1 . 已知
的展开式中含
项的系数为160,则实数a的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f8bb8f82df1f8584b8a9d8c8281fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae666ea089aeed6e8df798c81dd2f187.png)
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名校
2 . 已知集合
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933347fd4d93628c8a9cb6a540560471.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/273a61f0869406c75be25dab20ec0af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836147cc2b534de6b691c427643a0493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933347fd4d93628c8a9cb6a540560471.png)
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3 . 样本数据2,2,3,3,3,4,4,5,5,6的中位数和众数分别为( )
A.3和3 | B.![]() | C.4和3 | D.![]() |
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2024-06-12更新
|
535次组卷
|
2卷引用:2024届福建省宁德市普通高中毕业班五月质量检测数学试题
名校
4 . 函数
.若存在
,使得
为奇函数,则实数
的值可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cf6707c0f1c74f49465b0678ccea45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d32d1a5a0732c7e4af737555e44ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61593bf4a3ddaf2fb75e61e1e0ad47ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-06-07更新
|
289次组卷
|
2卷引用:2024届福建省宁德市普通高中毕业班五月质量检测数学试题
5 . 《缀术》中提出的“缘幂势既同,则积不容异”被称为祖暅原理,其意思是:如果两个等高的几何体在同高处被截得的两截面面积均相等,那么这两个几何体的体积相等.该原理常应用于计算某些几何体的体积.如图,某个西晋越窑卧足杯的上下底为互相平行的圆面,侧面为球面的一部分,上底直径为
,下底直径为6cm,上下底面间的距离为3cm,则该卧足杯侧面所在的球面的半径是__________ cm;卧足杯的容积是____________
(杯的厚度忽略不计)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d4428ff9e9eaf5a0b26c6b18668f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6d1d99afa158b4ba4fc0dae562fcc1.png)
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6 . “杨辉三角”是二项式系数在三角形中的一种几何排列.从第1行开始,第n行从左至右的数字之和记为
,如
的前
项和记为
,依次去掉每一行中所有的1构成的新数列2,3,3,4,6,4,5,10,10,5,...,记为
,
的前
项和记为
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1829194a3ae731497284f8935ceac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
A.![]() | B.![]() ![]() ![]() |
C.![]() | D.![]() |
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解题方法
7 . 已知
是两个单位向量,若
在
上的投影向量为
,则
与
的夹角为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10814bc3db929e79874befe96cf4e3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c86779e465e98e32df7e1de20a0a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0920be0508984a3c3a337b3a93c525c4.png)
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解题方法
8 . 在
中,角
的对边分别为
.已知
,且
.
(1)若
,垂足为
,求BD的长;
(2)若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/1c7b296d57f8134aa27d3910dad49e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80500f9866df4e15761a10e5e85e2ec1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b3722c29d3032abc99a8b1dd145e85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1810555c0c28fe352841322b85bbc6.png)
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9 . 在平行四边形
中,
,
,
.将
沿
翻折到
的位置,使得
.
平面
;
(2)在线段
上是否存在点
,使得二面角
的余弦值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd0e8f705192e7012805abde99adb2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e240a6378adf6d23ebf9cc710c9bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f29c3e772e56008790298824122792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be449ac37995493404101ba7d474360e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d7ec7877f4ce3166c1a0c587de156f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943feac8392ab6ce588420d6aa866ae9.png)
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解题方法
10 . 已知抛物线
的焦点为
是抛物线上的两个动点.若
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d0a522b36799e4bcc6e3645db4d4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b74c78c00d69876fbc50d9cad20f6db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36719f1e764ee0e719b65c49fae84677.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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