📚 Year 9 CIE Further Maths: Vocabulary & Terminology Quick-Memory Guide | Year 9 CIE 进阶数学：词汇术语速记指南
In Year 9 CIE Further Mathematics, building a strong command of technical vocabulary is just as important as mastering calculations. Terms like 'coefficient', 'asymptote', and 'mutually exclusive' are not merely jargon; they are the precise language that exam questions use to test your understanding. This guide breaks down the must-know terminology into logical categories, pairs each English term with its Chinese equivalent, and offers memory hacks to make recall faster and more reliable — helping you read questions correctly and express your reasoning with clarity.
在 Year 9 CIE 进阶数学中，牢固掌握专业术语与掌握计算同样重要。像 'coefficient'（系数）、'asymptote'（渐近线）、'mutually exclusive'（互斥）这样的词汇并非只是行话，它们是考题用来检验你理解程度的精准语言。本指南将必知术语分门别类，为每个英文词配以对应的中文表达，并提供速记技巧，让回忆变得更快、更牢靠——帮助你准确读题，并用清晰的逻辑表达推理。
1. Algebraic Expressions | 代数表达式
Variable (变量): A symbol, typically a letter, that represents an unknown number. Think of it as a container whose value can change. Memory hook: 'vary' + 'able' — able to vary.
Variable (变量)： 通常用字母表示的符号，代表未知数。把它想象成数值可以改变的容器。记忆法：能变的量。
Coefficient (系数): The number multiplying a variable. In 5x, 5 is the coefficient. Memory hook: 'co-' means together, and 'efficient' hints at doing the work — the number that works together with the variable.
Coefficient (系数)： 与变量相乘的数字。在 5x 中，5 是系数。记忆法：和变量一起起作用的数字。
Constant (常数): A fixed value that does not change. In the expression 3x + 7, 7 is the constant. Memory hook: 'con' + 'stant' — staying the same.
Constant (常数)： 固定不变的值。在表达式 3x + 7 中，7 是常数。记忆法：恒常不变。
Term (项): A single number, variable, or product of numbers and variables separated by + or − signs. Memory hook: think of each 'term' as a separate piece of an agreement, just like clauses in a contract.
Term (项)： 由加号或减号分隔的单个数字、变量或数字与变量的乘积。记忆法：像合同里的条款，每一‘项’独立存在。
2. Equations and Inequalities | 方程与不等式
Equation (方程): A statement that two expressions are equal, shown by an equals sign (=). Memory hook: 'equa-' like equal, so it’s a balance statement.
Equation (方程)： 表示两个表达式相等的语句，用等号 (=) 标示。记忆法：因相等而成‘方’程。
Inequality (不等式): wing that two expressions are not equal, using symbols like <, >, ≤, ≥. Memory hook: 'in-' (not) + 'equality' — not equal.
Inequality (不等式)： 表示两个表达式不相等的符号关系，使用 <、>、≤、≥ 等符号。记忆法：不相等，故称不等式。
Solution (解): A value that makes an equation or inequality true. Memory hook: the 'solution' solves the puzzle — it dissolves the problem.
Solution (解)： 使得方程或不等式成立的数值。记忆法：解题的钥匙，解开未知数。
Root (根): y hook: the root where the graph crosses the x-axis, like a tree root touching the ground.
Root (根)： 方程的另一个说法，特别适用于 f(x)=0 的情形。记忆法：图像与 x 轴的交点，如同树根扎入地面。
3. Sequences and Series | 数列与级数
Sequence (数列): An ordered list of numbers following a rule. Each number is a term. Memory hook: 'se-' (follow) + 'quence' (order) — numbers in order.
Sequence (数列)： 按规则排列的一列有序数字，每个数字称为一项。记忆法：按次序排列的一列数。
Arithmetic progression (等差数列): A sequence where the difference between consecutive terms is constant (common difference). Memory hook: 'arithmetic' sounds like 'a rhythm' — steady beat, steady difference.
Arithmetic progression (等差数列)： 相邻项之差为常数（公差）的数列。记忆法：节奏匀称，差值相等。
Geometric progression (等比数列): A sequence where each term is multiplied by a constant (common ratio) to get the next. Memory hook: 'geo-' like grow, because multiplying makes terms grow fast.
Geometric progression (等比数列)： 每一项乘以常数（公比）得到下一项的数列。记忆法：几何级增长，倍数翻滚。
nth term (第 n 项): A formula that gives any term of a sequence based on its position n. Memory hook: 'nth' means any position you choose — the general term.
nth term (第 n 项)： 根据位置 n 给出数列任意项的公式。记忆法：通项，无论第几位都能算出来。
4. Functions and Graphs | 函数与图像
Function (函数): A rule that assigns exactly one output for each input. Often written as f(x). Memory hook: a 'function' machine — input goes in, one output comes out.
Function (函数)： 为每个输入恰好分配一个输出的规则，常写作 f(x)。记忆法：函数像一台机器，输入进去，唯一输出出来。
Domain (定义域): The set of all possible input values (x-values). Memory hook: 'domain' sounds like 'own' — the x-values a function owns.
Domain (定义域)： 所有可能输入值（x 值）的集合。记忆法：函数自己的领地。
Range (值域): The set of all possible output values (y-values). Memory hook: the range of heights a ball can reach — outputs ‘range’ from low to high.
Range (值域)： 所有可能输出值（y 值）的集合。记忆法：函数输出的波动范围。
Asymptote (渐近线): A line that a graph approaches but never touches. Memory hook: 'a-' (not) + 'symptote' (fall together) — it never meets, just gets infinitely close.
Asymptote (渐近线)： 图像无限接近但永不相交的直线。记忆法：渐行渐近，却永不抵达。
Gradient (斜率/梯度): The steepness of a line, calculated as rise over run. Memory hook: 'grade' like the steepness of a hill — grading the slope.
Gradient (斜率/梯度)： 直线的倾斜程度，等于上升量除以水平移动量。记忆法：坡度等级。
5. Geometry – Lines and Angles | 几何 – 线与角
Parallel (平行): Lines that never meet, no matter how far they extend. Memory hook: 'para-' (beside) + 'allel' (each other) — running alongside each other forever.
Parallel (平行)： 无论延伸多远都不会相交的直线。记忆法：永伴同行，永不相交。
Perpendicular (垂直): Lines that intersect at a right angle (90°). Memory hook: 'per-' (through) + 'pend' (hang) — a plumb line hanging perfectly vertical, meeting the horizontal at 90°.
Perpendicular (垂直)： 相交成直角 (90°) 的直线。记忆法：如铅垂线与水平面垂直相交。
Bisector (平分线): A line that divides an angle or segment into two equal parts. Memory hook: 'bi-' (two) + 'sect' (cut) — cuts into two equal pieces.
Bisector (平分线)： 将角或线段分成相等两部分的线。记忆法：一刀两半，平分秋色。
Vertex (顶点): The corner point where two sides of a shape or two rays meet. Plural: vertices. Memory hook: 'vert' like convert or turn — the turning point of an angle.
Vertex (顶点)： 图形两条边或两条射线的交汇点。复数 vertices。记忆法：转折点，角的尖顶。
6. Geometry – Shapes and Properties | 几何 – 图形与性质
Polygon (多边形): A closed 2D shape with straight sides. Memory hook: 'poly' (many) + 'gon' (angles) — shape with many angles.
Polygon (多边形)： 由直边围成的封闭二维图形。记忆法：多角形。
Regular polygon (正多边形): All sides and all angles are equal. Memory hook: 'regular' means uniform, like a regular schedule — everything the same.
Regular polygon (正多边形)： 所有边和角都相等的多边形。记忆法：规则整齐，边角一致。
Congruent (全等): Exactly the same shape and size. Memory hook: 'con-' (together) + 'gruent' (agree) — shapes that agree perfectly.
Congruent (全等)： 形状和大小完全相同。记忆法：完全一致，可以重合。
Similar (相似): Same shape, but different size; corresponding angles equal, sides proportional. Memory hook: similar like siblings — same shape, different size.
Similar (相似)： 形状相同，大小不同；对应角相等，对应边成比例。记忆法：形相似，大小异。
Symmetry (对称): A balanced arrangement where one half mirrors the other. Line symmetry, rotational symmetry. Memory hook: 'sym-' (same) + 'metry' (measure) — same measure on both sides.
Symmetry (对称)： 一半镜像另外一半的平衡排列。线对称、旋转对称。记忆法：两边度量相同。
7. Trigonometry Basics | 三角学基础
Hypotenuse (斜边): The longest side of a right-angled triangle, opposite the right angle. Memory hook: 'hypo-' (under) + 'tenuse' (stretch) — the side stretching under the right angle.
Hypotenuse (斜边)： 直角三角形中最长的边，正对直角。记忆法：直角的对边，斜而最长。
Opposite (对边): The side facing a given angle (not the right angle). Memory hook: opposite means across from — stand opposite the angle and you see that side.
Opposite (对边)： 面对给定角（非直角）的边。记忆法：角对面那条边。
Adjacent (邻边): The side next to a given angle, forming the angle together with the hypotenuse. Memory hook: 'ad-' (to) + 'jacent' (lie) — lying next to the angle.
Adjacent (邻边)： 紧挨给定角的边，与斜边一起构成该角。记忆法：相邻的那条边。
Sine, Cosine, Tangent (正弦、余弦、正切): in a right triangle: sin = opp/hyp, cos = adj/hyp, tan = opp/adj. Memory hook: SOH CAH TOA — Silly Old Harry Caught A Herring Trawling Off America.
Sine, Cosine, Tangent (正弦、余弦、正切)： 直角三角形中边的比：sin = 对/斜，cos = 邻/斜，tan = 对/邻。记忆法：SOH CAH TOA —— 顺口溜记住比值关系。
8. Statistics – Data Handling | 统计 – 数据处理
Mean (平均数): Sum of all values divided by the number of values. Memory hook: 'mean' sounds like 'me an' average — it’s the everyday average.
Mean (平均数)： 所有数值之和除以数值个数。记忆法：均分公平的平均。
Median (中位数): The middle value when data is ordered. Memory hook: 'median' like 'medium' — the one in the middle.
Median (中位数)： 数据排序后处于中间的值。记忆法：中间的那一位。
Mode (众数): The most frequently occurring value. Memory hook: 'mode' sounds like 'most' — the most popular.
Mode (众数)： 出现频率最高的值。记忆法：最多人选的模式。
Range (极差): Difference between the largest and smallest data values. Memory hook: how far data ranges from low to high — the spread.
Range (极差)： 最大值与最小值的差。记忆法：数据跨度的范围。
Outlier (异常值): A data point that lies far away from the others. Memory hook: 'out' + 'lier' — it lies outside the main cluster.
Outlier (异常值)： 远离其他数据点的数值。记忆法：躺在外面的异类。
9. Probability Vocabulary | 概率词汇
Experiment (试验): A repeatable process with observable outcomes. Memory hook: like a science experiment — you do something and observe results.
Experiment (试验)： 可重复进行并能观测结果的步骤。记忆法：如同做实验，观察结果。
Outcome (结果): A possible result of an experiment. Memory hook: what 'comes out' of the trial.
Outcome (结果)： 试验的一个可能结果。记忆法：试验的产出。
Event (事件): A set of one or more outcomes. Memory hook: an 'event' is something that can happen — e.g., rolling an even number.
Event (事件)： 一个或多个结果组成的集合。记忆法：可以发生的事件，如掷出偶数。
Sample space (样本空间): The set of all possible outcomes. Memory hook: 'sample' like a menu sampling all possibilities.
Sample space (样本空间)： 所有可能结果的集合。记忆法：全部结果一览。
Mutually exclusive (互斥): Events that cannot happen at the same time. Memory hook: 'exclusive' like a club — you can't be in two at once.
Mutually exclusive (互斥)： 不可能同时发生的事件。记忆法：互相排斥，只能选一。
Independent events (独立事件): The occurrence of one does not affect the probability of the other. Memory hook: independent people don't influence each other — same with events.
Independent events (独立事件)： 一个事件发生与否不影响另一个事件概率。记忆法：各过各的，互不影响。
10. Sets and Logic | 集合与逻辑
Set (集合): A collection of distinct objects. Memory hook: a set of trading cards — a well-defined group.
Set (集合)： 一组明确不同的对象。记忆法：一套卡片，成员分明。
Element (元素): An object belonging to a set. Memory hook: 'element' like the basic ingredient — element of a set.
Element (元素)： 属于集合的对象。记忆法：集合里的基本成分。
Union (并集): The set containing all elements from both sets, denoted A ∪ B. Memory hook: 'union' like marriage — brings all members together.
Union (并集)： 包含两个集合所有元素的集合，记作 A ∪ B。记忆法：联合起来，全员到齐。
Intersection (交集): The set of elements common to both sets, denoted A ∩ B. Memory hook: 'inter-' (between) + 'section' — the overlapping section.
Intersection (交集)： 两个集合共同元素的集合，记作 A ∩ B。记忆法：交叉重叠的部分。
Universal set (全集): The set containing all objects under consideration, denoted ξ or U. Memory hook: the universe of everything relevant.
Universal set (全集)： 包含所考虑所有对象的集合，记作 ξ 或 U。记忆法：相关万物的总集合。
Complement (补集): Elements not in a set but in the universal set. Memory hook: what completes the set to make the whole — like a complement to a meal.
Complement (补集)： 在全集中但不在某集合的元素。记忆法：补充成全集的那部分。
11. Number Types and Properties | 数的分类与性质
Integer (整数): A whole number that can be positive, negative, or zero. Memory hook: 'integer' sounds like 'integral' — whole and complete.
Integer (整数)： 正整数、负整数或零。记忆法：完整无缺的数。
Rational number (有理数): A number that can be written as a fraction a/b where a and b are integers, b≠0. Memory hook: 'rational' like 'ratio' — can be expressed as a ratio.
Rational number (有理数)： 可写成分数 a/b 形式的数，a、b 为整数且 b≠0。记忆法：有理即能成比例。
Irrational number (无理数): A number that cannot be expressed as a simple fraction; its decimal never repeats or terminates, e.g., √2, π. Memory hook: 'ir-' (not) + 'rational' — not a ratio, unreasonable but real.
Irrational number (无理数)： 不能表示为简单分数的数；小数既不循环也不终止，如 √2、π。记忆法：不成比例，却真实存在。
Prime number (质数/素数): An integer greater than 1 with exactly two distinct factors: 1 and itself. Memory hook: 'prime' like first-class — only divisible by 1 and itself, no other factors.
Prime number (质数/素数)： 大于 1 且恰好只有两个不同因数的整数：1 和它自身。记忆法：质数如同基本元素，不能再分解。
Factor (因数): A number that divides another exactly. Memory hook: a 'factor' that makes something — breaks it into parts.
Factor (因数)： 能够整除另一个数的数。记忆法：构成因子的部件。
Multiple (倍数): The product of a number and any integer. Memory hook: 'multiple' like multiply — result of multiplying.
Multiple (倍数)： 一个数与任意整数的乘积。记忆法：乘出来的倍数。
12. Transformations and Symmetry | 变换与对称
Translation (平移): Sliding a shape without rotating or flipping; every point moves the same distance in the same direction. Memory hook: 'trans-' (across) + 'lation' (carrying) — carrying across without spinning.
Translation (平移)： 图形不旋转、不翻转的滑动；每一点沿同方向移动相同距离。记忆法：平移搬运，方向距离都相同。
Reflection (反射/轴对称): Flipping a shape over a mirror line. Memory hook: 're-' (back) + 'flect' (bend) — bending back like a mirror image.
Reflection (反射/轴对称)： 沿对称轴翻转图形。记忆法：镜中映像，反向弯折。
Rotation (旋转): Turning a shape about a fixed point through a given angle. Memory hook: 'rot-' like a wheel — spin around a centre.
Rotation (旋转)： 图形绕固定点转动一定角度。记忆法：轮转旋转。
Enlargement (放大/位似): Changing the size of a shape by a scale factor relative to a centre of enlargement. Memory hook: 'en-' (make) + 'large' — make larger or smaller, but keep proportions.
Enlargement (放大/位似)： 按比例因子相对于位似中心改变图形大小。记忆法：放大或缩小，形状比例不变。
Invariant (不变的): A property or point that does not change under a transformation. Memory hook: 'in-' (not) + 'variant' (changing) — unchanging, constant.
Invariant (不变的)： 在变换下保持不变的属性或点。记忆法：坚守不变。
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