解题方法
1 . 设等差数列
的公差为
,令
,记
分别为数列
的前
项和.
(1)若
,求数列
的通项公式;
(2)若数列
是公比为正数的等比数列,
,
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59214a46d47d4e9d45288588f8f737f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11aca5961a67d5aee3c03821ffad086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478421b81927e435cbcf5acafa89efd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b813b18bbb5bd16c3d6cb6da3790931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8850b13e872f581e16d8ebba91575b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847179a6e6e1a1268ab173586e4c8ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749a622e0249b075373103eb31ff50dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
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2 . 已知双曲线
是双曲线
的左顶点,直线
.
(1)设直线
过定点
,且交双曲线
于
两点,求证:直线
与
的斜率之积为定值;
(2)设直线
与双曲线
有唯一的公共点
.
(i)已知直线
与双曲线
的两条渐近线相交于两点
,求证:
;
(ii)过点
且与
垂直的直线分别交
轴、
轴于
两点,当点
运动时,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aae0adfafc94233b75cf5cf3d792678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edce7895b7c18ff6ada4f8975b414657.png)
(1)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
(2)设直线
![](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/ac047e91852b91af639feec23a9598b2.png)
(i)已知直线
![](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/fbbbc9c5353894f2c93c205c3ac04f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14da7a2daa1f7e1a5e3127a3060b35a3.png)
(ii)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38b9fcc365f60c8896d093edb46a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffbca194ac467f226654cbd444a1813.png)
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3 . 如图,在四棱锥
中,
是边长为2的正三角形,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810ee7bc82b6f452afb3fc18691abc3b.png)
,设平面
平面
.
(不要求写作法);
(2)线段
上是否存在一点
,使
平面
?请说明理由;
(3)若
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509385c384702090b9263822ea3d535b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810ee7bc82b6f452afb3fc18691abc3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fd798391ec66a29235c9e93d79025b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1084a42a7b7600ac9651a023de6d3401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebae74545340ce6971f437d129e9c659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23976db53f05b3d5d791c4d736a7184d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa145a3e4f18f784ddf4869e0bf904c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
名校
解题方法
4 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7550b87f0acd12417ef03dfc1be468.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-04更新
|
949次组卷
|
2卷引用:福建省龙岩市2024届高中毕业班三月质量检测数学试题
解题方法
5 . 已知
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71dddf05bd9986e353f734f1514b843f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f04d44d8e08c76a9f5bc24413cf49b.png)
A.![]() | B.![]() | C.![]() | D.2 |
您最近一年使用:0次
2024-03-04更新
|
1256次组卷
|
3卷引用:福建省龙岩市2024届高中毕业班三月质量检测数学试题
6 . 2023年秋季,支原体肺炎在我国各地流行,该疾病的主要感染群体为青少年和老年人.某市医院传染病科从该市各医院某段时间就医且年龄在70岁以上的老年人中随机抽查了200人,并调查其患病情况,将调查结果整理如下:
(1)试根据小概率值
的独立性检验,分析70岁以上老年人感染支原体肺炎与自身慢性疾病是否有关?
(2)用样本估计总体,并用本次抽查中样本的频率代替概率,从本市各医院某段时间就医且年龄在70岁以上的老年人中随机抽取3人,设抽取的3人中感染支原体肺炎的人数为
,求
的分布列和数学期望
.
附:
.
有慢性疾病 | 没有慢性疾病 | |
未感染支原体肺炎 | 60 | 80 |
感染支原体肺炎 | 40 | 20 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead9d6ff51996f3ebace6f212e11a9e4.png)
(2)用样本估计总体,并用本次抽查中样本的频率代替概率,从本市各医院某段时间就医且年龄在70岁以上的老年人中随机抽取3人,设抽取的3人中感染支原体肺炎的人数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c931474f58fa7c188670c0a94584729c.png)
![]() | 0.10 | 0.05 | 0.025 | 0.010 | 0.001 |
![]() | 2.706 | 3.841 | 5.024 | 6.635 | 10.828 |
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7 . 已知复数
满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f45b36715503c5335ecd7159af61ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d938e92eb228f6478890f1f471c8bb.png)
A.![]() | B.![]() | C.-8 | D.8 |
您最近一年使用:0次
8 .
的展开式中
的系数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c7cd44cb625ed4596f7fd95e4ab92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e2bd69747a7a90b575e97e2914aea4.png)
A.![]() | B.![]() | C.14 | D.49 |
您最近一年使用:0次
2024-03-04更新
|
1387次组卷
|
4卷引用:福建省龙岩市2024届高中毕业班三月质量检测数学试题
福建省龙岩市2024届高中毕业班三月质量检测数学试题(已下线)专题09 计数原理与随机变量及分布列(讲义)(已下线)专题7 三项式展开式问题浙江省海宁市第一中学2023-2024学年高二下学期3月阶段测试数学试题
9 . 已知函数
是大于0的常数,记曲线
在点
处的切线为
在
轴上的截距为
.
(1)若函数
,求
的单调区间;
(2)当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44adca0b35c59624c3210436974a8f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471050204eb30916555f5bb20bc4e8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff58702fa978040dc5b2a8a5c19304c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e2c8e7537453d4f72255deb779f9eb.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a644a122cd185f45b43ce054142be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a964b0caaeed0872176bceff242dbe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
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10 . 如图,在棱长为2的正方体
中,已知
分别是棱
的中点,点
满足
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9369aed2d8309af46ac3eaffb9cce537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d272066e90755925614f0d073ddf154c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e008a337c1d1c2f18dd2a50eaa7b2611.png)
A.不存在![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次