📚 Year 9 Cambridge Mathematics: Core Knowledge Checklist | Year 9 剑桥数学：核心知识点梳理
Mastering the Year 9 Cambridge Mathematics syllabus is essential for building the strong conceptual understanding needed for IGCSE success. This checklist brings together the most important topics you will encounter – from number and algebra to geometry and statistics – so you can review, practise and approach your assessments with confidence.
掌握 Year 9 剑桥数学课程内容是顺利衔接 IGCSE 的关键基础。本文梳理了数与代数、几何、统计概率等核心知识点，帮助你有条理地回顾考点、查漏补缺，以扎实的基本功迎接校内评测。
1. Number and Operations | 数与运算
Confidently perform the four operations with integers, fractions, decimals and directed numbers, following the correct order of operations (BIDMAS).
熟练进行整数、分数、小数及正负数的四则运算，并严格遵循 BIDMAS 运算顺序。
Convert seamlessly between fractions, decimals and percentages; solve problems involving percentage increase, decrease, reverse percentages and simple interest.
灵活转换分数、小数和百分数；能解决包含百分比增减、逆向百分比及单利的问题。
es, and express large or small numbers in standard form (e.g., 4.5 × 10³ or 6.02 × 10⁻²⁴).
掌握幂与根的运算，包括正整数指数和负指数；能将数字表示为标准形式，例如 4.5 × 10³ 或 6.02 × 10⁻²⁴。
Use ratio and proportion in real-life contexts; divide quantities into a given ratio and solve problems using the unitary method.
运用比与比例解决实际问题，如按给定比例分配总量，以及使用归一法求解。
2. Algebra: Expressions and Equations | 代数：表达式与方程
Simplify algebraic expressions by collecting like terms, and expand brackets such as 3(x + 2) or (x + 4)(x – 5).
通过合并同类项化简代数式，并展开括号，如 3(x + 2) 或 (x + 4)(x – 5)。
expressions by taking out common factors and using the difference of two squares, e.g., x² – 16 = (x + 4)(x – 4).
提取公因式以及利用平方差公式进行因式分解，例如 x² – 16 = (x + 4)(x – 4)。
Solve linear equations with unknowns on one or both sides, and represent simple linear inequalities on a number line.
解未知数在一边或两边的线性方程，并能用数轴表示简单的线性不等式解集。
arrange formulae to change the subject, for example make h the subject of A = ½(b₁ + b₂)h.
对公式进行主项变换，如从 A = ½(b₁ + b₂)h 中表示出 h。
3. Sequences and Patterns | 数列与规律
Recognise and continue number sequences using term-to-term rules, and identify whether a sequence is arithmetic, geometric or based on a special pattern (e.g., square numbers).
根据递推规律辨识并续写数列，能判断数列属于等差数列、等比数列还是基于平方数等特殊模式的数列。
Find the nth term of a linear sequence in the form an + b, for example: 5, 8, 11, 14, … has nth term 3n + 2.
求出线性数列的第 n 项公式，形如 an + b，如数列 5, 8, 11, 14, … 的通项为 3n + 2。
Tₙ = 3n + 2
Use the nth term to determine whether a given number belongs to the sequence or to find the position of a term.
利用第 n 项公式判断某个数是否在数列中，或求某项的位置序号。
4. Linear Graphs and Functions | 线性图像与函数
Plot and interpret straight-line graphs on the coordinate plane, and understand the concept of gradient and y-intercept.
在坐标平面上绘制并解读直线图像，理解斜率（梯度）和 y 轴截距的概念。
+ c; link the gradient m to parallel lines and identify lines of the form y = c and x = c.
以 y = mx + c 的形式写出直线方程；能将斜率 m 用于平行线的判断，并识别形如 y = c 和 x = c 的直线。
y = 2x – 3
Use a graph to solve simultaneous linear equations by finding the point of intersection.
通过图像交点求解联立线性方程组。
5. Geometry: Angles and Polygons | 几何：角度与多边形
Apply angle facts on a straight line (sum to 180°), at a point (sum to 360°), vertically opposite angles, and the angle properties of parallel lines (alternate, corresponding and co-interior angles).
熟练运用角的基本性质：平角 180°，周角 360°，对顶角相等，以及平行线下的内错角、同位角、同旁内角关系。
Calculate interior and exterior angles of regular and irregular polygons; the sum of exterior angles of any convex polygon is always 360°.
计算正多边形与不规则多边形的内角和外角；任意凸多边形的外角和恒为 360°。
Sum of interior angles = (n – 2) × 180°
Know the names and properties of triangles (scalene, isosceles, equilateral) and quadrilaterals (trapezium, parallelogram, rhombus, kite).
掌握各类三角形（不等边、等腰、等边）和四边形（梯形、平行四边形、菱形、筝形）的名称与性质。
6. Pythagoras' Theorem | 勾股定理
State and apply Pythagoras' theorem in right-angled triangles: a² + b² = c², where c is the hypotenuse.
陈述并运用勾股定理：在直角三角形中，a² + b² = c²，其中 c 为斜边。
a² + b² = c²
Calculate the length of any side of a right-angled triangle, and solve problems involving perpendicular lines in 2D shapes and real-life contexts.
计算直角三角形任意边长，并能解决二维图形中涉及垂直距离的实际问题。
Determine whether a triangle is right-angled by checking if the three sides satisfy the Pythagorean relationship (converse of Pythagoras).
通过验算三边是否满足勾股定理的逆命题，判断一个三角形是否为直角三角形。
7. Perimeter, Area and Volume | 周长、面积与体积
Calculate the perimeter and area of common shapes, including compound shapes – triangles, parallelograms, trapeziums, and circles (A = πr², C = 2πr or πd).
计算常见图形与组合图形的周长和面积，包括三角形、平行四边形、梯形和圆（A = πr², C = 2πr 或 πd）。
ncluding cuboids and cylinders) using the formula volume = area of cross-section × length.
利用体积 = 截面积 × 长度的公式，求棱柱（包括长方体和圆柱）的体积和表面积。
Convert between metric units of area (e.g., m² to cm²) and volume (cm³ to litres), and use volume in capacity problems.
进行面积单位换算（如 m² 与 cm²）和体积/容积单位换算（如 cm³ 与升），解决容量相关问题。
8. Transformations | 变换
Recognise and describe the four types of single transformation: reflection (in a mirror line), rotation (centre, angle and direction), translation (by a column vector), and enlargement (with a positive scale factor and centre).
识别并描述四种基本几何变换：反射（对称轴）、旋转（旋转中心、角度和方向）、平移（列向量）和放大（正比例因子与放大中心）。
Draw the image of a shape after a transformation on a coordinate grid and fully describe a transformation that maps a object to its image.
在坐标网格上绘制变换后的图形，并能完整描述一个将原图映射到像的变换。
Understand the effect of enlargements on side lengths, angles, perimeter and area; when a shape is enlarged by scale factor k, the area is multiplied by k².
理解放大变换对边长、角度、周长和面积的影响：当图形按比例因子 k 放大时，面积变为原来的 k² 倍。
9. Statistics and Data Handling | 统计与数据处理
Collect, organise and interpret data using frequency tables, bar charts, pie charts and stem-and-leaf diagrams.
使用频数表、条形图、饼图和茎叶图收集、整理和解读数据。
Calculate and compare measures of central tendency: mean, median and mode, and understand the range as a measure of spread.
计算并比较集中趋势量数：平均数、中位数和众数，并理解极差作为离散程度的衡量。
Draw and interpret scatter graphs; describe correlation (positive, negative or none) and use a line of best fit to make predictions.
绘制并解读散点图；描述相关关系（正相关、负相关或无相关），并利用最佳拟合线进行预测。
10. Probability | 概率
Place events on a probability scale from 0 (impossible) to 1 (certain); express probabilities as fractions, decimals or percentages.
将事件按概率尺度从 0（不可能）到 1（必然）排列；用分数、小数或百分数表示概率。
Calculate theoretical probabilities for equally likely outcomes, and use sample space diagrams for combined events (e.g., spinning two spinners or rolling two dice).
计算等可能结果的理论概率，并利用样本空间图处理组合事件（如同时转动两个转盘或掷两枚骰子）。
Distinguish between experimental and theoretical probability; understand that increasing the number of trials brings the relative frequency closer to the theoretical value.
区分实验概率与理论概率；理解随着试验次数增加，相对频率会趋于理论值。
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