Year 8 WJEC Maths Summer Prep & Bridge Course | Year 8 WJEC 数学：暑期预习与衔接课程

📚 Year 8 WJEC Maths Summer Prep & Bridge Course | Year 8 WJEC 数学：暑期预习与衔接课程

Welcome to the Year 8 WJEC Maths summer preparation and bridging course. This resource is designed to help you confidently step into Year 8 by revisiting essential Year 7 topics and introducing the key concepts you will meet in your new mathematics lessons. You will strengthen your number skills, build a solid algebraic foundation, develop geometry and measurement understanding, and learn to reason logically with data and probability. Each section is presented in a clear, bilingual format so you can grasp both the English mathematical language and the Chinese explanation.

欢迎来到 Year 8 WJEC 数学暑期预习与衔接课程。本资源旨在通过复习关键的七年级知识，并介绍你将在新数学课上遇到的核心概念，帮助你自信地迈入八年级。你将巩固数字技能，建立扎实的代数基础，加深对几何和测量的理解，并学习如何利用数据和概率进行逻辑推理。每个部分都以清晰的双语形式呈现，便于你同时掌握英文数学术语和中文解释。

1. Place Value and Number Operations | 位值与数字运算

Understanding place value up to millions and down to three decimal places is crucial for all further calculation work. You should be able to read, write, order and compare whole numbers and decimals, and round them to any given power of 10 or decimal place. Secure addition, subtraction, multiplication and division methods – including column methods and mental strategies – are expected. For multiplication, you must recall times tables up to 12 × 12 and use them to multiply two- and three-digit numbers.

理解从百万位到三位小数的位值对所有后续计算都至关重要。你需要能够读写、排序和比较整数与小数，并按照任意指定的十的幂次或小数位进行四舍五入。牢固掌握加减乘除的方法——包括竖式运算和心算策略——是先决条件。对于乘法，你必须熟记 12 × 12 以内的乘法表，并能运用它们计算两位数与三位数的乘法。

When working with negative numbers, use the number line to support addition and subtraction. Remember that subtracting a negative is equivalent to adding the positive. Order of operations (BIDMAS/BODMAS) must be applied consistently: Brackets first, then Indices, Division and Multiplication (left to right), and finally Addition and Subtraction (left to right).

处理负数时，利用数轴辅助加减运算。请记住，减去一个负数相当于加上其相反数。运算顺序（BIDMAS/BODMAS）必须严格执行：先算括号，再算指数，然后从左至右计算除法和乘法，最后从左至右计算加法和减法。

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

You must be able to simplify fractions, find equivalent fractions and convert between mixed numbers and improper fractions. Adding and subtracting fractions requires a common denominator; multiplication is done by multiplying numerators and denominators separately. To divide by a fraction, multiply by its reciprocal. Always express answers in their simplest form where appropriate.

你必须能够化简分数、寻找等价分数，并在带分数与假分数之间进行转换。分数加减需要先通分得到共同分母；分数乘法只需将分子相乘、分母相乘。除以一个分数等于乘以它的倒数。在适当情况下，务必将答案化为最简形式。

Convert fluently between fractions, decimals and percentages. For example, 3/8 = 0.375 = 37.5%. You should also find a percentage of a quantity and increase or decrease an amount by a given percentage, including in the context of real-life problems like discounts or VAT.

要能在分数、小数和百分比之间熟练转换。例如，3/8 = 0.375 = 37.5%。你还需要会求一个量的百分比，以及按给定百分比增加或减少一个数值，包括在折扣或增值税等实际生活问题中应用。

3. Algebra: Expressions and Substitution | 代数：表达式与代入

Algebra uses letters to represent unknown numbers or variables. You should be able to write algebraic expressions from word problems, for example, “n more than 5” is written as 5 + n. Simplify expressions by collecting like terms: 3a + 2b – a + 5b = 2a + 7b. Use the rules of indices for multiplication and division of the same variable, e.g., x³ × x² = x⁵.

代数使用字母表示未知数或变量。你应该能够根据文字题写出代数表达式，例如，“比5大n”写作 5 + n。通过合并同类项来化简表达式：3a + 2b – a + 5b = 2a + 7b。运用指数法则处理相同变量的乘除，例如 x³ × x² = x⁵。

Substitution means replacing letters with given numbers. If you know a = 3, b = –2, c = 0.5, then 2a + bc becomes 2×3 + (–2)×0.5 = 6 – 1 = 5. Always use brackets when substituting negative or fractional values to avoid sign errors.

代入是指用给定的数值替换字母。如果已知 a = 3, b = –2, c = 0.5，那么 2a + bc 就变为 2×3 + (–2)×0.5 = 6 – 1 = 5。代入负数或分数值时，始终使用括号以避免符号错误。

4. Solving Linear Equations | 解一元一次方程

An equation shows that two expressions are equal. To solve, you must keep the balance – whatever you do to one side you must do to the other. For simple equations like x + 7 = 12, subtract 7 from both sides: x = 5. For 3x = 18, divide both sides by 3: x = 6. For two-step equations, undo the addition/subtraction first, then the multiplication/division. Example: 2x – 5 = 9 → 2x = 14 → x = 7.

方程表示两个表达式相等。解方程时必须保持平衡——你对一边做什么操作，另一边也要同样操作。对于像 x + 7 = 12 这样的简单方程，两边同时减去7：x = 5。对于 3x = 18，两边除以3：x = 6。两步方程先处理加减后处理乘除。例如：2x – 5 = 9 → 2x = 14 → x = 7。

You will also meet equations with unknowns on both sides, e.g., 5x + 2 = 3x + 10. First, eliminate the smaller unknown term by subtracting 3x from both sides: 2x + 2 = 10, then solve. Always check your solution by substituting back into the original equation.

你还会遇到未知数出现在两边的方程，如 5x + 2 = 3x + 10。首先，通过两边减去较小的未知项 3x 来消去未知数：2x + 2 = 10，然后求解。始终将解代入原方程检验。

5. Angles and 2D Shapes | 角与二维图形

Learn the names and properties of triangles (scalene, isosceles, equilateral, right-angled) and quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium, kite). Know that angles on a straight line sum to 180°, angles around a point sum to 360°, and vertically opposite angles are equal. The interior angles of a triangle sum to 180°, and of a quadrilateral sum to 360°.

学习三角形的名称和性质（不等边三角形、等腰三角形、等边三角形、直角三角形）以及四边形的名称和性质（正方形、矩形、平行四边形、菱形、梯形、筝形）。要知道直线上的角之和为 180°，围绕一个点的角之和为 360°，对顶角相等。三角形内角和为 180°，四边形内角和为 360°。

Be able to calculate missing angles using these facts, and justify each step with a clear reason

Published by TutorHao | Year 8 Mathematics Revision Series | aleveler.com

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