1 . 已知函数
在区间
上的最小值为3.
(1)求常数
的值;
(2)当
时,将函数
的图象上所有点的横坐标缩短到原来的
(纵坐标不变)得到函数
,求函数
的单调递减区间、对称中心.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265384d62ae17af01c1562581a893ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
(1)求常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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2 . 已知
,
与
的夹角为
,
为
外接圆上一点,
与线段
交于点
.
,求
;
(2)设
.
(ⅰ)试用
的函数表示
;
(ⅱ)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89d64255de7162b1fa5f659732693daa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a41a475407451ed8427d0e7a483568c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eff576db012cc8a793b1afcb0b47fbe.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f7983aade7a7c61f065c5bd3569fbd2.png)
(ⅰ)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f14d13e081ed59bab413a9f30b62e3.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ef6d007c9539c08562fcc217ae131e.png)
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3 . 定义:
.若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c8894e0b37af5da23a1c1bffb32017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f9d41306133d059e2daa28edd6d824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ec7c99202b44d5d65239f65f155b6f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
4 . 已知向量
,
,
.
(1)若将函数
图象向左平移
个单位长度,再把得到的图象上所有点横坐标缩短为原来的
,得到函数
,试求
在
上的单调递减区间;
(2)锐角
中角A,B,C所对的边分别为a,b,c,若
,
,求
周长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f3ec8ca41f88b197335b44dc3c4f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d086d10f28658452c539d1ef8dacc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30351fb67c2df449163b052e1ff4ef9c.png)
(1)若将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c6c37ce441a8ed77c8e3953e8fe1f.png)
(2)锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39900a2d790732077ffb571427a134fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69def215d32ff6734ad883a0ca260a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
解题方法
5 . 在
中,内角
的对边分别是
,且
.
(1)求角
的大小;
(2)若
,且
的面积为
,求
边上的中线长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef0e289213adb19ea06f895c522f6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2099b865424058d46b742a1659dafd0.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82986ab38a4ae58593191ccae2a44f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcb5876e83a663aa11bc213425f2345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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6 . 校园里有个如图的半径为4,圆心角为
的扇形花坛
,P是圆弧
上一点(不包括A,B),点M,N分别在半径
,
上.为美化校园,分别在四边形
,
和
种植红色,黄色的牡丹花,其余地方种植绿草点缀.
为矩形,求其面积最大值;
(2)若种植黄色牡丹的
和
均为直角三角形,求它们面积之和的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](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/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b16c49d16305cf1afacc5a9e2bf7e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a163fbf4333651741cec447995092a19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35a9ec7088381262f8ca327bd377660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b16c49d16305cf1afacc5a9e2bf7e9a.png)
(2)若种植黄色牡丹的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a163fbf4333651741cec447995092a19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35a9ec7088381262f8ca327bd377660.png)
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7 . 在①
,②
,③
,这三个条件中任选一个补充在下面的横线上,并加以解答.
在
中,角
,
,
所对的边分别为
,
,
,且 .
(1)求角
的大小;
(2)若
为锐角三角形,
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef8ad9f9cf060771d47d36cde93afae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5455c52de0aef08eba4c104f99efeab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/949400f9ba875a3e230063573a423e74.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
解题方法
8 . 如图,在平面四边形ABCD中,E为线段BC的中点,
.
,求AE;
(2)若
,求AE的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb12049c4ca9c62d12c884bbaa9d09.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df54bb4e7febefb181ed69139d76317d.png)
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7日内更新
|
593次组卷
|
7卷引用:河北省保定市定州中学2023-2024学年高一下学期5月期中考试数学试题
名校
解题方法
9 . 如图,在扇形OAB中,半径
,圆心角
,F是扇形弧上的动点,矩形CDEF内接于扇形,设
,则矩形CDEF的面积的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc790cfaa59a808c25a7edb95dc29fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c22f040f353ab28a6e00ddd56913c2.png)
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10 . 函数
相邻的两个零点分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc574389b74c0e846657b2e24ffe115f.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd5543f6cc0a25deb6410dd48cce9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d3c0e7508ff7fd36faba07a0aa41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc574389b74c0e846657b2e24ffe115f.png)
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