📚 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
ite, 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 – t 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。
vert fluently between fractions, decimals and percentages. For example, 3/8 = 0.375 = 37.5% 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
iables. 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 – 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 – 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 – 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。
ides: 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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