Year 9 CCEA Further Mathematics: Glossary Quick Memorisation Guide | Year 9 CCEA 进阶数学：词汇术语速记指南

📚 Year 9 CCEA Further Mathematics: Glossary Quick Memorisation Guide | Year 9 CCEA 进阶数学：词汇术语速记指南

Mathematics has a rich vocabulary, and knowing the exact meaning of every term is the key to unlocking complex problems. This guide gathers the essential words you will meet in Year 9 CCEA Further Mathematics, organises them by topic and gives you clever memory hooks so you can learn them faster and recall them under pressure. Read each English explanation followed by its Chinese twin, and you will build a bilingual understanding that strengthens both your language and your logic.

数学拥有丰富的词汇，精确理解每一个术语是解开复杂问题的钥匙。本指南整理了你将在 Year 9 CCEA 进阶数学中遇到的核心词汇，按主题排列，并为你提供巧妙的记忆钩子，帮助你更快学习、在压力下顺利回忆。阅读每个英文解释及其对应的中文版本，你将建立起双语理解力，同时强化语言与逻辑能力。

1. Introduction: Why Vocabulary Matters | 引言：词汇为何重要

Words like 'coefficient' or 'perpendicular' are not just jargon — they are precise instructions. When you master them, exam questions become a conversation you already know how to join. This guide encourages you to say each term aloud, link it to a visual image, and test yourself regularly.

像 'coefficient'（系数）或 'perpendicular'（垂直）这样的词语不只是术语——它们是精确的指令。一旦你掌握它们，考题就变成了你早已懂得如何加入的对话。本指南鼓励你大声读出每个术语，将它和视觉图像联系起来，并定期进行自测。

2. Number and Place Value | 数与位值

Numbers are the raw ingredients of mathematics. The terms in this section help you describe size, order and the position of digits.

数字是数学的原材料。本节术语帮助你描述大小、顺序以及数字的位置。

• Integer: A whole number that can be positive, negative or zero, with no fractional part. Memory tip: 'integer' sounds like 'in the grid' — all whole numbers sitting neatly on the number line.

  整数：可以是正数、负数或零的完整数，没有小数部分。记忆技巧：'integer' 听起来像 'in the grid'——所有完整数整齐地排列在数轴上。

• Place value: The value of a digit based on its position in a number, such as units, tens, hundreds. Memory tip: think of each column as a 'place' with a power of 10 (10⁰, 10¹, 10²).

  位值：一个数字根据其在数中的位置而具有的值，如个位、十位、百位。记忆技巧：把每一列想成一个拥有10的幂的“位置”（10⁰, 10¹, 10²）。

• Negative number: A number less than zero, written with a minus sign. Memory tip: imagine a thermometer; below zero is negative territory.

  负数：小于零的数，用减号书写。记忆技巧：想象一个温度计；零度以下就是负数领地。

• Ascending order: Arranging numbers from smallest to largest. Memory tip: 'ascend' means go up, so values climb like steps.

  升序：将数字从小到大排列。记忆技巧：'ascend' 表示上升，因此数值像台阶一样向上攀升。

3. Fractions, Decimals and Percentages | 分数、小数与百分数

Parts of a whole can be expressed in three interchangeable forms. Knowing the vocabulary makes conversions effortless.

整体的一部分可以用三种可互换的形式表达。掌握这些词汇让转换变得毫不费力。

• Numerator: The top number in a fraction, showing how many parts we have. Memory tip: Up in nUmerator.

  分子：分数中上面的数，表示我们有多少份。记忆技巧：'numerator' 中的 'nu' 暗示 'number up'。

• Denominator: The bottom number in a fraction, showing the total number of equal parts. Memory tip: Denominator is down.

  分母：分数中下面的数，表示整体被等分的总份数。记忆技巧：'denominator' 以 'd' 开头，和 'down' 一样。

• Equivalent fractions: Different fractions that represent the same value, e.g. 1/2 = 2/4. Memory tip: 'equal value' fractions.

  等值分数：表示相同值但形式不同的分数，如 1/2 = 2/4。记忆技巧：价值相等（equal value）的分数。

• Percentage: A rate per hundred, symbol %. Memory tip: 'cent' means 100, so 'per cent' means for every 100.

  百分数：每一百份中的比率，符号为 %。记忆技巧：'cent' 指一百，因此 'per cent' 表示每一百。

4. Algebraic Foundations | 代数基础

Algebra gives us a way to generalise patterns using letters and symbols. These terms are the grammar of algebraic sentences.

代数让我们能够用字母和符号将模式一般化。这些术语就是代数语句的语法。

• Variable: A letter or symbol that stands for an unknown or changing value. Memory tip: it 'varies', so it can change.

  变量：表示未知或变化值的字母或符号。记忆技巧：它能变化（varies）。

• Coefficient: The number multiplied by a variable, e.g. in 3x, 3 is the coefficient. Memory tip: 'co' means together with the variable; it works 'with' it.

  系数：与变量相乘的数字，例如在 3x 中，3 是系数。记忆技巧：'co' 表示共同，它和变量一同工作。

• Expression: A combination of numbers, variables and operations, but without an equals sign. Memory tip: an expression is a phrase, not a full sentence (which would be an equation).

  表达式：数字、变量与运算的组合，但没有等号。记忆技巧：表达式就像一个短语，不是完整的句子（完整句子是方程）。

• Like terms: Terms that contain exactly the same variable raised to the same power, e.g. 2x and -5x. Memory tip: they 'look alike' in their variable part.

  同类项：包含完全相同的变量且该变量指数也相同的项，如 2x 和 -5x。记忆技巧：它们的变量部分“看起来相像”。

5. Equations and Inequalities | 方程与不等式

Once we have expressions, we can relate them with equals signs or inequality symbols to model real situations.

一旦有了表达式，我们就可以用等号或不等号将它们关联起来，以模拟真实情境。

• Equation thematical statement showing that two expressions are equal, using the = sign. Memory tip: 'equa' means equal; think of a balanced scale.

  方程：使用 = 号表明两个表达式相等的数学陈述。记忆技巧：'equa' 表示相等；想象一个平衡的天平。

• Inequality than or equal to). Memory tip: the open side of the symbol always faces the larger number.

  不等式：使用 >（大于）、<（小于）、≥（大于或等于）或 ≤（小于或等于）比较两个表达式的陈述。记忆技巧：符号的开口端永远朝向较大的数。

• Solve: To find the value(s) of the variable that make an equation true. Memory tip: solving 'unlocks' the mystery number.

  解：求出使方程成立的变量的值。记忆技巧：求解就是“解锁”那个神秘的数字。

• Root: A solution of an equation, especially when the expression equals zero. Memory tip: a root is where the function touches the ground (x-axis).

  根：方程的解，尤其当表达式等于零时。记忆技巧：根是函数触碰地面（x轴）的地方。

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6. Sequences and Patterns | 数列与模式

Recognising and describing patterns lies at the heart of mathematical thinking. Sequences help us predict what comes next.

识别并描述模式是数学思维的核心。数列帮助我们预测下一个结果。

• Sequence: An ordered list of numbers following a rule. Memory tip: think of a 'sequence' of events — one after another.

  数列：按照某种规则排列的一列有序数字。记忆技巧：想象一系列事件——一个接一个。

• Term: Each individual number in a sequence. Memory tip: term = an item in a list.

  项：数列中的每一个单独的数字。记忆技巧：项就是列表中的一个条目。

• nth term : The general rule that allows you to find any term in a sequence, written in terms of n (the position number). Memory tip: n stands for 'number of the term'. For an arithmetic sequence, aₙ = a₁ + (n - 1)d.

  第n项：能够让你求出数列中任意一项的通项规则，用 n（位置编号）表示。记忆技巧：n 代表“项的编号”。对等差数列，aₙ = a₁ + (n - 1)d。

• Arithmetic sequence: A sequence where the difference between consecutive terms is constant (the common difference). Memory tip: 'arithmetic' -> 'add or subtract' regularly.

  等差数列：相邻两项之差为常数（公差）的数列。记忆技巧：'arithmetic' 关联有规律的加减。

7. Geometry: Lines, Angles and Shapes | 几何：线、角与图形

Geometry is the study of space, shapes and their properties. Accurate vocabulary lets you describe figures and prove relationships.

几何学是研究空间、形状及其性质的学科。准确的词汇让你能够描述图形并证明关系。

• Acute angle: An angle measuring less than 90°. Memory tip: 'a cute' little angle, small and sharp.

  锐角：角度小于 90° 的角。记忆技巧：'a cute' 小小的角，又小又尖。

• Obtuse angle: An angle between 90° and 180°. Memory tip: 'obtuse' sounds like 'obtuse' = 'obvious big' — it is clearly larger than a right angle.

  钝角：角度在 90° 和 180° 之间的角。记忆技巧：'obtuse' 听起来像“明显大”——明显比直角大。

• Perpendicular: Two lines that meet at a right angle (90°). Memory tip: the symbol ⊥ looks like a little right angle; also 'perp' rhymes with 'sharp turn'.

  垂直：两条相交成直角（90°）的直线。记忆技巧：符号 ⊥ 像一个微型直角；也可记 'perp' 与 'sharp turn' 押韵。

• Parallel: Lines that never meet, staying the same distance apart. Memory tip: 'parallel' has parallel letter 'l's inside the word.

  平行：永不相交、始终等距的直线。记忆技巧：'parallel' 这个单词中间有平行的字母 'l'。

• Regular polygon: A polygon with all sides equal and all angles equal. Memory tip: 'regular' means 'normal' in shape — everything the same.

  正多边形：所有边相等且所有角相等的多边形。记忆技巧：'正' 意味着形状标准——一切都相同。

8. Coordinates and Linear Graphs | 坐标与线性图像

Coordinates allow us to pinpoint locations on a plane. Together with linear graphs, they link algebra with geometry.

坐标让我们能够在平面上精准定位。与线性图像一起，它们把代数与几何连接起来。

• Coordinates: A pair of numbers (x, y) showing a point's horizontal and vertical position. Memory tip: 'x is a cross, then wise up' — go along the corridor (x), then up the stairs (y).

  坐标：一对数字 (x, y)，表示一个点的水平位置和垂直位置。记忆技巧：先沿着走廊走（x），再上楼（y）。

• Origin: The point (0, 0) where the axes intersect. Memory tip: the 'origin' is where the journey starts.

  原点：坐标轴相交的点 (0, 0)。记忆技巧：'origin' 是旅程开始的地方。

• Gradient line is, usually represented by m. Memory tip: gradient = rise / run. Think of climbing a 'grade'.

  斜率：表示一条直线有多陡的度量，常用 m 表示。记忆技巧：斜率 = 垂直变化 / 水平变化。想象爬坡的“坡度”。

• Linear graph: A straight-line graph representing a linear equation. Memory tip: 'linear' contains 'line'.

  线性图像：表示线性方程式的直线图。记忆技巧：'linear' 含有 'line'。

9. Statistics and Averages | 统计与平均数

Statistics help us collect, organise and interpret data. Averages summarise a whole data set with a single representative number.

统计学帮助我们收集、整理和解读数据。平均数用一个代表性的数字总结整个数据集。

• Mean: The sum of all data values divided by the number of values. Memory tip: 'mean' requires 'meaningful' sharing — add them all and share equally.

  平均数（均值）：所有数据值之和除以值的个数。记忆技巧：'mean' 是有意义的分享——全部加起来再均分。

• Median: The middle value when data are arranged in order. Memory tip: median sounds like 'medium' or 'middle'.

  中位数：数据按顺序排列后位于中间的值。记忆技巧：median 听起来像 'medium'（中间）。

• Mode: The value that appears most often. Memory tip: 'mode' = 'most' frequent.

  众数：出现次数最多的值。记忆技巧：'mode' 听起来像 'most'（最多）。

• Range: The difference between the largest and smallest data values. Memory tip: range tells you how far the data 'ranges' from end to end.

  极差：最大值与最小值之差。记忆技巧：范围告诉你数据从一端到另一端的“幅度”。

10. Probability and Sets | 概率与集合

Probability measures how likely events are to happen. Set language gives us a clear way to group and compare outcomes.

概率衡量事件发生的可能性大小。集合语言为我们提供了一种清晰的方式来分组和比较结果。

• Probability rtain. Memory tip: probability = number of favourable outcomes / total number of outcomes.

  概率：一个在 0 和 1 之间的数，表示可能性；0 表示不可能，1 表示必然。记忆技巧：概率 = 有利结果数 / 所有可能结果数。

• Sample space: The set of all possible outcomes of an experiment. Memory tip: it is the 'space' containing all 'samples' (outcomes).

  样本空间：一项试验所有可能结果组成的集合。记忆技巧：它是容纳所有“样本”（结果）的“空间”。

• Set: A well-defined collection of objects or numbers. Memory tip: a set is like a team — all members are listed inside curly brackets {}.

  集合：一个明确定义的对象或数字的汇集。记忆技巧：一个集合就像一支队伍——所有成员列在大括号 {} 内。

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