> For the complete documentation index, see [llms.txt](https://www.juzisan.site/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://www.juzisan.site/zhong-xiao-xue-bian-cheng/1.-shu-xue.md).

# 1.数学

数学软件使用 **Wolfram Mathematica**

linux 下可以使用，从[官网下载](https://www.wolfram.com/download-center/?source=footer) linux 版本，下载自动变成中文版。

清除变量

```mathematica
Clear["Global`*"]
```

LaTex 公式 需要`$$$$`四个符号

[github下载智慧中小学教材PDF](https://github.com/happycola233/tchMaterial-parser)

## 1. 小学四年级下

笼子里有若干只鸡和兔。从上面数，有 35 个头；从下面数，有 94 只脚。鸡和兔各有几只？ 解：设鸡的数量为 x ，兔的数量为 y

```mathematica
Solve[{x + y == 35, x*2 + y*4 == 94}, {x, y}]
```

***显示输出：***$${{x\to 23,y\to 12}}$$

## 2. 中学七年级上

做大小两个长方体纸盒，尺寸如下（单位：cm）：

|     | 长    | 宽  | 高  |
| --- | ---- | -- | -- |
| 小纸盒 | a    | b  | c  |
| 大纸盒 | 1.5a | 2b | 2c |

(1)做这两个纸盒共用料多少平方厘米？ (2)做大纸盒比做小纸盒多用料多少平方厘米？ 解：

（1）

```mathematica
( 2*ab + 2*bc + 2*ca ) + ( 6*ab + 8*bc + 6*ca)
```

***显示输出：***$$=8 ab + 10 bc + 8 ca$$

（2）

```mathematica
( 6*ab + 8*bc + 6*ca) - ( 2*ab + 2*bc + 2*ca )
```

***显示输出：*** $$=4 ab + 6 bc + 4 ca$$

## 3. **中学七年级下**

***1. 解三元一次方程组*** $$\begin{cases} 3x+4z=7,\ 2 x + 3 y + z = 9,\ 5 x - 9 y + 7 z = 8 \end{cases}$$

```mathematica
Solve[{3x+4z==7, 2x+3y+z==9, 5x-9y+7z==8}, {x,y,z}]
```

***显示输出：***

$$\left{\left{x\to 5,y\to \frac{1}{3},z\to -2\right}\right}$$

***解不等式：***$$\frac{2+x}{2} \ge \frac{2x-1}{3}$$

```mathematica
Reduce[(2 + x)/2 \[GreaterSlantEqual] (2 x - 1)/3, x]
```

***显示输出：*** $$x \ge 8$$

***3. 解不等式组：*** $$\begin{cases} 2 x - 1 > x + 1 \ x + 8 < 4 x - 1 \end{cases}$$

```mathematica
Reduce[2 x - 1 > x + 1 && x + 8 < 4 x - 1, x]
```

***显示输出：***$$x > 3$$

***求下面不等式组的整数解：*** $$\begin{cases} 5 x + 2 > 3(x - 1), \ \frac{1}{2} x-1 \le 7 - \frac{1}{2} x, \end{cases}$$

```mathematica
Reduce[5 x + 2 > 3 (x - 1) &&  1/2 x - 1 \[LessSlantEqual] 7 - 3/2 x, x, Integers]
```

***显示输出：***$$x=-2\lor x=-1\lor x=0\lor x=1\lor x=2\lor x=3\lor x=4$$

## 4. 中学八年级上

***计算：***$$(x+y) \left(x^2-x y+y^2\right)$$

```mathematica
Simplify[(x + y) (x^2 - x y + y^2)]
```

***显示输出：*** $$x^3+y^3$$

***计算：***$$8 a^3 b^2+12 a b^3 c$$

```mathematica
Factor[8 a^3 b^2 + 12 a b^3 c]
```

***显示输出：***$$4 a b^2 \left(2 a^2+3 b c\right)$$

***计算：***$$\frac{6 x^2-12 x y+6 y^2}{3 x-3 y}$$

```mathematica
Simplify[(6 x^2 - 12 x y + 6 y^2)/(3 x - 3 y)]
```

***显示输出：***$$2 (x-y)$$

***计算：***$$\frac{(a-1) \left(a^2-4 a+4\right)}{\left(a^2-4\right) \left(a^2-2 a+1\right)}$$

```mathematica
Factor[Simplify[((-1 + a) (4 - 4 a + a^2))/((-4 + a^2) (1 - 2 a + a^2))]]
```

***显示输出：*** $$\frac{a-2}{(a-1) (a+2)}$$

***计算：***$$\frac{1}{2 p-3 q}+\frac{1}{2 p+3 q}$$

```mathematica
Factor[1/(2 p + 3 q) + 1/(2 p - 3 q)]
```

***显示输出：*** $$\frac{4 p}{(2 p-3 q) (2 p+3 q)}$$

***计算：*** $$\frac{1}{2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+\cdots +\frac{1}{(n-1) n}+\frac{1}{n (n+1)}=$$

```mathematica
Factor[Sum[1/(n*(n + 1)), {n, 1, n}]]
```

***显示输出：***$$\frac{n}{n+1}$$

## 5.**中学八年级下**

***1. 求解***

当$$x$$是怎样的实数时，$$\sqrt{x-2}$$在实数范围内有意义？

解：

```mathematica
Reduce[Sqrt[x - 2] \[GreaterSlantEqual] 0, x]
```

***显示输出：*** $$x\geq 2$$

## 6.中学九年级上

***求解*** 一元二次方程$$a x^2+b x+c=0$$求根公式：

```mathematica
Solve[a x^2 + b x + c == 0, x]
```

***显示输出：*** $$\left{\left{x\to \frac{-\sqrt{b^2-4 a c}-b}{2 a}\right},\left{x\to \frac{\sqrt{b^2-4 a c}-b}{2 a}\right}\right}$$

$$\left{\left{x\to \frac{-b+\sqrt{b^2-4 a c}}{2 a}\right},\left{x\to \frac{-b-\sqrt{b^2-4 a c}}{2 a}\right}\right}$$

$$x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}$$


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://www.juzisan.site/zhong-xiao-xue-bian-cheng/1.-shu-xue.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.