽卷)辽宁省名校联盟2023-2024学年高三上学期第三次联考数学模拟卷A
2022高三·全国·专题练习
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4 . 使
有唯一的解的
有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abeca43e7cc430e3761a5eb3cef580fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.不存在 | B.1个 | C.2个 | D.无穷多个 |
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5 . 七巧板是一种古老的中国传统智力玩具.如图,边长为
的七巧板左下角为坐标原点,其中各点的横、纵坐标均为整数.当函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d117a826cb528e760ca35e498383d59c.png)
经过的顶点数最多时,
的值为( )
![](https://img.xkw.com/dksih/QBM/2022/4/5/2951709161218048/2952814577582080/STEM/0908542b61c1449b8173b2312e7f5289.png?resizew=371)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d117a826cb528e760ca35e498383d59c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232a53492b6921112c366640bd1cdf78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4efd1637e49d25851fc02b351d31cf.png)
![](https://img.xkw.com/dksih/QBM/2022/4/5/2951709161218048/2952814577582080/STEM/0908542b61c1449b8173b2312e7f5289.png?resizew=371)
A.1 | B.2 | C.1或![]() | D.1或2 |
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6 . 下列命题中是真命题的个数为( )
①函数
的对称轴方程是
;
②函数
的一个对称轴方程是
;
③函数
的图象关于点
对称;
④函数
的值域为
.
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117226ad16b55079d5fac91d3efe7626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974f7eeb0b47c5f7e74b04465a6a7452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a2ec02caf837c6e7e0b76dd9acc7f0.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3ed2dbcb54759b7700f60aa016a4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95c64782df35b9dfa69431761d82ad6.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3ed2dbcb54759b7700f60aa016a4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e83d322ea744883053d048735ed7a16.png)
A.1 | B.2 | C.3 | D.4 |
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7 . 把
的图象向左平移
个单位,再把所得图象各点的横坐标缩短为原来的
倍,再把所得图象各点的纵坐标伸长为原来的2倍,得到函数
的图象,若
对
成立,则
①
的一个单调递增区间为
;
②
的图象向右平移
个单位得到的函数是一个偶函数,则
的最小值为
;
③
的对称中心为
;
④若关于x的方程
在区间
上有两个不相等的实根,则n的取值范围为
.其中,
判断正确的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6cc0e2b71c0bbc477f15420d2cfa2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3200e6aa922be0e0675d52c3d799750d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec2b153baae853850533aee2b5d8b3b.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f07948e9258b482a2164ac871f90f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a779bc72e99260a531b88acdfbb39277.png)
④若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b12ff508a0b321c8c57468509e1963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6232413a655f772f53b7fabbc9c332b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02c5c46e01d8419b7a810494b4ed6ca.png)
判断正确的序号是( )
A.①② | B.①③ | C.③④ | D.①③④ |
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4卷引用:云南省昭通市2022届高三期末数学(文)试题
解题方法
8 . 让·巴普蒂斯·约瑟夫·傅里叶,法国欧塞尔人,著名数学家、物理学家.他发现任何周期函数都可以用正弦函数和余弦函数构成的无穷级数来表示,如定义在R上的偶函数
满足
,且当
时,有
,已知函数
有且仅有三个零点,则a的取值范围是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c96ed911dff63f46366019d59824ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2a6f74e83314b53741267b8e90c1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cdde751120c6deab563a6f7f8cf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d71bb7ac3c4219499a434527cd0357.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 已知函数
,则下列结论错误的是( )
①
时,函数
图象关于
对称;②函数
的最小值为-2;③若函数
在
上单调递增,则
;④
,
为两个不相等的实数,若
且
的最小值为
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b3fd9d4fa63d1bae1a76a90f0ff9dc.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dcee772e6187ac31d7f8d69b0487000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e1c64c42b7f3b7fdc396d4756cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe0e99cd239e789a9df7b181e98a10b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787f2c8b1d9d1ef0cf740d2fd9b25a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2dc6d650e0885a1001c7a102b9c981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc191ebded559cc4e6752b9a4e2727c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05a467ddaa138590b3b56615c2c42a5.png)
A.②③ | B.②④ | C.①③④ | D.②③④ |
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解题方法
10 . 已知定义在
上的函数
满足
,且当
时,
,则当函数
在
有零点时,关于其零点之和有以下阐述:①零点之和为
;②零点之和为
;③零点之和为
;④零点之和为
.其中结果有可能成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd51b3cbd5dc46c1788178fd89dfb9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6c15bdab83062afbd50f88ee49b596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039f9392112593405d4c0f1bea7d31f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b007c480872b6a9ee5f909d7ccc8a725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b199d124fb9a5bc8438c9884f04534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
A.①② | B.②③ | C.③④ | D.②③④ |
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3卷引用:四川省泸州市泸县第二中学2020-2021学年高一下学期第一次月考数学(文)试题
四川省泸州市泸县第二中学2020-2021学年高一下学期第一次月考数学(文)试题(已下线)期末复习【真题训练】-2020-2021学年新教材高一数学下册单元复习一遍过(沪教版2020必修第二册)广西岑溪市2020-2021学年高一下学期期末数学试题