把下列各数用数轴表示出来,并用“<”连接起来.
,
,
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead4951a963f4074512ab092d395d583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c960e3b875cdceca0011c74b4fc5b56d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30910e13e6818d721f845f4b9432585e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb3528d985a77044680e3fb9bd49c8e3.png)
更新时间:2022-07-28 09:11:08
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解答题-作图题
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【推荐1】画出数轴,把下列各数及它们的相反数表示在数轴上,并将这些数按从小到大的顺序用“<”连接.2,0,-
,-3.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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名校
【推荐2】画一条数轴,并在数轴上表示:3.5和它的相反数,
和它的倒数,绝对值等于3的数,最大的负整数和它的平方,并把这些数由小到大用“<”号连接起来.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
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名校
【推荐1】在数轴上表示下列各数,再用“<”把各数连接起来:
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/203b4c1b97dcb87dacb9fc636699f86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4f47d27d32b7f205cd916f49623f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2384167ae61cf3183559acb3006898a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f9f82b39cc1adf62725a51d4b735fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/203b4c1b97dcb87dacb9fc636699f86e.png)
![](https://img.xkw.com/dksih/QBM/2019/11/22/2339413848244224/2339611734089728/STEM/bce8760590ea41d18a9c9093c38439c0.png?resizew=301)
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解答题-作图题
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适中
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【推荐2】画出数轴,将下列各数表示在数轴上,并用“
”连接.
,0,
,
,3,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89117f3793e604ce6793f258369051b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33416936750a9caf9e877f02c3ad6b0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6ddf31b7d9225a4239883af72d153b.png)
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解答题-计算题
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适中
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【推荐1】若关于
二元一次方程组
.
(1)求方程组的解
、
(用含
的代数式表示);
(2)若
,求
的取值范围;
(3)在(2)的条件下化简
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9e3707042e9ce2cf8ce44d2c988db2.png)
(1)求方程组的解
![](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/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9261a45b3df71edf72919cc24b9a22f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)在(2)的条件下化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25365926ce6adaec96846bbe7240393.png)
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解答题-计算题
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【推荐2】已知,数
,
,
在数轴上的位置如图:
(1)判断正负,用“
”或“
”连接:
_____
,
_____
,
_____
.
(2)化简
![](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://img.xkw.com/dksih/QBM/editorImg/2023/11/30/4f9250bb-1f2f-42da-965d-8dfa5499f27e.png?resizew=365)
(1)判断正负,用“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1810555c0c28fe352841322b85bbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e4d93d6487777af953af02c1be6f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77e9b8e1c407081d01c8542b55ba395.png)
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解答题-计算题
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解题方法
【推荐1】概念学习:规定:求若干个相同的有理数(均不等于0)的除法运算叫做除方,如2÷2÷2,(﹣3)÷(﹣3)÷(﹣3)÷(﹣3)等.类比有理数的乘方,我们把2÷2÷2记作2③,读作“2的圈3次方”,
(﹣3)÷(﹣3)÷(﹣3)÷(﹣3)记作(﹣3)④,读作“﹣3的圈4次方”,一般地,把
(a≠0)记作aⓝ,读作“a的圈n次方”.
初步探究:
(1)直接写出计算结果:2③= ,
⑤= ;
(2)关于除方,下列说法错误的是
A.对于任何正整数n,1ⓝ=1; B.3④=4③
C.负数的圈奇数次方结果是负数,负数的圈偶数次方结果是正数.
深入思考:
我们知道,有理数的减法运算可以转化为加法运算,除法运算可以转化为乘法运算,有理数的除方运算如何转化为乘方运算呢?
(3)试一试:仿照上面的算式,将下列运算结果直接写成幂的形式.
(﹣3)④= ;5⑥= ;
⑩= .
(4)算一算:
④-4③×8.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/18/6c1f03b7-74e9-4b5e-96d4-faee3a9fab04.jpg?resizew=386)
(﹣3)÷(﹣3)÷(﹣3)÷(﹣3)记作(﹣3)④,读作“﹣3的圈4次方”,一般地,把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f7ea1bb0fc777f693c6977fc020f78.png)
初步探究:
(1)直接写出计算结果:2③= ,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb91bc11d2fd9933cda5c3b7b3c785f.png)
(2)关于除方,下列说法错误的是
A.对于任何正整数n,1ⓝ=1; B.3④=4③
C.负数的圈奇数次方结果是负数,负数的圈偶数次方结果是正数.
深入思考:
我们知道,有理数的减法运算可以转化为加法运算,除法运算可以转化为乘法运算,有理数的除方运算如何转化为乘方运算呢?
(3)试一试:仿照上面的算式,将下列运算结果直接写成幂的形式.
(﹣3)④= ;5⑥= ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb91bc11d2fd9933cda5c3b7b3c785f.png)
(4)算一算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f893854964a487dbff4c375455f6c0da.png)
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【推荐2】数学课外小组的同学发现,很多计算法则逆用时会有神奇的效果.如同底数幂的乘法法则为
(其中
,
、
为正整数),类似的,我们规定关于任意正整数
、
的一种新运算:
(其中
、
为正整数).
例如:
,则
;
.
请根据这种新运等解决以下问题:
(1)若
,则
________________;
(2)在(1)成立的前提下,当
,求
的值;
(3)若
,化简:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c4041aeaf2cb6085d57d3b760fa11e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d6f3f855cfee71ac03a54628e003c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
例如:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94dcba2f076197a08ea4cf76d4379fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b91cfa7431e1edccfce987d2d673ea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe244e1c4272a442d1a46a397246ca9.png)
请根据这种新运等解决以下问题:
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f209c5f0fd5434e6999bb6186ff3ba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8d437a261c80bb03fdb8e6a62af2b0.png)
(2)在(1)成立的前提下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f78cebf45b79e0298a41c5252e771e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855cce75456d2e60a46b582b8fe33a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb146a7990833f73083bd4db07697b0d.png)
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