名校
解题方法
1 . 在世界环保意识日益强化,石油资源日渐沽竭的今天,以氢气做动力源的研究已成为一大课题.当年马自达坚持下来的转子发动机(如图1)从结构上讲是最适合燃烧氢气,而且最“干净”,因为氢燃烧完后排出的是水蒸气,对环境没有任何污染.马自达公司改制了RX-7型跑车的转子发动机,使它可以用氢做燃料.以正四面体的四个顶点为球心,以正四面体的棱长为半径的四个球的相交部分围成的几何体(如图2)被称为“勒洛四面体”,它表面上任意两点间的距离最大值与正四面体棱长相等,能在两个平行平面间自由转动,并且始终保持与两平面都接触,因此它能像球一样来回滚动.转子发动机的设计正是利用了这一原理.转子引擎只需转一周,各转子便有一次进气、压缩、点火与排气过程,相当于往复式引擎运转两周,因此具有小排气量就能成就高动力输出的优点.另外,由于转子引擎的轴向运动特性,它不需要精密的曲轴平衡就可以达到非常高的运转转速.若正四面体ABCD的棱长为2,将对应的勒洛四面体ABCD放进一个正方体纸盒中,若该勒洛四面体可以在纸盒内任意转动,则该纸盒棱长的最小值为__________ ;若在勒洛四面体ABCD内放一个小正方体零件,该零件可以在勒洛四面体ABCD内任意转动,则该零件棱长的最大值为__________ .
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昨日更新
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23次组卷
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2卷引用:山西省介休市第一中学校2022-2023学年高二上学期开学考试数学试题
2 . (1)计算:
;
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85568cb2d7877a51bab9c4ab69cb1861.png)
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c1b49e9fda4a970a10e11acb7a61fb2.png)
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3 . 如图,抛物线
(常数
)与x轴的负半轴交于点G,顶点为Q,过Q作
轴交x轴于点M且交双曲线
于点P,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/f8bfcb06-ec69-4380-b5ce-59a313fb8e14.jpg?resizew=136)
(1)求k值;
(2)当
时,求PQ的长;
(3)当P是QM的中点时,求t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee7615480a873c1de3ea9f01336729f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d1668b8e80d00f85e5836f6ae9dd36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f71bd0858d8190bf7f892cbfb2d46ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026207eb5bd1429a700a1eda0f4e1823.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/f8bfcb06-ec69-4380-b5ce-59a313fb8e14.jpg?resizew=136)
(1)求k值;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
(3)当P是QM的中点时,求t的值.
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4 . 已知
是二次函数
图象上的一系列点,其中
,记
(n为正整数),令
,则S的值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb1b052b4fbeab908e1e3d4a2903f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5109eb35b9c16fc5e128198a1819a44c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f74cba0f2dcda7e483808b7aaaabb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c414502a9d5420715cb39e6fc2d64c47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeaeefb8d052ab78155b326f7392555d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
5 . 正方形边长等于
,通过它的中心引一条直线,已知正方形的四个顶点到这条直线的距离的平方之和恒为定值,则这个定值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
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6 . 如图,小睿为测量公园的一凉亭AB的高度,他先在水平地面点E处用高1.5m的测角仪DE测得∠ADC=31°,然后沿EB方向向前走3m到达点G处,在点G处用高1.5m的测角仪FG测得∠AFC=42°.求凉亭AB的高度.(A,C,B三点共线,AB⊥BE,AC⊥CD,CD=BE,BC=DE.结果精确到0.1m)(参考数据:sin31°≈0.52,cos31°≈0.86,tan31°≈0.60,sin42°≈0.67,cos42°≈0.74,tan42°≈0.90)
![](https://img.xkw.com/dksih/QBM/2023/11/23/3374009401016320/3376892260655104/STEM/e8d9f61dd61d47bd8c839eb3e41202e9.png?resizew=315)
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7 . 环保局对某企业排污情况进行检测,结果显示,所排污水中硫化物的浓度超标,即硫化物的浓度超过最高允许的
,环保局要求该企业立即整改,在
天以内
含
天
排污达标,整改过程中,所排污水中硫化物的浓度
与时间
天
的变化规律如图所示,其中线段
表示前
天的变化规律,从第
天起,所排污水中硫化物的浓度
与时间
成反比例关系
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/e6dcb5f3-7db2-41ec-a56e-343f816bfc7e.png?resizew=148)
(1)求整改过程中硫化物的浓度
与时间
的函数表达式(要求标注自变量
的取值范围)
(2)该企业所排污水中硫化物的浓度,能否在
天以内
含
天
排污达标?为什么?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b768f6382f0c0433af84576413ff092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae24921f8d0ec1105c435c43ac95838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/285912b40e1dce8bfc029df88115c961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/e6dcb5f3-7db2-41ec-a56e-343f816bfc7e.png?resizew=148)
(1)求整改过程中硫化物的浓度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)该企业所排污水中硫化物的浓度,能否在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
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8 . 如图,已知抛物线
与
轴交于点
,
点
位于点
的左侧
,
为顶点,直线
经过点
,与
轴交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/e0a9c546-00c0-40e2-b6bd-2571429892f3.png?resizew=122)
(1)求线段
的长;
(2)沿直线
方向平移该抛物线得到一条新拋物线,设新抛物线的顶点为
,若点
在反比例函数
的图象上.求新抛物线对应的函数表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e61e0a1bc2ab34fe0cd1de9f59b0e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a920a78c48e71749017d40e01caa3a3.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/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/e0a9c546-00c0-40e2-b6bd-2571429892f3.png?resizew=122)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)沿直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e76d09a7face9b72ac0890f47b90ad.png)
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名校
解题方法
9 . 直线过点
,直线
:
过点
,且把
分成面积相等的两部分,其中靠近原点的那部分是一个三角形,则直线
的方程为
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10 . 如图,在半径为3的圆
中,
、
都是圆
的半径,且
,点
是劣弧
上的一个动点(点
不与点
、
重合),延长
交射线
于点
.
(1)如果设
,
,求
关于
的函数解析式,并写出定义域;
(2)当
时,点
在线段
上,且
,点
是线段
上一点,射线
与射线
交于点
,如果以点
、
、
为顶点的三角形与
相似,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/23/6bcaa0f8-5ea9-45fa-a4c6-be213150a2ef.png?resizew=148)
(1)如果设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bfc0387785bf3c60f75ed3d34cc98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531944b051cb8e0714370f050c5633f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818ae50f8482cb0a961d1b5ce2077c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fc28f622892dd18bbbac95d541acfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ed92a6827783abceb6357e9369117a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13366eb23da383f4cd8c74986ef07ff7.png)
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