Year 8 Edexcel Maths: Core Knowledge Points Overview | Year 8 Edexcel 数学：核心知识点梳理

📚 Year 8 Edexcel Maths: Core Knowledge Points Overview | Year 8 Edexcel 数学：核心知识点梳理

Welcome to your complete revision guide for Year 8 Edexcel Maths. This article summarises the essential topics you will encounter in the curriculum, including number skills, algebra, geometry, statistics, and probability. Each section is designed to reinforce your understanding with clear explanations and practical examples.

欢迎阅读 Year 8 Edexcel 数学的完整复习指南。本文总结了课程涵盖的核心主题，包括数、代数、几何、统计与概率。每个部分都通过清晰的解释和实用示例来巩固你的理解。

1. Integers, Powers and Roots | 整数、幂与根

You should be able to add, subtract, multiply and divide integers (positive and negative whole numbers). Remember the rules: multiplying or dividing two numbers with the same sign gives a positive result, while different signs give a negative result.

你应当能够对整数（正整数和负整数）进行加、减、乘、除运算。记住规则：同号两数相乘或相除得正，异号得负。

Powers (indices) indicate repeated multiplication. For example, 3² means 3 × 3 = 9, and 5³ means 5 × 5 × 5 = 125. The square root (√) is the inverse of squaring. √64 = 8 because 8² = 64. Cube roots work similarly: ∛27 = 3 because 3³ = 27.

幂（指数）表示重复相乘。例如，3² 表示 3 × 3 = 9，5³ 表示 5 × 5 × 5 = 125。平方根 (√) 是平方的逆运算。√64 = 8，因为 8² = 64。立方根与之类似：∛27 = 3，因为 3³ = 27。

You must also be familiar with the order of operations (BIDMAS/BODMAS): Brackets, Indices, Division/Multiplication (left to right), Addition/Subtraction (left to right). Always apply this hierarchy to simplify expressions correctly.

你必须熟悉运算顺序（BIDMAS/BODMAS）：括号、指数、除法/乘法（从左到右）、加法/减法（从左到右）。始终遵循此层级来正确化简表达式。

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2. Fractions, Decimals and Percentages | 分数、小数与百分比

You need to convert fluently between fractions, decimals and percentages. For instance, 1/4 = 0.25 = 25%. To convert a fraction to a decimal, divide the numerator by the denominator. To change a decimal to a percentage, multiply by 100.

你需要熟练在分数、小数和百分比之间进行转换。例如，1/4 = 0.25 = 25%。将分数转换为小数，用分子除以分母；将小数转换为百分比，乘以 100。

When adding or subtracting fractions, find a common denominator first. For multiplication, simply multiply numerators together and denominators together. To divide by a fraction, multiply by its reciprocal.

进行分数的加减运算时，先找到公分母。乘法直接分子乘分子、分母乘分母。除以一个分数等于乘以它的倒数。

Percentage increase and decrease are key skills. To increase £40 by 5%, find 5% of £40 (£2) and add to get £42. Alternatively, multiply by 1.05. For a decrease of 15%, multiply by 0.85.

百分比增减是核心技能。将 40 英镑增加 5%，先计算 40 的 5%（2 英镑）再加起来得到 42 英镑。或者乘以 1.05。减少 15% 则乘以 0.85。

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3. Ratio and Proportion | 比与比例

Ratio compares quantities in the same unit. A ratio like 3:2 tells you that for every 3 of one thing, there are 2 of another. You can simplify ratios by dividing both parts by their greatest common factor. The ratio £1:20p must first be converted to the same units: 100p:20p, which simplifies to 5:1.

比用来比较相同单位的数量。比如 3:2 表示每 3 份对应另一样东西的 2 份。你可以用最大公因数同时除两边的数来化简比。比例如 1 英镑:20 便士，需先转换为相同单位：100p:20p，化简为 5:1。

Proportion links two quantities that change together. Direct proportion means when one doubles, the other doubles. If 5 pens cost £3, 10 pens cost £6. Unitary method (finding the value of one item first) helps solve problems.

比例联系了两个同时变化的量。正比例意味着一个量翻倍，另一个也翻倍。如果 5 支笔花费 3 英镑，那 10 支笔花费 6 英镑。归一法（先求单一物品的价值）有助于解题。

Dividing a quantity in a given ratio: to split £50 in the ratio 2:3, add the parts (2+3=5), one part is £10, then the shares are £20 and £30.

按给定比例分配数量：将 50 英镑按 2:3 分配，总份数为 2+3=5，每份为 10 英镑，则分配结果分别为 20 英镑和 30 英镑。

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4. Algebraic Expressions and Simplification | 代数表达式与化简

Algebra uses letters to represent unknown numbers. An expression like 3a + 2b + a – b can be simplified by collecting like terms: 3a + a = 4a, and 2b – b = b, giving 4a + b.

代数使用字母表示未知数。像 3a + 2b + a – b 这样的表达式可以通过合并同类项来化简：3a + a = 4a，2b – b = b，得到 4a + b。

Expanding brackets uses the distributive law. For example, 5(2x + 3) becomes 5×2x + 5×3 = 10x + 15. For double brackets, like (x + 2)(x + 5), multiply each term: x² + 5x + 2x + 10, then simplify to x² + 7x + 10.

去括号使用分配律。例如，5(2x + 3) 变成 5×2x + 5×3 = 10x + 15。对于双重括号如 (x + 2)(x + 5)，逐项相乘：x² + 5x + 2x + 10，然后化简为 x² + 7x + 10。

Factorising is the reverse of expanding. To factorise 6x + 9, find the highest common factor (3), so 6x + 9 = 3(2x + 3). You can check by expanding back.

因式分解是展开的逆运算。要分解 6x + 9，找到最大公因数 3，因此 6x + 9 = 3(2x + 3)。你可以通过展开来进行检验。

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5. Linear Equations | 线性方程

Solving equations means finding the value of the unknown. For one-step equations like x + 7 = 12, subtract 7 from both sides to get x = 5. For 3x = 18, divide both sides by 3: x = 6.

解方程就是找到未知数的值。对于一步方程如 x + 7 = 12，两边同时减去 7 得到 x = 5。对于 3x = 18，两边同时除以 3：x = 6。

Two-step equations require reverse BIDMAS. Solve 2x – 5 = 11: first add 5 (2x = 16), then divide by 2 (x = 8). Always do the opposite operation in reverse order.

两步方程需要反向 BIDMAS。解 2x – 5 = 11：首先加 5（2x = 16），然后除以 2（x = 8）。始终按反向顺序进行相反的运算。

Equations with the unknown on both sides, like 5x + 2 = 3x + 10, collect x terms: 5x – 3x = 10 – 2, so 2x = 8, x = 4.

未知数在方程两边的情况，如 5x + 2 = 3x + 10，将含 x 的项移到一边：5x – 3x = 10 – 2，所以 2x = 8，x = 4。

Always check your solution by substituting it back into the original equation.

始终将解代入原方程进行检验。

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6. Sequences and the nth Term | 数列与第 n 项

A number sequence follows a rule. Linear sequences increase or decrease by the same amount each time. For the sequence 4, 7, 10, 13, …, the term-to-term rule is ‘add 3’. The nth term gives a formula: start with 3n, then adjust to match the first term. Here, when n=1, 3×1 = 3, but the first term is 4, so add 1: nth term = 3n + 1.

数列遵循某种规则。线性数列每次增加或减少相同的量。对于数列 4

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