解题方法
1 . 《易经》是阐述天地世间关于万象变化的古老经典,如图所示的是《易经》中记载的几何图形——八卦图.图中正八边形代表八卦,中间的圆代表阴阳太极图,其余八块面积相等的图形代表八卦田.已知正八边形
的边长为
,点P是正八边形
边上的一点,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83b9f01e806bf74042ba41b26423022.png)
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2卷引用:辽宁省大连市滨城高中联盟2023-2024学年高一下学期5月期中考试数学试题
2 . 函数
的图象如图所示,图中阴影部分的面积为
,则函数
的解析式为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473c9fea4cdded9be6f12958770c0cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997b5842f3d4eae1989debee9ae41b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
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2卷引用:辽宁省大连市滨城高中联盟2023-2024学年高一下学期5月期中考试数学试题
解题方法
3 . 已知函数
.
(1)若
,,求函数
解析式;
(2)已知
,函数
图象向右平移
个
单位,得到函数
的图象,
是
的一个零点,若函数
在
(
且
)上恰好有10个零点,求
的最小值;
(3)已知函数
,在第(2)问条件下,若对任意
,存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ab71ec0fd3d719b7ff7206bed7d504b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c4020b17f7ad2d5f179b3f6b01898e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2091dc47caec0c6734eb058375d8a294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e8d6f968dd1b47482f1808f2c53c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9895bf4192f5c55c16f8270d53c49b13.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/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26927f1f0be044942dfce30c3607158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8de7d589969f21c7693508cfca0c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e538686939002a2ba06670615144c73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caece05b586ec9e2d6f1ec69449550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b56a0bc723618e7cdac994882c807bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 关于平面向量,有下列四个命题,其中说法错误的是( )
A.点![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若向量![]() ![]() ![]() ![]() ![]() |
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5 . 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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解题方法
6 . 函数
的定义域为
,
为奇函数,且
为偶函数,当
时,
.
①A,B是锐角
的内角,
;
②
;
③
;
④
.
其中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105068fe440b555880e9c566e6fd3f5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d7661d3fc28f785b438ad8c8f9d240a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4e9ed540a4aff2db2f887b81e0b982.png)
①A,B是锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a673984ab88416f50a8496242427cdbe.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f227bbeda10306a74beb7cb2e5df2d.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45691cfa763ee20fcfc741fcdb74d8f4.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/220b656c067ac8a548f1f7926c80dd38.png)
其中正确的有( )
A.②③④ | B.①② | C.①②④ | D.①②③ |
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7 . 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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名校
解题方法
8 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161d39fa1cb0e994941c02bd4ab971b1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8529a52e32b12244bd535641221e83e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161d39fa1cb0e994941c02bd4ab971b1.png)
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2卷引用:辽宁省大连市第二十四中学2023-2024学年高一下学期5月期中数学试题
名校
解题方法
9 . 已知
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9fcaa804011c37873b03ee284504fe.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef966cdd137b3b10e290201b4d17542e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c98ce1bd8a5ffe3e18b4033d4ade5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc282dae4ac9132196ac5d13f63b901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f836697b6e7daec4ab093779fff51923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9fcaa804011c37873b03ee284504fe.png)
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名校
解题方法
10 . 已知
,
分别为该三角形的垂心、外心,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91219670f597461ea7c6b7f259ff039a.png)
A.若![]() ![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() |
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