Core Knowledge Checklist for Year 10 Edexcel Mathematics | Year 10 Edexcel 数学核心知识点梳理

📚 Core Knowledge Checklist for Year 10 Edexcel Mathematics | Year 10 Edexcel 数学核心知识点梳理

Year 10 is a pivotal stage in the Edexcel GCSE Mathematics course, where students consolidate foundational topics and begin more advanced problem-solving. This checklist outlines essential concepts across the key strands—Number, Algebra, Ratio, Geometry, Probability, and Statistics—ensuring students are well-prepared for the challenges of Year 11 and the final examinations.

Year 10 是 Edexcel GCSE 数学课程的关键阶段，学生在此巩固基础主题，并开始更高级的问题解决。这份清单概述了关键领域（数、代数、比例、几何、概率和统计）的基本概念，确保学生为 Year 11 及最终考试的挑战做好充分准备。

1. Number – Fractions, Decimals, Percentages | 分数、小数和百分比

Mastery of fractions, decimals, and percentages is fundamental. You must be able to add, subtract, multiply, and divide fractions, including mixed numbers. Converting between fractions, decimals, and percentages fluently is essential for many exam questions. A key skill is calculating percentage increase or decrease using a multiplier. For example, to increase a value by 15%, multiply by 1.15. Reverse percentages allow you to find the original amount after a percentage change: divide by the multiplier (e.g., after a 20% increase, divide by 1.2).

掌握分数、小数和百分比是基础。你必须能够进行分数的加减乘除，包括带分数。在分数、小数和百分比之间灵活转换对许多考题至关重要。一项关键技能是使用乘数计算百分比增减。例如，要将一个值增加 15%，乘以 1.15。逆向百分比可用于在百分比变化后找到原始值：除以乘数（例如，增加 20% 后，除以 1.2）。

You should also be able to convert recurring decimals into fractions using an algebraic approach. For a recurring decimal like 0.373737…, set x = 0.373737…, multiply by 100 to get 100x = 37.3737…, subtract to obtain 99x = 37, so x = 37/99.

你还应能使用代数方法将循环小数转换为分数。例如，对于 0.373737… 这样的循环小数，设 x = 0.373737…，乘以 100 得 100x = 37.3737…，相减得到 99x = 37，因此 x = 37/99。

2. Algebraic Expressions and Equations | 代数表达式与方程

Algebraic fluency involves simplifying expressions by collecting like terms, expanding brackets (including double brackets and the grid method), and factorising by taking out common factors or using the difference of two squares: a² – b² = (a + b)(a – b). Solving linear equations with unknowns on both sides, including those with brackets, is a core Year 10 skill. You should also be able to form and solve equations from word problems and geometric contexts.

代数流畅性包括通过合并同类项来简化表达式、展开括号（包括双括号和网格法），以及通过提取公因数或平方差公式进行因式分解：a² – b² = (a + b)(a – b)。解含括号、未知数在等号两边的线性方程是 Year 10 的核心技能。你还应能根据文字问题和几何情境列方程并求解。

Factorising quadratic expressions of the form x² + bx + c is introduced in Year 10. You need to find two numbers that multiply to c and add to b. This skill underpins solving quadratic equations later.

Year 10 还会介绍 x² + bx + c 形式的二次表达式的因式分解。你需要找到两个数，积为 c，和为 b。这项技能是后期解二次方程的基础。

(x + p)(x + q) = x² + (p + q)x + pq

3. Linear Graphs | 线性图

Linear graphs are straight lines plotted on the coordinate plane. The equation of a line is commonly written as y = mx + c, where m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis). You must be able to calculate the gradient from two points (change in y ÷ change in x) and interpret the meaning in context. Identifying parallel lines (same gradient) and perpendicular lines (product of gradients = −1) is also essential.

线性图是在坐标平面上绘制的直线。直线方程通常写作 y = mx + c，其中 m 是斜率（倾斜度），c 是 y 轴截距（直线与 y 轴交点的纵坐标）。你必须能够根据两点计算斜率（y 的变化量 ÷ x 的变化量），并理解其实际意义。识别平行线（斜率相同）和垂直线（斜率的乘积为 −1）也必不可少。

m = (y₂ – y₁) / (x₂ – x₁)

4. Ratio and Proportion | 比例与比例关系

Ratio compares the sizes of two or more quantities. You need to simplify ratios, share a quantity into a given ratio, and solve problems involving ratios and fractions. Direct proportion means two quantities increase or decrease at the same rate, modelled by y = kx. Inverse proportion means as one quantity increases, the other decreases, modelled by y = k/x. Understanding graphical representations of proportional relationships is also tested.

比例比较两个或多个量的大小。你需要化简比例、按给定比例分配一个量，并解决涉及比例和分数的问题。正比例意味着两个量以相同的速率增加或减少，用 y = kx 表示。反比例意味着一个量增加时另一个量减少，用 y = k/x 表示。理解比例关系的图形表示也是考查内容。

y ∝ x and y ∝ 1/x

5. Angles and Polygons | 角与多边形

You should know basic angle facts: angles on a straight line sum to 180°, angles around a point sum to 360°, vertically opposite angles are equal. When parallel lines are cut by a transversal, alternate angles are equal, corresponding angles are equal, and co-interior (allied) angles sum to 180°. For polygons, the sum of interior angles of an n-sided polygon is (n – 2) × 180°. The sum of exterior angles of any convex polygon is 360°. Regular polygons have equal sides and angles.

你应知道基本角度知识：直线上的角之和为 180°，绕一点的角之和为 360°，对顶角相等。当平行线被一条截线切割时，内错角相等，同位角相等，同旁内角之和为 180°。对于多边形，n 边形的内角和为 (n – 2) × 180°。任意凸多边形的外角和为 360°。正多边形的边和角都相等。

Sum of interior angles = (n – 2) × 180°

6. Perimeter, Area and Volume | 周长、面积与体积

You must be able to calculate the perimeter of 2D shapes, including the circumference of a circle: C = πd or C = 2πr. Area formulas required: rectangle (length × width), triangle (½ × base × height), parallelogram (base × vertical height), trapezium (½(a + b)h), circle (πr²). For 3D shapes, volume of a prism = area of cross-section × length. Cylinders are prisms with circular cross-section: volume = πr²h. Surface area involves summing the areas of all faces.

你必须能够计算二维图形的周长，包括圆的周长：C = πd 或 C = 2πr。需要掌握的面积公式：矩形（长

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