📚 Year 9 WJEC Maths: Vocabulary & Terminology Quick Memorisation Guide | 九年级 WJEC 数学：词汇术语速记指南
Mastering mathematical vocabulary is one of the quickest ways to boost your confidence in Year 9 WJEC Maths. When you understand the precise meaning of terms, questions become less confusing and explanations clearer. This guide pairs each key term with a plain English definition and a Chinese translation, along with a quick memory tip where useful. Use it for daily review or last-minute revision.
掌握数学词汇是提升WJEC九年级数学自信心的最快途径之一。当你理解术语的精确含义时，题目会变得不那么令人困惑，解题思路也更清晰。本指南为每个关键术语提供简明英文定义与中文翻译，并在适当处附上速记提示。可供日常复习或考前冲刺使用。
1. Integers, Decimals and Place Value | 整数、小数与位值
Integer: An integer is a whole number that can be positive, negative, or zero, with no fractional or decimal part. For example, -5, 0 and 8 are integers. Think of the word ‘integral’ – complete and unbroken.
整数：整数是可以为正、负或零的整数，没有小数或分数部分。例如-5、0和8都是整数。记忆提示：整数就像“完整”无缺的数字。
Decimal: A decimal is a number that uses a decimal point to separate the whole part from the fractional part, such as 3.14 or 0.6. The digits after the point represent tenths, hundredths, thousandths and so on.
小数：小数是用小数点将整数部分与小数部分分开的数，如3.14或0.6。小数点后的数字依次表示十分位、百分位、千分位等。
Place value: The value of a digit determined by its position in a number. In 427, the 4 is worth 400 (hundreds), the 2 is worth 20 (tens) and the 7 is worth 7 (ones). In decimals, the first place after the point is tenths.
位值：一个数字在数中根据位置而具有的值。在427中，4代表400（百位），2代表20（十位），7代表7（个位）。在小数中，小数点后第一位是十分位。
Negative number: A number less than zero, written with a minus sign, e.g. -3. These are used for temperatures below zero, debts or depths below sea level.
负数：小于零的数，书写时带负号，例如-3。负数用于表示零下温度、债务或海平面以下的深度。
Significant figure (s.f.): A meaningful digit used to express a number to a certain degree of accuracy. The first significant figure is the first non-zero digit when reading from left to right. For example, 0.0052 rounded to 1 s.f. is 0.005, and to 2 s.f. is 0.0052 itself.
有效数字（s.f.）：用于表示数字精度的有意义数字。从左向右读取时，第一个非零数字即为第一个有效数字。例如，0.0052四舍五入到1个有效数字为0.005，到2个有效数字则为0.0052本身。
2. Fractions, Decimals and Percentages | 分数、小数和百分数
Fraction: A way of representing a part of a whole, written as numerator over denominator, such as ¾. The horizontal line means division: 3 divided by 4.
分数：表示整体的一部分，写作分子/分母，如¾。分数线表示除法：3除以4。
Numerator: The top number in a fraction, showing how many equal parts are taken. In ⅝, 5 is the numerator.
分子：分数中上方的数字，表示取了多少等份。在⅝中，5是分子。
Denominator: The bottom number in a fraction, showing the total number of equal parts the whole is divided into. In ⅝, the denominator is 8.
分母：分数中下方的数字，表示整体被分成的总等份数。在⅝中，分母是8。
Improper fraction: A fraction where the numerator is greater than or equal to the denominator, such as ⁷⁄₄. Its value is at least 1.
假分数：分子大于或等于分母的分数，如⁷⁄₄。其值至少为1。
Mixed number: A number consisting of a whole number and a proper fraction, e.g. 1¾. It represents the sum of the whole and the fraction.
带分数：由一个整数和一个真分数组成的数，例如1¾。它表示整数与分数的总和。
Percentage: A fraction out of 100, denoted by the symbol %. 45% means 45 out of 100 or 0.45. ‘Per cent’ means ‘per hundred’.
百分数：以100为分母的分数，用符号%表示。45%表示每100份中的45份，或0.45。“Percent”意为“每百”。
Equivalent fractions: Fractions that represent the same value, even though they use different numerators and denominators, such as ½ = ²⁄₄ = ³⁄₆.
等值分数：表示相同值但分子分母不同的分数，如½ = ²⁄₄ = ³⁄₆。
3. Ratio and Proportion | 比和比例
Ratio: A way of comparing two or more quantities, showing how many times one value contains another. Written with a colon, e.g. 3:2. The order matters – 3:2 is not the same as 2:3.
比：比较两个或多个数量的方式，表示一个值是另一个值的多少倍。用冒号书写，如3:2。顺序很重要——3:2与2:3不同。
Simplify a ratio: To divide every part of a ratio by the same common factor until the terms are the smallest possible whole numbers. 10:15 simplifies to 2:3 by dividing both sides by 5.
化简比：将比中每一项除以同一个公因数，直至各项成为最小可能的整数。10:15除以5后化简为2:3。
Proportion: A statement that two ratios are equal, or a way of showing how a total is shared. In direct proportion, as one quantity increases, the other increases at the same rate. Often set up as fractions: a/b = c/d.
比例：表示两个比相等的陈述，或表示总量如何分配的方式。在正比例中，一个量增加时，另一个以相同速率增加。常设为分数形式：a/b = c/d。
Unitary method: A technique for solving proportion problems by first finding the value of one unit, then scaling up or down. For example, if 5 oranges cost £1.50, find the cost of 1 orange (30p) and then multiply for any number.
归一法：解决比例问题的一种技巧，先求出一个单位的量，再放大或缩小。例如，若5个橙子1.50英镑，先求1个橙子的价钱（30便士），然后乘以任意数量。
4. Algebraic Expressions and Simplifying | 代数表达式与化简
Variable: A symbol, usually a letter, that stands for an unknown number or a number that can change. In the expression 3x + 2, x is the variable.
变量：通常用字母表示的符号，代表未知数或可变化的数。在表达式3x + 2中，x是变量。
Term: A single number, variable, or the product of numbers and variables separated by + or − signs. In 5a + 3b − 7, the terms are 5a, 3b and -7.
项：单个数字、变量，或由加减号分隔的数字与变量的乘积。在5a + 3b − 7中，项为5a、3b和-7。
Coefficient: The number multiplying a variable in a term. In 4y, the coefficient of y is 4. If no number is shown, the coefficient is 1 (e.g. p means 1p).
系数：项中与变量相乘的数字。在4y中，y的系数是4。如果没有显示数字，则系数为1（例如p表示1p）。
Constant: A term with a fixed value, containing no variables. In 2n + 5, 5 is the constant.
常数：具有固定值的项，不含变量。在2n + 5中，5是常数。
Like terms: Terms that contain exactly the same variable(s) raised to the same power. Only like terms can be combined by addition or subtraction. 3x and 5x are like terms; 3x and 3x² are not.
同类项：所含变量及其幂次完全相同的项。只有同类项可以通过加减合并。3x和5x是同类项；3x和3x²不是。
Expand brackets: To multiply each term inside a bracket by the term outside. 3(a + 4) expands to 3a + 12. Double brackets such as (x + 2)(x + 3) expand to x² + 5x + 6.
去括号：将括号外的项乘以括号内的每一项。3(a + 4)展开为3a + 12。双括号如(x + 2)(x + 3)展开为x² + 5x + 6。
Factorise: The reverse of expanding; writing an expression as a product of its factors. For example, 6x + 9 factorises to 3(2x + 3). Look for the highest common factor.
因式分解：展开的逆过程；将一个表达式写成其因式的乘积。例如，6x + 9因式分解为3(2x + 3)。寻找最大公因数。
5. Solving Linear Equations | 解线性方程
Equation: A mathematical statement that shows two expressions are equal, using an equals sign. 2x + 5 = 11 is an equation; 2x + 5 is an expression.
方程：用等号表示两个表达式相等的数学陈述。2x + 5 = 11是方程；2x + 5则是表达式。
Solve: To find the value(s) of the variable that make the equation true. The solution to x + 4 = 10 is x = 6.
解：求出使方程成立的变量的值。x + 4 = 10的解是x = 6。
Balance method: A visual way of solving equations by performing the same operation on both sides to keep the equation balanced. Imagine a scale: whatever you do to one side, you must do to the other.
平衡法：一种通过对方程两边进行相同运算来求解的直观方法。想象一座天平：对一边做什么，对另一边也必须做同样的操作。
Inverse operation: The opposite mathematical operation used to isolate the variable. Addition and subtraction are inverses; multiplication and division are inverses. To solve 3x = 12, you divide both sides by 3 (the inverse of multiplication).
逆运算：用于分离变量的相反数学运算。加法与减法互为逆运算，乘法与除法互为逆运算。解3x = 12时，两边同除以3（乘法的逆运算）。
Unknown: The symbol, often x or y, that represents the number we are trying to find in an equation.
未知数：方程中代表待求数字的符号，通常是x或y。
6. Linear Inequalities | 线性不等式
Inequality: A mathematical sentence comparing two expressions using inequality signs instead of an equals sign. It shows that one side is greater than, less than, or not equal to the other.
不等式：使用不等号而非等号比较两个表达式的数学句子。它表示一边大于、小于或不等于另一边。
Greater than (>) and Less than (<): > means the left side is larger than the right; < means the left side is smaller. The open side of the symbol faces the larger number. 7 > 3 is read as ‘7 is greater than 3’.
大于 (>) 与小于 (<)：> 表示左边比右边大；< 表示左边比右边小。符号的开口朝向较大的数。7 > 3读作“7大于3”。
Greater than or equal to (≥) and Less than or equal to (≤): ≥ includes the equality case, so the number can be equal to or larger than the given value. x ≥ 4 means x can be 4, 5, 6… and is shown on a number line with a closed circle.
大于等于 (≥) 与小于等于 (≤)：≥ 包含等于的情况，因此数可以等于或大于给定值。x ≥ 4 表示 x 可以是 4、5、6… 并在数轴上用实心圆点表示。
Solution set: All values that satisfy an inequality. For x > -1, any number greater than -1 is in the solution set. Often represented on a number line with an open circle for strict inequalities and a closed circle for inclusive ones.
解集：满足不等式的所有值。对于 x > -1，任何大于-1的数都在解集中。常在数轴上用空心圆圈表示严格不等式，用实心圆点表示包含等号的不等式。
7. Sequences and Patterns | 数列与规律
Sequence: An ordered list of numbers following a rule. Each number in the list is called a term. 3, 6, 9, 12… is a sequence with a rule ‘add 3’.
数列：按某种规则排列的一列有序数字。其中的每个数称为项。3, 6, 9, 12… 是一个规则为“加3”的数列。
Term-to-term rule: A rule that tells you how to get from one term to the next in a sequence. For 5, 10, 15, 20…, the term-to-term rule is ‘add 5’.
项间法则：说明如何从数列的一个项得到下一个项的规则。对于5, 10, 15, 20…，项间法则是“加5”。
Position-to-term rule (nth term): A formula that allows you to find any term in a sequence directly by its position number, n. For the sequence 4, 7, 10, 13…, the nth term is 3n + 1. To find the 10th term, substitute n = 10 to get 3(10) + 1 = 31.
位置至项的规则（第n项）：一种公式，能让你直接根据位置编号n找到数列中的任一项。对于数列4, 7, 10, 13…，第n项为3n + 1。要找到第10项，代入n = 10得3(10) + 1 = 31。
Arithmetic (linear) sequence: A sequence where the difference between consecutive terms is constant. This difference is called the common difference. 2, 5, 8, 11… has a common difference of +3.
等差数列（线性数列）：相邻两项之差为常数的数列。这个差称为公差。2, 5, 8, 11… 的公差为+3。
8. Angles and Properties of Shapes | 角度与图形性质
Angle: The measure of turn between two straight lines that meet at a point, measured in degrees (°). A full turn is 360°.
角：两条直线在一点相交时，衡量其张开程度的量，以度(°)为单位。一整圈为360°。
Acute angle: An angle that measures between 0° and 90°. Think ‘a-cute little angle’ – it is small and sharp.
锐角：角度在0°到90°之间的角。记忆：锐（acute）意为尖锐的小角。
Right angle: Exactly 90°, often marked with a small square in the corner of a diagram. A quarter turn.
直角：恰好90°，图中常在角处用小方块标记。为四分之一圈。
Obtuse angle: An angle between 90° and 180°. It is larger than a right angle but less than a straight line.
钝角：角度在90°到180°之间。比直角大，但小于平角。
Reflex angle: An angle between 180° and 360°. It is the larger angle when two lines meet.
优角：角度在180°到360°之间。是两条直线相交时较大的那个角。
Vertically opposite angles: When two lines cross, the angles opposite each other are equal. These are called vertically opposite angles.
对顶角：当两条直线相交时，彼此相对的角相等。这些角称为对顶角。
Parallel lines angle rules: When a line crosses two parallel lines, corresponding angles are equal, alternate angles are equal, and co-interior (allied) angles sum to 180°.
平行线角度法则：当一条线与两条平行线相交时，同位角相等，内错角相等，同旁内角之和为180°。
9. Perimeter, Area and Volume | 周长、面积和体积
Perimeter: The total distance around the outside of a 2D shape. For a rectangle, add the lengths of all four sides: P = 2l + 2w.
周长：二维图形外边界的总距离。对于长方形，将所有四边长相加：P = 2l + 2w。
Area: The amount of space inside a 2D shape, measured in square units (cm², m²). Rectangle area = length × width.
面积：二维图形内部空间的大小，以平方单位（cm², m²）计量。长方形面积 = 长 × 宽。
Volume: The amount of space occupied by a 3D object, measured in cubic units (cm³, m³). Volume of a cuboid = length × width × height.
体积：三维物体所占空间的大小，以立方单位（cm³, m³）计量。长方体体积 = 长 × 宽 × 高。
π (pi): The constant ratio of the circumference of any circle to its diameter, approximately 3.14 or ²²⁄₇. Circumference = π × diameter or 2πr, and area of a circle = πr².
π (圆周率)：任何圆的周长与其直径的恒定比值，约为3.14或²²⁄₇。圆周长 = π × 直径 或 2πr，圆面积 = πr²。
Formula: A mathematical rule expressed in symbols. For example, the area of a triangle is ½ × base × height, written as A = ½bh.
公式：用符号表示的数学规则。例如，三角形的面积是½ × 底 × 高，写作 A = ½bh。
Surface area: The total area of all faces of a 3D solid. For a cube, it is 6 × (side length)².
表面积：三维立体所有面的总面积。对于立方体，为6 × (边长)²。
10. Transformations: Translation, Reflection, Rotation, Enlargement | 变换：平移、反射、旋转、放大
Transformation: The movement or resizing of a shape on a coordinate grid. The original shape is the object, and the shape after transformation is the image.
变换：形状在坐标网格上的移动或大小变化。原始图形称为原像，变换后的图形称为影像。
Translation: A slide that moves a shape without turning, flipping or resizing it. Described by a column vector (x above y), e.g. (4, -3) means move 4 right and 3 down.
平移：不旋转、不翻转、不改变大小的滑动。用列向量（x在上，y在下）描述，如(4, -3)表示向右4、向下
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