1 . 已知集合
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54de2455dfd7028974f0b9254f9299a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d0a7fab64bbd0b5c7b74b5d15157bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
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名校
2 . 已知集合
,其中实数
是常数.
(1)求集合A与集合
;
(2)若对任意的
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea3ac2f45b27e6f22bddfdc1ca0ef72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)求集合A与集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 如图,点
均在
轴的正半轴上,
,
,…,
分别是以
为边长的等边三角形,且顶点
均在函数
的图象上.
个等边三角形的边长
;
(2)设数列
的前
项和为
,求
.
(3)已知数列
的通项
,数列
中,
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce1e808127c5672eb1b47024e54c9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb99c20237aca8ff2ba640c28fbc5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a619e2751f422ae187505e95339d02fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b80801bd92f36541707eea1229685e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699bdb06cc1a8e431fd96fdd06f6d2f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a6e162176d244084d154bc50b598eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d876a9e0ab9abc3880410cfde910eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ef48976a52cc4a2be7c46a98426c0a.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267c99ff3f6386113dbaa7b1e49612da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e1ee88beaddafb0d0a185c3a8e0dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a655f0f5afe3673c421af8a677b5154c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8427946085d576e0696e06cf4463c30f.png)
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4 . 有甲乙两个骰子,甲骰子正常且均匀,乙骰子不正常且不均匀,经测试,投掷乙骰子得到6点朝上的概率为
,若投掷乙骰子共6次,设恰有3次得到6点朝上的概率为
,
是
的极大值点.
(1)求
;
(2)若
且等可能地选择甲乙其中的一个骰子,连续投掷3次,在得到都是6点朝上的结果的前提下,求这个骰子是乙骰子的概率;
(3)若
且每次都等可能地选择其中一个骰子,共投掷了10次,在得到都是6点朝上的结果的前提下,设这10次中有
次用了乙骰子的概率为
,试问当
取何值时
最大?并求
的最大值(精确到0.01).(参考数据
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098e663b79254b0a2e0e00f92bd14b8d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098e663b79254b0a2e0e00f92bd14b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcbd28fefa404513768b10747e2291a.png)
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解题方法
5 . 已知抛物线
,动直线
与抛物线
交于
,
两点,分别过点
、点
作抛物线
的切线
和
,直线
与
轴交于点
,直线
与
轴交于点
,
和
相交于点
.当点
为
时,
的外接圆的面积是
.
(1)求抛物线
的方程;
(2)若直线
的方程是
,点
是抛物线
上在
,
两点之间的动点(异于点
,
),求
的取值范围;
(3)设
为抛物线
的焦点,证明:若
恒成立,则直线
过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf5f0df2579e567038baa206cb0b016f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b3a91ccf6028608cd03df7072f6536.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912bae66a2b7cc1caa4cd0333796ec41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a07da1731feb22da90850241b3580f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
6 . 已知长方体
中,
,点
为矩形
内一动点,记二面角
的平面角为
,直线
与平面
所成的角为
,若
,则三棱锥
体积的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a871dabec7b93bd9fcf74602ece936d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c911b404bbb8f8d5f1470585fa31ad97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa3205b1df826d63914dcb55bb3ab43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7a43b5f03e1e911ea2e82da91301a8.png)
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7 . 已知集合
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431212aa7d769932f012f3bb33ca2316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
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解题方法
8 . 如图,扇形
所在圆的半径为3,它所对的圆心角为
,点
满足
,点
是线段
上的一点,
,点
是弧
上的一点.
是弧
的中点,求
与
夹角的余弦值;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1860dc8259793593c78a05288652f3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065852037c585d69d962c39f3b69f826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a014dff8997c661055229de29c61cfc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8eb37a4dd75318dcbd836395e575bd.png)
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解题方法
9 . 设全集
,集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0dc8098ad6f31bdd87771ca9cfa33a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1cca6339c5856ce75b91f032e90551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e40b430ead18cee0e3fe6056e533708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fed3bd5bc925cf990e057f43395bff.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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昨日更新
|
175次组卷
|
2卷引用:湖北省宜昌市夷陵中学等校2023-2024学年高二下学期5月联合测评数学试题
解题方法
10 . 如图,函数
的部分图象如图所示,已知点
为
的零点,点
为
的极值点,
,则函数
的解析式为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62de064d515f09067e8ddfb8ab16c403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65436512ecbaefba4ac8123c55094211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38bd093169da55a14d82a033729b6f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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