1 . 计算:
(1)
.
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5bc6d6cc43878b939033a1642baeb2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591a17ff509ef4f980dcd2567f3526dc.png)
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2 . 计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0aec2942259819ee36327844bf6f84.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0aec2942259819ee36327844bf6f84.png)
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2024-04-09更新
|
123次组卷
|
3卷引用:浙江省绍兴市柯桥区柯桥区浙光中学2023-2024学年八年级下学期第一次月考数学试题
3 . 计算:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bfe30380decb4ba3f9a6b0598ed922.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26592a6be349e10a3bebab0d9077fa3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bfe30380decb4ba3f9a6b0598ed922.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801108697d5cf8047330664fbe669614.png)
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4 . 计算(需写出计算过程):
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb9261a50cc989b1d34fe199d0e5e85.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abb1982279208b53bc6db76131e64519.png)
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5 . 已知
是方程
的一个解,则m的值为_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78f07fa951d88cd20dae635e326e7a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e31e313a4c7b77bacf7a53bae9463f.png)
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6 . 计算:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788e4ee042da991f88e45ee828ea15b7.png)
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2024-04-04更新
|
431次组卷
|
4卷引用:2024年浙江省金华市东阳市中考二模数学试题
2024年浙江省金华市东阳市中考二模数学试题2024年广东省深圳市蛇口育才教育集团中考一模数学试题湖北省黄冈市黄梅县多校联考2023-2024学年九年级下学期期中数学试题(已下线)抢分通关07 锐角三角函数解决实际问题(2易错7题型)-备战2024年中考数学抢分秘籍(全国通用)
7 . 我们知道形如
,
的数可以化简,其化简的目的主要是把原数分母中的无理数化为有理数.如:
,
.这样的化简过程叫做分母有理化.我们把
叫做
的有理化因式,
叫做
的有理化因式.利用有理化因式,可以得到如下结论:①
;②设有理数a,b满足
,则
;③
;④已知
,则
;以上结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf30225033ed65ba166c6f25ffa2ff52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46d903100e4258ef742d56efdeeb156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e13086a7dd306655c58926773a80a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6631a036244034b582312289cd0ce6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab46ea0cba2d06283fae3d864a2329e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47cfe4e08c06bde245e58aa22485044c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51a4f6d6a05b6fb6e3160a665d13d806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f538b8da9794174c7b0bf67c54ac8ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289295fad0d1c11fc74470e8bb0c6be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3cc9f76c7b756e3a77811e3b475bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc1f48f40d6aa2219122ded96bf8ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9d406a76e15e4216175219db0c9b34.png)
A.①③ | B.①② | C.①④ | D.③④ |
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8 . 计算
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ef3bfe73e5b623736c50171e42a224.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ef3bfe73e5b623736c50171e42a224.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49900d0abd350b3ae192d11a61dcc9b.png)
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9 . 计算:
(1)
;
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701611ab767255ff49f6cacf348770cc.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a96855c56f4af27b8224a9127229ed.png)
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10 . 【阅读】我们将
与
称为一对“对偶式”,
因为
,所以构造“对偶式”,再将其相乘可以有效地将
和
中的“
”去掉,于是二次根式的除法可以这样计算:如![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c78d9b11fb443069fb7e09ea86822ce.png)
.像这样,通过分子、分母同乘一个式子把分母中的根号化去,叫做分母有理化.
根据以上材料,理解并运用材料提供的方法,解答下列问题:
(1)对偶式
与
之间的关系是____________;
A.互为相反数 B.绝对值相等 C.互为倒数
(2)已知
,
,化简
,
;
(3)解方程:
.
[提示:令
,
].
(4)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a989c4fbf0ff34cedb365d2dda47f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175d0c99e866f1db915462a91b356ef3.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50036f42d68bcb48ee54bf6a8e76856f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9928ba39cdd5878aced506d3dbb9fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b87033f1efe85e559a9a3efc985be9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa0dba76fbef65983ebf043218ea5e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c78d9b11fb443069fb7e09ea86822ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755d7e08b98c26303f2f61de7e7ddd2.png)
根据以上材料,理解并运用材料提供的方法,解答下列问题:
(1)对偶式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab46ea0cba2d06283fae3d864a2329e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47cfe4e08c06bde245e58aa22485044c.png)
A.互为相反数 B.绝对值相等 C.互为倒数
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e4636f3b6eb54711c4410fa831f623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add3e1ba560da4c0904e016eb85940b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(3)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e95857b9fcde7b45e59ef3d498e456.png)
[提示:令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab49c882cfe6fc298a74b8dbfa5cd815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50036f42d68bcb48ee54bf6a8e76856f.png)
(4)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75fd7e405a9928ae2642a15050b1446.png)
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