名校
1 . 已知函数
,若函数
的最小值恰好为0,则实数
的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1328e7d04052f002d4b3bd78d3529e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 定义在
上的函数
满足
为偶函数,
为奇函数,且当
时,
.当
时,函数
与
图象的交点个数为______ .
![](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/0e81e15b871dd32b2438ef8025bcc42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e356a6e54a669fda721085096c8416db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08869ffa8b997472fbc4deee60ae0d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/facd6be947e37552dfa0565d1f21e380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4eccc8b4cef84da4388fc696fef97a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8898d891410dd22bff5d1d2a3cf340e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2024-06-07更新
|
258次组卷
|
2卷引用:贵州省部分学校2024届高三下学期联考数学试卷
解题方法
3 . 已知点P是椭圆
上除顶点外的任意一点,过点P向圆
引两条切线
,
,设切点分别是M,N,若直线
分别与x轴,y轴交于A,B两点,则
面积的最小值是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f88c102345ea2d5d61771f42075453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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名校
解题方法
4 . 已知椭圆
的左、右焦点分别为
为
上一点,且
,若
,
的外接圆面积是其内切圆面积的25倍,则椭圆
的离心率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ce2b47812fce4b17fd813d0e4cce21.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b76e364a93cd78537c6c97b88021f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ed463bf16c78a4bbb9d3acff922afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7affd8a277498fd39b4a2a95d649f45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141fb75b0807d4428756cdb2437adf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ce2b47812fce4b17fd813d0e4cce21.png)
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解题方法
5 . 已知
,若
,均有不等式
恒成立,则实数
的取值范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bdf8772caa266bda0087cd3c3172bca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136a003907c455bfd58875c96c138772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe181d0702abc25b3ce7d2259189ff41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2024-04-16更新
|
639次组卷
|
3卷引用:贵州省黔西南州部分学校2023-2024学年高三下学期第一次模拟考试数学试卷
6 . 第24届北京冬奥会开幕式由一朵朵六角雪花贯穿全场,为不少人留下深刻印象.六角雪花曲线是由正三角形的三边生成的三条1级Koch曲线组成,再将六角雪花曲线每一边生成一条1级Koch曲线得到2级十八角雪花曲线(如图3)……依次得到n级
角雪花曲线.若正三角形边长为1,我们称∧为一个开三角(夹角为
),则n级
角雪花曲线的开三角个数为__________ ,n级
角雪花曲线的内角和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446a5809055d7efef04d6bc01292478c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae6358af7332d7609bf8d18467487d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae6358af7332d7609bf8d18467487d3.png)
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解题方法
7 . 如果复数
,
,
,
在复平面内对应的点分别为
,
,
,
,复数z满足
,且
,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9edf13e16f94717233962e7ec2fa079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897b3236850f1925308136357d4d5899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed343cf3cad4644ea3d9ca0bd37a8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6391054f48da6b0e007e8210677f49b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8477bcc87b1401970171bf57b9ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c1fd680a5d355178273c6d6025eb80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276bdeecec8e10c149c9653fa5f5facb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cf49f5ddfb0682255be5cbba1d3626d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8af0ca09b38b3ee491816d8bf097c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2d67a223c5b9fd87c060ec8c006d6b.png)
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解题方法
8 . 双曲线
:
(
,
)的左、右焦点分别为
,
,过点
直线
与双曲线右支交于
,
两点,点
是
轴上一点,
,
,则双曲线
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f30acc34f4ee1077532ae6808af2ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aec335cbb956999b4c53130c548cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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解题方法
9 . 三等分角大约是在公元前五世纪由古希腊人提出来的,它和“立方倍积问题”“化圆为方问题”并称为“古代三大几何难题”.公元六世纪时,数学家帕普斯曾证明用一固定的双曲线可以解决“三等分角问题”.某同学在学习过程中,借用帕普斯的研究,使某锐角
的顶点与坐标原点
重合,点
在第四象限,且点
在双曲线
的一条渐近线上,而
与
在第一象限内交于点
.以点
为圆心,
为半径的圆与
在第四象限内交于点
,设
的中点为
,则
.若
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20b5646427bee93f9d0542f91f374b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a58f9947538051854639fb05d876d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ed200cdcec3e0461dc5974f7d3f8d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bca735ba25c34964d96a4923cf797a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
10 . 已知直四棱柱
的棱长均4,且
,则以
为球心,
为半径的球面与侧面
的交线长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f427d187aad86252e188bd0649bfd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbff61fe9d4e93d7cc338489d1c99c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
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