1 . 已知数列
的前n项和为
,且满足
,则
( )
![](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/234605545a58197b26d52799abbb17b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fbdd2e3efbef1ff014df55b242eced.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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今日更新
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399次组卷
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3卷引用:河北省张家口市2024届高三下学期第三次模拟考试数学试卷
名校
解题方法
2 . 为了选拔雏鹰计划的预备人员,某地区教育局对高一年级新生进行了测试(测试分为初试和复试).现共有400名学生参加初试,且所有学生的初试成绩
近似服从正态分布
,根据以往入选同学的初试和复试成绩走势,本届复试作出如下规定:①初试成绩高于91分者免于复试,直接确定为雏鹰计划的预备人员;②初试成绩高于80分且不超过91分的学生有资格参加复试,下图为从以往入围雏鹰计划预备人员的所有同学中随机抽取的20名同学的的初试和复试成绩.
(2)复试试题由两道数学题和两道物理题构成,已知数学题的难度系数为0.5(可以理解为进入复试的学生答对每道数学题目的概率是0.5),物理题目的难度系数均为
,能否答对这些题目相互独立,每个考生需答完四个题目,至少答出其中三个即通过复试并确定为雏鹰计划的预备人员,如果本次确定为雏鹰计划的预备人员数目不能超过33人,请确定物理试题的难度系数
的取值范围.
附:若随机变量
服从正态分布
,则
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0210a70d3664db67006ecd0cbc88e864.png)
(2)复试试题由两道数学题和两道物理题构成,已知数学题的难度系数为0.5(可以理解为进入复试的学生答对每道数学题目的概率是0.5),物理题目的难度系数均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
附:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfc26b8bdcd1fd3781c4593217c725e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04398619f7b3251b93fb34cc14930f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14360db70f4872cf5b47f12090fc211b.png)
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解题方法
3 . 已知函数
.
(1)求函数
的最值;
(2)若
,设曲线
与
轴正半轴的交点为
,该曲线在点
处的切线方程为
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd14ea273c21800c00132219688c61c.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c28eea59d06bd471fb15d2111014817.png)
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解题方法
4 . 如图所示,在棱长为2正方体
中,
分别为
的中点,
为侧面
内的动点(不包含边界),且
//平面
,
是三角形
内一动点(包含边界),且直线
与直线
的夹角等于直线
与直线
的夹角,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c427d77e282b60f0d65cd332a281b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03a049b1a67f3bfd2f11b3521a141cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f348ed8a1690d3ed02aa64459ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59375dfae3a8ec264204cfe78caac97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9104c2027ce95a663dfd92d68835a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
A.存在点![]() ![]() |
B.点![]() ![]() |
C.三棱锥![]() ![]() |
D.过点![]() ![]() ![]() ![]() ![]() |
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解题方法
5 . 已知函数
,若存在
使得
,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd2c7b8627bd16e0fc05cfff8ae880d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6440574a832dc3d79d8172b07bc5fc6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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解题方法
6 . 已知函数
,若
,则
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571bdbe6e09cf983787cb70c4b811d64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6cc553a81e66a1b15d457aa39a72917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
7 . 函数
的函数值表示不超过
的最大整数,例如,
.下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1550a97c21c1d71c9e95dde569668be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2ae14cdf62d0a69dda9a58d1ea9640.png)
A.函数![]() ![]() |
B.若![]() ![]() |
C.![]() |
D.所有满足![]() ![]() ![]() |
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8 . 已知椭圆
短轴长为2,椭圆
上一点
到
距离的最大值为3.
![](https://img.xkw.com/dksih/QBM/2024/5/26/3504894981390336/3520242638839808/STEM/32c129353263403684caca44141869ef.png?resizew=151)
(1)求
的取值范围;
(2)当椭圆
的离心率达到最大时,过原点
斜率为
的直线
与
交于
两点,
分别与椭圆
的另一个交点为
.
①是否存在实数
,使得
的斜率
等于
?若存在,求出
的值;若不存在,说明理由;
②记
与
交于点
,求线段
长度的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9059420851d219dba2189975f8eb5178.png)
![](https://img.xkw.com/dksih/QBM/2024/5/26/3504894981390336/3520242638839808/STEM/32c129353263403684caca44141869ef.png?resizew=151)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7708c156249bb475564027f73313fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2ec2e454afe8452a6f1714a986aa38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235557c7e459c7100787e436826c198e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f963b16dcebd808b41842febc329a6.png)
①是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e08d5c04f0431fb57b33a01717b599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4b2e1a496f0df7918efed76a51f34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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34次组卷
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2卷引用:江苏省扬州市2024届高三下学期高考考前调研测试数学试题
解题方法
9 . 已知圆C:
,直线l:
,若l与圆C交于A,B两点,设坐标原点为O,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ca01d1c400707e011745ad16199da13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef6d00ddabcb1bb41fae534f5183ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df09bff72dab3e6555a0597b638a3bd0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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33次组卷
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2卷引用:2024届广西壮族自治区贵港市高考模拟预测数学试题