📚 Year 9 CIE Mathematics Core Knowledge Points Checklist | Year 9 CIE 数学：核心知识点梳理
This guide provides a structured overview of the essential topics in the Year 9 CIE Mathematics curriculum. It is designed to help students consolidate their understanding, identify key concepts, and build a strong foundation for IGCSE. Each section pairs an English explanation with its Chinese translation, covering number, algebra, geometry, statistics, and probability in a clear, exam-focused manner.
本指南系统梳理了 Year 9 CIE 数学课程的核心知识点，旨在帮助学生巩固理解、明确重点概念，为 IGCSE 打下坚实基础。每个板块均以英文和中文对照讲解，涵盖数、代数、几何、统计与概率等内容，紧扣考试要点，条理清晰。
1. Number and Operations | 数与运算
Understand place value and the four operations with integers, including negative numbers. Perform calculations using the correct order of operations (BIDMAS/BODMAS: Brackets, Indices, Division/Multiplication, Addition/Subtraction).
理解位值以及整数的四则运算，包括负数的运算。按照正确的运算顺序（BIDMAS/BODMAS：括号、指数、乘除、加减）进行计算。
Identify and work with factors, multiples, prime numbers, and prime factor decomposition. Use the highest common factor (HCF) and lowest common multiple (LCM) to solve problems.
识别并运用因数、倍数、质数以及质因数分解。利用最大公因数（HCF）和最小公倍数（LCM）解决问题。
Round numbers to a given number of decimal places or significant figures, and estimate answers to check the reasonableness of results.
将数字四舍五入到指定的小数位数或有效数字，并估算结果以检验答案的合理性。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
Convert fluently between fractions, decimals, and percentages. Order a mix of these forms by converting them to the same representation.
熟练进行分数、小数和百分数之间的互化。通过转化成同一种表示形式，对混合形式的数进行排序。
Add, subtract, multiply, and divide fractions, including mixed numbers. Understand that 'of' in a fractional context means multiplication.
进行分数的加减乘除运算，包括带分数。理解分数语境中的“的”表示乘法。
Calculate a percentage of a quantity, express one quantity as a percentage of another, and solve percentage increase/decrease problems.
计算一个数量的百分之几，将一个数量表示为另一个数量的百分比，并解决百分数增减问题。
3. Ratio and Proportion | 比与比例
Use ratio notation to compare two or more quantities, simplify ratios, and divide a quantity into a given ratio. Recognise the link between ratios and fractions.
使用比的符号比较两个或多个量，化简比，并将一个量按给定比例分配。理解比与分数的联系。
nship y = kx. Identify when two quantities are in direct proportion from a table or graph.
使用归一法解决正比例问题，并理解关系式 y = kx。通过表格或图像判断两个量是否成正比例。
Apply ratio and proportion to real-life contexts such as recipes, scale drawings, and map scales (e.g., 1 : n).
将比和比例应用于实际情境，如食谱、比例图和地图比例尺（例如 1 : n）。
4. Algebraic Expressions and Formulae | 代数表达式与公式
g like terms, and use the distributive law to expand brackets, such as a(b + c) = ab + ac.
用字母表示变量并写出代数表达式。通过合并同类项化简表达式，并运用分配律展开括号，如 a(b + c) = ab + ac。
Substitute positive and negative numbers into formulae and evaluate the result. Rearrange simple formulae to change the subject.
将正数和负数代入公式并求值。对简单公式进行变形以更换主项。
luding the laws for multiplication and division of powers: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ.
处理代数中的指数，包括幂的乘法和除法法则：aᵐ × aⁿ = aᵐ⁺ⁿ，aᵐ ÷ aⁿ = aᵐ⁻ⁿ。
5. Equations and Inequalities | 方程与不等式
Solve linear equations with the unknown on one or both sides, using inverse operations to isolate the variable. Always check your answer by substituting back.
利用逆运算求解未知数在一边或两边的线性方程，将变量分离。始终通过代回原方程检验答案。
Construct and solve equations from word problems, translating real-life situations into algebraic language.
根据文字题构建并求解方程，将现实情境转化为代数语言。
Represent inequalities on a number line using open and closed circles. Solve simple linear inequalities and list integer solutions.
在数轴上用空心圆和实心圆表示不等式。求解简单的线性不等式，并列出整数解。
6. Sequences | 数列
Recognise and continue linear (arithmetic) sequences by finding the common difference. Generate terms of a sequence given the nth term or a term-to-term rule.
通过寻找公差识别并延续线性（等差）数列。给定第 n 项公式或项间递推规则，生成数列的项。
Find and use the nth term of an arithmetic sequence, usually in the form an + b. Use this to find any term or check whether a number belongs to the sequence.
找出并使用等差数列的第 n 项公式，通常形如 an + b。利用公式求任意项或判断某数是否属于该数列。
Explore non-linear sequences, such as square numbers and cube numbers, and describe their patterns in words.
探索非线性数列，如平方数和立方数，并用语言描述其规律。
7. Geometry: Angles and Shapes | 几何：角与形状
Know and use angle facts: angles on a straight line sum to 180°, angles around a point sum to 360°, vertically opposite angles are equal.
掌握并运用角度基本事实：直线上的角之和为 180°，绕一点一周的角之和为 360°，对顶角相等。
Identify and calculate angles in triangles (sum to 180°) and quadrilaterals (sum to 360°). Classify triangles by sides (scalene, isosceles, equilateral) and angles (acute, right, obtuse).
识别并计算三角形（内角和为 180°）和四边形（内角和为 360°）中的角。按边（不等边、等腰、等边）和角（锐角、直角、钝角）对三角形进行分类。
Understand properties of parallel lines: corresponding angles, alternate angles, and co-interior (allied) angles are used to find unknown angles.
理解平行线的性质：利用同位角、内错角和同旁内角求未知角。
8. Perimeter, Area and Volume | 周长、面积与体积
πd or C = 2πr. Calculate the area of rectangles, triangles, parallelograms, and trapezia.
计算直线图形的周长，以及使用公式 C = πd 或 C = 2πr 计算圆的周长。计算矩形、三角形、平行四边形和梯形的面积。
g A = πr². Solve problems involving composite shapes by splitting them into simpler parts.
使用公式 A = πr² 求圆的面积。将组合图形分割为简单图形来解决问题。
Calculate the surface area and volume of cubes, cuboids, and right prisms. Use appropriate units (e.g., cm³, m²) and convert between them.
计算立方体、长方体和直棱柱的表面积与体积。使用合适的单位（如 cm³、m²）并进行单位换算。
9. Statistics and Data Handling | 统计学与数据处理
Collect, organise, and present data using frequency tables, bar charts, pie charts, and line graphs. Choose the most suitable diagram for a given data type.
使用频数表、条形图、饼图和折线图收集、整理和展示数据。为给定数据类型选择最合适的图表。
Calculate the mean, median, mode, and range for a set of discrete data. Understand the advantages and disadvantages of each average.
计算一组离散数据的平均数、中位数、众数和极差。理解每种平均数的优缺点。
Interpret and construct scatter graphs to explore the relationship between two variables. Describe correlation as positive, negative, or none, and draw a line of best fit where appropriate.
解读并绘制散点图以探索两个变量之间的关系。将相关性描述为正相关、负相关或无相关，并在适当时画出最佳拟合线。
10. Probability | 概率
Use the probability scale from 0 to 1, expressing probabilities as fractions, decimals, or percentages. Understand that the probabilities of all possible outcomes sum to 1.
使用 0 到 1 的概率尺度，用分数、小数或百分数表示概率。理解所有可能结果的概率之和为 1。
using the formula P(event) = (number of favourable outcomes) / (total number of outcomes).
对于等可能结果，使用公式 P(事件) = （有利结果数）/（总结果数）计算理论概率。
Use sample space diagrams and two-way tables to list all outcomes for combined events. Estimate probability from relative frequency in experiments.
使用样本空间图和双向表列出组合事件的所有结果。通过实验中的相对频率估计概率。
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