📚 Year 9 CAIE Mathematics: Essential Vocabulary Memorisation Guide | CAIE 九年级数学核心词汇速记指南
Mastering mathematical vocabulary is the first step towards fluency in Year 9 CAIE Mathematics. This guide breaks down the most important terms across all key topics, pairing clear English definitions with direct Chinese translations. Each entry includes a simple memory trick to help you recall the meaning instantly during lessons, homework, and exams. Use these paired explanations to build a strong bilingual foundation that will support deeper problem-solving.
掌握数学词汇是精通九年级CAIE数学的第一步。本指南涵盖所有核心课题的关键术语，将清晰的英文定义与准确的中文翻译一一对照。每个词条都附有简单易记的记忆技巧，帮助你在课堂、作业和考试中快速调取含义。运用这些中英对照的解释，你将打下坚实的双语基础，从而更好地攻克难题。
1. Number & Arithmetic Terminology | 数与算术术语
Integer: A whole number that can be positive, negative, or zero, without any fractional or decimal parts. Memory trick: 'Integer' sounds like 'in-te-grit,' think of complete, unbroken pieces.
整数：可以是正数、负数或零的完整数字，没有分数或小数部分。记忆法：'Integer' 音似“完整颗粒”，想象一颗颗完整的豆子。
greater than 1 that has exactly two distinct factors: 1 and itself. (Example: 7 = 1 × 7). Memory trick: 'Prime' means first-class; a prime number only accepts 1 and itself as its 'VIP guests.'
质数（素数）：大于1且只有两个不同因数的数：1 和它本身。（例：7 = 1 × 7）。记忆法：'Prime' 有“首要”之意；质数只认1和自身为“VIP嘉宾”。
Factor: A number that divides exactly into another number without leaving a remainder. Memory trick: Think of a 'factory' that produces the original number by multiplying with another factor.
因数：能整除另一个数而没有余数的数。记忆法：把因数想象成“工厂零件”，与另一个因数相乘就能生产出原来的数。
Multiple: The result of multiplying a number by an integer. For example, multiples of 4 are 4, 8, 12, 16... Memory trick: 'Multiple' sounds like 'multiply'; it grows by repeated addition just like steps on a staircase.
倍数：一个数与整数相乘的结果。例如4的倍数是4、8、12、16……记忆法：“倍数”就是一次次加出来的阶梯，像楼梯逐级上升。
Reciprocal: The number obtained by swapping the numerator and denominator of a fraction. The reciprocal of a is 1/a (when a ≠ 0). Memory trick: 'Reciprocal' is like a 're-flip-procal'; flip the fraction upside down.
倒数：将一个分数的分子和分母交换后得到的数。a (a≠0)的倒数是1/a。记忆法：“倒数”就是“倒过来数”，把分数翻转。
2. Algebraic Fundamentals | 代数基础
Variable: A symbol, usually a letter, that represents an unknown or changing quantity. Memory trick: 'Variable' means able to vary — think of a letter that can take different values.
变量：通常用字母表示的符号，代表未知或可变的数量。记忆法：“变量”就是可变的量，想象一个字母可以换成不同的数字。
Coefficient: The number placed in front of a variable; it multiplies the variable. In 5x, 5 is the coefficient. Memory trick: 'Coefficient' works together ('co-') with the variable to represent a term.
系数：变量前面的数字，它与变量相乘。在5x中，5就是系数。记忆法：“系数”与变量合作（“协”同），构成一个项。
Term: A single number, variable, or the product of numbers and variables separated by + or − signs. Memory trick: Think of each 'term' as a separate ingredient in a recipe that you add or subtract.
项：由一个数、一个变量或数与变量的乘积组成，通过加号或减号分隔。记忆法：把每个“项”看作食谱里单独的一份材料，你决定加或减。
Expression: A combination of terms, operators, and possibly brackets without an equals sign. Example: 3x + 2y − 7. Memory trick: An 'expression' expresses a value but doesn't state equality.
表达式（代数式）：由项、运算符和括号组合而成，没有等号。如3x + 2y − 7。记忆法：“表达式”只表达一个算式，不建立相等关系。
Simplify: To rewrite an expression in its most compact form by collecting like terms. Memory trick: 'Simplify' is like tidying a messy desk — gather similar items together.
化简：通过合并同类项把表达式写成最紧凑的形式。记忆法：“化简”就像整理杂乱的桌面——把同类的东西归拢到一起。
3. Fractions, Decimals & Percentages | 分数、小数与百分比
Numerator: The top part of a fraction, showing how many parts we take. Memory trick: 'Numerator' tells the 'number' of pieces you count (North = top).
分子：分数中上面的部分，表示取了多少份。记忆法：“分子”就像房顶上的“子”，数一数取了几片。
Denominator: The bottom part of a fraction, indicating the total number of equal parts. Memory trick: 'Denominator' sounds like 'down-nominator' — it names the size of the pieces at the bottom.
分母：分数中下面的部分，表示整体被分成多少等份。记忆法：“分母”在底下，好比地基，决定了每一份的大小。
Equivalent fractions: Fractions that represent the same value, created by multiplying or dividing numerator and denominator by the same number. Memory trick: 'Equivalent' = 'equal value' — different looks, same amount.
等值分数：表示相同数值的分数，通过将分子和分母同乘或同除以一个数得到。记忆法：“等值”就是价值相等——外貌不同，分量一样。
Improper fraction: A fraction where the numerator is greater than or equal to the denominator, e.g. 7/4. Memory trick: 'Improper' means the top is too heavy — it's top-heavy.
假分数：分子大于或等于分母的分数，如7/4。记忆法：“假”分数就是头重脚轻，上面的比下面的大。
centage of the original amount. Formula: Percentage increase = (increase ÷ original) × 100%. Memory trick: Think of 'in-' as going up; calculate the rise relative to the starting point.
百分比增长：一个数值相对于原始值的增长部分，以百分数表示。公式：增长百分比 = (增长量 ÷ 原量) × 100%。记忆法：“增”加的量除以“原”来的量，再乘100，看涨了多少。
4. Ratio, Rate & Proportion | 比、率与比例
Ratio: A way to compare two or more quantities, showing their relative sizes. Written as a:b or a to b. Memory trick: 'Ratio' is like a 'recipe-oh' — a recipe always uses ratios of ingredients.
比：比较两个或多个数量相对大小的方法，写作a:b或a比b。记忆法：'Ratio' 类似“配比”，就像食谱里材料的比例。
Rate: A ratio comparing two quantities with different units, such as km per hour (km/h). Memory trick: 'Rate' often mentions time — think of heart 'rate' or speed 'rate'.
率：比较两个不同单位数量的比，如千米每小时 (km/h)。记忆法：“率”常与时间挂钩，如速率、心率，强调单位时间内的变化。
Proportion: An equation stating that two ratios are equal. Often written as a/b = c/d. Memory trick: 'Proportion' has 'port' like 'portion' — the two portions are balanced.
比例：表示两个比相等的等式。常写作 a/b = c/d。记忆法：“比例”含有“例”字，两个例子等价；两边份额均衡。
ortion: A relationship where two quantities increase or decrease at the same rate. y = kx. Memory trick: 'Direct' means they move together in the same direction — as one doubles, the other doubles.
正比例：两个量以恒定速率同增同减的关系，y = kx。记忆法：“正”就是方向一致，一个变两倍，另一个也变两倍。
5. Equations & Inequalities | 方程与不等式
Equation: A mathematical sentence that states two expressions are equal, using the '=' sign. Memory trick: Think of a balance scale — both sides must weigh exactly the same.
方程：用等号“=”连接两个表达式，表明它们相等。记忆法：想象一架天平，两边必须完全平衡。
Solution (root): A value that makes an equation true when substituted for the variable. Memory trick: 'Solution' solves the puzzle; plug it in and both sides match.
解（根）：代入变量后使方程成立的数值。记忆法：“解”就是答案，填进去，等号两边就握手言和了。
< (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to). Memory trick: The open side of the symbol always faces the larger quantity — like a hungry mouth eating the bigger meal.
不等式：用 < (小于)、> (大于)、≤ (小于等于)、≥ (大于等于) 连接两个表达式的比较语句。记忆法：开口永远朝着较大的数，就像张大嘴要吃掉更大的那份。
Integer solution: A solution to an inequality that is a whole number. For example, if x > 2 and x < 5, integer solutions are 3 and 4. Memory trick: List all whole numbers that fit between the boundaries.
整数解：不等式的解为整数的情形。如 x > 2 且 x < 5，整数解是 3 和 4。记忆法：在边界之间把所有合适的整数一个个挑出来。
6. Geometry: Angles & Lines | 几何：角与线
Acute angle: An angle measuring between 0° and 90°. Memory trick: 'A-cute' little angle — small and sharp, like the tip of a pencil.
锐角：度数在0°和90°之间的角。记忆法：“锐”利的小角，像铅笔尖一样尖细。
Obtuse angle: An angle greater than 90° but less than 180°. Memory trick: 'Obtuse' sounds like 'ob-large' — bigger than a right angle, fat and wide.
钝角：大于90°且小于180°的角。记忆法：“钝”角好比不锋利的大开口，胖乎乎的。
Perpendicular lines: Two lines that intersect at a right angle (90°). Memory trick: The symbol ⟂ looks like a corner of a square. 'Perpendicular' reminds of 'perfect corner'.
垂直线：相交成直角（90°）的两条直线。记忆法：符号 ⟂ 像正方形的角。'Perpendicular' 可联想“完美拐角”。
Parallel lines: Lines in a plane that never meet, no matter how far they are extended. Marked with arrow symbols. Memory trick: 'Parallel' has two l's side by side, just like parallel tracks.
平行线：同一平面内永不相交的直线，用箭头标记。记忆法：'Parallel' 中间有两条 l 并排，就像平行的铁轨。
Bisect: To divide an angle or a line segment into two equal parts. Memory trick: 'Bi-' means two, '-sect' means cut — cut into two identical halves.
平分：把一个角或一条线段分成两个相等的部分。记忆法：“Bi-”是二，“sect”是切，切成完全一样的两半。
7. Properties of Shapes | 图形的性质
Quadrilateral: A polygon with four sides. Examples: square, rectangle, rhombus, trapezium. Memory trick: 'Quad' means four, like a quad bike with four wheels.
四边形：有四条边的多边形。如正方形、矩形、菱形、梯形。记忆法：'Quad' 意思是四，就像四个轮子的四轮摩托。
Parallelogram: A quadrilateral with two pairs of parallel sides. Opposite sides are equal in length. Memory trick: 'Parallelogram' starts with 'parallel' — its opposite sides never meet.
平行四边形：两组对边分别平行的四边形。对边长度相等。记忆法：名称里有“平行”，对边永不相遇。
Polygon: A closed 2D figure with straight sides. Names depend on the number of sides (pentagon - 5, hexagon - 6, octagon - 8). Memory trick: 'Poly' means many, 'gon' means angle — many angles closed together.
多边形：由直线段围成的封闭二维图形。按边数命名（五边形、六边形、八边形）。记忆法：'Poly' 是多，'gon' 是角，拼在一起就是多个角围成的形状。
Regular polygon: A polygon where all sides and all interior angles are equal. Memory trick: 'Regular' means all parts follow the same rule — everything is symmetrical and equal.
正多边形：所有边长和内角都相等的多边形。记忆法：“正”就是规矩，每条边每个角都一样大。
8. Area, Perimeter & Volume | 面积、周长与体积
erimeter: The total distance around the outside of a shape. For a rectangle, P = 2(l + w). Memory trick: 'Peri-' means around, 'meter' means measure — measure around the shape.
周长：图形外边线的总长度。长方形周长 P = 2(长+宽)。记忆法：“周”就是环绕一周，“长”是长度，绕场跑一圈的距离。
Area: The amount of space inside a 2D shape, measured in square units. Memory trick: Imagine covering the shape with square tiles — count how many fit.
面积：二维图形内部空间的大小，以平方单位计量。记忆法：想象用方砖铺满图形，数数用了多少块。
Volume: The amount of space occupied by a 3D object, measured in cubic units. Memory trick: 'Volume' can also mean loudness — but here it's how much 3D space you 'fill up'.
体积：三维物体占据的空间大小，以立方单位计量。记忆法：'Volume' 也有音量的意思，这里指能“填满”多大的立体空间。
Surface area: The total area of all faces of a 3D solid. Memory trick: Think of unwrapping the solid into a net and finding the area of the entire wrapper.
表面积：三维立体所有面的总面积。记忆法：把立体展开成平面图（展开图），计算整张“包装纸”的面积。
9. Transformations & Symmetry | 变换与对称
Translation: Sliding a shape from one position to another without rotating, resizing, or flipping. Every point moves the same distance in the same direction. Memory trick: 'Translation' is like sliding a book across a table — no turning, just shifting.
平移：将图形从一个位置滑移到另一个位置，不旋转、不改变大小、不翻转。每一点移动的距离和方向相同。记忆法：像在桌上推一本书，只移动不转圈。
Reflection: Flipping a shape over a mirror line (line of reflection) to produce a mirror image. Memory trick: 'Reflection' is what you see in a mirror — the image is reversed but the same size.
反射（翻转）：把图形沿着一条镜面线（对称轴）翻折，得到镜像。记忆法：“反射”就是照镜子的镜像，左右颠倒但大小不变。
Rotation: Turning a shape about a fixed point (centre of rotation) through a given angle and direction. Memory trick: Imagine a spinning windmill — the blades rotate around a centre.
旋转：绕着一个固定点（旋转中心）按给定角度和方向转动图形。记忆法：像风车叶片绕中心转动，位置变化但形状大小不变。
Line symmetry: A shape has line symmetry if one half is the mirror image of the other half when folded along a line. Memory trick: The fold line is the line of symmetry — fold and the two halves match perfectly.
线对称：如果一个图形沿一条直线对折后完全重合，则它具有线对称。记忆法：这条对折线就是对称轴，折过来两边严丝合缝。
10. Statistics & Data Handling | 统计与数据处理
Mean: The average, calculated by adding all values and dividing by the number of values. Memory trick: 'Mean' means 'average' — share the total equally among all.
平均数（均值）：所有数值相加后除以个数得到的平均值。记忆法：“平均”就是把总数公平分给每个人。
Median: The middle value when data is arranged in order. If there are two middle numbers, it's the mean of those two. Memory trick: 'Median' sounds like 'medium' — it sits right in the middle of the road.
中位数：将数据排序后位于正中间的值。如果有两个中间数，则取它们的平均数。记忆法：“中位数”就是中间那个数，像道路中线。
Mode: The value that appears most frequently in a data set. Memory trick: 'Mode' and 'most' both start with 'mo' — most often seen value.
众数：数据集中出现次数最多的值。记忆法：“众”就是人多，出现频率最高的那个数。
Range: The difference between the largest and smallest values in a data set. It measures spread. Memory trick: 'Range' stretches from the minimum to the maximum — it covers the whole spread.
极差（范围）：数据中最大值与最小值的差，衡量数据的分散程度。记忆法：“范围”从最小的延伸到最大的，覆盖整个跨度。
Discrete data: Data that can only take specific, separate values (often whole numbers). Example: number of students. Memory trick: 'Discrete' means distinct — you can't have half a student, so values jump in steps.
离散数据：只能取特定、可分离的值（常为整数）。如学生人数。记忆法：“离散”就是一个个分开的，你不可能有半个学生，数值只能跳着走。
11. Probability | 概率
Probability: A measure of how likely an event is to happen, expressed as a fraction, decimal, or percentage between 0 (impossible) and 1 (certain). Memory trick: 'Prob-ability' = the ability (chance) that something will probably occur.
概率：衡量事件发生可能性的量，用0（不可能）到1（必然）之间的分数、小数或百分数表示。记忆法：“概”率就是大概可能的程度，越接近1越肯定。
Outcome: A possible result of a probability experiment. Memory trick: An 'outcome' is what comes out after the trial.
结果：概率试验中可能出现的某一个情形。记忆法：“结果”就是试验后跑出来的那个答案。
Event: A set of one or more outcomes that we are interested in. Memory trick: An 'event' is a collection of outcomes — like the event 'rolling an even number' includes 2, 4, 6.
事件：由感兴趣的一个或多个结果组成的集合。记忆法：“事件”比单个结果大，比如“掷出偶数”这个事件包含了2、4、6几个结果。
Sample space: The set of all possible outcomes of an experiment. Often shown as a list or a grid. Memory trick: 'Sample space' is the full menu of everything that could happen.
样本空间：一项试验所有可能结果的集合，常用列表或表格表示。记忆法：“样本空间”就是全部可能选项的菜单，无一遗漏。
Mutually exclusive: Two events that cannot happen at the same time. Memory trick: 'Mutually exclusive' means they exclude each other — like turning left and turning right at the same instant.
互斥事件：两个不可能同时发生的事件。记忆法：“互相排斥”，有你没我，就像同时向左转和向右转。
12. Graphs & Coordinates | 图形与坐标
Cartesian plane: A two-dimensional grid formed by a horizontal x-axis and a vertical y-axis. Points are located using ordered pairs (x, y). Memory trick: 'Cartesian' comes from Descartes who said 'I think, therefore I locate points'. Think of the plane as a map with x and y streets.
笛卡尔平面：由水平x轴和垂直y轴构成的二维网格，用有序数对 (x, y) 定位。记忆法：想象一张地图，x街和y街交叉就能找到位置。
Origin: The point (0, 0) where the x-axis and y-axis intersect on a coordinate plane. Memory trick: 'Origin' is where everything starts — the centre of the graph.
原点：坐标平面上x轴和y轴的交点 (0, 0)。记忆法：“原”点就是一切的起点，就像旅程的出发点。
Gradient (slope): A measure of steepness of a line, calculated as rise over run (change in y / change in x). Memory trick: 'Gradient' sounds like 'grade' — how steep the grade of a hill is.
斜率（坡度）：衡量直线陡峭程度的量，等于铅垂变化除以水平变化（Δy/Δx）。记忆法：爬坡的“坡”度；斜率越大，坡越陡。
Intercept: The point where a line crosses an axis. The y-intercept is where the line meets the y-axis. Memory trick: 'Intercept' means to cut across — the line cuts the axis at that point.
截距：直线与坐标轴相交的点。y轴截距是直线与y轴的交点。记忆法：“截”就是切断，直线在此处切过轴线。
Linear graph: A straight-line graph whose equation can be written in the form y = mx + c. Memory trick: 'Linear' has 'line' inside — the graph is a single straight line.
线性图：方程可写成 y = mx + c 形式的直线图。记忆法：'Linear' 里藏着 'line'，所以画出来就是一条笔直的线。
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