名校
1 . 利用反证法证明“已知
,求证:
中,至少有一个数大于20.”时,首先要假设结论不对,即就是要假设( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7267291073b77eab69d5d01383c045d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874781ab5711bff6ee8c9cbad5b3b3dc.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2021-09-04更新
|
96次组卷
|
2卷引用:陕西省宝鸡市金台区2020-2021学年高二下学期期中理科数学试题
名校
2 . 如图1,直角梯形
中,
,
,
,
为
的中点,现将
沿着
折叠,使
,得到如图2所示的几何体,其中
为
的中点,
为
上一点,
与
交于点
,连接
.请用空间向量知识解答下列问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/786e3828-c164-4ab2-b188-132893bc5e5f.png?resizew=403)
(1)求证:
∥平面
;
(2)若三棱锥
的体积为
,求平面
与平面
的夹角
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3753faebdc15d2d2e598d5ffc4487a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b43490ca09467a4c8cd8cfe91c94e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321f96c4f808afe67cf565ca74ae0351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/786e3828-c164-4ab2-b188-132893bc5e5f.png?resizew=403)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065f7ff90e26ff382aa7b709955ad1b9.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3ad76c5b79648e73a91065ef847f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6734b2bef8750392d3c5c08b5d878505.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2022-12-08更新
|
279次组卷
|
3卷引用:陕西省榆林市神木中学2021-2022学年高二上学期第四次检测理科数学试题
名校
3 . 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)
您最近一年使用:0次
4 . 在代数运算中有下列乘法公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02afa7c7ab445f4332b1aa67d00874cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6f5f4ad27d1ca1028de903270ac3b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c6199ef03b3c389c4dcf15f48b1bf2.png)
.
(1)观察上述结果,你能做出怎样的猜想?
(2)证明你的猜想,并判断
是否是99的倍数?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02afa7c7ab445f4332b1aa67d00874cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6f5f4ad27d1ca1028de903270ac3b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c6199ef03b3c389c4dcf15f48b1bf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf7616d4e0060ca37d9526f4f17111e.png)
(1)观察上述结果,你能做出怎样的猜想?
(2)证明你的猜想,并判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac869d216f9d7281770cedd34a420d95.png)
您最近一年使用:0次
2021-09-10更新
|
128次组卷
|
2卷引用:陕西省咸阳市永寿中学2020-2021学年高二下学期第二次月考理科数学试题
名校
5 . 已知实数
满足
,则下列结论的证明更适合用反证法的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45900deae0489e87fe448948e8091c4.png)
A.证明![]() | B.证明![]() |
C.证明![]() | D.证明![]() |
您最近一年使用:0次
2021-08-30更新
|
121次组卷
|
5卷引用:陕西省西安市莲湖区信德中学2020-2021学年高二下学期期中理科数学试题
解题方法
6 . 已知三棱锥
的侧棱
,
.且
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712424741462016/2714552814379008/STEM/066009fd8dd34da6bfd4fa60669921d0.png?resizew=195)
(1)证明:
;
(2)求点M到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd1bc6147d69777b26a35d48522f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1f2daed50be20359046d8019f13b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5511eb89a3eca96985ede732a3e78e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8dcb266efb6ab5561259f0eb0ad2c3c.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712424741462016/2714552814379008/STEM/066009fd8dd34da6bfd4fa60669921d0.png?resizew=195)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac3b144cadc3c155f9bcc54766364a5.png)
(2)求点M到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
7 . 已知函数
.
(1)证明:
仅有一个零点,且该零点为负数.
(2)判断
,
的大小,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85fbde4d1d77324c6755b6898c363803.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b90da5f9f40bcd8c26d4ffb64824439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0c79b85a9494414257356025bc4993.png)
您最近一年使用:0次
2021-08-12更新
|
161次组卷
|
3卷引用:陕西省西安市莲湖区信德中学2020-2021学年高二下学期期中理科数学试题
8 . 以单位圆为工具,根据三角函数定义证明:
,
.(提示,同圆中,等角所对弦长相等.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac64bd6e38ccf03ef6593ac5b5bbd6b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6739328fd4604784c78e0f5d88726c6e.png)
您最近一年使用:0次
名校
解题方法
9 . 核酸检测也就是病毒DNA和RNA的检测,是目前病毒检测最先进的检验方法,在临床上主要用于新型冠状乙肝、丙肝和艾滋病的病毒检测.通过核酸检测,可以检测血液中是否存在病毒核酸,以诊断机体有无病原体感染.某研究机构为了提高检测效率降低检测成本,设计了如下试验,预备12份试验用血液标本,其中2份阳性,10份阴性,从标本中随机取出
份分为一组,将样本分成若干组,从每一组的标本中各取部分,混合后检测,若结果为阴性,则判定该组标本均为阴性,不再逐一检测;若结果为阳性,需对该组标本逐一检测.以此类推,直到确定所有样本的结果.若每次检测费用为
元,记检测的总费用为
元.
(1)当
时,求
的分布列和数学期望;
(2)(ⅰ)比较
与
两种方案哪一个更好,说明理由;
(ⅱ)试猜想100份标本中有2份阳性,98份阴性时,
和
两种方案哪一个更好(只需给出结论不必证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)(ⅰ)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
(ⅱ)试猜想100份标本中有2份阳性,98份阴性时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe08722cf9300fe188dbbb71989c06c9.png)
您最近一年使用:0次
2021-05-16更新
|
1032次组卷
|
8卷引用:陕西省2021届高三下学期教学质量检测测评(五)理科数学试题
陕西省2021届高三下学期教学质量检测测评(五)理科数学试题山西省吕梁市2021届高三三模数学(理)试题(已下线)“超级全能生”2021届高三全国卷地区5月联考试题(乙卷)数学(理)试题(已下线)“超级全能生”2021届高三全国卷地区5月联考试题(甲卷)数学(理)试题(已下线)期末综合检测01-2020-2021学年高二数学下学期期末专项复习(苏教版选修2-2、2-3)(已下线)8.7 均值与方差在生活中的运用(精练)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)(已下线)2020年高考江苏数学高考真题变式题21-25题安徽省合肥市第六中学2022届高三下学期高考前诊断暨预测理科数学试题