1 . 已知椭圆
:
经过
,
两点,M,N是椭圆
上异于T的两动点,且
,直线AM,AN的斜率均存在.并分别记为
,
.
(1)求证:
为常数;
(2)证明直线MN过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c5ad47223dcd7afbd03a26c7f6bb37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032a2eb83561061db7c31d35a93a328f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
(2)证明直线MN过定点.
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6卷引用:四川省广安市2023届高三第二次诊断数学(文)试题
名校
解题方法
2 . 在直角坐标系
中,设
为抛物线
(
)的焦点,
为
上位于第一象限内一点.当
时,
的面积为1.
(1)求
的方程;
(2)当
时,如果直线
与抛物线
交于
,
两点,直线
,
的斜率满足
.证明直线
是恒过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a5f7aa32000ae7ed868721278834bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2ce6d23fb52cc513580a8f0e6760c2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e30c5909e71d420de79eadd5061cda.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2c1be4b46eb936b47e4ca870922fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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6卷引用:四川省广安市2024届高三第二次诊断性考试数学(文)试题
名校
3 . 已知
,
,
均为正数,且
.
(1)是否存在
,
,
,使得
,说明理由;
(2)证明:
.
![](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/1a57e060f61f7efa54982bda67db483a.png)
(1)是否存在
![](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/5882aba406145a4755d3bc184b8aee30.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31270f0a9cb69c97225271fb354847db.png)
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10卷引用:四川省广安市2024届高三第二次诊断性考试数学(文)试题
解题方法
4 . 已知函数
.
(1)若
存在极值,求
的取值范围;
(2)若
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20a21999ea818acdfb48d3641f70d3b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fe2115d883d13561e28006d3f6143b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e0c59c93623fecf375c5beb1cdd2087.png)
您最近一年使用:0次
2024-03-27更新
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1242次组卷
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6卷引用:四川省广安市2024届高三第二次诊断性考试数学(文)试题
名校
解题方法
5 . 设函数
.
(1)解不等式
;
(2)令
的最小值为
,正数
满足
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2790f3349fae2119070e9a512717aa9e.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155834bf3412ebac9896c0cce9e2cb31.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ccb77ba53e986204cd158abb87bcbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4336688b5b9fb6d91400401756cc45e8.png)
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11卷引用:四川省广安市2024届高三一模数学(文)试题
6 . 如图,在三棱锥
中,
为
边上的一点,
,
,
,
.
平面
;
(2)设点
为边
的中点,试判断三棱锥
的体积是否有最大值?如果有,请求出最大值;如果没有,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94b7928ff6145cccd4b64b0010a585d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75935f499493a6bdf92cab5ed82abe1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a910c896750506ffc2f8e29ce96435bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd3eb538f36e6e722e4ce125266b99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03203dd5ac79dd8c6707e4340773359.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aef45a3fcc6e34ece114d4315747a0f.png)
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6卷引用:四川省广安市2024届高三第二次诊断性考试数学(文)试题
四川省广安市2024届高三第二次诊断性考试数学(文)试题2024届四川省遂宁市等3地高三二模文科数学试题四川省雅安市2024届高三下学期二诊数学(文)试题四川省乐山市2024届高三第二次调查研究考试文科数学试题(已下线)专题13.7空间中的距离和夹角问题-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)6.6简单几何体的再认识-【帮课堂】(北师大版2019必修第二册)
7 . 如图,在三棱柱
中,直线
平面
,平面
平面
.
;
(2)若
,在棱
上是否存在一点
,使得四棱锥
的体积为
?若存在,指出点
的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ad7c180d6d084ecb25f23cb6fe9b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1de5964353beb55c5058b2a431eecaf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9008767d531e72e94dee8452aedca97a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de04ac3f924d139c7ea15a0b230db6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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|
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|
9卷引用:四川省广安市2024届高三一模数学(文)试题
四川省广安市2024届高三一模数学(文)试题四川省遂宁市2024届高三一模数学(文)试题四川省雅安市2024届高三一模数学(文)试题四川省资阳市2024届高三二模数学(文)试题四川省眉山市2024届高三一模数学(文)试题(已下线)重难点12 立体几何必考经典解答题全归类【九大题型】(已下线)第15讲 8.6.3平面与平面垂直(第2课时)-【帮课堂】(人教A版2019必修第二册)(已下线)专题8.8 空间中的线面位置关系大题专项训练【七大题型】-举一反三系列(已下线)专题突破:空间几何体的动点探究问题-同步题型分类归纳讲与练(人教A版2019必修第二册)
名校
解题方法
8 . 如图,四边形ABCD为长方形,
平面ABCD,
,点E,F分别为AD,PC的中点.
(1)证明:
∥平面PBE;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7909a880816dcd6886774124ac86b55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/29/74f7a2eb-9ab4-4671-ab03-170a43a23efa.png?resizew=170)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea56f8a50404ac066bc2099bc58ff58.png)
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2023-11-08更新
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3卷引用:四川省广安市第二中学校2024届高三上学期第二次月考数学(文)试题
名校
解题方法
9 . 如图,在三棱锥
中,
平面
,
,
,
分别为
,
的中点,且
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/fb539780-7d6a-4624-9a35-8c15f02e8468.png?resizew=162)
(1)证明:平面
平面
,
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd051fedb6691e2183e658f1fe487ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ddad21a6de8f54e65123d274c0098c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/fb539780-7d6a-4624-9a35-8c15f02e8468.png?resizew=162)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4739ad948445af72d585fe29c745929b.png)
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2023-11-27更新
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6卷引用:四川省广安第二中学校2023-2024学年高三上学期第二次月考理科数学试题
名校
解题方法
10 . 已知动圆过定点
,且与直线
相切.
(1)求动圆圆心C的轨迹的方程.
(2)设A、B是轨迹C上异于原点O的两个不同点,直线OA和OB的倾斜角分别为
和
,当
,
变化且
为定值
,证明直线AB恒过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
(1)求动圆圆心C的轨迹的方程.
(2)设A、B是轨迹C上异于原点O的两个不同点,直线OA和OB的倾斜角分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
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|
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4卷引用:四川省广安第二中学校2023-2024学年高三上学期第二次月考理科数学试题