📚 Year 9 CCEA Maths: Core Knowledge Checklist | Year 9 CCEA 数学：核心知识点梳理
This article is your complete guide to the key topics in Year 9 CCEA Mathematics. It brings together essential areas such as number, algebra, geometry, and statistics, giving you a clear checklist to support your revision. Work through each section to strengthen your skills and build confidence before moving on to GCSE-level work.
本文是 Year 9 CCEA 数学核心话题的完整指南。它汇集了数、代数、几何和统计等重要领域，为你提供一份清晰的复习清单。逐一梳理每个部分，在进入 GCSE 阶段之前巩固技能、树立信心。
1. Number Operations and Order of Operations | 数字运算与运算顺序
Fluency with the four operations (addition, subtraction, multiplication and division) for whole numbers and decimals is essential. You should be confident using both mental methods and written column methods. Remember to check your answers by estimating roughly what the result should be.
熟练掌握整数和小数的四则运算（加、减、乘、除）至关重要。你应该既能心算，也能使用竖式笔算，并通过估算大致结果来检验答案。
The order of operations, often remembered by BIDMAS or BODMAS, tells you the sequence to follow: Brackets first, then Indices (powers, like squares and cubes), then Division and Multiplication working from left to right, and finally Addition and Subtraction from left to right. For example, 10 − 2 × 3 equals 4, not 24.
运算顺序，通常记为 BIDMAS 或 BODMAS，告诉你遵循的次序：先算括号，再算指数（如平方、立方），然后从左到右计算乘除，最后从左到右计算加减。例如，10 − 2 × 3 等于 4，而不是 24。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
You need to move fluently between fractions, decimals and percentages. To change a fraction to a decimal, divide the numerator by the denominator. Multiply a decimal by 100 to get a percentage. Common equivalents such as 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25% and 3/4 = 0.75 = 75% should be automatic.
你需要能在分数、小数和百分数之间自如转换。分数转小数，用分子除以分母；小数乘以 100 得到百分数。应该熟记常用的等价关系，如 1/2 = 0.5 = 50%，1/4 = 0.25 = 25%，3/4 = 0.75 = 75%。
Performing percentage increase and decrease is a core skill. To increase an amount by 15%, multiply by 1.15; to decrease by 15%, multiply by 0.85. When adding or subtracting fractions, find a common denominator first. Multiply fractions by multiplying numerators and denominators separately, and divide by flipping the second fraction and multiplying.
百分数的增减是一项核心技能。一个数增加 15%，乘以 1.15；减少 15%，乘以 0.85。对分数进行加减运算时，先找到公分母。分数相乘时，分子乘分子、分母乘分母；分数相除则把第二个分数倒过来再相乘。
3. Ratio and Proportion | 比率与比例
A ratio compares the sizes of two or more quantities. You should be able to simplify a ratio by dividing all parts by their highest common factor, and write it in the form 1 : n where appropriate. For example, 8 : 12 simplifies to 2 : 3, or 1 : 1.5.
比率用来比较两个或更多量的大小。你应该能将比率化简，所有项除以它们的最大公因数，并在需要时写成 1 : n 的形式。例如，8 : 12 化简为 2 : 3，或写成 1 : 1.5。
When sharing a quantity in a given ratio, first find the total number of parts. Divide the total amount by the number of parts to find the value of one part, then multiply by the parts for each share. Direct proportion problems involve keeping the ratio between two variables constant; if one doubles, the other doubles.
按给定比例分配一个量时，先求出总份数。用总量除以总份数得到一份的量，再乘以各自的份数。正比例问题中两个变量的比值保持不变；一个加倍，另一个也加倍。
4. Algebraic Expressions | 代数表达式
Algebra uses letters to stand for unknown numbers or variables. An expression contains terms, which are combined with addition and subtraction. A term like 5xy has a coefficient (5) and variables (x and y). You must collect like terms by adding or subtracting their coefficients; for example, 3a + 4a simplifies to 7a, while 2a + 3b cannot be combined further.
代数用字母表示未知数或变量。表达式由项组成，各项通过加减连接。一个项如 5xy 含有一个系数（5）和变量（x 和 y）。必须合并同类项，即加减它们的系数；例如 3a + 4a 化简为 7a，而 2a + 3b 则不能进一步合并。
Expanding brackets uses the distributive law: multiply the term outside by every term inside. For instance, 4(x + 3) = 4x + 12. Factorising is the reverse process; look for the highest common factor and place it outside brackets, e.g. 6x + 9 = 3(2x + 3).
展开括号运用分配律：外面的项与括号内每一项相乘。例如，4(x + 3) = 4x + 12。因式分解是逆过程；找出最大公因数并放在括号外面，如 6x + 9 = 3(2x + 3)。
5. Solving Linear Equations | 解线性方程
A linear equation has the unknown raised to the power of 1, such as 2x + 5 = 11. The goal is to isolate the unknown by performing the same operation on both sides. Always start by simplifying each side if necessary, then undo addition or subtraction, and finally division or multiplication.
线性方程中未知数的最高次数为 1，如 2x + 5 = 11。目标是通过在两边执行相同的运算来分离未知数。必要时先化简两边，然后移走加减，最后处理乘除。
When the unknown appears on both sides, collect the variable terms on one side and constants on the other. Equations containing brackets should be expanded first. If there are fractional coefficients, multiply every term by the lowest common denominator to clear fractions. Always verify your solution by substituting it back into the original equation.
当未知数出现在等号两边时，把含变量的项移到一边，常数移到另一边。含有括号的方程应该先展开。如果有分数系数，用最小公分母乘以每一项以消去分母。一定要把解代回原方程进行检验。
6. Sequences and the nth Term | 数列与第 n 项
A number sequence follows a rule. In an arithmetic (linear) sequence, the difference between consecutive terms is constant. For example, in the sequence 4, 9, 14, 19, … the common difference is +5. The nth term formula allows you to find any term without listing all previous terms.
数列按某一规律排列。在等差（线性）数列中，相邻两项的差是常数。例如，数列 4, 9, 14, 19, … 的公差是 +5。第 n 项公式令你无需列出前面所有项就能求出任意一项。
To find the nth term of an arithmetic sequence, use the rule an + b, where a is the common difference and b is the value needed to make the first term work. For the sequence 4, 9, 14, 19, …, the nth term is 5n − 1. Check: n = 1 gives 5(1) − 1 = 4, n = 2 gives 9, and so on. Be able to generate terms from a formula and to find whether a given number is a term in the sequence.
要找出等差数列的第 n 项，使用 an + b 形式，其中 a 是公差，b 是使首项成立的调整值。数列 4, 9, 14, 19, … 的第 n 项为 5n − 1。验证：n = 1 得 5(1) − 1 = 4，n = 2 得 9，以此类推。要能从公式生成项，并判断某个给定的数是否为数列中的一项。
7. Angles and Polygons | 角与多边形
You should know the names and properties of angles: acute, obtuse, reflex, right, straight, and a full turn. On parallel lines, corresponding angles are equal, alternate angles are equal, and co-interior (allied) angles sum to 180°. These facts help calculate missing angles in diagrams.
你应知道各类角的名称和性质：锐角、钝角、优角、直角、平角以及周角。在平行线上，同位角相等，内错角相等，同旁内角互补（和为 180°）。这些定理可用于计算图形中的未知角。
The interior angles of a triangle always add up to 180°. For any polygon, the sum of interior angles is (n − 2) × 180°, where n is the number of sides. The sum of exterior angles of any convex polygon is always 360°. In a regular polygon, all sides and angles are equal, so each interior angle is (n − 2) × 180° ÷ n.
三角形的内角和总是 180°。对于任意多边形，内角和为 (n − 2) × 180°，其中 n 是边数。任意凸多边形的外角和恒为 360°。在正多边形中，所有边和角都相等，因此每个内角为 (n − 2) × 180° ÷ n。
8. Perimeter, Area and Volume | 周长、面积与体积
Perimeter is the distance around a shape. For rectangles, use 2(length + width). The area of a rectangle is length × width; a triangle is ½ × base × height; a parallelogram is base × perpendicular height; a trapezium is ½ × (sum of parallel sides) × height. Memorise these formulas and apply them with correct units.
周长是围绕一个形状的总距离。矩形的周长为 2(长 + 宽)。矩形的面积为长 × 宽；三角形的面积为 ½ × 底 × 高；平行四边形的面积为底 × 垂直高；梯形的面积为 ½ × (上下底之和) × 高。熟记这些公式并使用正确的单位。
The circumference of a circle is C = 2πr or C = πd, and the area is A = πr². Volume measures the space inside a 3D object. For prisms, the volume is area of cross-section × length. Cylinders are a type of prism, so V = πr²h. Use π ≈ 3.14 or the π key on a calculator as directed, and always include appropriate units (cm, cm², cm³).
圆的周长为 C = 2πr 或 C = πd，面积为 A = πr²。体积衡量三维物体所占空间。棱柱的体积为横截面积 × 长度。圆柱体是一种棱柱，因此 V = πr²h。按要求使用 π ≈ 3.14 或计算器上的 π 键，并始终带上合适的单位（cm, cm², cm³）。
9. Coordinates and Linear Graphs | 坐标与线性图
Coordinates are written as ordered pairs (x, y). You should be able to plot points in all four quadrants, reading x first, then y. A linear equation can be represented by a straight line. To draw a line like y = 2x + 1, construct a table of values, choose three x-values, calculate the y-values, plot the points, and join them with a straight edge.
坐标表示为有序数对 (x, y)。你应该能在所有四个象限描点，先读 x 坐标，再读 y 坐标。线性方程可用一条直线表示。要画出如 y = 2x + 1 的直线，先建一个数值表，取三个 x 值，计算对应的 y 值，描点，再用直尺连线。
The equation of a straight line is often written as y = mx + c, where m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis). Lines with the same gradient are parallel. Recognise that vertical lines have equations of the form x = a, and horizontal lines y = b.
直线方程常写成 y = mx + c 的形式，其中 m 是斜率（倾斜度），c 是 y 轴截距（直线与 y 轴的交点）。斜率相同的直线互相平行。要认识到垂直线方程为 x = a，水平线方程为 y = b。
10. Data Handling and Averages | 数据处理与平均数
Data can be summarised using measures of average and spread. The mode is the most common value, the median is the middle value in an ordered list, and the mean is found by summing all values and dividing by how many there are. The range (largest value minus smallest) gives a measure of spread.
数据可以用平均数与离散程度指标来概括。众数是最常出现的数值，中位数是有序数列里居中的值，平均数则是所有值的总和除以数据个数。极差（最大值减最小值）反映出数据的分散程度。
Statistical diagrams include bar charts for discrete data, pie charts for showing proportions, and scatter graphs for investigating relationships between two variables. On a scatter graph, if points show an upward trend there is positive correlation; a downward trend suggests negative correlation; no clear pattern indicates no correlation. Be careful not to confuse correlation with causation.
统计图包括表示离散数据的条形图、展示比例的饼图，以及用于考察两个变量关系的散点图。在散点图中，如果点呈上升趋势，则为正相关；下降趋势为负相关；无明显规律则没有相关。注意不要混淆相关关系与因果关系。
11. Introduction to Probability | 概率入门
Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). For equally likely outcomes, theoretical probability = number of successful outcomes ÷ total number of possible outcomes. Probabilities can be expressed as fractions, decimals or percentages.
概率用来衡量事件发生的可能性，量表从 0（不可能）到 1（必然）。对于等可能的结果，理论概率 = 成功结果数 ÷ 所有可能结果的总数。概率可以用分数、小数或百分数表示。
Mutually exclusive events cannot happen at the same time. The probability of either one event or the other occurring is found by adding their individual probabilities. The sum of probabilities of all possible outcomes is 1, so the probability of an event NOT happening is 1 − P(event). Use sample space diagrams or simple tree diagrams to list all outcomes systematically.
互斥事件不能同时发生。两个互斥事件中任一发生的概率等于它们各自概率之和。所有可能结果的概率总和为 1，所以某事件不发生的概率为 1 − P(事件)。可以使用样本空间图或简单的树形图来系统列出所有结果。
Published by TutorHao | Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply