1 . 如图所示的散点图,现选用两种回归模型,模型A:用线性回归模型,计算出相关系数
;模型B:用指数回归模型,计算出转化为线性回归方程所对应的相关系数
,则一定有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/11/bca786f4-f78d-49b1-b866-985fee116fd4.png?resizew=147)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/11/bca786f4-f78d-49b1-b866-985fee116fd4.png?resizew=147)
A.![]() | B.![]() | C.![]() | D.无法确定 |
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2 . 如图,圆C:
与圆O:
内切于点A,当圆C沿圆O逆时针方向无滑动地滚动一周时,圆C上的定点P(开始在点A)运动的轨迹是一个三叶轮.已知圆C上的定点P按这种运动方式从点A开始运动(B是两圆的切点).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/fddcfe0b-943a-40b1-a8ab-159fe401e6ab.png?resizew=170)
(1)若
,求点P的坐标;
(2)若
,求点P的轨迹关于
的参数方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9df0d79e42d86b0def4caa10dffa75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08227ca941898eb34941f446ca8b1de8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/fddcfe0b-943a-40b1-a8ab-159fe401e6ab.png?resizew=170)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d162c29b1e484cfc87350dd68f00b85.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb7e00f8bacce4d649b535449f04568c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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3 . 世界锦标赛简称
,是方程式汽车赛中最高级别.所谓“方程式”赛车是按照国际汽车联合会(
)规定的标准制造的赛车,目前西南交通大学实验室制造了一种新的方程式赛车,已知这种赛车的位移和时间的关系满足
,则
时赛车的瞬时速度是______ (米/秒).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80ecb6b5d5eca464b3f099513c08fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2078a37bb0faada51bc3796efcfe864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15a13b4190ac3d5feaee27a4c97b21b.png)
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2023-03-02更新
|
291次组卷
|
3卷引用:四川省成都市锦江区嘉祥外国语高级中学2020-2021学年高二下学期期中考试理科数学试题
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4 . 已知函数
有两个零点
,
,则下列说法:
①函数
有极大值点
,且
;
②
;
③
;
④若对任意符合条件的实数
,曲线
与曲线
最多只有一个公共点,则实数
的最大值为
.其中正确说法的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/620809df01729bc526807d556a5e2b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31cdc61764eef3fbe2dc5fafaa2efb39.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4900c67f4b57fa430c4bd863f8e896.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d406c2022d92072bd3f4a93d0e472c82.png)
④若对任意符合条件的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd661503039022b395ff97b9d91aa66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2df754f77604928c25690dde22b753.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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5 . 为了调研雄安新区的空气质量状况,某课题组对雄县、容城、安新3县空气质量进行调查,按地域特点在三县内设置空气质量观测点,已知三县内观测点的个数分别为6,y,z依次构成等差数列,且6,y,
成等比数列,若用分层抽样的方法抽取12个观测点的数据,则容城应抽取的数据个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b79e2486f480ed7e153809489a524f6.png)
A.2 | B.4 | C.6 | D.8 |
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6 . 设四面体
中,有
条棱长为
,其余
条棱长为
.
(1)
时,求
的取值范围;
(2)
时,求
的取值范围;
(3)
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e6155764141e88750b8c15fc7b606db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbd5bb726a08c308b48373afebbb768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
7 . 已知底面边长和斜高长均为2的正四棱锥被平行于底面的平面所截得的正棱台为
,且满足
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9dcbb4a05aa3b0cf780baa4489556e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
(2)求棱台的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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8 . 均值不等式
可以推广成均值不等式链,在不等式证明和求最值中有广泛的应用,具体为:
.
(1)证明不等式
.
(2)上面给出的均值不等式链是二元形式,其中
指的是两个正数的平方平均数不小它们的算数平均数,类比这个不等式给出对应的三元形式,即三个正数的平方平均数不小于它们的算数平均数,并尝试用分析法证明猜想.(
个数的平方平均数为
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72dc44cb9d5684d5377141fcd393c415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ece659f1e648942b5c9f7155685dcc.png)
(1)证明不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b40495f9b82c312c90382cb0a1b75f.png)
(2)上面给出的均值不等式链是二元形式,其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7806d740bdb93071c7580a9c6db0d09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40a7ac954477ada360785f8fe82a162.png)
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9 . 已知集合
,
若将集合
中的数按从小到大排成数列
,则有
,
,
,
,…,依次类推,将数列依次排成如图所示的三角形数阵,则第六行第三个数为( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/27/7afbb1a5-3b4b-4508-8717-e97fb8f956ee.png?resizew=129)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3612d5af5bad7059ffe0eb9b72a7d3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18e278273fdd2a0f46be69d2d7c46ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014aff9b566cfacbb6a6c01d341a1cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cad7da74bcd75d50fc54fb6786a4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6689ce2f9ac81f8091427a0697a3bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8388a73bf5c9c1c064f690b68186ed.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/27/7afbb1a5-3b4b-4508-8717-e97fb8f956ee.png?resizew=129)
A.247 | B.735 | C.733 | D.731 |
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10 . 下面几种推理中是演绎推理的是( )
A.![]() ![]() ![]() |
B.某班张三、李四、王五身高都超过1.8米,猜想该班同学身高都超过1.8米 |
C.猜想数列1×2,2×3,3×4,…的通项公式为![]() |
D.由平面直角坐标系中两点![]() ![]() ![]() ![]() ![]() ![]() |
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