1 . 已知等差数列
满足,
,公差
,且22,
,
成等比数列.
(1)求数列
的通项公式;
(2)若数列
的通项公式为
,求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b71ef6cb9c5d494692d40a9ef279f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfe23848f9ed53463f2d75885c56178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042edb1bede0472d8d14cc45f66d25d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6fb7d0e49d52979bc79920019ab8979.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267c99ff3f6386113dbaa7b1e49612da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e24c0b6a5964ad028bac5e8c10c6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2024-06-07更新
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2卷引用:广东省潮州市华南师范大学附属潮州学校2023-2024学年高二下学期阶段二教学质量检测数学试卷
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2 . 某圆拱梁的示意图如图所示,该圆拱的跨度AB是36m,拱高OP是6m,在建造时,每隔3m需要一个支柱支撑,求支柱
的长(参考数据
2.45,结果精确到0.1m).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3cd19fa6b46b0f84127e40aaa8a66c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1fa0fc035ce6bbba67af947d423f84.png)
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3 . 如图,一个几何体是由一个正三棱柱内挖去一个倒圆锥组成,该三棱柱的底面正三角形的边长为2,高为4.圆锥的底面内切于该三棱柱的上底面,顶点在三棱柱下底面的中心处.
(2)求该几何体的表面积.
(2)求该几何体的表面积.
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4 . 已知向量
,且
与
的夹角为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e3430cc976da11493e693783796939.png)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c9abe1f8fb33024df04558987daf1f.png)
(2)若
,求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10814bc3db929e79874befe96cf4e3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786954a4502555f3455f4a41df1b0786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fe4e713c108e118522a99ecd683924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ede7d953b17fc5153c45029218ecc83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e3430cc976da11493e693783796939.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c9abe1f8fb33024df04558987daf1f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b190b5fb977d012e536ce8cfe6e430a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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5 . 已知函数
,
(1)求
;
(2)若直线
与曲线
相切于点
,求切点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c59508c69247cbe5f85fbbcfbbc070.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383acb6637f314601906b2b617c823bc.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67e9e6d8cf55f060ae0d7c48f51e814b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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6 . 已知函数
.
(1)讨论函数
的单调性;
(2)若存在正数
,使
成立,求
的取值范围;
(3)若
,证明:对任意
,存在唯一的实数
,使得
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe008fe11acbc34a61c7f44c5811be57.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若存在正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d41acc47493556617fe7b9e55093d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9e6a220e85fa5a1d7c773bb143d46f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d701701514d29d22d56e8a35f797d267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99851fb4df35dfb2c4efd4a839b901f.png)
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2024-04-18更新
|
1739次组卷
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4卷引用:广东省潮州市华南师范大学附属潮州学校2023-2024学年高二下学期阶段二教学质量检测数学试卷
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7 . 设
、
分别是
的边
、
上的点,
,
,
.
(1)若
(
、
为实数),求
的值;
(2)若
(
、
为实数),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74a61581d965458316280968241e4c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f3ddfd586ae5432f0c06e5b1a76ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a936641949d6f9daa1e9bb2679b5fc1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cea8f02768bdd7e869290d042a5748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7345f310975ddb40dca94b5135c35dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0ee8fc6d8bbd11a0cf66a86207bd69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061baa765d2939a416300de14c45b8ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf97cb5e2fa09745dbb21b9bcfe9e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698533f7cec9ad4a58bbf307bbdc93d5.png)
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8 . 在
中,角
的对边分别为
.
(1)若
,求
的值;
(2)若
,求
边上的高;
(3)若
,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)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c47577e18a3c1a161dd838b1554274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a744add7947909f8e0ab790dcf76dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8ea25b4ae2fbbe8e2388f58ca2d5d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1311f32edf13f8caee5edb03f24a7ba.png)
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9 . 阅读以下材料,解决本题:我们知道①
;②
.由①-②得
,我们把最后推出的式子称为“极化恒等式”,它实现了没有夹角参与的情况下将两个向量的数量积化为“模”的运算.如图所示的四边形
中,
,
为
中点.
,求
的面积;
(2)若
,求
的值;
(3)若
为平面
内一点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b99b4343c4203c548394d359864bca39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fedd0e00920793446fd97cb1b9fc8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2149e23b4eaceaee7409f7bf9d7e70e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e9a6363be202df9530a291ab85730a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf93b48e3851a4ad9d2d8913db8130b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb961bd7db3adb76af2d4cedb611bd7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4695ef2ef8930aa9e515db3efb3411e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b847ccdc479d753206a89eb94e37754.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892966a4071cdf7a0424e461499f4f71.png)
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10 . 在复平面内,复数
对应的点的坐标为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f62004f00ae1e4b9f77df9e5bfc4e7.png)
,且
为纯虚数(
是z的共轭复数).
(1)求m的值;
(2)复数
在复平面对应的点在第一象限,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f62004f00ae1e4b9f77df9e5bfc4e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce271fca2cfe209bc311fbe3080bafc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160b0638cf392d3073a89580e992a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
(1)求m的值;
(2)复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4dd95efd7f87c60490d7874ac8e9ae.png)
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2024-04-03更新
|
863次组卷
|
5卷引用:广东省潮州市饶平县第二中学2023-2024学年高一下学期第一次月考数学试题
广东省潮州市饶平县第二中学2023-2024学年高一下学期第一次月考数学试题(已下线)高一下学期期中考试--重难点突破及混淆易错规避(苏教版2019必修第二册)福建省部分优质高中2023-2024学年高一下学期期中质量检测数学试题江苏省连云港市七校2023-2024学年高一下学期期中考试数学试题(已下线)第10章:复数章末综合检测卷(新题型)-【帮课堂】(人教B版2019必修第四册)