名校
解题方法
1 . 如图①所示,在
中,
,D,E分别是AC,AB上的点,且
.将
沿DE折起到
的位置,使
,如图②所示.M是线段
的中点,P是
上的点,
平面
.
的值.
(2)证明:平面
平面
.
(3)求点P到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8a150b70d722fa1d8725c622fe621e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2fef4031c10abc18c8747af6b9a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3834a4bb20d2b065695dbf53091b065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7f2f4a3efed30b487543e35fa6100c.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677df39c6c9f1fc7700e1eb8cdf9854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
(3)求点P到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
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7卷引用:河北省保定市定州市第二中学2023-2024学年高一下学期5月月考数学试题
2 . 已知函数
.
(1)若
,求
的单调区间;
(2)若
恒成立,求
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0aefefa22770c10304803252d376532.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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昨日更新
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266次组卷
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3卷引用:2024届河北省保定市九县一中三模联考数学试题
名校
解题方法
3 . 如图,四棱锥
中,面
和面
均垂直于面
.
面
;
(2)若底面
是边长为2的正方形,直线
与面
所成的角为
.
(i)求直线
与面
所成角的正弦值;
(ii)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2246c0e92e8cc344f636ea8f8f9037e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9332d230f25309248ff2a6161f060229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若底面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
(i)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
(ii)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d639bc8b486be1176e595f82511f50.png)
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4 . 已知
中,角
的对边分别是
,
,
,且
.
(1)求角A的大小;
(2)求
的最大值;
(3)若
,
为
边上靠近B点的三等分点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516983449108347c9bbf5dd2a72ab3dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d90d7f054e8f0346479e1999622f11cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8c463f847a2360d2ce5d2de4f17be4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452e15519f305e5afbc184116b4691a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2758285d3c1d8c16784edbc5f572fc26.png)
(1)求角A的大小;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dfa04ed69eb5e36931c076e0cf3f01e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
解题方法
5 . 如图,已知
分别是三棱锥
棱
上的点.
为平行四边形,证明:
面
;
(2)若
分别是
的中点,且
,直线
和直线
所成角为
,求直线
和直线
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d45053e5879b431923e0d53b57091f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068eeefc0c19329cc04ff28ba51ac090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce3da36477d98f47fff39520e496617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1e6d86c5142ba1576cc277dbf32994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1655c164ebe93332ef4d9fed6bdeb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7288db347b6e10d3d679d4030c857a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
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6 . 如图,已知正方体
的棱长为1,点P为对角线
上的动点,点N为棱
上的动点(不含端点),点M为线段
的中点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bb1548ddc0e5536a35b1bd78c4e7cd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
7 .
中,
.
;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e291115f0eb743765a70d18404eb8991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e5d4f93699f8dcffb0e7840ca5597e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e715833d14ea5cad4e199947b02c5921.png)
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8 . 已知
外接圆的圆心为M,半径为r,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c1b00aa17d7376561138a18d3d8cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f3b22560c36768d7938cb94d8bec3b.png)
A.![]() | B.![]() | C.2 | D.3 |
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名校
解题方法
9 . 设
为随机事件,且
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037d14f62d2bdf2b66aa7b8473858f9f.png)
A.事件![]() ![]() |
B.若三个事件![]() ![]() |
C.若事件![]() ![]() |
D.若![]() ![]() |
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名校
解题方法
10 . (1)已知
,关于x的方程
的一个虚根为
,求
的值;
(2)已知复数
满足:
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360ff131c51a4ef6745538c18cec92c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1146110d4382c714c10de00dd1273b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36c3dd5d956edd552444e019d8e158c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)已知复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0832095149659ac7fbe35eba945d4b34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a40e2b6c49f849119ad4a3f2e79530.png)
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