2024七年级下·全国·专题练习
1 . 如图,在直角坐标系中,第一次将
变换成
,第二次将
变换成
,第三次将
变换成
,已知
,
,
,
;
,
,
,
.
变换成
,则
的坐标是 ,
的坐标是 .
(2)若按(1)找到的规律将
进行了
次变换,得到
,比较每次变换中三角形顶点有何变化,找出规律,推测
的坐标是 ,
的坐标是 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb99c20237aca8ff2ba640c28fbc5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb99c20237aca8ff2ba640c28fbc5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef3e5e30a5d97b80edfa260b43c3e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef3e5e30a5d97b80edfa260b43c3e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d24434eb8bf365cb3145a89771ff95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71a512987761644b8d7fac755fd89c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d104ab5ca1f4839f522e224f6cf0ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98588e87c23e3457b2601e8e9e3a9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2694a3c4b93cb6b142692eca80a4bb76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f605a7fc2f1064fe14882ee426839db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4b7e01e33e0b7a93c9ea2dc23f0d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee65ee129ab0db9f84b085b01a94937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cebca5a278cfdc35447cbc58cfa001d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d24434eb8bf365cb3145a89771ff95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5bb157a604f1da055ad90bd91ac234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a821e643d5fae24caed0faa6d423dad6.png)
(2)若按(1)找到的规律将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75e563a1219cc5b71503a618ecfb7d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
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2 . 如图,在平面直角坐标系
中,
,
,
,
是边长为1个单位长度的小正方形的顶点,开始时,顶点
,
依次放在点
,
的位置,然后向右滚动,第1次滚动使点
落在点
的位置,第2次滚动使点
落在点
的位置,…,按此规律滚动下去,则第2025次滚动后,顶点
的坐标是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/8455657dde27aabe6adb7b188e031c11.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/ff32d26c8d44f5fb4813a19c1030a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0573e2af8a0dc8c6a1c0af067a324f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb442fb1fe1a5d9768cf11c3e1b7ec5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfa2a6d9749a619edf80bad8b3e4962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 乙炔
是最重要的一种炔烃,在工业中可用以照明、焊接及切断金属(氧炔焰),炔烃属于有机化合物,简单的炔烃化合物有乙炔
、丙炔
、丁炔
、戊炔
,…,按照此规律,设一个炔烃分子的碳原子
个数为
(
),请用
表示炔烃分子的氢原子
个数是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c23aaf94cac4e27edd27e6dc718c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c23aaf94cac4e27edd27e6dc718c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a1d480ecd8ce897ea26d920984db0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7be9ee948b86040c6abbccf49e47473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4a263b2791cf4bec5aa70a375c67c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5d2e85c02a030b0eeba5a366686256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8201de1621b4b5bd752a555ef2bf33.png)
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4 . 观察下列等式,解答问题.
;
;
;
…
(1)请直接写出第5个等式: ;
(2)利用上述规律,比较
与
的大小;
(3)直接写出
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f8486603d3f472cd3998c1f2d53eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8164b7483fb50871ac417e371c3c9d46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8611c9dcc5c6092cd7e8522472888278.png)
…
(1)请直接写出第5个等式: ;
(2)利用上述规律,比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01de824ecc30e0e06f88bd12b045b7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148bbb64339fc5e504ec52fe1ba4bb8e.png)
(3)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c00ca246c88bce442e1220f42a55df.png)
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5 . 观察下列运算:
①由
,得
;
②由
,得
;
③由
,得
.
(1)通过观察,将你发现的规律用含有
的式子表示出来,并注明
的取值;
(2)利用你发现的计算
.
①由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916801280e639ddc0700afba2adfe28d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46916ae4936e634cd05abc59f5a6246e.png)
②由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d8e46976fa60bacb93dca7af921bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c64e7bdb41d097a271b68f9ede41c7bc.png)
③由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed79024949e5704ca4f71aebb0934464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdd10d410047ebef943410ff67882cad.png)
(1)通过观察,将你发现的规律用含有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)利用你发现的计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32f7b7d6bbb1ce8f2e7df367c64dd5d.png)
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6 . 某综合实践小组准备研究心率(每分钟心跳次数)与跳绳活动(每分钟跳
次左右)持续时间的关系,用实测心率占最大心率的百分比(也叫相对心率)来描述运动后的即时心率与跳绳持续时间的关系(最大心率
年龄).该小组在九年级随机抽取了
位男生(年龄都是
岁),测试了跳绳持续时间与相对心率,通过计算平均数后得到的数据如下表:
(2)该小组请教体育和保健老师后知道,随着跳绳持续时间增加,平均相对心率随之增加且增加的速度越来越慢,
.他们计算表中
的值,画出散点图如图所示,发现
是
(a是常数)的反比例函数,求y与x之间的函数表达式.
(3)该小组查阅资料发现:热身运动合适的心率范围是最大心率的
,减脂运动合适的心率范围是最大心率的
,有氧耐力运动(锻炼心肺功能)和无氧耐力运动的合适心率范围分别是最大心率的
和
,从健康角度考虑,相对心率不应超过
.根据这些信息,请你给学校设计一套男生跳绳持续时间的训练方案.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3864983798fe836a591e13783fd9e82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01e3a9170a88e7ed5a56f39fa8bff0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
跳绳持续时间x(单位:秒) | 0 | … | ||||
平均相对心率y(%) | … |
(2)该小组请教体育和保健老师后知道,随着跳绳持续时间增加,平均相对心率随之增加且增加的速度越来越慢,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689a2ea53b540ea8206ca9a5dc575bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1319d7833906fbe49d5ab4082ded3be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e432bd9a68492b6e31468a565946212b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbab003d7e5b9b7ff3cfc0b9c0d8e62.png)
(3)该小组查阅资料发现:热身运动合适的心率范围是最大心率的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d882432bd56b4c22c4d3941df10c73e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d8a00feefe9d96085469819728c745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccf57a3de2722116d048d1f51b384fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8a45e7c8dd7495c927b870fcab724f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c4bf61e073c899494b2fb3b767b108.png)
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7 . 某数学兴趣小组为了研究多边形中从一个顶点可以作几条对角线,以及该多边形中对角线的总条数与边数的关系,他们决定从以下图形开始寻找规律.
点出发的所有对角线;
(2)根据探究,整理得到下面表格:
①表格中
______,
______;(用含n的代数式表示)
②拓展应用:
若该校要举办足球比赛,总共有
个班级参加比赛,规定每个班级都要和其他班级比赛一次,请计算总共要比赛多少场.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)根据探究,整理得到下面表格:
多边形的边数 | 4 | 5 | 6 | 7 | 8 | …… | |
从一个顶点出发的对角线的条数 | 1 | 2 | 3 | 4 | 5 | …… | |
多边形对角线的总条数 | 2 | 5 | 9 | 14 | 20 | …… |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
②拓展应用:
若该校要举办足球比赛,总共有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0b71b8d2c183154221f717ce09077b.png)
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7日内更新
|
69次组卷
|
2卷引用:安徽省六安市霍邱县2023-2024学年八年级下学期月考数学试题
8 . 观察:下列等式
,
,
…据此规律,当
时,代数式
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77fc530917ade098f3a481f1ada4bd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c97f3e0b3eb6ad36aaba9e6c3c6bbe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfdc088d5384f01280e91e9b5964a40c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1291e3208f7011fd93bc6baed1e4f439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1d7a4c2f3e85a04e5c32d845eb3312.png)
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9 . 如图,在平面直角坐标系中,动点P按箭头所示的方向做折线运动,第一次从原点运动到
,第二次从
运动到
,第三次从
运动到
,第四次从
运动到
,第五次从
运动到
,第六次从
运动到
……,按这样的运动规律(向右始终保持运动一个单位长度,向上或向下比前一次的向下或向上都多运动一个单位长度),经过第2024次,点P的坐标是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991c1f0c963104740e50cfff6f29a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991c1f0c963104740e50cfff6f29a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a20a61d384b658080b92d8c1a9e7c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a20a61d384b658080b92d8c1a9e7c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbfff9a05b85a815235a94098f994e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbfff9a05b85a815235a94098f994e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcab2c5c85301cf851418b1f57402d22.png)
A.(1011,506) | B.(1011,![]() | C.(1012,506) | D.(1012,![]() |
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10 . 如图1,
中,
,
,
,点D,E分别为
,
的中点,点P为
上一个动点,过点E作
,垂足为点Q,设
,C,Q两点的距离为
,E,Q 两点的距离为
.小明根据学习函数的经验,对函数
和
随自变量x的变化而变化的规律进行了探究.
(1)自变量x的取值范围是 .
(2)通过取点、画图、测量,得到了x与y的几组值,如下表:
请直接写出
;
(3)如图2,在平面直角坐标系
中,描出以补全后的表中各对对应值为坐标的点,画出
随自变量x的变化而变化的函数图象.
(4)结合画出的函数图象,解决问题:当
为等腰三角形时,x的值约为
.(数值保留一位小数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c545764505bb00578a870c5e39493a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cd4a1c8087ef697d82b321a3331211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28719b1c54dd019b73f255e4f8b9973b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc37d3558570e6bbb9c98e08d5641a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38703a1be638e22eb5d06e315fbff406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469490cb0402f8cf5a51a143dd9e124f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
(1)自变量x的取值范围是 .
(2)通过取点、画图、测量,得到了x与y的几组值,如下表:
x/![]() | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
![]() ![]() | 0 | 0.93 | 2.25 | 3.72 | 4.73 | m | 4.88 | 4.68 | 4.47 | 4.30 | 4.16 |
![]() ![]() | 3 | 3.69 | 4.48 | 4.98 | 4.75 | n | 3.25 | 2.68 | 2.24 | 1.31 | 1.66 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
(3)如图2,在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
(4)结合画出的函数图象,解决问题:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86643348a8164750d9aefcfe20fecb7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
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