📚 Year 8 Cambridge Mathematics: Summer Preview and Bridging Course | 剑桥八年级数学：暑期预习与衔接课程
Welcome to the Year 8 Cambridge Mathematics Summer Preview and Bridging Course. This resource is designed to help you consolidate the key concepts from Year 7 and get a head start on the exciting topics awaiting you in Year 8. By working through these sections, you will build confidence in core areas such as algebra, geometry, statistics, and problem-solving, ensuring a smooth transition and a strong foundation for the IGCSE journey ahead.
欢迎参加剑桥八年级数学暑期预习与衔接课程。本资源旨在帮助你巩固七年级的关键概念，并为八年级即将学习的精彩内容提前做好准备。通过逐一学习这些章节，你将在代数、几何、统计和问题解决等核心领域建立信心，确保平稳过渡并为未来的IGCSE学习奠定坚实基础。
1. Review of Integers and Decimals | 整数与小数的复习
g that subtracting a negative is the same as adding a positive. For example, 5 - (-3) = 5 + 3 = 8. Multiplication and division with negatives follow the rule: same signs give a positive result, different signs give a negative result.
整数是正整数、负整数和零。你应该熟练掌握负数的加减运算，记住减去一个负数等于加上它的相反数。例如，5 - (-3) = 5 + 3 = 8。负数的乘除法遵循规则：同号得正，异号得负。
Decimals extend place value to tenths, hundredths, thousandths and beyond. In Year 8, you will work with decimals in measurements, money and calculations. Practice multiplying and dividing decimals by 10, 100 and 1000, which shifts the decimal point. Also, rounding decimals to a given number of decimal places is a vital skill.
小数将位值扩展到十分位、百分位、千分位等。在八年级，你会用到小数进行测量、货币和计算。练习将小数乘以和除以10、100和1000，这涉及小数点的移位。此外，将小数四舍五入到指定的小数位数是一项重要技能。
2. Fractions, Percentages and Ratios | 分数、百分数和比
Fractions represent parts of a whole. You will review equivalent fractions, simplifying fractions to their lowest terms, and converting between improper fractions and mixed numbers. For instance, 11/4 as a mixed number is 2 3/4.
分数表示整体的一部分。你将复习等值分数、将分数化为最简形式，以及假分数与带分数之间的转换。例如，11/4 化为带分数是 2 3/4。
onvert between fractions, decimals and percentages is crucial. For example, 3/5 = 0.6 = 60% calculate a percentage of a quantity and solve percentage increase and decrease problems.
百分数是分母为100的分数。能够在分数、小数和百分数之间进行转换至关重要。例如，3/5 = 0.6 = 60%。你还将学习如何计算一个数量的百分之几，并解决百分比增减问题。
Ratios compare quantities. Simplify ratios by dividing both sides by their highest common factor. For example, 8:12 simplifies to 2:3. You will also divide quantities in a given ratio, such as sharing £50 in the ratio 2:3.
比用来比较数量。通过将两边同时除以它们的最大公约数来化简比。例如，8:12 化简为 2:3。你还要学会按给定比例分配数量，比如按 2:3 分享 50 英镑。
3. Introduction to Algebra: Expressions and Equations | 代数入门：表达式与方程
to stand for unknown numbers. You can form expressions like 3n + 2 from word descriptions: "multiply a number by 3 and add 2" ng expressions means collecting like terms, e.g., 2a + 3a = 5a, and 4x - x + 2y = 3x + 2y.
代数用字母（变量）代表未知数。你可以根据文字描述写出表达式，如 3n + 2 表示“一个数乘3再加2”。化简表达式就是合并同类项，比如 2a + 3a = 5a，以及 4x - x + 2y = 3x + 2y。
one-step equations: x + 5 = 12 → x = 7. Then progress to two-step equations, for instance:
方程表示两个表达式相等。解方程就是找出变量的值。先从一步方程开始：x + 5 = 12 → x = 7。然后进阶到两步方程，例如：
2x - 3 = 9 → 2x = 12 → x = 6
Always check your solution by substituting it back into the original equation.
始终把解代回原方程检验。
4. Coordinates and Linear Graphs | 坐标与线性图像
t (-3, 4) is in the second quadrant. You will learn to generate coordinates from a linear equation like y = 2x + 1 by choosing x-values and calculating y-values, then plotting and connecting the points to form a straight line.
坐标写作 (x, y) 的形式。你在四个象限的直角坐标网格上描点。理解负坐标很重要：点 (-3, 4) 在第二象限。你将学习如何从线性方程如 y = 2x + 1 生成坐标，通过选取 x 值并计算对应的 y 值，然后描点并连成一条直线。
he gradient is 2 and it intercepts the y-axis at (0, 1). This foundational understanding prepares you for deeper study of linear functions.
直线图 y = mx + c 有斜率（坡度）m 和 y 轴截距 c（即与 y 轴的交点）。对于 y = 2x + 1，斜率为 2，与 y 轴交于点 (0, 1)。这一基础理解为你今后深入学习线性函数做好准备。
5. Angles and Properties of Shapes | 角度与图形性质
Angle rules are essential in geometry. On a straight line, angles sum to 180°. Around a point, angles sum to 360°. Vertically opposite angles are equal. For example, if two lines intersect, the angles opposite each other are the same.
角度规则在几何中必不可少。在一直线上，角度之和为180°。绕着一点，角度之和为360°。对顶角相等。例如，两条直线相交，相对的两个角大小相等。
Triangles have interior angles summing to 180°. You can find a missing angle by subtracting the known angles from 180°. Quadrilaterals sum to 360°. You will also explore properties of polygons, such as the sum of interior angles of a pentagon being 540°, and learn to identify line and rotational symmetry.
三角形内角和为180°。你可以用180°减去已知角的和来求未知角。四边形内角和为360°。你还会探索多边形的性质，例如五边形内角和为540°，并学习识别线对称和旋转对称。
6. Perimeter, Area and Volume | 周长、面积和体积
× width, triangle area = ½ × base × height, parallelogram area = base × perpendicular height, trapezium area = ½ × (sum of parallel sides) × height. Always use the correct units.
周长是图形一周的长度。对于矩形，周长 = 2(长 + 宽)。面积衡量二维图形内部的空间：矩形面积 = 长 × 宽，三角形面积 = ½ × 底 × 高，平行四边形面积 = 底 × 垂直高，梯形面积 = ½ × (上下底之和) × 高。始终使用正确的单位。
, a box of 2 cm by 3 cm by 4 cm has volume 24 cm³. It is useful to visualise nets of 3D shapes to understand their surface area as well.
体积衡量三维图形内部的空间。立方体和长方体的体积 = 长 ×
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