1 . 如图,在四棱锥P-ABCD中,底面ABCD为正方形,PA⊥底面ABCD,
,E为线段PB的中点.
![](https://img.xkw.com/dksih/QBM/2021/11/23/2857383004266496/2859171813531648/STEM/1954850c2fa448bf9c165695635d81fd.png?resizew=164)
(1)若F为线段BC上的动点,请证明:平面AEF⊥平面PBC;
(2)若F为线段BC,CD,DA上的动点(不含A,B),
,三棱锥A-BEF的体积是否存在最大值?如果存在,求出最大值;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://img.xkw.com/dksih/QBM/2021/11/23/2857383004266496/2859171813531648/STEM/1954850c2fa448bf9c165695635d81fd.png?resizew=164)
(1)若F为线段BC上的动点,请证明:平面AEF⊥平面PBC;
(2)若F为线段BC,CD,DA上的动点(不含A,B),
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
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2021-11-25更新
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11卷引用:2020届内蒙古鄂尔多斯市第一中学高三下学期第一次模拟考试数学(文)试题
2020届内蒙古鄂尔多斯市第一中学高三下学期第一次模拟考试数学(文)试题四川省雅安市2020届高三第一次诊断性考试数学(文)试题四川省资阳市2019-2020学年高三上学期第二次诊断考试数学(文)试题四川省广安遂宁资阳等七市2019-2020学年高三上学期第一次诊断性考试数学(文)试题2020届四川省眉山市高三第一次诊断性考试数学(文)试题2020届高三1月(考点07)(文科)-《新题速递·数学》(已下线)专题04 立体几何——2020年高考真题和模拟题文科数学分项汇编(已下线)考点27 空间直线、平面的垂直-备战2021年新高考数学一轮复习考点一遍过四川省南充高级中学2021-2022学年高二上学期期中考试数学(文)试题(已下线)2020年高考全国2数学文高考真题变式题21-23题四川省泸州市泸县第五中学2021-2022学年高二下学期第一学月(3月)考试文科数学试题
名校
2 . 已知六面体
如图所示,
平面
,
,
,
,
,
,
是棱
上的点,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/a0926a18-9656-43ba-b267-a7664637ef10.png?resizew=154)
(1)求证:直线
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fe4da569e7b983b02ad25f8654d220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2395720e6d6aeb7efdcd8e921849acf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a61dfd9a6b9b882a4444fdaea63f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3483f39cd5a2c761166d5e0669e2b9cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/a0926a18-9656-43ba-b267-a7664637ef10.png?resizew=154)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a6d0c77bcbe4a0ba21f57fe8b71c08.png)
您最近一年使用:0次
2020-04-20更新
|
304次组卷
|
2卷引用:2020届内蒙古鄂尔多斯市高考模拟考试(4月)理科数学试题
解题方法
3 . 如图,在四棱锥
中,已知
,
,
,
,
,点
是线段
的中点.
![](https://img.xkw.com/dksih/QBM/2020/4/19/2444928964935680/2445688796692480/STEM/dea13fd4664e4eb99157a9249d9494f8.png?resizew=164)
(1)证明:
平面
;
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b72c6d2ae4924f930c437542b3356a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8c7d2b78ab2452b0a57925241dbdb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2020/4/19/2444928964935680/2445688796692480/STEM/dea13fd4664e4eb99157a9249d9494f8.png?resizew=164)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0684e0b09b04661c602437982c0397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9af60b519ca962e0b0ff04838a2092.png)
您最近一年使用:0次
2020-04-20更新
|
294次组卷
|
2卷引用:2020届内蒙古鄂尔多斯市高考模拟考试(4月)文科数学试题
解题方法
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e28f1467b6892df1d15ec306667f9711.png)
(1)解不等式
;
(2)若
均为正实数,且满足
,
为
的最小值,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e28f1467b6892df1d15ec306667f9711.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0dd18467feea8eb478f4669a32c2d57.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d86be2de99fbf7f99cd54ab399146b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30125d853264dae1e08136384c7ea91.png)
您最近一年使用:0次
2020-04-20更新
|
278次组卷
|
2卷引用:2020届内蒙古鄂尔多斯市高考模拟考试(4月)理科数学试题
名校
解题方法
5 . 如图所示,三国时代数学家赵爽在《周髀算经》中利用弦图,给出了勾股定理的绝妙证明.图中包含四个全等的直角三角形及一个小正方形(阴影),设直角三角形有一内角为
,若向弦图内随机抛掷500颗米粒(米粒大小忽略不计,取
),则落在小正方形(阴影)内的米粒数大约为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/be59c85b-d074-484f-a973-1b671be594eb.png?resizew=105)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47bb3f35e3db7c1f3a3dd3eb20151b5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/be59c85b-d074-484f-a973-1b671be594eb.png?resizew=105)
A.134 | B.67 | C.182 | D.108 |
您最近一年使用:0次
2020-02-18更新
|
619次组卷
|
7卷引用:2020届内蒙古鄂尔多斯市第一中学高三下学期第一次模拟考试数学(理)试题
名校
解题方法
6 . 如图,在四棱锥
中,底面
是平行四边形,
平面
,
是棱
上的一点,满足
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/1147598c-b995-4ba3-8bae-0bac67b22528.png?resizew=189)
(Ⅰ)证明:
;
(Ⅱ)设
,
,若
为棱
上一点,使得直线
与平面
所成角的大小为30°,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/1147598c-b995-4ba3-8bae-0bac67b22528.png?resizew=189)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec78c2154c5972efd438a6555afaf2d.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7794325335aa508186003c333e95ed5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.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/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb08a3eed3af2bdcb9d30e8b142de47f.png)
您最近一年使用:0次
2020-03-15更新
|
640次组卷
|
3卷引用:2020届内蒙古鄂尔多斯市第一中学高三下学期第一次模拟考试数学(理)试题
7 . 在直角坐标系
中,圆
的参数方程为
(
为参数),经过变换
,得曲线
.以坐标原点为极点,
轴正半轴为极轴建立极坐标系.
(Ⅰ)求曲线
的极坐标方程.
(Ⅱ)若
,
为曲线
上的动点,且
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227d865a2286728fa4ad40e2f603dcc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349a465a45a731182861b2ade790b16a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)若
![](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/ac51bffb8f476896081027b33f7ec25d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dcb4841ae7bb1d5f91837094cdfcf2c.png)
您最近一年使用:0次
8 . 选修4-4:坐标系与参数方程
在平面直角坐标系
中,以坐标原点
为极点,以
轴正半轴为极轴,建立极坐标系,若直线
的参数方程为
(
为参数,
为
的倾斜角),曲线
的极坐标方程为
,射线
,
,
与曲线
分别交于不同于极点的三点
.
(1)求证:
;
(2)当
时,直线
过
两点,求
与
的值.
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016018e300f13c73032cadbed7b0341e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/69cf89e94eb51129f144d9809ec290f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c54258755a1798a586a77765e2b0066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e2fe56780c2e547dc3cd914f4645a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0f637ff074c2775c68b5d4f3fc78c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7acfaf50163857cafa4b3c9529b362.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6be9659a58847ac85a05596d0610544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
14-15高三上·浙江嘉兴·期中
名校
9 . 设数列
,其前
项和
,又
单调递增的等比数列,
,
.
(Ⅰ)求数列
,
的通项公式;
(Ⅱ)若
,求数列
的前n项和
,并求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bec4712b63ee0d5c03db27cfd89228b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89b2d40598a899ed515748dd4a2f21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea74a5cf39bd1149aed1ce6c8ba0c895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3746eccce36898ba84a8b7b0149cb727.png)
(Ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eadf5b7deed402237ff92eba48c5aa6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1056f02e4a7e9b8fd479519eec2d9b3.png)
您最近一年使用:0次
2016-12-03更新
|
4089次组卷
|
10卷引用:2020届内蒙古鄂尔多斯市第一中学高三下学期第一次模拟考试数学(理)试题
2020届内蒙古鄂尔多斯市第一中学高三下学期第一次模拟考试数学(理)试题河南省信阳市2020届高三上学期第二次教学质量检测(期末)数学(文)试题(已下线)2015届浙江省桐乡第一中学等四校高三上学期期中联考理科数学试卷【全国百强校】浙江省杭州第十四中学2019届高三8月月考数学试题2020届河南省南阳市高三上学期期末数学(理)试题2020届河南省信阳市高三第二次教学质量检测数学(理)试题2020届河南省开封市第五中学高三第四次教学质量检测数学(理)试卷(已下线)考点21 求和方法(第1课时)练习-2021年高考数学复习一轮复习笔记(已下线)第七单元 不等式 (B卷 滚动提升检测)-2021年高考数学(文)一轮复习单元滚动双测卷(已下线)第七单元 不等式(B卷 滚动提升检测)-2021年高考数学(理)一轮复习单元滚动双测卷
10 . 菱形
的边长为3,
与
交于
,且
.将菱形
沿对角线
折起得到三棱锥
(如图),点
是棱
的中点,
.
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571690935828480/1571690941358080/STEM/7c8ac682f24f4000b1999f348f8257e0.png)
(1)求证:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
平面
;
(2)求三棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571690935828480/1571690941358080/STEM/8be10f238c784020b0186ce859901036.png)
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571690935828480/1571690941358080/STEM/504d13a626c54fe0a65fe0bbcf2998a4.png)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571690935828480/1571690941358080/STEM/8be10f238c784020b0186ce859901036.png)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571690935828480/1571690941358080/STEM/36079a296c4a401cb936944196898404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9750a7d1bb1183c137a781bd22534f58.png)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571690935828480/1571690941358080/STEM/aced89df99ca49afb859d0fb6b75c90d.png)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571690935828480/1571690941358080/STEM/ea5f1e12dfa946898d5f5abe739f4ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58d599eccb35873cb9bb905af30fbc8.png)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571690935828480/1571690941358080/STEM/7c8ac682f24f4000b1999f348f8257e0.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4237f6a1fc115bb790aa10704b7908c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75328601c7217bf4a80eaf35b935991d.png)
(2)求三棱锥
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571690935828480/1571690941358080/STEM/19cb9427b70046aaa4284dda844df99b.png)
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