1 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数),以原点
为极点,
轴正半轴为极轴建立极坐标系.
(1)求曲线
的极坐标方程;
(2)设
是曲线
上的两点,且
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b2288fe9338cd9edd18c386aec04da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
2024-06-10更新
|
179次组卷
|
3卷引用:陕西省铜川市2024届高三第三次模拟考试理科数学试题
解题方法
2 . 榫卯结构是中国古代建筑文化的瑰宝,在连接部分通过紧密的拼接,使得整个结构能够承受大量的重量,并且具有较高的抗震能力.这其中木楔子的运用,使得榫卯配合的牢度得到最大化满足,木楔子是一种简单的机械工具,是用于填充器物的空隙使其牢固的木橛、木片等.如图为一个木楔子的直观图,其中四边形
是边长为2的正方形,且
均为正三角形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,则该木楔子的外接球的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb6bc33be59a39d0bf6530d02715b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee16d92c14db93561e0163ff0df8c85.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知甲种杂交水稻近五年的产量数据为
,乙种杂交水稻的产量数据为
,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e12b5f5fdfc83418b60497a79b27ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/775c817cdc35413b6cbd1e19e9a5d381.png)
A.甲种的样本极差小于乙种的样本极差 |
B.甲种的样本平均数等于乙种的样本平均数 |
C.甲种的样本中位数等于乙种的样本中位数 |
D.甲种的样本方差大于乙种的样本方差 |
您最近一年使用:0次
解题方法
4 . 已知函数
,则下列说法中不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7521e281dcd1326dc2b10fe3bd5caa97.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() |
您最近一年使用:0次
5 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若函数
存在零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e8fc13d0e5024b0d85d67c2b469851e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
6 . 如图,四棱锥
的底面是正方形,
平面
,点
是
的中点,
是线段
上(包括端点)的动点,
.
平面
;
(2)若直线
与平面
的夹角为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b610c9b9948d88eda8de0fb8d1cf972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b70cef0b79ca64acbb67dc667fc53b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb7162483d12c18cd4d1ab2acc28c49.png)
您最近一年使用:0次
解题方法
7 . 已知函数
.
(1)求不等式
的解集;
(2)记函数
的最小值为
,若正数
满足
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5a5654771a93b966e0e0086e1f6112.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5e587ca42942c63cf7ba196a355a81.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7c2c9f402b4f83ee6c0474c7964487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ce569853573f27b862f5e32b9963d5.png)
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8 . 过抛物线
焦点
的直线
交
于
两点,若直线
垂直于
轴,则
的面积为2,其中
为原点.
(1)求抛物线
的方程;
(2)抛物线
的准线上是否存在点
,使得当
时,
的面积为
.若存在,求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/7789a500686c7a73770404ead6af0590.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/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)抛物线
![](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/9d3835e6398d18d162afebc92cd2ae9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
9 . 学校团委和工会联合组织教职员工进行益智健身活动比赛.经多轮比赛后,由教师甲、乙作为代表进行决赛.决赛共设三个项目,每个项目胜者得10分,负者得
分,没有平局.三个项目比赛结束后,总得分高的获得冠军.已知教师甲在三个项目中获胜的概率分别为
,各项目的比赛结果相互独立.甲、乙获得冠军的概率分别记为
.
(1)判断甲、乙获得冠军的实力是否有明显差别(若
,则认为甲、乙获得冠军的实力有明显差别,否则认为没有明显差别);
(2)用
表示教师甲的总得分,求
的分布列和数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44986287ed599f86a23cfffe788cc76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3909a0f8cb807f821e987b8e141b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3c5a4887dfe02b02ee90d740151e1d.png)
(1)判断甲、乙获得冠军的实力是否有明显差别(若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce986d3907d57d5f7e31bbe631a10e7.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次
10 . 已知点
为
外接圆的圆心,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c507d5157851d4a24bfbdecaeb3c071b.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c47d2fe38ec0c1b4f7f82035a2fa40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c507d5157851d4a24bfbdecaeb3c071b.png)
您最近一年使用:0次