1 . 已知递增数列
的前n项和为
,且
,
.
(1)求数列
的通项公式;
(2)设
.
(ⅰ)求数列
的通项公式;
(ⅱ)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84c2e4a2a86ffc252955c06e9b567e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37b430b94a1afdb43f2a80782627c02.png)
(ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f3d151cbe277608d3a6cfbbe3f5eb9a.png)
您最近一年使用:0次
名校
2 . 已知函数
,
,其中
.
(1)若
,求实数a的值
(2)当
时,求函数
的单调区间;
(3)若存在
使得不等式
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cd20be84d4a5c153adc0dcaeffcf84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f09d8c5f6875b04965d79e787dca3ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67bad806be39af278f3cb7f77da2645a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d101c4394ba31350bfdadf5b25c4e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
您最近一年使用:0次
昨日更新
|
72次组卷
|
2卷引用:天津市河西区2023-2024学年高三下学期总复习质量调查(三)数学试卷
名校
解题方法
3 . 已知在锐角
中,角A,
,
所对的边分别为
,
,
,且
.
(1)求角
的大小;
(2)当
时,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95921d7458b14d0f4335f6c8dd5b0a56.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5742b2684d00be50a66e01c9acb6b51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
名校
解题方法
4 . 已知
,
分别为椭圆
的左、右焦点,焦距为2,
,
分别为椭圆C的上、下顶点,椭圆C的右顶点为A,直线
,
的斜率之积为
.
(1)求椭圆C的标准方程;
(2)设过右顶点A的直线
与C交于另外一点B,与
垂直的直线
与
交于点M,与y轴交于点N;若
,且
(O为坐标原点),求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b93e3f4eb68d7e137c034d9d32094be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8671e4ccb0d0da8b6cf19b0669fe76d9.png)
(1)求椭圆C的标准方程;
(2)设过右顶点A的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/5ded51ed307a019fb209cf5fa31bed4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8928625ad6575b6ce7545178005b59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次
解题方法
5 . 在
中,内角A,B,C所对的边分别为a,b,c,已知
,
.
(1)求
的值;
(2)设函数
.
(ⅰ)求
的定义域和最小正周期;
(ⅱ)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09eebab59213386449a726b75065bf76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1321c2d0bfa223b176e4e6a1286b98.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/721e29b775e696045f44a4b1e7f74ef2.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bbb30744d9c00e52b9055019ebb4e3.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2231c2f7241d4fb4c48c3105700ea0c2.png)
您最近一年使用:0次
6 . 已知等差数列
,满足
,
,正项数列
的前
项和为
,且
.
(1)求数列
和
的通项公式;
(2)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c445ae9b9b8e23fbafe3bf32cd58b8.png)
(3)在
,
之间插入1个数
,使
成等差数列,在
,
之间插入2个数
,
,使
成等差数列,
;在
,
之间插入
个数
,使
成等差数列.
①求
;
②求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83f24b32abf4b2cb15e326063e84a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/5fc5eac09ed870c6711d94e558a25a9b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c445ae9b9b8e23fbafe3bf32cd58b8.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37711dd13e400346369d9d366018de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e524013b85f8ecda29773f0fbcaf7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ffd1d0d2f8ac94173a589eb526851c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf922f855f5c6ba4f76ce9c72ab5465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50503e7c9b6e485253285cdd0c7df30b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95931effbd59c43e8ed1ea09962b84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c12353dfeb825f6b593d46b94a24af2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119dc692b6bb23baba1e27a909c4b6b2.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc38dee83ec4bbaed6f62c55e59f4f4.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ee33508bf5c846d5bd5c19d7b6844f.png)
您最近一年使用:0次
解题方法
7 . 已知等差数列
的前
项和为
,
,
,数列
是公比大于1的等比数列,且
,
.
(1)求
,
的通项公式;
(2)数列
,
的所有项按照“当
为奇数时,
放在
的前面;当
为偶数时,
放在
的前面”的要求进行“交叉排列”,得到一个新数列
:
,
,
,
,
,
,
,…,求数列
的前7项和
及前
项和
;
(3)是否存在数列
,满足等式
成立,若存在,求出数列
的通项公式,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/a8a0eecb5b800fce9ae10aed86ffee62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7f18ec0020048985d101969880d93e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90221b91dabf8a382486cdb4fea5d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a738600092c6dbff35a59954f8b0788.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1f7ed820a91b5e6fb31606ece9b9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95184a1a20419163065949815e54f174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f0818bdac0985b3a823200d552f29f.png)
(3)是否存在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebaf7c9df85e98dd4317b05a890b1c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
您最近一年使用:0次
解题方法
8 . 在
中,内角
所对的边分别为
,
,
,
.
(1)求角
的大小:
(2)求
的值;
(3)求
的值.
![](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/c18f4e1a24fc4a8672e39bfdf5e2e1af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5bac75f36bb1dc5c8190d4dbe681d.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f22fd382ec53fc639f32eac8ff96529.png)
您最近一年使用:0次
名校
解题方法
9 . (1)篮球运动员甲投篮一次得3分的概率为
,得2分的概率为
,得0分的概率为0.5(投篮一次得分只能为3分,2分,1分或0分),其中
,已知甲投篮一次得分的数学期望为1.
ⅰ)求
的最大值;
ⅱ) 求
的最小值;
(2)有甲、乙两个鱼缸,甲鱼缸中有
条金鱼和
条锦鲤,乙鱼缸中有4条金鱼和3条锦鲤,先从甲鱼缸中随机捞出一条鱼放入乙鱼缸,再从乙鱼缸中随机捞出一条鱼,若从乙鱼缸中捞出的是金鱼的概率为
,求
的最小值;
(3)总结用基本不等式求最值的条件和方法.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367658f927132c870bd5316ef30a1605.png)
ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
ⅱ) 求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7085101464667694a0a0b6e49768f65a.png)
(2)有甲、乙两个鱼缸,甲鱼缸中有
![](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/fa5a1a2ee471c67aa5264c0991d05421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483bd525deb09a595f5a791a071588b1.png)
(3)总结用基本不等式求最值的条件和方法.
您最近一年使用:0次
10 . 已知
,且
.
(1)求
,
的值;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1eca7f8e63042b1c98badc0d9e36af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353b4f6ed38b5bd83d2f0fa64d686cef.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8c56d09485b718a85ed23f637e2d77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a86df8b3934891c1d2e9016f6c4477.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f15d37ff33a395f8d35659abf4a34f0f.png)
您最近一年使用:0次