Year 7 Edexcel Maths: Formula & Theorem Quick Reference | 七年级Edexcel数学：公式定理速查手册

📚 Year 7 Edexcel Maths: Formula & Theorem Quick Reference | 七年级Edexcel数学：公式定理速查手册

Welcome to the Year 7 Edexcel Maths quick reference guide. This handbook summarises the essential formulas, theorems and key concepts you need to know. Keep it handy for homework, revision and tests.

欢迎使用七年级 Edexcel 数学速查手册。本手册总结了你需要掌握的关键公式、定理和重要概念。方便你在做作业、复习和考试时查阅。

1. Number and Place Value | 数与位值

The place value of a digit tells you how much it is worth depending on its position in a number (e.g. in 3,482 the digit 3 is worth 3 thousands).

位值告诉你一个数字根据它在一个数中的位置值多少（例如在 3,482 中，数字 3 值是 3 千）。

When rounding to the nearest 10, 100 or 1000, look at the digit immediately to the right. If it is 5 or more, round up; otherwise round down.

将数字四舍五入到最近的 10、100 或 1000 时，看紧邻右侧的数字。如果它大于或等于 5，则向上舍入；否则向下舍去。

Negative numbers are numbers less than zero. On a number line they lie to the left of zero.

负数是小于零的数。在数轴上它们位于零的左侧。

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2. Addition, Subtraction, Multiplication & Division | 加法、减法、乘法与除法

Addition and multiplication are commutative: a + b = b + a and a × b = b × a.

加法和乘法满足交换律：a + b = b + a，a × b = b × a。

The associative law for addition: (a + b) + c = a + (b + c). For multiplication: (a × b) × c = a × (b × c).

加法结合律：(a + b) + c = a + (b + c)。乘法结合律：(a × b) × c = a × (b × c)。

The distributive law connects multiplication and addition: a × (b + c) = a × b + a × c.

分配律将乘法和加法联系起来：a × (b + c) = a × b + a × c。

When dividing, we can use the inverse relationship: if a ÷ b = c, then b × c = a.

除法使用逆运算关系：如果 a ÷ b = c，那么 b × c = a。

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3. Fractions, Decimals & Percentages | 分数、小数与百分数

A fraction represents a part of a whole. The top number is the numerator, the bottom is the denominator.

分数表示整体的一部分。上面的数是分子，下面的数是分母。

To add or subtract fractions with the same denominator, keep the denominator and add/subtract the numerators: a/c ± b/c = (a ± b)/c.

同分母分数相加减，分母不变，分子相加减：a/c ± b/c = (a ± b)/c。

To multiply fractions, multiply the numerators and multiply the denominators: a/b × c/d = ac/bd.

分数相乘，分子相乘，分母相乘：a/b × c/d = ac/bd。

To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d = a/b × d/c.

除以一个分数，等于乘以它的倒数：a/b ÷ c/d = a/b × d/c。

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 by 100 and add the % sign.

将小数转换为百分数，乘以 100 并加上百分号。

Part = (Percentage ÷ 100) × Whole

部分 = (百分数 ÷ 100) × 整体

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4. Ratio and Proportion | 比与比例

A ratio compares quantities using division. The ratio a:b means a parts to b parts.

比通过除法比较数量。比例 a:b 表示 a 份对 b 份。

To simplify a ratio, divide both terms by their highest common factor.

化简比例，将两项同时除以它们的最大公因数。

Two quantities are in direct proportion if one is a constant multiple of the other: y = kx.

如果两个量一个是另一个的常数倍，则它们成正比：y = kx。

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5. Algebra: Expressions & Equations | 代数：表达式与方程

A variable is a symbol (usually a letter) that stands for an unknown number.

变量是一个表示未知数的符号（通常是字母）。

An expression is a combination of variables, numbers and operations, like 3x + 2y.

表达式是由变量、数字和运算符号组成的式子，如 3x + 2y。

To simplify expressions, collect like terms: 2a + 3a = 5a; 4x + 2y – x = 3x + 2y.

化简表达式要合并同类项：2a + 3a = 5a；4x + 2y – x = 3x + 2y。

An equation states that two expressions are equal, e.g. x + 5 = 12. Solve by performing the same operation on both sides.

方程表示两个表达式相等，例如 x + 5 = 12。解方程时在等号两边进行相同的运算。

One-step equation solving: if x + 3 = 7, subtract 3: x = 4; if 4x = 20, divide by 4: x = 5.

一步解方程：如果 x + 3 = 7，两边减 3 得 x = 4；如果 4x = 20，两边除以 4 得 x = 5。

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6. Sequences | 数列

A sequence is an ordered list of numbers following a rule. The term-to-term rule tells you how to get from one term to the next.

数列是按一定规则排列的一列数。项间规则告诉你如何从一项得到下一项。

An arithmetic sequence has a common difference d between consecutive terms.

等差数列相邻两项之间有一个公差 d。

nth term of an arithmetic sequence: T(n) = a + (n − 1)d

等差数列的第 n 项：T(n) = a + (n − 1)d

Where a is the first term, d is the common difference, and n is the term position.

其中 a 是首项，d 是公差，n 是项的位置。

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7. Geometry: Angles & Lines | 几何：角与线

Angles are measured in degrees (°). A right angle = 90°, a straight angle = 180°, a full turn = 360°.

角以度（°）为单位。直角 = 90°，平角 = 180°，一周角 = 360°。

Vertically opposite angles are equal. When two lines intersect, the angles opposite each other are equal.

对顶角相等。两条直线相交时，相对的两个角相等。

Angles on a straight line add up to 180°. Angles around a point add up to 360°.

直线上的角之和为 180°。点周围的角之和为 360°。

The sum of interior angles of a triangle is always 180°.

三角形的内角和总是 180°。

The sum of interior angles of a quadrilateral is 360°.

四边形的内角和是 360°。

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8. Properties of 2D Shapes | 二维图形的性质

Triangles can be classified by sides: equilateral (all sides equal), isosceles (two equal sides), scalene (no equal sides).

三角形按边分类：等边三角形（三边相等）、等腰三角形（两边相等）、不等边三角形（三边都不等）。

Triangles by angles: acute (all angles < 90°), right-angled (one angle = 90°),

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