解题方法
1 . 已知实数
,记
.若函数
在区间
上的最小值为
,则
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29607289153a461696170c1cd668d40e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87db566129388307bdf3f8eea81ce4c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2 . 如果一个非空集合
上定义了一个运算
,满足如下性质,则称
关于运算
构成一个群.
(1) 封闭性,即对于任意的
,有
;
(2) 结合律,即对于任意的
,有
;
(3) 对于任意的
,方程
与
在
中都有解.
例如,整数集
关于整数的加法(
)构成群,因为任意两个整数的和还是整数,且满足加法结合律,对于任意的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526c6e33166cdaadce9d0226b67642c7.png)
,方程
与
都有整数解;而实数集
关于实数的乘法(
)不构成群,因为方程
没有实数解.
以下关于“群”的真命题有( )
①自然数集
关于自然数的加法(
)构成群;
②有理数集
关于有理数的乘法(
)构成群;
③平面向量集关于向量的数量积(
)构成群;
④复数集
关于复数的加法(
)构成群.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd94e5c210921dfbe11796b1fc97cee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd94e5c210921dfbe11796b1fc97cee.png)
(1) 封闭性,即对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9cbad1e8b405feac6e8fe403f024b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d114f63ee7e47c04170f88f50da421fb.png)
(2) 结合律,即对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d4ef2c168b3dba086f2485c3c9cc7c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f85669796a75bc41a4c73d983df4e470.png)
(3) 对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9cbad1e8b405feac6e8fe403f024b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2f15046971cccda1b8d71b6619a4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592d41e37ffe434aa96117acdeef06ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
例如,整数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed24e42ca43303878d653316e149170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4cd9a7068de096606d1ab991f5e6da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526c6e33166cdaadce9d0226b67642c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed24e42ca43303878d653316e149170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333b4fe0a74ea21932b6954c63b3c794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea1301a10396933e82b070621bacbef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086adfb67fd14ad6b4acdf96d1b65449.png)
以下关于“群”的真命题有( )
①自然数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6e5e4edd3db682d6f0e57aca5e4d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4cd9a7068de096606d1ab991f5e6da.png)
②有理数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a064c152c8d7225a1cf14a247f2ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
③平面向量集关于向量的数量积(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97ec04a1aa7ac6fce72d589864940a2.png)
④复数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616bf4b8ecad92ea0d882024ef56bb37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4cd9a7068de096606d1ab991f5e6da.png)
A.0个; | B.1个; | C.2个; | D.3个. |
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解题方法
3 . 在下列关于实数
的四个不等式中,恒成立的是_______ .(请填入全部正确的序号)
①
;②
;③
;④
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759c09917e5728d75bf5cfdb5b4a807f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf3e4ab16184e30ccb223f42e7f3623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6627943e258550c27076ff81e2ac71c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0076f770e001e05a5545101e2a112135.png)
您最近一年使用:0次
4 . 已知
是虚数单位,复数
是纯虚数,则实数
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b240e3590fbdc76843358fe00c3f9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
5 . 如图1所示,
是水平放置的矩形,
,
.如图2所示,将
沿矩形的对角线
向上翻折,使得平面
平面
.
的体积
;
(2)试判断与证明以下两个问题:
① 在平面
上是否存在经过点
的直线
,使得
?
② 在平面
上是否存在经过点
的直线
,使得
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
(2)试判断与证明以下两个问题:
① 在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49b2f51d88feb313b735e8077117abb.png)
② 在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0bcc3c5b41a01362779683f5b70710c.png)
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解题方法
6 . 江南某公园内正在建造一座跨水拱桥.如平面图所示,现已经在地平面以上造好了一个外沿直径为20米的半圆形拱桥洞,地平面与拱桥洞外沿交于点
与点
. 现在准备以地平面上的点
与点
为起点建造上、下桥坡道,要求:①
;②在拱桥洞左侧建造平面图为直线的坡道,坡度为
(坡度为坡面的垂直高度和水平方向的距离的比);③在拱桥洞右侧建造平面图为圆弧的坡道;④在过桥的路面上骑车不颠簸.
(2)并按你的方案计算过桥道路的总长度;(精确到0.1米)
(3)若整个过桥坡道的路面宽为10米,且铺设坡道全部使用混凝土.请设计出所铺设路面的相关几何体,提出一个实际问题,写出解决该问题的方案,并说明理由 (如果需要,可通过假设的运算结果列式说明,不必计算).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7af3106d29fa975bfb43fc75779a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b981bcf37604ce11a7f5ccf90a21eee8.png)
(2)并按你的方案计算过桥道路的总长度;(精确到0.1米)
(3)若整个过桥坡道的路面宽为10米,且铺设坡道全部使用混凝土.请设计出所铺设路面的相关几何体,提出一个实际问题,写出解决该问题的方案,并说明理由 (如果需要,可通过假设的运算结果列式说明,不必计算).
您最近一年使用:0次
7 . 正四棱锥
底面边长为2,高为3,则点
到不经过点
的侧面的距离为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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解题方法
8 . 某高中随机抽取
名学生,测得他们的身高(单位:cm),按照区间
,
,
,
,
分组,得到样本身高的频率分布直方图(如下图所示).
(2)将身高在
,
,
区间内的学生依次记为
,
,
三个组,用分层抽样的方法从三个组中抽取6人.
① 求从这三个组分别抽取的学生人数;
② 若要从6名学生中抽取2人,求
组中至少有1人被抽中的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439f8009ecaf546e38642730be395ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54a698346cc649ac6ba6494e550e3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b34472a3d4a69d9ddbbf37af28200c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f394452e6c8f72f528eff39892c03a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbdec146b2b2a81cc6e94cbe14c4600.png)
(2)将身高在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b34472a3d4a69d9ddbbf37af28200c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f394452e6c8f72f528eff39892c03a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbdec146b2b2a81cc6e94cbe14c4600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
① 求从这三个组分别抽取的学生人数;
② 若要从6名学生中抽取2人,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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名校
9 . 我们称如图的曲线为“爱心线”,其上的任意一点
都满足方程
,现将一边在x轴上,另外两个顶点在爱心线上的矩形称为心吧.若已知点
“爱心线”上任意一点的最小距离为
,则用
表示心吧面积的最大值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a07a272938c36238a41bda3e275620b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b2e664656b4242a8a264eca64ef005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
您最近一年使用:0次
2024-04-19更新
|
339次组卷
|
3卷引用:上海市静安区2024届高三下学期期中教学质量调研数学试卷
10 . 在![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
中,角
、
、
的对边分别为
、
、
,已知
,
,
.
(1)求角
的大小;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23725094c363fd158166a8698971694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb75557d217f59ef1f33e8da1ac0d09.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3281ca4f80fa22bfc42125dd86ca2e2a.png)
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