名校
1 . 设
和
是两个等差数列,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9107b183a776ead2abb6430d12991e81.png)
,其中
表示
,
,
,
这
个数中最大的数.
(1)若
,
,求
,
,
的值;
(2)若
为常数列,证明
是等差数列;
(3)证明:或者对任意正数
,存在正整数
,当
时,
;或者存在正整数
,使得
,
,
,
,
是等差数列.
![](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/9107b183a776ead2abb6430d12991e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4139f450eede11d86247de12a5b431b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f1d0271713debdf8f0542ab79f32e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637f94c79ddadc15f305bed8adc45733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ff259bff098430a6512d0e4f6fb2d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db84454f051d418a4904fa423ab8b304.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)证明:或者对任意正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b137a34d2d5b20671b7a3c7a29606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c738db07e589f0345db84933cfcb189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829442c6473c94fde041595bc18530d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2bfc84267380660a800786986bb09f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f49a990d5bd3557d6449bb8dd91a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f49a990d5bd3557d6449bb8dd91a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
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名校
解题方法
2 . 已知椭圆
的离心率为
,左右焦点分别为
,
是椭圆上一点,
,
.
(1)求椭圆的方程;
(2)过点
的直线与椭圆交于
两点,
为线段
中点.
(i)求证:
点轨迹方程为
;
(ii)
为坐标原点,射线
与椭圆交于点
,点
为直线
上一动点,且
,求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a74e28144cbed9111d17dd239136f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6b646abc8ee6b9c8558d898f2af4be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74404619ad5699e6c44c947fb569600f.png)
(1)求椭圆的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0a807a550b61acd46aa4f8677dd6d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62518b67e16e5c04a2d6be20c476fb0.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fb85c78522640bcaf889f89ad89de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fb85c78522640bcaf889f89ad89de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a281a22f6ce9def698919a6d1a04c389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
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解题方法
3 . 如图,已知
中
为直角,
是线段
上任意一点(不含端点),沿直线
将
折成
,所成二面角
的平面角为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172f1b400d9ddec4ea01f6fd040b3802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0a49b9a3976893039103a7ba3727e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa19f78fd19c8e5601bba0f52e438ca6.png)
A.![]() | B.![]() ![]() ![]() |
C.![]() | D.![]() ![]() ![]() |
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解题方法
4 . 已知a,
,
是虚数单位,
,
在复平面上对应的点分别A、B.
(1)若
是实数,求
的最小值;
(2)设O为坐标原点,记
,若
,且点C在y轴上,求
与
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f05683157eb845db949d888899d0f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c484d60171548d3b143f4d664b1c9c1c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf36d6c7ecd9fb710f8b7237c488471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d401876b078e318413b8ad876c54b7be.png)
(2)设O为坐标原点,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc170fc6c893de77fdbb1d5a9b34814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4876efa91f38d11ce12fed2e1fbf2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
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名校
解题方法
5 . 已知椭圆
:
的左、右焦点分别为
、
,焦距为
,点
在
上.
(1)求椭圆
的标准方程;
(2)已知点
,点
为椭圆
上一点,求
周长的最大值;
(3)过
的右焦点
,且斜率不为零的直线
交
于
、
两点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](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/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a20dc43538548ac95367b0a5695fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.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/432cdf18ddf26951722aea97b22c2f34.png)
(3)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ea1c3fe8431260ecb8dffcdae8d570.png)
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名校
6 . 已知有穷数列
的首项为1,末项为12,且任意相邻两项之间满足
,则符合上述要求的不同数列
的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5ae60c8ef83e4798fac7bc7d327af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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7 . 设集合
,点P的坐标为
,满足“对任意
,都有
”的点P构成的图形为
,满足“存在
,使得
”的点P构成的图形为
.对于下述两个结论:①
为正方形以及该正方形内部区域;②
的面积大于32.以下说法正确的为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03cd04b82dda9c0d2dd0957ffc407d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9712a0071f6d0d78d17ce18f6084cad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3693b84b83679c30b1035750d9b4f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deebd2c36a5e644a566f1980091359bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9712a0071f6d0d78d17ce18f6084cad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3693b84b83679c30b1035750d9b4f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e32039addb008103a2a8344225214a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deebd2c36a5e644a566f1980091359bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e32039addb008103a2a8344225214a.png)
A.①、②都正确 | B.①正确,②不正确 |
C.①不正确,②正确 | D.①、②都不正确 |
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名校
8 . 若存在实数
及正整数
使得
在
内恰有2024个零点,则满足条件的正整数
的值有______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c1173fe5c1b3445534e1d2cbe5d738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0b396c8cd1754fb25acce89a06d280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2024-05-28更新
|
382次组卷
|
3卷引用:上海市行知中学2023-2024学年高一下学期期中数学试题
名校
解题方法
9 . 某景点的票价为5元,售票窗口只有2张5元并有足够多的门票.现有4人持一张5元,5人持一张10元来买票,则没有顾客需要等待找钱的概率为________ .(结果用最简分数表示)
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10 . 已知函数
,其中
.
(1)若
,
,求
的对称中心;
(2)若
,函数
图象向右平移
个单位,得到函数
的图象,
是
的一个零点,若函数
在
(
,
且
)上恰好有8个零点,求
的最小值;
(3)已知函数
,在第(2)问条件下,若对任意为
,存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc83360ee915013086a987281278639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb73539af255bde55d682b0d0ca735f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9ceace94f41fcf47aa3ba6ca444a6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f95e85ce6707ff4161cc675665c557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9895bf4192f5c55c16f8270d53c49b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8440725e1df5ca0990b572dd84127914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0d3f5247aced48d54b594ec3522628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e538686939002a2ba06670615144c73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caece05b586ec9e2d6f1ec69449550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b56a0bc723618e7cdac994882c807bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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