名校
解题方法
1 . (1)证明:当
时,
;
(2)已知正项数列
满足
.
(i)证明:数列
为递增数列;
(ii)证明:若
,则对任意正整数
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca947e8ea00b7a485097ecafd2dfcae9.png)
(2)已知正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f91f8b7476e67db488d85c3a14ffa6d.png)
(i)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
(ii)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f2db682457da2d4abd0e7cca1bdf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d8a310323506a3c2f3626dec8d781f.png)
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2 . 已知椭圆
的离心率为
,点
在
上.
(1)求椭圆
的方程;
(2)过点
的直线
交椭圆
于
两点(异于点
),过点
作
轴的垂线与直线
交于点
,设直线
的斜率分别为
.证明:
(i)
为定值;
(ii)直线
过线段
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e90064d012356de1877aa697cd6d6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f2a72c6d7780757ab065fb29f47526.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
(ii)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ec05e3cec27677ded7b4aecaa62d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
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名校
解题方法
3 . 已知
的内角
的对边分别为
,且满足
.
(1)求角
的大小;
(2)若
为锐角三角形且
,求
面积的取值范围.
![](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/a0d927c5817cf25e519432a63e1538c5.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/3cd07e8a88a2413704e90721ab49315f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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|
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|
2卷引用:重庆市巴蜀中学校2024届高三下学期模拟预测数学试卷
名校
4 . 为考察某种药物预防疾病的效果,进行动物试验,得到如下的列联表(单位:只):
(1)请将上面的列联表补充完整;
(2)依据
的独立性检验,能否认为药物有效呢?从概率的角度解释得到的结论;
(3)为了进一步研究,现按分层抽样的方法从未患病动物中抽取10只作为样本,从该样本中随机抽取4只,设其中未服用药物的动物数为
,求
的分布列及期望.
附表及公式:
.
药物 | 疾病 | 合计 | |
未患病 | 患病 | ||
未服用 | 50 | 40 | |
服用 | |||
合计 | 75 | 200 |
(2)依据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0298d106f2b72aadf3cffce041a25da6.png)
(3)为了进一步研究,现按分层抽样的方法从未患病动物中抽取10只作为样本,从该样本中随机抽取4只,设其中未服用药物的动物数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附表及公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d7bf7318494281c0634ab5aee4831e.png)
![]() | 0.15 | 0.10 | 0.05 | 0.025 |
![]() | 2.072 | 2.706 | 3.841 | 5.024 |
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5 . 如图,已知在正三棱柱
中,
为边
的中点.
;
(2)求三棱锥
的体积;
(3)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0bb803cd8c9c8d598416c2816aef6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa8345302e8036af33d4598282144d7.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa58d518fe175f71265a2e405f1d253.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ceb31247add8ca7b0853e801e1d125.png)
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6 . 已知抛物线
的焦点为
,其准线与
轴的交点为
,过点
的直线
与抛物线
交于
,
两点(
点位于
点右方).若
为
的角平分线,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff24d4627c643c5aeee873c6e1e626aa.png)
__________ ;直线
的斜率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4fb72e39d79b7a0cd892fa5fa34bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed24d7acba0b3a7ebf4d520296424a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff24d4627c643c5aeee873c6e1e626aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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7 . 已知函数
图象的一个对称中心为
,且
在
上单调递增,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629ab2b9cf61f4b02419beb7754767a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b212e0d4339cbd3d236a807547ebf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed440b9f974492068a68203e5029f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
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|
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8 . 已知每门大炮击中目标的概率都是0.6,现有14门大炮同时对某一目标各射击一次,则最有可能击中目标__________ 次.
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解题方法
9 . 已知实数
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4edfef181ed229ed1a3bb2295be7db9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
10 . 已知随机事件
满足
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55693a57bf5575d696bb0aad4b5113f5.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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