名校
1 . 已知函数
过原点
.
(1)求
的值;
(2)求函数
在
上的零点;
(3)下表是应用“五点法”进行的列表,请填写表中缺失的数据.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9694cdd0765955f8c2868f34b9fb0ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b6a9ffffc0c461881b427c543924cd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4ad588acc23503dca49ca80c4495d4.png)
(3)下表是应用“五点法”进行的列表,请填写表中缺失的数据.
0 | |||||
0 | 1 | 0 | 0 | ||
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2 . 已知整数
,集合
,
,
,满足
,对任意的
,都有
且
.记
.
(1)若
,写出两组满足条件的集合
,
并写出相应的
;
(2)证明:
;
(3)求
的所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652fd852e080c91df90888d0449d63d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c7bb58dca886fc65d874e2b30040c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f906607b8f6606742f496f73fff2ffd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431acf301f0cf1e414b532de94708474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd31439e275791f4fcd3d22b5ae30ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab4a9bfa50054c808dd8190305d0abd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.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/ce4a2681390214200443ae07c01a4abe.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607a272bff596f86f25dd99f5a69fbbe.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4a2681390214200443ae07c01a4abe.png)
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3 . 声音是由物体振动产生的,每一个纯音都是由单一简谐运动产生的乐音,其数学模型为
,其中
表示振幅,响度与振幅有关;
表示最小正周期,
,它是物体振动一次所需的时间;
表示频率,
,它是物体在单位时间里振动的次数.下表为我国古代五声音阶及其对应的频率
:
小明同学利用专业设备,先弹奏五声音阶中的一个音,间隔
个单位时间后,第二次弹奏同一个音(假设两次声音响度一致,且不受外界阻力影响,声音响度不会减弱),若两次弹奏产生的振动曲线在
上重合,根据表格中数据判断小明弹奏的音是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37088e84230a522586eb9e60089c54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dceb375cbb5f7cad9129f22aabf8bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02f1e2590c1c301b820a4a717529b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
音 | 宫 | 商 | 角 | 徵 | 羽 |
频率 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb22d8add89d149400c5e6221b47d77.png)
A.宫 | B.商 | C.角 | D.徵 |
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4 . 假设某飞行器在空中高速飞行时所受的阻力
满足公式
,其中
是空气密度,
是该飞行器的迎风面积,
是该飞行器相对于空气的速度,
是空气阻力系数(其大小取决于多种其他因素),反映该飞行器克服阻力做功快慢程度的物理量为功率
. 当
不变,
比原来提高
时,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed280544911aa91a07b26a2ed09e39c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171102a883b22fe6ca578efc8926f5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a344acb1ed9c08dc5f355ff74d01bafa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae5e401a716bc52bed83b53c447eacb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522fdf99d6e1ae6757428932e5d319db.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.为使![]() ![]() ![]() |
D.为使![]() ![]() ![]() |
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名校
解题方法
5 . 在现实生活中,一个符合实际的函数模型经常是将不同的函数组合得到的,如听音乐家演奏音乐时,我们听到的声音常常就是多种不同乐器产生的声波叠加的结果.在学习了向量和三角函数后,人大附中某研学小组利用所学知识研究若干振幅相同,同频同向的简谐波叠加后,得到新的简谐波的振幅和初相规律,该小组把
(N为正整数)叠加,研究
中的
和
,其中
.
(1)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
______ .
(2)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2073aefa188a89d515b9d32de5d89c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e289d2f03b9a42c8f61858f1c3b32e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52d236ed8d14f8135a0a63d41a351fe.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb55d413f1ab722e17747c8e99f6c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722068b39032dd59c01afdba985d65be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
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6 . 在人大附中
节活动的入场券中有如下图形,单位圆
与
轴相切于原点
,该圆沿
轴向右滚动,当小猫头鹰位于最上方时,其对应
轴的位置正好是
,若在整个运动过程中当圆
滚动到与出发位置时的圆相外切时(此时记圆心为
),此时小猫头鹰位于
处,圆
与
轴相切于
,则劣弧AB所对应的扇形面积是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.1 | B.2 | C.![]() | D.![]() |
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7 . 某公园为了美化游园环境,计划修建一个如图所示的总面积为
的矩形花园.图中阴影部分是宽度为1m的小路,中间
,
,
三个矩形区域将种植牡丹、郁金香、月季(其中
,
区域的形状、大小完全相同).设矩形花园的一条边长为
,鲜花种植的总面积为
.
的代数式表示
;
(2)当
的值为多少时,才能使鲜花种植的总面积最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c084f46accb2bd9638261edba4a0ba.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3bde6ef2ee5b749b4d48d706543cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baaa2d65026770c5505f8adeb450e43b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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名校
8 . 一架飞机从北京向南飞行1935公里到达广州,假设在广州白云国际机场上空的等待航线是圆形,飞机到达机场上空后,继续沿原航线向南飞行20公里后,开始在直径40公里的圆形等待航线上飞行,飞机每15分钟飞行一周,如图所示,设飞机在等待航线上飞行的时间为t小时,飞机从北京出发向南的飞行距离 为
,
可以近似地 表示为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb17843c51402a1f7cd9b07542597b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb17843c51402a1f7cd9b07542597b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43e4f18894a6b698cc313a052449e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
您最近一年使用:0次
9 . 设A,B为两个非空有限集合,定义
其中
表示集合S的元素个数.某学校甲、乙、丙、丁四名同学从思想政治、历史、地理、物理、化学、生物这6门高中学业水平等级性考试科目中自主选择3门参加考试,设这四名同学的选考科目组成的集合分别为
,
,
,
.已知
{物理,化学,生物},
{地理,物理,化学},
{思想政治,历史,地理},给出下列四个结论:
①若
,则
{思想政治,历史,生物};
②若
,则
{地理,物理,化学};
③若
{思想政治,物理,生物},则
;
④若
,则
{思想政治,地理,化学}.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069ec439d599e7989e74f4c4ac91d65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911cdb689ca80557ce076cb49b3ee498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3dabace330ccdd9755fbcf32d5d6343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b625192d7398634a02ea24fa78ed87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef354e5c5ff828cc8d27c71badd40f98.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d10b9f228c9a255aca3ace899db760d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b4f81050636eac5b4f064fa0f06313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a41bbaf9ee8f16ee2ab343dc164a8e48.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231bca548a6ffe3013474743e1b5d039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
其中所有正确结论的序号是
您最近一年使用:0次
10 . 按国际标准,复印纸幅面规格分为
系列和
系列,其中
系列以
,
,…等来标记纸张的幅面规格,具体规格标准为:
①
规格纸张的幅宽和幅长的比例关系为
;
②将
(
)纸张平行幅宽方向裁开成两等份,便成为
规格纸张(如图).
规格纸张裁剪其他规格纸张.共需
规格纸张40张,
规格纸张10张,
规格纸张5张.为满足上述要求,至少提供
规格纸张的张数为( )
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea68b25c2e09c6aa70843052e43c422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa7e89c5d3ca8e70330ac3010005100.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea68b25c2e09c6aa70843052e43c422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526ddee4ed97b917d9e4cc4542c72a37.png)
②将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e2edb08ade32f10e715ec57755d7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c4efdbc64857469c666dd78a4a7019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90db8321e9bb3b8fdfbff204fe958c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea68b25c2e09c6aa70843052e43c422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b553e2a281714677e29a5e97dd7d5a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2ba909c3435f8212c1da4fae36ee19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa7e89c5d3ca8e70330ac3010005100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea68b25c2e09c6aa70843052e43c422.png)
A.6 | B.7 | C.8 | D.9 |
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