1 . 已知无穷数列
,构造新数列
满足
,
满足
,
,
满足
,若
为常数数列,则称
为
阶等差数列;同理令
,
,
,
,若
为常数数列,则称
为
阶等比数列.
(1)已知
为二阶等差数列,且
,
,
,求
的通项公式;
(2)若
为
阶等差数列,
为一阶等比数列,证明:
为
阶等比数列;
(3)已知
,令
的前
项和为
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22e75bf99dcb0fe32f66fa90a74f9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc06ff2f65c456efb6a114e67b62cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d16e3ca4fb65342b0e9a0594d661ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf623a6dd661f87cf64ea150072fd78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcbdf91bb5a49f293f9b52ac8dcfa35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1ca0ac3789432a3d1ce975a9a6f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ab5abd104649f9a3c231df9a55813a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1ca0ac3789432a3d1ce975a9a6f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69c653f3a05dd25f6affdba7baeab38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0606df3b6fbc6fcf863f9c59e0e54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab214e5f34d976717284bed52c645e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e796a0144ff9b3329c7064a01c5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a4b318fa151fab14b3857942ed3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07418f1fa0f6569b50944b5a13ffa021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7778648d93a10ed66ddd99672d3ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.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/a2a5a414f3f5d724058a2e887f3d1c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3fec47d2dd2b8099d86c87b6e57de8.png)
您最近一年使用:0次
7日内更新
|
463次组卷
|
3卷引用:浙江省宁波市镇海中学2024届高三下学期适应性测试数学试卷
2 . 若某次乒乓球练习中,乒乓球发球后先后击中已方桌面
和对方桌面
,且
长为60英寸,球在
中点
处到达最高点,高度为
英寸,乒乓球网位于
上靠近
的三等分点
处,网高为6英寸,球恰好沿着网的上边界越过,其轨迹图象如下:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 如图1,在梯形
中,
,
是线段
上的一点,
,
,将
沿
翻折到
的位置.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/211d1e84-85c7-440e-972e-c6d64ffebc7f.png?resizew=616)
(1)如图2,若二面角
为直二面角,
,
分别是
,
的中点,若直线
与平面
所成角为
,
,求平面
与平面
所成锐二面角的余弦值的取值范围;
(2)我们把和两条异面直线都垂直相交的直线叫做两条异面直线的公垂线,点
为线段
的中点,
,
分别在线段
,
上(不包含端点),且
为
,
的公垂线,如图3所示,记四面体
的内切球半径为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb15c7f8fd604976818ff6de254b6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/211d1e84-85c7-440e-972e-c6d64ffebc7f.png?resizew=616)
(1)如图2,若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9d5946fba71d0623ab27f24c6b57fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e184efd65dfaa5d62242c482d2158d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
(2)我们把和两条异面直线都垂直相交的直线叫做两条异面直线的公垂线,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bb1c5af4c7a9376882867e07690b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bb1c5af4c7a9376882867e07690b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da424b529ab73775b90cd4089d18419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57d8c0d92f5b6bede99e8d9d227e40.png)
您最近一年使用:0次
解题方法
4 . 已知棱长为1的正方体
是空间中一个动平面,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89656654ebe90dfe1f2c243afde60c5d.png)
A.设棱![]() ![]() ![]() ![]() |
B.设棱![]() ![]() ![]() ![]() |
C.正方体的12条棱在平面![]() |
D.四面体![]() ![]() |
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5 . 曲线的法线定义:过曲线上的点,且垂直于该点处切线的直线即为该点处的法线.已知点
是抛物线
上的点,
是
的焦点,点
处的切线
与
轴交于点
,点
处的法线
与
轴交于点
,与
轴交于点
,与
交于另一点
,点
是
的中点,则以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfb23a9e07213cb76990dbedfc7feca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97afdeaa1d4433cffe5005446fcbbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
A.点![]() ![]() |
B.![]() ![]() |
C.![]() |
D.过点![]() ![]() ![]() |
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6 . 已知离心率为
的双曲线
与x轴交于A,B两点,B在A的右侧.在E上任取一点
,过点B作直线QB垂直PA交于点Q,直线PB、QA分别交y轴于不同的两点M,N.
(1)求双曲线E的方程;
(2)求证:直线
与直线
的斜率乘积为定值;
(3)三角形MNB的外接圆是否过x轴上除B点之外的定点,若是,求出该定点坐标:若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9c7f26c2b768d5bae9fc062d431348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2dde6ab3c91e54f052de132494a5e5.png)
(1)求双曲线E的方程;
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(3)三角形MNB的外接圆是否过x轴上除B点之外的定点,若是,求出该定点坐标:若不是,请说明理由.
您最近一年使用:0次
7 . 定义满足
的实数
为函数
的然点.已知
.
(1)证明:对于
,函数
必有然点;
(2)设
为函数
的然点,判断函数
的零点个数并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477ac2d23b77b49c205952d8cda5a981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27dc87cafb7a8d3bed4b4a7e82155a6.png)
(1)证明:对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7b784381c282fc5f788485316c943c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19105fc2ee351fdb367614762992929.png)
您最近一年使用:0次
8 . 抛物线C:
,椭圆M:
,
.
(1)若抛物线C与椭圆M无公共点,求实数r的取值范围;
(2)过抛物线上点
作椭圆M的两条切线分别交抛物线C于点P,Q,当
时,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e61e0a1bc2ab34fe0cd1de9f59b0e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181820d1a015068701cfdbdf48b24c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
(1)若抛物线C与椭圆M无公共点,求实数r的取值范围;
(2)过抛物线上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8adb3358f321cc2c429b9c20674b271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b38040230a7f5674f13c690e780ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
您最近一年使用:0次
9 . 已知函数
,
,记
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699f767ccf837c2bf8019d03451849c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd17ae52ccb646646e43237c0697495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f92ac0144b7ab2c33c46d7347ffe0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00b23ab45465b96c7d1c385b56080d.png)
A.若正数![]() ![]() ![]() ![]() |
B.若正数![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.![]() ![]() ![]() |
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10 . 在空间直角坐标系Oxyz中,
,
,若直线AB与平面xOy交于点
,点P的轨迹方程为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6377767f356676a837aff1b90ef3749c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c231fdd1209eca78428f4b2fd803c31e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7836750ff40c856e6aeb9ce0e239895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad86ba09055ed2abe5b4299463b7b74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
A.1 | B.![]() | C.2 | D.![]() |
您最近一年使用:0次