1 . 设函数
.
(1)若
,求曲线
在点
处的切线方程;
(2)若函数
在区间
内单调递增,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3cf85e80663b8cf9f1700939d7f100a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a2a34b4317deffa40ba34e269c2b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
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2 . 已知函数
,
,若关于x的方程
有三个不同实数根,则实数t的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff003550d99ab3862156a75df7f18521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/601089d902cdde95507fb4db1af1823d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5388b496b66261c9f8fbc9e741ea73e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 已知抛物线
的焦点为
,抛物线
的焦点为
,
,A,B,C为
上不同的三点.
(1)求
的标准方程;
(2)若直线
过点
,且斜率
,求
面积的最小值;
(3)若直线
,
与
相切,求证:直线
也与
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4428756f1088ce78ed97cbcea99775f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c9c87eba774f6bc072663d32d11fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e2a53d1a4b083d0f4d0b64ed0d0353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d165046175c70690335c3c8ce97b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3738fa0ab2ac2aa1da705ea85f3b9b21.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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4 . 某地为了了解学生的睡眠时间,根据初中和高中学生的人数比例采用分层抽样,抽取了40名初中生和20名高中生,调查发现初中生每天的平均睡眠时间为8小时,方差为2,高中生每天的平均睡眠时间为7小时,方差为1.根据调查数据,估计该地区中学生睡眠时间的总体方差约为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 设A,B是两个随机事件,且
,
,则下列正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2dc39b48969812063cc9d265489e10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f265833907c74d5d9771f0383c6b76.png)
A.若![]() | B.![]() |
C.![]() | D.A与B有可能是对立事件 |
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名校
解题方法
6 . 已知定义在
上的函数
满足
,且
,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1ba677dc12c5304da89bc2e95dd4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ca2e66c203f9aab0b30cf06e72d7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23437d77a112dc274b70dd0295bf723.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() |
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2024-06-11更新
|
691次组卷
|
3卷引用:辽宁省葫芦岛市协作校2023-2024学年高三下学期第一次考试数学试卷
解题方法
7 . 集合
的整数元素的个数为
,数列
的前n项和为
,满足
,
,且
,都有
成立,下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd5eb55b7d5afbbc2e9adbfbd2c6da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a48e76200db6510369b47b3dcdeba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c0e76cc052b81d0534979470a89cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/076e60926a8baccb37ecba4b571ed128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9544eeec3735c96416b28aa01bb92c7.png)
A.数列![]() ![]() |
B.![]() |
C.实数![]() ![]() |
D.数列![]() |
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8 . 设数阵
,其中
.设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac98f22d559df85afd6cde2122982c1b.png)
,其中
,
且
.定义变换
为“对于数阵的每一列,若其中有t或
,则将这一列中所有数均保持不变;若其中没有t且没有
,则这一列中每个数都乘以
”(
),
表示“将
经过
变换得到
,再将
经过
变换得到
,…,以此类推,最后将
经过
变换得到
.记数阵
中四个数的和为
.
(1)若
,
,写出
经过
变换后得到的数阵
,并求
的值;
(2)若
,
,求
的所有可能取值的和;
(3)对任意确定的一个数阵
,证明:
的所有可能取值的和不大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd0a32496c35c7a9ec330bdd02808829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d989c2c5a405c4d9a20e470f5bd96ab3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac98f22d559df85afd6cde2122982c1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f8daacbdbb8b2ff092d4c56057c729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96b51fbf91d105af6afbd5b2966185a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b08c58baacec3cd0c0a06e267fa9ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c88248a34d270530f9d01570a911878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e93d044f7bde4330e206b4edd2bd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97add95cc99b7846691dbdd91ef0f3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97add95cc99b7846691dbdd91ef0f3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b2c2aa49dc4520fcc7fe01f1776301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad42dbc5fa989573d079ff58c9bd837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd680d9d3352bfe69d373054ab106a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9e38f3101bb9a37b307ce245c57b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/841f2788fc89aafb399653dcf5c373c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3233aed5e30e9988e1676b4392dd4dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a6254dbc0b14828d000e1901ae21eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9cce113f874ea096ee027d0c7d2ad27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9cce113f874ea096ee027d0c7d2ad27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca99f73e0e80bfa74b06d4d28ed09c4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21f1d68a3e838d14d000d02301ce78c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39979f11a0fd0a8d9d726a1b48260f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd680d9d3352bfe69d373054ab106a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca99f73e0e80bfa74b06d4d28ed09c4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21f1d68a3e838d14d000d02301ce78c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07225d468ccf6abe4f258d74cd8ba08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca99f73e0e80bfa74b06d4d28ed09c4.png)
(3)对任意确定的一个数阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd680d9d3352bfe69d373054ab106a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca99f73e0e80bfa74b06d4d28ed09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b9a5f1362c12e1ea8f6fc0d9d787ac.png)
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9 . 如图,在五面体
中,底面
是菱形,
,
.
;
(2)
,M是
的中点,O为
的中点,
且
,
.
①求证:
平面
;
②求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedd51383f8f047f565191b128cec637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6469878a955cc09fac22ba5aea3fb962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0953f077bbdf4a6d5889b8cda088fb67.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/884bb2f05bbc2ce8a34b8601269768f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93af9774200946261f0ccba3e6eeba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108ebf3215a544f65ff55283bda648b9.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de7ea432599108b34a0ccaa0f2c75e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
②求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
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解题方法
10 . 某商场为调查手机卖场各品牌手机在晚上19:30到21:00时段的销售情况,随机抽取了某一周该时段的销售数据,并要求每个品牌只抽取一个款式的手机,且不考虑价格波动.
销售利润率是指:一部手机销售价格减去出厂价格得到的利润与该手机销售价格的比值.
(1)从该公司本周该时段卖出的手机中随机选一部,求这部手机利润率高于0.07的概率;
(2)从该公司本周该时段卖出的销售单价为4800元的手机中随机选取2部,求这两部手机的利润率不同的概率;
(3)销售一部步步高手机获利
元,销售一部三星手机获利
元,…,销售一部vivo手机获利
元,依据上表统计数据,随机销售一部手机获利的期望为
,设
,试判断
与
的大小.
手机品牌 | 步步高 | 三星 | 华为 | 苹果 | vivo |
销售总额(万元) | 1.92 | 1.8 | 4.8 | 4.8 | 2.52 |
销售量 | 4 | 3 | 10 | 6 | 7 |
销售利润率 | 0.1 | 0.07 | 0.06 | 0.05 | 0.08 |
(1)从该公司本周该时段卖出的手机中随机选一部,求这部手机利润率高于0.07的概率;
(2)从该公司本周该时段卖出的销售单价为4800元的手机中随机选取2部,求这两部手机的利润率不同的概率;
(3)销售一部步步高手机获利
![](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/ee9b42973c53907f09f2de384c42fc5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abd6ab8372512c420c76f9437665d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0c4c71089ffa8b2d6c7a58848325c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abd6ab8372512c420c76f9437665d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85481cd7e94130ef3aa05b4a39e79cd.png)
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