名校
1 . 如图,三棱柱
中,
,
,
.
;
(2)若平面
⊥平面
,
,动点P在线段
上,且
的正弦值为
,求
与
成角余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d89ba4036a5d18ec4abed44d7fd8e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baa3d0db9ad31d33c2883a6efed1dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29e8a1eefb6776168969a1155c9e9c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba985fb50a9078a839b66bf1d1eadea9.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4908fad3dc6fe1b0675c870328f043ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f776a27765b22790d41eb7b1c79b296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2022-04-08更新
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551次组卷
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2卷引用:新疆石河子市第一中学2022届高三3月第一周模拟数学(理)试题
名校
2 . 如图,在平面四边形
中,
,
,
,将
沿
翻折,使点D到达点S的位置,且平面
平面
.
![](https://img.xkw.com/dksih/QBM/2022/3/24/2943275641487360/2944364991422464/STEM/e8000755-0ee8-4376-84e9-ec1e0efb7da2.png?resizew=166)
(1)证明
;
(2)若E为
的中点,直线
与平面
所成角的正弦值为
,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35333abd7f02d663d15251bc5cbbf921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78307cd417504554a4e2276fe24d1162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2022/3/24/2943275641487360/2944364991422464/STEM/e8000755-0ee8-4376-84e9-ec1e0efb7da2.png?resizew=166)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f797c40604a39f2d81bae5e13d5ef89a.png)
(2)若E为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b5e290c6b2c5508a3bf6117afbf7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f91414bbba4600fce6f12441b670d6e.png)
您最近一年使用:0次
2022-03-26更新
|
436次组卷
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2卷引用:新疆维吾尔自治区2022届高三第二诊断性测试数学(理)试题(问卷)
3 . 如图,在三棱柱
中,平面
平面
,
是正三角形,
是
的中点.
,直线
与平面
所成的角为
.
![](https://img.xkw.com/dksih/QBM/2022/4/6/2952462021271552/2952929727406080/STEM/dd5c0e22eb2c4b1a8e8b4c3e652e707b.png?resizew=208)
(1)求证:
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91cbafbd47a57b0a24799ca61af682f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://img.xkw.com/dksih/QBM/2022/4/6/2952462021271552/2952929727406080/STEM/dd5c0e22eb2c4b1a8e8b4c3e652e707b.png?resizew=208)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb689000fa7a3b425be3196d8b0f32af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6102b9c37374eb50ef133bdc92e662a0.png)
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名校
4 . 如图,在三棱柱
中,侧面
是矩形,
,
,
,
,E,F分别为棱
,BC的中点,G为线段CF的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/4580a8a0-2fc6-44f1-a032-02c820b15434.png?resizew=144)
(1)证明:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404005c9bb408214fe5bafee7507e175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/4580a8a0-2fc6-44f1-a032-02c820b15434.png?resizew=144)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874acc16deb1b13c54d8f9ee2ad09922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770d42343599d3f26f0e0de8d5849f52.png)
您最近一年使用:0次
2022-03-07更新
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1774次组卷
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10卷引用:新疆2022届高三诊断性自测(第二次)数学(理)试题
新疆2022届高三诊断性自测(第二次)数学(理)试题三省三校(黑龙江哈师大附中、东北师大附中、辽宁实验中学)2022届高三下学期第一次模拟数学(理)试题(已下线)二轮拔高卷01-【赢在高考·黄金20卷】备战2022年高考数学(理)模拟卷(全国卷专用)山西省太原市2022届高三二模数学(理)试题陕西省西安市长安区第一中学2022届高三下学期六模理科数学试题福建省南平市浦城县第三中学2023届高三上学期数学期中测试模拟卷试题(3)(已下线)三省三校2022届高三下学期第一次模拟数学(理)试题变式题16-20江西省丰城中学、新建二中2022-2023学年高二下学期6月期末联考数学试题福建省泉州市现代中学2022-2023学年高二上学期期中数学试题江苏省无锡市市北高级中学2023-2024学年高二上学期期中数学试题
5 . “工艺折纸”是一种把纸张折成各种不同形状物品的艺术活动,在我国源远流长,某些折纸活动蕴含丰富的数学内容,例如:用一张圆形纸片,按如下步骤折纸(如下图1)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/ad068b94-e800-4af8-b41e-ef7ec45324a2.png?resizew=503)
步骤1:设圆心是E,在圆内异于圆心处取一点,标记为F;
步骤2:把纸片折叠,使圆周正好通过点F;
步骤3:把纸片展开,并留下一道折痕;
步骤4:不停重复步骤2和3,就能得到越来越多的折痕(如图2).
已知这些折痕所围成的图形是一个椭圆.若取半径为4的圆形纸片,设定点F到圆心E的距离为2,按上述方法折纸.
(1)以点F,E所在的直线为x轴,线段EF的中垂线为y轴,建立坐标系,求折痕所围成的椭圆C(即图1中M点的轨迹)的标准方程.
(2)如图3,若直线m:
与椭圆C相切于点P,斜率为
的直线n与椭圆C分别交于点A,B(异于点P),与直线m交于点Q.证明:
,
,
成等比数列.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/ad068b94-e800-4af8-b41e-ef7ec45324a2.png?resizew=503)
步骤1:设圆心是E,在圆内异于圆心处取一点,标记为F;
步骤2:把纸片折叠,使圆周正好通过点F;
步骤3:把纸片展开,并留下一道折痕;
步骤4:不停重复步骤2和3,就能得到越来越多的折痕(如图2).
已知这些折痕所围成的图形是一个椭圆.若取半径为4的圆形纸片,设定点F到圆心E的距离为2,按上述方法折纸.
(1)以点F,E所在的直线为x轴,线段EF的中垂线为y轴,建立坐标系,求折痕所围成的椭圆C(即图1中M点的轨迹)的标准方程.
(2)如图3,若直线m:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791693c447c67da455b0ac3d777f2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e9f93b4a4a99c3671b3bbad56a8e65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39711520ae2c8b2e030be65d3cc4360.png)
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2022-02-04更新
|
562次组卷
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6卷引用:新疆昌吉州2022届高三第二次诊断性测试数学(理)试题
新疆昌吉州2022届高三第二次诊断性测试数学(理)试题新疆维吾尔自治区昌吉回族自治州2022届高三第二次诊断性测试数学(文)试题安徽省蚌埠市2021-2022学年高三上学期第二次教学质量检查理科数学试题安徽省蚌埠市2021-2022学年高三上学期第二次教学质量检查文科数学试题(已下线)专题五检测 解析几何-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)(已下线)专题29 弦长问题及长度和、差、商、积问题-2
名校
解题方法
6 . 如图,
是圆
的直径,
圆
所在的平面,
为圆周上一点,
为线段
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896502985490432/2902018382725120/STEM/619cdb34-0f14-4d8d-bbb4-0562a2ba7ca2.png?resizew=187)
(1)证明:平面
平面
.
(2)若
为
的中点,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590388ae64b699fe42b71de76ba3d28d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff7ad82b0938145af6a5ffa2c9596d8.png)
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896502985490432/2902018382725120/STEM/619cdb34-0f14-4d8d-bbb4-0562a2ba7ca2.png?resizew=187)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8711675c09d3eaf3d49ff795ff5f79f.png)
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2022-01-25更新
|
1477次组卷
|
10卷引用:新疆昌吉州2022届高三上学期第二次高考质量检测数学(理)试题
7 . 已知椭圆C的短轴的两个端点分别为A(0,1),B(0,
),焦距为
.
(1)求椭圆C的方程;
(2)已知直线y=m与椭圆C有两个不同的交点M,N,设D为直线AN上一点,且直线BD,BM的斜率之积为
,证明:点D在x轴上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆C的方程;
(2)已知直线y=m与椭圆C有两个不同的交点M,N,设D为直线AN上一点,且直线BD,BM的斜率之积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
您最近一年使用:0次
名校
8 . 如图,在多面体
中,
为等边三角形,
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/3/9/2932461285335040/2932518452912128/STEM/1bd5e457823e453e9340d63eae2abca1.png?resizew=187)
(1)证明:
平面
;
(2)求锐二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164a4df60a15587971e883cf557b5ce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af620f6d204d310d8e3f267fdd6c3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1394fc01d91ffe8e6826cab0c933be3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee90881c743e2cff2e3128d6bdb86174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://img.xkw.com/dksih/QBM/2022/3/9/2932461285335040/2932518452912128/STEM/1bd5e457823e453e9340d63eae2abca1.png?resizew=187)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9c89e28bb3b5ce434e8ebea6363339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678b28fddb166d90878d24d6e5481080.png)
(2)求锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d76403bac26df50d934d93586f8a11.png)
您最近一年使用:0次
2022-03-09更新
|
660次组卷
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5卷引用:新疆昌吉州2022届高三下学期高考适应性第一次诊断性测试数学(理)试题
新疆昌吉州2022届高三下学期高考适应性第一次诊断性测试数学(理)试题(已下线)专题20 平行垂直与空间向量在立体几何中的应用-2022届高考数学一模试题分类汇编(新高考卷)河北省部分重点中学2022届高三下学期期中数学试题上海市大同中学2022届高三下学期期中数学试题江西省上饶市第一中学2022-2023学年高二上学期期中数学试题
解题方法
9 . 如图,
是棱长为1的正方体.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253610491904/2716459014283264/STEM/2ba922eb-cbfe-4ad5-8d72-87a494325831.png?resizew=284)
(1)求证:平面
平面
;
(2)在棱
上是否存在点
,使得二面角
的平面角与二面角
的平面角相等,如果存在,求出
的长,如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253610491904/2716459014283264/STEM/2ba922eb-cbfe-4ad5-8d72-87a494325831.png?resizew=284)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0fbd88fdb064072eedd136e9cb41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d9cb67314af122defeaa715365a9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a7ba7cd0c654714c967a900513ba16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
您最近一年使用:0次
解题方法
10 . 已知椭圆
过点
,焦距长
,一直线
交椭圆
于
,
两点.
(1)求椭圆
的方程;
(2)若点
为
轴上一点且
=
,求证:直线
过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182c81fb1c5e6d1a57a5f34a31ee69a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73aad2b1c1aa100a0840ae32435c1965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33e5d0dbdd0f15854f0d7dd8b53058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7e4900636034c67e37e73e9a29e2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2021-11-11更新
|
828次组卷
|
4卷引用:新疆克拉玛依市2019届高三三模数学(理)试题
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