1 . 如图从边长为
的正方形纸片中剪去一个边长为
的正方形
,剩余部分沿虚线剪拼成一个长方形(不重叠无缝隙),则长方形的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac31a93a98fe8440ba9b0745108286a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce9f51cde151c95baf51d929c6d8430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073bd7cec3f5d4d0107a2b6affcf59c2.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2 . 有一个三位数,其3个数字排列组成的最大三位数与最小三位数之差恰好等于原三位数,则这个三位数是__________ .
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3 . 如图,四边形
是边长为
的正方形,四边形
是边长为
的正方形,点
在线段
上,连接
,
.
的代数式表示
的面积;
(2)用含
的代数式表示阴影部分面积
,并求出当
时,阴影部分面积
是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f43677db00ba65a7f96fc49627d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95db6323116a56609a72faf88b6bc270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8b62dc033d86ee9e561b8903796701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa485cf3776f36aaf4abaadaf30fb85.png)
(2)用含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b92d80a91fddf3d4c93cf5b6250ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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4 . 某居民小区为提高业主的宜居环境,准备在小区内一个长为
米,宽为
米的长方形休闲广场上修建宽度均为
米的健身跑道.
(2)如图2,若修建两纵一横的三条健身跑道,且剩余部分的面积为
平方米.当
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80088a26565c2c74de651f736b700103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03261a2ca2c6da2ff4c76a98806aa12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)如图2,若修建两纵一横的三条健身跑道,且剩余部分的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7123ef4a654494c80b94613eec9f1f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b104867a12d24a353d94858c2fa17c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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5 . 已知自然数
小于50,且
和
有大于1的公因数,则所有
的可能值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027c1937834a3c3820d18e9e43a17617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7daeec0d64080ca37093b63dfad94b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.18 | B.20 | C.30 | D.40 |
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6 . 任意一个个位数字不为0的四位数
,都可以看作由前面三位数和最后一位数组成,交换这个数的前面三位数和最后一位数的位置,将得到一个新的四位数
,记
,例如:
,则
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876621d84b863cd5c3031f4f79328c9a.png)
______ ;若四位数
,满足
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29798b00a9b78327cef9cb03537a7920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b4e7834b3a969a23182b07151ba2ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0808e9e889dbaa5884461477fe0131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3296679c56d99df86a374fff85d2044e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876621d84b863cd5c3031f4f79328c9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21bcd0763cefb1b59afc8d9bda4341a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe821cb5c7711d441b12855291e49d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5646744ea382c9cfaadaba939be01a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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7 . 如图1,在平面直角坐标系中,点A在y轴上,点B、点C在x轴上,
平分
交x轴于点H,
平分
交
的延长线于点D.
,求
的度数.
(2)如图2,连接
,则
平分
,做
于点K,探究
与
的数量关系,并证明结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d29e7c4d6216690152430b09f9cf0c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93c1a847fc62d79450fc26b6911feba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650362bbb54273f96eb35df79751b52c.png)
(2)如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd94dd51562ecbee6edd4265326b765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5031363bc487f62b2ae5fdf2c07b8e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b30bfdeff02c9070211480e09c543f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344a0de153f126156200d43faa6a5eb.png)
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8 . 实践课上,老师出示了两个长方形,如图1,长方形的两边长分别为
,
;如图2,长方形的两边长分别为
,
.(其中m为正整数 )
(1)图1中长方形的面积
_______;图2中长方形的面积
_______;
(2)比较
与
的大小;
(3)现有一面积为25的正方形,其周长与图1中的长方形周长相等.求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103960317959f836983c4b624f8fa460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2c1ec3153d6b86778f01cb90027029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8401bb16895bde1550fb7cb6047c777d.png)
(1)图1中长方形的面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3dabace330ccdd9755fbcf32d5d6343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b625192d7398634a02ea24fa78ed87.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(3)现有一面积为25的正方形,其周长与图1中的长方形周长相等.求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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9 . 若
,
,则
,
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9433c6aed1dbbacc64ea6e5a1a8e8132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752fc19132f170d96d6234b1a0b03feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-05-13更新
|
115次组卷
|
2卷引用:江苏省南京市联合体2023-2024学年七年级下学期期中考试数学试题
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10 . 对于个位数字不为零的任意三位数
,将其个位数字与百位数字对调得到
,则称
与
互为“对称数”,将互为“对称数”的两个数的差的绝对值与33的商记为
,例如当
时,
.
(1)
,
;
(2)求
的值;
(3)对于任意三位数
,其百位上的数字为
,十位上的数字为
,个位上的数字为
,满足:
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c693e0770a0b97749f792a25a4ed8615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c693e0770a0b97749f792a25a4ed8615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f915234c028fd025f1577e387f6d1a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fc301e48690c60a2a9f237c6266906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0371b0ce4a1d8d99a6049db6fb1962f2.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdfdee1a0913464c908009a03a35481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58859fae8f15f41bea534ade850d7d85.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47dfda0a97fca673533b6510a5901ce2.png)
(3)对于任意三位数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d216cab17d5426c933d96ae5e8acb82f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f915234c028fd025f1577e387f6d1a6.png)
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