📚 Year 7 WJEC Mathematics: Quick Reference Formula & Theorem Handbook | 7年级 WJEC 数学公式定理速查手册
Welcome to your quick-reference companion for Year 7 WJEC Mathematics. This handbook brings together all the key formulas, rules and theorems you will meet in class, organised by topic. Keep it with you when you are revising, doing homework or preparing for tests. Each entry gives the English statement or formula first, followed by its Chinese translation so you can build your bilingual mathematical vocabulary.
欢迎使用7年级 WJEC 数学速查手册。本手册将课堂中会遇到的所有重要公式、法则和定理按主题汇集在一起。复习、做作业或准备测试时，请把它放在手边。每一条目先给出英文陈述或公式，再配上中文翻译，帮助你建立双语数学词汇。
1. Number Types and Operations | 数字类型与运算
A factor is a whole number that divides exactly into another number with no remainder.
因数是能整除另一个数且没有余数的整数。
The multiples of a number are the results of multiplying that number by whole numbers.
一个数的倍数是指这个数乘以整数所得的结果。
A prime number is a number greater than 1 that has exactly two distinct factors: 1 and itself.
质数是大于1且恰好只有两个不同因数（1和它本身）的数。
A square number is the result of multiplying a whole number by itself.
平方数是将一个整数自乘一次得到的结果。
The order of operations is remembered by BIDMAS: Brackets, Indices, Division and Multiplication (left to right), Addition and Subtraction (left to right).
运算顺序可以通过 BIDMAS 记住：括号、指数、除法和乘法（从左到右）、加法和减法（从左到右）。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
To convert a fraction to a decimal, divide the numerator by the denominator.
将分数转换为小数，用分子除以分母。
To convert a decimal to a percentage, multiply the decimal by 100 and write the '%' symbol.
将小数转换为百分比，将小数乘以100并加上百分号 '%'。
To convert a percentage to a fraction, write the percentage over 100 and simplify.
将百分比转换为分数，把百分数写在分母100上，然后化简。
Common fraction, decimal and percentage equivalents are useful to learn by heart:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
常记下列常见分数、小数和百分比的等价关系：1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%。
3. Negative Numbers | 负数
Adding a negative number is the same as subtracting its positive value.
5 + (−3) = 5 − 3 = 2
加上一个负数等同于减去它的绝对值：5 + (−3) = 5 − 3 = 2。
Subtracting a negative number is the same as adding its positive value.
5 − (−3) = 5 + 3 = 8
减去一个负数等同于加上它的绝对值：5 − (−3) = 5 + 3 = 8。
When multiplying or dividing two integers: same signs give a positive answer, different signs give a negative answer.
两个整数相乘或相除时：同号得正，异号得负。
4. Algebraic Expressions and Substitution | 代数表达式与代入求值
You can simplify an expression by collecting like terms.
2a + 3a = 5a
你可以通过合并同类项来化简表达式：2a + 3a = 5a。
You can multiply a term by a number or a variable.
4 × b = 4b, a × a = a²
可以用数或变量乘以项：4 × b = 4b，a × a = a²。
Substitution means replacing letters with given numbers to find the value of an expression.
If x = 3, then 2x + 1 = 2×3 + 1 = 7
代入求值是指用给定的数字替换字母，计算表达式的值：若 x = 3，则 2x + 1 = 2×3 + 1 = 7。
5. Solving Equations | 解方程
To solve a one-step equation, perform the inverse operation on both sides of the equals sign.
x + 7 = 15 ⇒ x = 15 − 7 = 8
解一步方程，要在等号两边同时进行逆运算：x + 7 = 15 ⇒ x = 15 − 7 = 8。
When a variable is multiplied by a number, divide both sides by that number.
4y = 20 ⇒ y = 20 ÷ 4 = 5
当变量乘以一个数时，两边同时除以那个数：4y = 20 ⇒ y = 20 ÷ 4 = 5。
Always check your solution by substituting it back into the original equation.
始终通过将解代回原方程来检查答案。
6. Sequences | 数列
A number sequence is a list of numbers that follow a rule. Each number is called a term.
数列是按照一定规则排列的一列数。每个数称作一项。
In an arithmetic sequence, you add or subtract the same number (the common difference) to get from one term to the next.
在等差数列中，每项加上或减去同一个数（公差）得到下一项。
For the sequence 3, 5, 7, 9, … the term-to-term rule is 'add 2'.
nth term = 2n + 1
对于数列 3, 5, 7, 9, … 项与项之间的规则是“加2”。第 n 项公式为：2n + 1。
To find the nth term of an arithmetic sequence, multiply the common difference by n and adjust with the value of the first term.
要找出等差数列的第 n 项，用公差乘以 n，再根据首项的值进行调整。
7. Angles | 角
An acute angle measures less than 90°; a right angle is exactly 90°; an obtuse angle is between 90° and 180°; a reflex angle is greater than 180°.
锐角小于90°；直角恰好为90°；钝角在90°到180°之间；反角大于180°。
Angles on a straight line add up to 180°.
a + b = 180°
平
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