📚 Year 7 Cambridge Mathematics: Core Topics Review | Year 7 剑桥数学：核心知识点梳理
This article provides a structured overview of the essential topics covered in Year 7 Cambridge Lower Secondary Mathematics. From number operations to geometry and data handling, each section summarises key concepts to support revision and consolidation. The paired Chinese and English explanations help bilingual learners master the material with confidence.
本文系统梳理了 Year 7 剑桥初中数学的核心知识点，涵盖从数的运算到几何与数据处理的关键内容。每个部分都以中英对照的形式概括重要概念，帮助双语学习者巩固基础，自信掌握数学内容。
1. Number and Place Value | 数与位值
Understand place value for integers up to millions. For example, in 3 456 789, the digit 4 represents four hundred thousand (400 000). Read and write large numbers using both digits and words.
理解数百万以内整数的位值。例如，3 456 789 中，数字 4 代表四十万（400 000）。学会用数字和文字两种方式读写大数。
Round numbers to the nearest 10, 100, 1000 or a given decimal place. Knowing when to round up or down is essential for estimation.
把数四舍五入到最接近的十、百、千或指定的小数位。判断向上舍入还是向下舍入对于估算很重要。
ymbols <, > and =. Place numbers on a number line to visualise their relative sizes.
运用符号 <、> 和 = 比较整数与小数的大小，并排序。在数轴上标出数字，以便直观理解它们的相对大小。
2. Fractions, Decimals and Percentages | 分数、小数和百分数
Recognise equivalent fractions, decimals and percentages: ½ = 0.5 = 50%. Convert between these three forms fluently.
认识等值的分数、小数和百分数：½ = 0.5 = 50%。在三者之间熟练地进行转换。
Add, subtract, multiply and divide fractions with different denominators. Use common denominators or keep-change-flip for division.
对异分母分数进行加、减、乘、除。使用通分，或在做除法时运用“倒数相乘”的方法。
Calculate percentages of quantities, e.g., 15% of 200 = 30. Solve problems involving percentage increase and decrease.
计算一个数量的百分之几，如 15% of 200 = 30。解决涉及百分比增减的实际问题。
Compare and order fractions, decimals and percentages by converting them to the same form. Understand that ¾ is greater than 0.7.
通过转化为相同形式，比较分数、小数和百分数并排序。理解 ¾ 大于 0.7。
3. Integers and Negative Numbers | 整数与负数
rs on a number line. Adding a negative is equivalent to subtraction: 5 + (−3) = 5 − 3 = 2.
在数轴上处理负数。加上一个负数等同于减法：5 + (−3) = 5 − 3 = 2。
e number results in addition: 7 − (−2) = 7 + 2 = 9. Recognise the double-negative pattern.
减去一个负数会变成加法：7 − (−2) = 7 + 2 = 9。认识“负负得正”的规律。
Understand absolute value as the distance from zero. |−8| = 8 and |5| = 5. Use it in contexts like temperature or elevation.
理解绝对值是数到零的距离。|−8| = 8，|5| = 5。在温度、海拔等情境中运用绝对值。
de with negative integers: negative × negative = positive, positive × negative = negative.
进行负整数的乘除运算：负数 × 负数 = 正数，正数 × 负数 = 负数。
4. Algebraic Expressions and Equations | 代数表达式与方程
Use letters to represent unknown values. An expression like 3a + 2b cannot be solved but can be simplified when values are known.
用字母表示未知数。像 3a + 2b 这样的表达式无法解出，但在已知数值时可以进行化简。
Simplify expressions by collecting like terms. For example, 5x + 3y − 2x + y = 3x + 4y.
通过合并同类项化简表达式。例如，5x + 3y − 2x + y = 3x + 4y。
uations such as x + 7 = 12 or 4y = 20 using inverse operations. Present solutions clearly.
运用逆运算解一元一次方程，例如 x + 7 = 12 或 4y = 20。清晰地呈现解的过程。
le formulas from patterns or real-life situations, e.g., the perimeter of a square P = 4s.
根据规律或实际情景写出简单公式，例如正方形的周长公式 P = 4s。
5. Sequences and Functions | 数列与函数
Recognise arithmetic sequences and describe term-to-term rules. For 2, 5, 8, 11, …, the rule is “add 3 each time”.
识别等差数列并描述相邻项之间的变化规律。数列 2, 5, 8, 11 … 的规律是“每次加 3”。
Find the n-th term of simple linear sequences. The n-th term for 5, 8, 11, 14 is 3n + 2.
求简单线性数列的第 n 项。数列 5, 8, 11, 14 的第 n 项为 3n + 2。
Use function machines with inputs and outputs. A rule “×3 then −4” can be expressed as y = 3x − 4.
使用带有输入和输出的函数机器。规则“×3 然后 −4”可表达为 y = 3x − 4。
Distinguish between position-to-term rules and term-to-term rules. Practise generating terms using both approaches.
区分“位置到项”规则与“项到项”规则。练习用这两种方法生成数列的项。
6. Geometry: Angles and Shapes | 几何：角与图形
Identify and name angles: acute (less than 90°), right (90°), obtuse (between 90° and 180°) and reflex (greater than 180°).
识别并命名角：锐角（小于 90°）、直角（90°）、钝角（90° 至 180° 之间）和优角（大于 180°）。
Use angle facts: angles on a straight line sum to 180°, angles around a point sum to 360°, vertically opposite angles are equal.
运用角度基本性质：直线上的角之和为 180°，绕一点的角之和为 360°，对顶角相等。
square, rectangle, parallelogram, rhombus, trapezium). Sum of angles in a triangle = 180°.
了解三角形的性质（等边三角形、等腰三角形、不等边三角形）和四边形的性质（正方形、矩形、平行四边形、菱形、梯形）。三角形内角和为 180°。
Calculate unknown angles by setting up simple equations, e.g., in an isosceles triangle, base angles are equal.
通过建立简单方程求未知角，例如，在等腰三角形中底角相等。
7. Measures: Perimeter, Area and Volume | 测量：周长、面积与体积
meter of rectilinear shapes by adding side lengths. For a rectangle, perimeter = 2(l + w).
通过边长相加计算直线围成图形的周长。对于矩形，周长 = 2(长 + 宽)。
ht) and parallelograms (A = base × perpendicular height). Use appropriate units (cm², m²).
求矩形面积（A = 长 × 宽）、三角形面积（A = ½ × 底 × 高）和平行四边形面积（A = 底 × 垂直高）。使用正确的单位（cm²、m²）。
d cuboids using V = l × w × h. Recognise that volume is measured in cubic units (cm³, m³).
用公式 V = 长 × 宽 × 高 计算正方体和长方体的体积。知道体积以立方单位（cm³、m³）计量。
cm, m, km), mass (g, kg) and capacity (ml, L). Use conversion factors like 1 km = 1000 m.
在公制长度单位（mm、cm、m、km）、质量单位（g、kg）和容量单位（ml、L）之间进行换算。运用换算系数，如 1 km = 1000 m。
8. Ratio and Proportion | 比率与比例
Understand ratio as a way to compare parts of a whole. The ratio 2 : 3 means for every 2 of the first, there are 3 of the second.
理解比率是对整体各部分进行比较的方式。比例 2 : 3 表示第一部分有 2 份时，第二部分有 3 份。
Simplify ratios to their simplest form by dividing by common factors, e.g., 10 : 15 simplifies to 2 : 3.
通过除以公因数，将比例简化为最简形式。例如 10 : 15 简化为 2 : 3。
Divide quantities in a given ratio. To divide £50 in the ratio 2 : 3, first find the value of one share (total parts = 5, one share = £10).
按照给定比例分配数量。将 £50 按 2 : 3 分配，先求出一份的金额（总份数 = 5，一份为 £10）。
tion: if one quantity doubles, the other doubles. Constant of proportionality k in y = kx.
认识正比例关系：一个量翻倍，另一个量也翻倍。在 y = kx 中，k 为比例常数。
Solve simple recipe and scale problems, e.g., adapting a recipe for 4 people to serve 10 people.
解决简单的食谱配方和缩放问题，例如将 4 人份的食谱调整为 10 人份。
9. Statistics | 统计学
Collect and organize data using tally charts and frequency tables. Group data into equal class intervals where appropriate.
使用划记表和频数表收集与整理数据。在合适时，将数据分组到相等的组距中。
Represent data using bar charts, line graphs and simple pie charts. Choose the best representation for the data type.
用柱状图、折线图和简单的饼图展示数据。根据数据类型选择最合适的图示方式。
Calculate the mean (average) by summing all values and dividing by the number of values. Find the median, mode and range of a small data set.
通过求和并除以数据个数计算平均数（均值）。求出一组小数据的众数、中位数和极差。
Interpret charts and draw conclusions. Describe trends, compare frequencies and identify outliers if present.
解读统计图并得出结论。描述趋势，比较频数，如存在异常值则识别出来。
10. Probability | 概率
Describe the likelihood of events using words such as impossible, unlikely, even chance, likely and certain.
用词汇描述事件发生的可能性：不可能、不太可能、等可能、很可能和一定发生。
Assign probabilities on a scale from 0 (impossible) to 1 (certain). An event with an even chance has probability ½ or 0.5.
在 0（不可能）到 1（一定）的尺度上标记概率。等可能事件的概率为 ½ 或 0.5。
ty as: P(event) = number of favourable outcomes / total number of equally likely outcomes.
计算理论概率：P(事件) = 有利结果的数量 / 所有等可能结果的总数。
Use probability to predict outcomes in simple experiments, such as rolling a fair dice or spinning a spinner.
运用概率预测简单实验的结果，例如掷均匀骰子或转动转盘。
11. Problem Solving and Reasoning | 问题解决与推理
Break down multi-step word problems by identifying key information, planning a strategy and carrying out calculations in logical order.
将多步应用题分解为关键信息，规划解题策略，并按照逻辑顺序进行计算。
Apply number, algebra, geometry and data skills in unfamiliar contexts. Check answers for reasonableness.
在不熟悉的情境中运用数、代数、几何和统计技能。检查答案的合理性。
Use mathematical reasoning to explain why a statement is true or false, such as “the sum of two odd numbers is always even”.
运用数学推理来解释一个命题的真伪，例如“两个奇数的和总是偶数”。
skills and mental strategies. For example, estimate 23.8 × 4.1 by rounding to 20 × 4 = 80.
培养估算能力和心算策略。例如，将 23.8 × 4.1 四舍五入为 20 × 4 = 80 进行估算。
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