名校
解题方法
1 . 在平面直角坐标系
中,
,
分别是双曲线
:
的左,右焦点,设点
是
的右支上一点,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad0c75ce33673ec4c425896e8619e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c465763b60ec542adce65c94b0e31cf.png)
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2卷引用:黑龙江省哈尔滨市第二十四中学校2024届高三下学期第三次模拟测试数学试题
名校
解题方法
2 . 如图,在四棱锥
中,
平面
,
,
,
,
,
,
分别为
,
的中点.
的体积;
(2)求直线
与平面
所成线面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/487530f6d17b94493d03b004aa3462d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3e27f6e6d1592408508cc9fd14d480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fc203fe37519a2fef5ed3f7f2e46d94.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149596fee6ed1e2d19fd8dadc14a8baf.png)
您最近一年使用:0次
名校
解题方法
3 . 已知箱中有若干个大小相同的红球和白球,每次抽一个球,若抽到白球,则放回并再次抽球,若抽到红球,则不再抽取.设每次抽到红球的概率为p(
),记X为停止抽球时所抽取的次数,X的数学期望为
.
(1)若最多抽4次,且
,求X的分布列及数学期望;
(2)在成功概率为p(
)的伯努利试验中,记X为首次成功时所需的试验次数,X的取值为所有正整数,此时称离散型随机变量X的概率分布为几何分布.若抽球一直进行下去,则X服从几何分布.
①求恰好第k次抽到红球的概率
;
②求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
(1)若最多抽4次,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e5a154944cfae71a14d3da122dd08e.png)
(2)在成功概率为p(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
①求恰好第k次抽到红球的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef133b0fd53a48310a82c18729575abd.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
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4 . 如图,在三棱柱
中,侧面
为矩形,M,N分别为AC,
的中点.
平面
;
(2)若二面角
的余弦值为
,
,
为正三角形,求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72bf4c36a2bbc4d9557a722db1c48ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc731c3d83f42275103a59f6c752a8dc.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1648474605a022df2f48184862d998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24de84a0b508ffdde407cde13fdbd1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc731c3d83f42275103a59f6c752a8dc.png)
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5 . 已知函数
(
).
(1)讨论
的单调性;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b65b1ee5601ff5aa4c64d2fbfcbfe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d32d1a5a0732c7e4af737555e44ff9.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f88a76f947e7022ef0c5efd6db060c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/511c60ab2eabf536ed2a863ef435c7d6.png)
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名校
解题方法
6 . 已知数列
前n项的积为
,数列
满足
,
(
,
).
(1)求数列
,
的通项公式;
(2)将数列
,
中的公共项从小到大排列构成新数列
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c7a0ac368e5fcb20ac099f51aea7be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46bf3911496403b6e7eedf87667fff52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)将数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
名校
解题方法
7 . 定义域为
的函数
,对任意x,
,
,且
不恒为0,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cccdff49c3efe6e7a7dbbf69db9319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82bde53de43dda74249725823c0e6610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() | B.![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() |
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8 . 已知圆C:
,直线l:
(
),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550d183b05000722c74baf25eb4a6741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5c5829ddf6feec8fc9709fbc63776c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
A.直线l恒过定点![]() |
B.存在实数m,使得直线l与圆C没有公共点 |
C.当![]() |
D.圆C与圆![]() |
您最近一年使用:0次
名校
解题方法
9 . 过抛物线
上的一点P作圆C:
的切线,切点为A,B,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81338417602aa3f61f2f62a63fb1184a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6cdb2806bd5c212f64a36648553514.png)
A.4 | B.![]() | C.6 | D.![]() |
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解题方法
10 . 已知四棱锥
的底面
是棱长为2的菱形,
,若
,且
与平面
所成的角为
为
的中点,点
在线段
上,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
平面
.
;
(2)求平面
与平面
夹角的大小.
![](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/2996d02ef58faec7918d55e5e7a59860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27dd7473bc61f631d788b152b16363f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad573edaad2b4dc616a0a3eb1fc92f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b2857b27a9ac7c6c9f87f6217caa49.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次