📚 Year 9 CCEA Maths: Quick Vocabulary & Terminology Memorisation Guide | Year 9 CCEA 数学：词汇术语速记指南
Mastering mathematical vocabulary is essential for success in Year 9 CCEA Maths. This guide provides clear definitions, paired with Chinese translations, and memory tips to help you quickly learn and recall key terms. By linking words to their meanings, you’ll improve your problem-solving skills and exam confidence.
掌握数学词汇是在 CCEA 九年级数学中取得成功的关键。本指南提供清晰的定义、中文翻译以及记忆技巧，帮助你快速学习并回忆关键术语。将词汇与其含义联系起来，你将提高解题能力和考试信心。
1. Number Family | 数的家族
Natural numbers are the counting numbers starting from 1 (1, 2, 3, …). They do not include zero or negative numbers.
自然数是从 1 开始的计数数 (1, 2, 3, …)。它们不包括零或负数。
Whole numbers include all natural numbers together with zero (0, 1, 2, 3, …).
整数包括所有自然数以及零 (0, 1, 2, 3, …)。
Integers are whole numbers and their negative counterparts (… -3, -2, -1, 0, 1, 2, 3 …). They have no fractional part.
整数是正整数、负整数和零 (… -3, -2, -1, 0, 1, 2, 3 …)，没有小数部分。
Rational numbers are any numbers that can be written as a fraction a/b, where a and b are integers and b ≠ 0. This includes terminating and recurring decimals.
有理数是任何可以写成分数 a/b 形式的数，其中 a 和 b 是整数且 b ≠ 0。包括有限小数和循环小数。
Irrational numbers cannot be expressed as exact fractions. Their decimal forms neither terminate nor repeat, such as π and √2.
无理数不能用精确的分数表示。它们的小数形式既不终止也不循环，例如 π 和 √2。
Real numbers consist of all rational and irrational numbers. In Year 9, you mainly work within the real number system.
实数由所有有理数和无理数组成。九年级主要是在实数范围内学习。
2. Factors, Multiples and Primes | 因数、倍数与质数
A factor is a whole number that divides another number exactly, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12.
因数是一个能整除另一个数的整数，整除后没有余数。例如，12 的因数有 1, 2, 3, 4, 6 和 12。
A multiple is the result of multiplying a given whole number by another integer. Multiples of 5 are 5, 10, 15, 20, …
倍数是将一个给定的整数乘以另一个整数所得的结果。5 的倍数有 5, 10, 15, 20, …
A prime number has exactly two distinct factors: 1 and the number itself. Examples: 2, 3, 5, 7, 11.
质数恰好有两个不同的因数：1 和它本身。例如：2, 3, 5, 7, 11。
A composite number has more than two factors. For instance, 8 has factors 1, 2, 4, 8.
合数有两个以上的因数。例如，8 的因数有 1, 2, 4, 8。
Highest common factor (HCF) is the largest factor shared by two or more numbers. For 12 and 18, HCF = 6.
最大公因数 (HCF) 是两个或多个数共有的最大因数。12 和 18 的最大公因数为 6。
Lowest common multiple (LCM) is the smallest multiple shared by two or more numbers. For 4 and 5, LCM = 20.
最小公倍数 (LCM) 是两个或多个数共有的最小倍数。4 和 5 的最小公倍数为 20。
Memory Tip: Think of ‘factor’ as a number that ‘fits into’ another like pieces of a whole; ‘multiple’ is what you get when you ‘multiply up’.
记忆窍门：把 ‘factor’（因数）想象成能“镶嵌”进另一个数的碎片；’multiple’（倍数）则是“乘上去”得到的结果。
3. Fractions, Decimals and Percentages | 分数、小数和百分数
The numerator is the top number of a fraction, indicating how many parts are taken. The denominator is the bottom number, showing the total number of equal parts the whole is divided into.
分子是分数中上面的数，表示取了多少份。分母是下面的数，表示整体被等分的总份数。
A proper fraction has a numerator smaller than its denominator, e.g. 3/4. An improper fraction has a numerator larger than or equal to its denominator, e.g. 7/4.
真分数的分子小于分母，例如 3/4。假分数的分子大于或等于分母，例如 7/4。
A mixed number combines a whole number and a proper fraction, such as 1½ (one and a half).
带分数由一个整数和一个真分数组合而成，例如 1½（一又二分之一）。
Equivalent fractions name the same portion of a whole even though they use different numbers, e.g. 1/2 = 2/4 = 3/6.
等价分数尽管使用不同的数字，但表示整体中的相同部分，例如 1/2 = 2/4 = 3/6。
A percentage means ‘out of 100’; it is a special fraction with denominator 100. 45% equals 45/100.
百分数意为“每一百中的”，是分母为 100 的特殊分数。45% 等于 45/100。
To convert between forms, remember: fraction → decimal: divide numerator by denominator; decimal → percentage: multiply by 100; percentage → fraction: write over 100 and simplify.
进行形式转换时记住：分数 → 小数：用分子除以分母；小数 → 百分数：乘以 100；百分数 → 分数：写成 100 分之后化简。
4. Algebraic Expressions | 代数表达式
A variable is a symbol, usually a letter like x or y, that represents an unknown or changeable value.
变量是一个符号，通常用 x 或 y 等字母表示，代表未知或可变化的值。
A constant is a fixed number that does not change, such as 5 in the expression 3x + 5.
常数是一个固定不变的数值，例如表达式 3x + 5 中的 5。
A term is a single number, variable, or product of numbers and variables. In 4x² + 2x – 7, there are three terms.
项是一个单独的数、变量或数与变量的乘积。在 4x² + 2x – 7 中，有三项。
A coefficient is the numerical factor multiplying a variable in a term. In 4x², the coefficient is 4.
系数是项中与变量相乘的数字因数。在 4x² 中，系数为 4。
An expression is a collection of terms linked by operation symbols but with no equals sign. Example: 2a + 5b – 3.
表达式是由运算符号连接的项的组合，没有等号。例如：2a + 5b – 3。
Like terms have exactly the same variable part to the same power; they can be combined. 3x and -5x are like terms.
同类项具有完全相同的变量部分且指数相同；它们可以合并。3x 和 -5x 是同类项。
Expanding brackets means multiplying each term inside the bracket by the term outside, e.g. 3(m + 2) = 3m + 6.
展开括号是指将括号外的项与括号内的每一项相乘，例如 3(m + 2) = 3m + 6。
Factorising is the reverse of expanding: you express an expression as a product, e.g. 3m + 6 = 3(m + 2).
因式分解是展开的逆运算：你将一个表达式表示为乘积形式，例如 3m + 6 = 3(m + 2)。
Memory Tip: ‘Expand’ opens up the expression; ‘factorise’ packs it back into a product.
记忆窍门：’Expand’（展开）是把表达式打开；’factorise’（分解）是把它打包回乘积。
5. Equations, Formulae and Inequalities | 方程、公式与不等式
An equation is a mathematical statement showing two expressions are equal, connected by an equals sign ‘=’. Example: 2x + 3 = 11.
方程是一个数学陈述，用等号 ‘=’ 连接两个相等的表达式。例如：2x + 3 = 11。
The solution to an equation is the value of the variable that makes the equation true. For x + 5 = 8, the solution is x = 3.
方程的解是使方程成立的变量的值。对于 x + 5 = 8，解是 x = 3。
A formula is a special equation that shows the relationship between different quantities, such as A = lw for area of a rectangle.
公式是一种特殊的方程，表示不同量之间的关系，例如矩形的面积公式 A = lw。
An inequality compares two expressions using symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to). Example: x > 4 means x can be any number greater than 4.
不等式用符号比较两个表达式：< (小于), > (大于), ≤ (小于或等于), ≥ (大于或等于)。例如：x > 4 表示 x 可以是任何大于 4 的数。
Solving inequalities is similar to solving equations, but remember if you multiply or divide by a negative number, the inequality sign reverses.
解不等式与解方程类似，但记住：如果乘以或除以一个负数，不等号方向要反转。
6. Angles and Their Relationships | 角及其关系
An angle is formed when two rays meet at a common point called the vertex. It is measured in degrees (°).
角由两条射线在称为顶点的公共点相交形成。以度数 (°) 量度。
Acute angle: between 0° and 90°. Right angle: exactly 90°. Obtuse angle: between 90° and 180°. Straight angle: exactly 180°. Reflex angle: between 180° and 360°.
锐角：0° 至 90° 之间。直角：恰好 90°。钝角：90° 至 180° 之间。平角：恰好 180°。优角：180° 至 360° 之间。
Complementary angles add up to 90°. Supplementary angles add up to 180°.
互余角之和为 90°。互补角之和为 180°。
Vertically opposite angles are formed when two lines intersect; they are always equal in measure.
对顶角由两条直线相交形成；它们的度数总是相等。
Adjacent angles share a common vertex and side but do not overlap.
邻角共享一个公共顶点和一条公共边，但不重叠。
A bearing is a three-figure degree measurement used to describe direction, measured clockwise from north.
方位角是一个三位数的度数度量，用于描述方向，从正北开始顺时针测量。
7. Triangles and Quadrilaterals | 三角形与四边形
An equilateral triangle has all three sides equal and every angle 60°.
等边三角形三条边都相等，每个角都是 60°。
An isosceles triangle has two equal sides and two equal base angles.
等腰三角形有两条相等的边和两个相等的底角。
A scalene triangle has no equal sides and no equal angles.
不等边三角形没有相等的边，也没有相等的角。
A right-angled triangle contains one 90° angle. The side opposite the right angle is the hypotenuse, the longest side.
直角三角形包含一个 90° 角。直角所对的边是斜边，即最长的边。
Quadrilaterals are four-sided polygons. A square has four equal sides and four right angles. A rectangle has opposite sides equal and four right angles.
四边形是四边形多边形。正方形有四条相等的边和四个直角。长方形对边相等且有四个直角。
A parallelogram has both pairs of opposite sides parallel. A rhombus is a parallelogram with all sides equal. A trapezium has exactly one pair of parallel sides.
平行四边形两组对边分别平行。菱形是所有边相等的平行四边形。梯形只有一组对边平行。
The sum of interior angles in any quadrilateral is 360°.
任意四边形的内角和为 360°。
8. Symmetry, Reflection, Rotation, Translation | 对称、反射、旋转、平移
Line symmetry (reflective symmetry) means a shape can be folded along a line so that both halves match exactly; this line is the line of symmetry.
线对称（反射对称）指一个图形沿某条直线对折后，两部分完全重合；这条直线就是对称轴。
Rotational symmetry is when a shape looks exactly the same after being rotated around its centre by a certain angle. The order of rotational symmetry is how many times it matches itself within a full turn.
旋转对称是指一个图形绕其中心旋转一定角度后与自身完全重合。旋转对称的阶数是在一整圈内它能与自身重合的次数。
A reflection is a transformation that flips a shape over a mirror line; the image is congruent but reversed.
反射是一种变换，将图形沿镜面线翻转；其像与原图形全等但方向相反。
A rotation turns a shape about a fixed centre point; you must state the centre, angle and direction (clockwise/anticlockwise).
旋转绕着一个固定中心点转动图形；你需要说明旋转中心、角度和方向（顺时针/逆时针）。
A translation slides a shape without turning or flipping; it is described by a vector, often as a column vector showing movement in x and y directions.
平移在不转动、不翻转的情况下滑动图形；它由一个向量描述，通常是用列向量表示沿 x 和 y 方向的移动。
Congruent shapes are identical in shape and size. Similar shapes have the same angles and proportional side lengths.
全等图形形状和大小完全相同。相似图形角度相同，对应边成比例。
9. Measures: Length, Area, Volume, Capacity, Mass | 度量：长度、面积、体积、容量、质量
Perimeter is the total distance around the outside of a 2D shape; measured in units like mm, cm, m, km.
周长是围绕二维图形外部的总距离；以毫米、厘米、米、千米等为单位。
Area is the amount of surface a shape covers; measured in square units (mm², cm², m²).
面积是图形覆盖的表面大小；以平方单位 (mm², cm², m²) 度量。
Volume is the space occupied by a 3D object; measured in cubic units (cm³, m³).
体积是三维物体所占的空间；以立方单位 (cm³, m³) 度量。
Capacity refers to the amount a container can hold, typically measured in millilitres (ml) and litres (l). 1 l = 1000 ml, 1 cm³ = 1 ml.
容量指容器所能容纳的量，通常以毫升 (ml) 和升 (l) 度量。1 升 = 1000 毫升，1 立方厘米 = 1 毫升。
Mass is the amount of matter in an object, measured in grams (g) and kilograms (kg). 1 kg = 1000 g.
质量是物体所含物质的多少，以克 (g) 和千克 (kg) 度量。1 千克 = 1000 克。
Metric prefixes help scale units: milli- means 1/1000, centi- means 1/100, kilo- means 1000.
公制前缀帮助换算单位：milli- 表示 1/1000，centi- 表示 1/100，kilo- 表示 1000。
10. Statistics: Averages and Range | 统计：平均数与极差
Mean (arithmetic average) is calculated by adding all values and dividing by the number of values. For the set 3, 7, 8, the mean is (3+7+8)÷3 = 6.
平均数（算术平均值）是将所有数值相加后除以数值的个数。对于数据集 3, 7, 8，平均数为 (3+7+8)÷3 = 6。
Median is the middle value when data are arranged in order. For an even number of values, it is the mean of the two middle numbers.
中位数是将数据按顺序排列后位于中间的数。若数据个数为偶数，则为中间两个数的平均值。
Mode is the value that appears most frequently. A set can have one mode, more than one mode, or no mode at all.
众数是出现次数最多的数值。一组数据可以有一个众数、多个众数或没有众数。
Range is the difference between the highest and lowest values, measuring how spread out the data is. Range = maximum – minimum.
极差是最大值与最小值的差，衡量数据的
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