📚 Year 8 CCEA Mathematics: Core Topics Revision | Year 8 CCEA 数学：核心知识点梳理
This comprehensive guide covers the essential knowledge areas of the Year 8 CCEA mathematics curriculum. Each section pairs clear English explanations with a Chinese translation, helping you master Numbers, Algebra, Geometry, Statistics and Probability step by step.
本全面指南涵盖 Year 8 CCEA 数学课程的核心知识领域。每个小节都将清晰的英文解释与中文翻译配对，帮助你逐步掌握数、代数、几何、统计和概率。
1. Number and Place Value | 数字和位值
Recognise the value of each digit in whole numbers up to 10 million and in decimal numbers with up to three decimal places (tenths, hundredths, thousandths).
能识别一千万以内整数以及最多三位小数（十分位、百分位、千分位）中每一位数字的值。
Round whole numbers to the nearest 10, 100, 1000 or to a given number of decimal places, and use this to check answers for reasonableness.
将整数四舍五入到最近的 10、100、1000 或指定的小数位数，并用此方法检查答案的合理性。
Compare and order positive and negative integers, decimals and fractions by considering place value or converting to a common form.
通过比较位值或转换成统一形式，对正整数、负整数、小数和分数进行大小比较与排序。
2. Fractions, Decimals and Percentages | 分数、小数和百分数
actors, and recognise equivalent fractions, decimals and percentages (e.g., 2/5 = 0.4 = 40%).
通过找出公因数将分数约分至最简形式，并能识别等值的分数、小数和百分数（如 2/5 = 0.4 = 40%）。
Perform additions and subtractions with fractions that have different denominators by finding a common denominator, and multiply or divide a fraction by an integer.
通过寻找公分母对异分母分数进行加减运算，并能将分数与整数相乘或相除。
Calculate a percentage of a quantity, and increase or decrease an amount by a percentage, using both mental methods and written calculations.
运用心算和笔算方法求一个数量的百分数，以及按一定百分数对某个量进行增减。
3. Ratios and Proportion | 比率和比例
orm using a colon (e.g., 6:10 = 3:5) and understand that the order of the numbers matters.
用冒号写出比率的最简形式（如 6:10 = 3:5）并理解数字的顺序很重要。
Relate ratios to fractions and percentages – for example, a ratio of 1:3 means one part is 1/4 of the total.
将比率与分数和百分数联系起来――例如，比率 1:3 表示一部分占总量的 1/4。
Solve simple proportion problems such as scaling up a recipe or working with currency conversions, using direct proportion and the unitary method.
运用正比例和归一法解决简单的比例问题，如按比例缩放食谱配方或进行货币换算。
4. Negative Numbers and Integers | 负数和整数
Understand negative numbers in real contexts such as temperature, elevation below sea level or bank balances, and order them on a number line.
理解负数在现实场景中的含义，如温度、海平面以下的海拔或银行余额，并能在数轴上排序。
Add and subtract integers including negative numbers: e.g., 3 – (-5) = 8, and recognise the rules for multiplying and dividing with negative numbers.
对包含负数的整数进行加减运算，如 3 – (-5) = 8，并认识负数乘除的符号规则。
Apply the order of operations (BIDMAS) when calculations involve negative integers, being especially careful with subtraction and directed numbers.
在涉及负整数的运算中运用运算顺序（BIDMAS），尤其小心减法和带符号数。
5. Algebraic Expressions and Equations | 代数表达式和方程
Use letters to represent unknown numbers or variables, and write simple algebraic expressions from word descriptions (e.g., 'five more than x' becomes x + 5).
用字母表示未知数或变量，并能根据文字描述写出简单的代数表达式（如 '比 x 大 5' 写作 x + 5）。
Simplify expressions by collecting like terms: 3a + 2b + 5a – b becomes 8a + b.
通过合并同类项化简表达式：3a + 2b + 5a – b 化简为 8a + b。
Substitute positive and negative integers into simple expressions and formulas, then use the results to evaluate real-life relationships.
将正整数和负整数代入简单的表达式和公式，再利用结果评价实际生活关系。
Solve one-step and two-step linear equations such as 2x – 3 = 11 by performing inverse operations.
通过逆运算解一步和两步线性方程，如 2x – 3 = 11。
6. Sequences and Patterns | 序列与模式
Recognise and continue linear number sequences, describing the term-to-term rule (e.g., add 4, subtract 3).
识别并延续线性数列，描述逐项规则（如加 4、减 3）。
Find the nth term of an arithmetic sequence and use it to generate terms – initially in words (e.g., 'double the position and add 1').
求出等差数列的第 n 项并用以生成各项――起初用文字表达（如 '将位置数加倍再加 1'）。
Explore patterns involving shapes and diagrams, linking them to number sequences and writing simple position-to-term rules.
探究涉及图形和图表的模式，将其与数字序列联系起来，并写出简单的位置-项规则。
7. Coordinates and Graphs | 坐标与图形
Read and plot coordinates in all four quadrants, understanding that the first number is the x-coordinate (horizontal) and the second is the y-coordinate (vertical).
能在四个象限中读取和绘制坐标，理解第一个数是 x 坐标（水平）而第二个数是 y 坐标（垂直）。
Construct a table of values for a simple linear relationship and plot the resulting points to draw a straight-line graph.
为一个简单的线性关系构建数值表，并描点绘制直线图形。
s parallel to the axes, such as x = -3 and y = 5, and understand their special properties.
识别并画出平行于坐标轴的直线，如 x = -3 和 y = 5，并理解其特殊性质。
8. Angles and Shapes | 角度与形状
Classify angles as acute, right, obtuse, straight and reflex, and estimate their sizes in degrees before measuring with a protractor.
将角分类为锐角、直角、钝角、平角和优角，并在用量角器测量前先估计其度数。
Apply angle rules: angles on a straight line sum to 180°, angles around a point sum to 360°, and vertically opposite angles are equal.
运用角度规则：平角之和为 180°，周角之和为 360°，对顶角相等。
Know that the sum of interior angles in a triangle is 180° and in a quadrilateral is 360°, and use this to find missing angles.
知道三角形内角和为 180°，四边形内角和为 360°，并用此求未知角度。
9. Perimeter, Area and Volume | 周长、面积和体积
Calculate the perimeter of rectangles, triangles and compound shapes made from rectangles, giving answers with correct units.
计算矩形、三角形和由矩形组成的复合图形的周长，用正确的单位给出答案。
e (½ × base × height) and parallelogram (base × perpendicular height), using mm², cm², m².
求矩形（长 × 宽）、三角形（½ × 底 × 高）和平行四边形（底 × 垂直高）的面积，使用 mm²、cm²、m²。
ength × width × height, understanding that volume is measured in cubic units mm³, cm³, m³.
用长 × 宽 × 高的公式计算立方体和长方体的体积，理解体积以立方单位 mm³、cm³、m³ 计量。
10. Transformations and Symmetry | 变换与对称
Perform reflections of shapes in a given mirror line on a coordinate grid, and describe a reflection by stating the line of symmetry.
在坐标网格上以给定对称轴进行图形的反射变换，并通过陈述对称轴来描述反射。
Translate a shape by a given vector or description (e.g., '3 right, 2 down') and recognise that the shape remains unchanged in size and orientation.
通过给定向量或描述（如 '右 3、下 2'）平移图形，并认识到图形的大小和方向保持不变。
Rotate a shape 90° or 180° about a centre, and identify the order of rotational symmetry in 2D figures.
围绕中心将图形旋转 90° 或 180°，并确定平面图形的旋转对称阶数。
11. Statistics and Data Handling | 统计与数据处理
Collect and organise discrete and continuous data using frequency tables, and choose appropriate charts to represent the data (bar charts, pictograms, line graphs).
使用频数表收集和整理离散数据与连续数据，并选择合适的图表呈现数据（条形图、象形图、线图）。
Calculate the mean, median, mode and range of a set of numbers, knowing that the mean is the sum divided by the count, and the median is the middle value when ordered.
计算一组数据的平均数（均值）、中位数、众数和极差，知道均值是总和除以个数，中位数是排序后的中间值。
Interpret pie charts and other statistical diagrams, using fractions or percentages to calculate actual values where necessary.
解读饼图及其他统计图，必要时使用分数或百分数计算实际值。
12. Introduction to Probability | 概率初步
Use a probability scale from 0 to 1, expressing the likelihood of events with words such as impossible, unlikely, even chance, likely and certain.
使用从 0 至 1 的概率尺度，用不可能、不太可能、等可能、很可能和确定等词语表示事件的可能性。
Calculate the probability of a single event as the number of favourable outcomes divided by the total number of possible outcomes, assuming all outcomes are equally likely.
在假设所有可能结果等可能的条件下，将有利结果数除以所有可能结果的总数来计算单一事件的概率。
List all the possible outcomes of a simple experiment using a sample space diagram, and explain why probabilities sum to 1 for exhaustive mutually exclusive events.
使用样本空间图列出简单实验的所有可能结果，并解释为什么互斥且穷举的事件的概率之和为 1。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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