📚 Year 8 WJEC Further Mathematics: Vocabulary Quick Revision Guide | 八年级 WJEC 进阶数学词汇术语速记指南
Mastering mathematical vocabulary is essential for success in Year 8 WJEC Further Mathematics. This guide provides clear definitions of key terms spanning number, algebra, geometry, statistics and probability. Each entry pairs an English explanation with its Chinese equivalent, helping you build confidence and fluency in problem-solving while preparing for assessments.
掌握数学词汇是八年级 WJEC 进阶数学取得成功的关键。本指南涵盖了数字、代数、几何、统计与概率等关键术语的清晰定义。每个词条都配有英文解释和对应的中文说明，帮助你在解题和备考中建立自信与流畅度。
1. Number and Arithmetic Vocabulary | 数字与算术词汇
Integer: A whole number that can be positive, negative, or zero, but not a fraction or decimal. Examples: −7, 0, 15.
整数：正整数、负整数或零，不是分数或小数。例如：−7、0、15。
Prime number: A number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Example: 2, 3, 5, 7, 11.
质数（素数）：大于 1 且只有两个不同正因数的数：1 和它自身。例如：2、3、5、7、11。
Factor: A whole number that divides another number exactly, leaving no remainder. For instance, the factors of 12 are 1, 2, 3, 4, 6 and 12.
因数：能整除另一个数而没有余数的整数。例如，12 的因数有 1、2、3、4、6 和 12。
Multiple: The product obtained when a number is multiplied by an integer. The multiples of 5 are 5, 10, 15, 20, …
倍数：一个数与整数相乘所得的积。5 的倍数有 5、10、15、20 ……
Highest Common Factor (HCF): The largest factor shared by two or more numbers. The HCF of 18 and 24 is 6.
最大公因数：两个或更多数共有的最大的因数。18 和 24 的最大公因数是 6。
Lowest Common Multiple (LCM): The smallest multiple that is common to two or more numbers. The LCM of 4 and 6 is 12.
最小公倍数：两个或更多数共有的最小的倍数。4 和 6 的最小公倍数是 12。
Square number hen an integer is multiplied by itself. Example: 25 is a square number because 5 × 5 = 25.
平方数：一个整数与其自身相乘得到的结果。例如，25 是平方数，因为 5 × 5 = 25。
Cube number : The result when an integer is multiplied by itself twice. Example: 8 is a cube number because 2 × 2 × 2 = 8.
立方数：一个整数与其自身相乘两次得到的结果。例如，8 是立方数，因为 2 × 2 × 2 = 8。
Index (power) many times the base is multiplied by itself. In 3⁴, the index is 4, meaning 3 × 3 × 3 × 3.
指数（幂）：写在底数右上角的小数字，表示底数自身相乘的次数。在 3⁴ 中，指数是 4，表示 3 × 3 × 3 × 3。
Standard form ers using powers of 10. The general form is a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
标准形式：利用 10 的幂来书写非常大或非常小的数字的方法。一般形式为 a × 10ⁿ，其中 1 ≤ a < 10 且 n 为整数。
Significant figures (sf): The meaningful digits in a number, used to express its precision. The first non-zero digit is the first significant figure.
有效数字：一个数字中有意义的数位，用来表示其精确度。第一个非零数字是第一个有效数字。
2. Algebraic Terminology | 代数术语
Variable: A symbol, usually a letter, that represents an unknown or changeable value. In the expression 4x + 2, x is the variable.
变量：一个符号，通常是一个字母，表示未知或可变的值。在表达式 4x + 2 中，x 是变量。
Constant: A fixed value that does not change. In 3y + 5, the number 5 is a constant.
常量：一个固定不变的数值。在 3y + 5 中，数字 5 是常量。
Term: A single mathematical entity, which may be a number, a variable, or numbers and variables multiplied together. In 2a + 3b − 7, there are three terms: 2a, 3b and −7.
项：单一的数学实体，可以是一个数字、一个变量，或数字与变量的乘积。在 2a + 3b − 7 中，有三项：2a、3b 和 −7。
Coefficient: The numerical factor of a term that contains a variable. In 5x, the coefficient is 5.
系数：含有变量的项中的数字因数。在 5x 中，系数是 5。
Expression mbers, variables and operations (+, −, ×, ÷) without an equals sign. Example: 2p + 3q − 1.
表达式：数字、变量和运算符号（+、−、×、÷）的组合，没有等号。例如：2p + 3q − 1。
Simplify (collect like terms): To reduce an expression to its simplest form by combining terms that have the same variable raised to the same power. 3x + 5x simplifies to 8x.
化简（合并同类项）：通过合并具有相同变量和相同指数的项，将表达式化为最简形式。3x + 5x 化简为 8x。
Expand brackets: To multiply each term inside a set of brackets by the term outside, removing the brackets. For example, 2(a + 3) expands to 2a + 6.
去括号展开：将括号外的项乘以括号内的每一项，从而去掉括号。例如，2(a + 3) 展开得到 2a + 6。
Factorise (common factor): To rewrite an expression as a product of its factors, often by taking out the highest common factor. 4x + 6 factorises to 2(2x + 3).
因式分解（提取公因数）：将一个表达式重写为它的因数的乘积，通常通过提取最大公因数。4x + 6 分解为 2(2x + 3)。
Substitution iable with a numerical value in an expression or formula. If x = 2, then 3x + 1 becomes 7.
代入法：在表达式或公式中将变量替换为数值的过程。若 x = 2，则 3x + 1 为 7。
Formula ls sign, connecting two or more variables. Example: A = l × w for the area of a rectangle.
公式：使用符号和等号表达的数学规则，连接两个或多个变量。例如，长方形的面积公式为 A = l × w。
3. Equations and Inequalities | 方程与不等式
Equation tement showing that two expressions are equal, using an equals sign. Example: 2x + 5 = 11.
方程：表示两个表达式相等的数学陈述，使用等号。例如：2x + 5 = 11。
Solve: To find the value(s) of the variable that make the equation true.
解方程：求出使方程成立的变量的值。
Solution (root) he value of the unknown that satisfies the equation. For x + 3 = 7, the solution is x = 4.
解（根）：满足方程的未知数的值。对于 x + 3 = 7，解是 x = 4。
Linear equation t : An equation where the highest power of the variable is 1, producing a straight line when graphed. Example: y = 2x + 1.
线性方程：变量的最高次幂为 1 的方程，其图像是一条直线。例如：y = 2x + 1。
Unknown: The variable in an equation whose value needs to be determined.
未知数：方程中需要确定其值的变量。
Balance method oth sides to keep the equation balanced. Adding 3 to both sides of x − 3 = 7 gives x = 10.
天平法：通过对方程两边执行相同的操作来保持方程平衡的解题技术。在 x − 3 = 7 两边加 3，得到 x = 10。
Inverse operation: The opposite mathematical operation that undoes another. Addition and subtraction are inverse operations; multiplication and division are inverses.
逆运算：能撤销另一种运算的相反数学运算。加法和减法互为逆运算，乘法和除法互为逆运算。
Inequality ing two expressions using symbols <, >, ≤, or ≥. Example: x > 3 means x is greater than 3.
不等式：使用符号 <、>、≤ 或 ≥ 比较两个表达式的数学陈述。例如：x > 3 表示 x 大于 3。
Symbols: <, >, ≤, ≥: 'Less than', 'greater than', 'less than or equal to', and 'greater than or equal to' respectively. They define a range of possible values.
符号：<, >, ≤, ≥：分别表示“小于”、“大于”、“小于或等于”和“大于或等于”。它们定义了一个可能值的范围。
Satisfy at : An inequality is satisfied by any value that makes the statement true. The inequality n > 2 is satisfied by n = 5, but not by n = 1.
满足：任何使不等式成立的数值都称满足该不等式。不等式 n > 2 被 n = 5 满足，但不被 n = 1 满足。
4. Sequences and Patterns | 序列与模式
Sequence: An ordered list of numbers or objects that follows a specific rule. Each number in the sequence is called a term.
序列：按照特定规则排列的一列数字或物体。序列中的每个数字称为一项。
Term: An individual number or element in a sequence. In the sequence 2, 4, 6, 8, …, the first term is 2.
项：序列中的单个数字或元素。在序列 2、4、6、8 …… 中，第一项是 2。
Arithmetic sequence s is constant. This difference is called the common difference (d). Example: 3, 7, 11, 15, … (d = 4).
等差数列：相邻两项的差是一个常数的序列。这个差称为公差（d）。例如：3、7、11、15 ……（d = 4）。
Common difference (d): The fixed amount added to each term to get the next term in an arithmetic sequence.
公差 (d)：在等差数列中，每一项加上一个固定数得到下一项，这个固定数就是公差。
Geometric sequence lying the previous term by a constant, called the common ratio (r). Example: 2, 6, 18, 54, … (r = 3).
等比数列：每一项都是前一项乘以一个常数得到的序列，这个常数称为公比（r）。例如：2、6、18、54 ……（r = 3）。
Common ratio (r): The constant multiplier used to find consecutive terms in a geometric sequence.
公比 (r)：在等比数列中用来得到连续各项的常数乘数。
nth term uence directly, based on its position (n). For an arithmetic sequence: aₙ = a₁ + (n − 1)d.
第 n 项：一个公式，可以根据项的位置 n 直接求出数列中的任何一项。等差数列：aₙ = a₁ + (n − 1)d。
aₙ = a₁ + (n − 1)d
Position-to-term rule: A rule that links the position number (n) directly to the term value. For the sequence 5, 10, 15, 20, …, the rule is 5n.
位置-项规则：将位置编号 n 直接与项的值联系起来的规则。对于序列 5、10、15、20 ……，规则是 5n。
Term-to-term rule: A rule that tells you how to get from one term to the next. Example: start at 3, add 2 each time.
项-项规则：告诉你如何从一项得到下一项的规则。例如：从 3 开始，每次加 2。
Triangular numbers: A sequence of numbers that can form an equilateral triangle. The nth triangular number is ½ n(n+1). The sequence begins 1, 3, 6, 10, 15, …
三角形数：能排列成等边三角形的数列。第 n 个三角形数为 ½ n(n+1)。数列开头为 1、3、6、10、15 ……
Square numbers (as a sequence): The sequence 1, 4, 9, 16, 25, … where the nth term is n².
平方数序列：序列 1、4、9、16、25 ……，其中第 n 项为 n²。
Fibonacci-like sequences: Sequences where each term is the sum of the two preceding terms. The classic Fibonacci sequence starts 1, 1, 2, 3, 5, 8, …
类斐波那契数列：每一项是前两项之和的数列。经典的斐波那契数列以 1、1、2、3、5、8 …… 开始。
5. Coordinates and Linear Graphs | 坐标与线性图
Coordinate: A pair of numbers (x, y) that defines the position of a point on a grid. The first number is the x-coordinate, the second is the y-coordinate.
坐标：一对数字 (x, y)，定义点在网格上的位置。第一个数是 x 坐标，第二个数是 y 坐标。
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