📚 Year 7 WJEC Advanced Maths: Essential Vocabulary Quick-Reference Guide | WJEC 七年级进阶数学：核心词汇速记指南
Mastering advanced mathematics at Year 7 level requires a strong command of the key vocabulary used in the WJEC curriculum. Without knowing what terms like 'BIDMAS', 'integer', or 'perimeter' mean, pupils can find it difficult to understand questions and explain their reasoning. This quick-reference guide breaks down the essential terms topic by topic, providing clear definitions and simple memory tricks to help you learn and retain them faster.
要在七年级进阶数学中取得优异成绩，你必须牢牢掌握 WJEC 课程中使用的核心词汇。如果不理解 “BIDMAS”、“整数” 或 “周长” 等术语的含义，就很难读懂题目并进行逻辑推理。这份速记指南按主题梳理了必学术语，并附上清晰定义和简单的记忆窍门，帮助你更快地学习和记住它们。
1. Number and Place Value | 数字与位值
Integer: A whole number that has no fractional or decimal part. It can be positive, negative, or zero. For example, -6, 0, 15 are all integers. Think of 'integer' as something 'intact' or whole.
整数：没有分数或小数部分的完整数字，可以是正数、负数或零。例如 -6、0、15 都是整数。可以把“整数”想象成“完整的”数。
Negative Number: A number less than zero, written with a minus sign (-). For instance, -3 is three degrees below zero. Visualise a thermometer going down to remember its direction on a number line.
负数：小于零的数，用负号 (-) 表示。例如，-3 表示零下三度。想象温度计下降的场景，就能记住它在数轴上的方向。
Place Value: The value of a digit based on its position in a number. In 583, the digit 5 is in the hundreds place, so it means 500. Use a place value chart with columns: Thousands, Hundreds, Tens, Ones, to break down large numbers.
位值：数字中某一位数字根据其位置所代表的值。在 583 中，数字 5 在百位上，表示 500。借助位值表（千位、百位、十位、个位）可以轻松拆分大数。
Greater than (>) and Less than (<): These symbols compare values. Imagine a hungry crocodile whose open mouth always faces the larger number. For example, 12 > 9 means 12 is greater than 9, and 4 < 10 means 4 is less than 10.
大于号 (>) 和小于号 (<)：用来比较数的大小。可以想象一头饥饿的鳄鱼，它的大嘴总是朝向较大的数字。例如 12 > 9 表示 12 大于 9，4 < 10 表示 4 小于 10。
Round (to the nearest 10, 100): Making a number simpler while keeping its value close to the original. Look at the digit to the right: if it is 5 or more, round up; if it is 4 or less, round down. Think '5 to the sky, 4 to the floor'.
四舍五入（到最近的十、百）：简化数字但保持数值接近原来。看右边的数字：如果是 5 或以上就进一，4 或以下就舍去。记住口诀“五上天，四下地”。
2. Operations and BIDMAS | 四则运算与运算顺序
Sum, Difference, Product, Quotient multiplication (×). The quotient is the result of division (÷). Note the operation words: 'sum' links to addition, 'difference' to subtraction.
和、差、积、商：和是加法（+）的结果。差是减法（−）的结果。积是乘法（×）的结果。商是除法（÷）的结果。阅读题目时，看到“和”就要用加法，“差”就用减法。
BIDMAS (or BODMAS): This tells you the correct order of operations. B – Brackets, I – Indices (powers/orders, e.g., 2³), D – Division, M – Multiplication, A – Addition, S – Subtraction. Division and multiplication have equal priority and are done left to right, as are addition and subtraction. A popular mnemonic is 'Big Elephants Destroy Mice And Snails'.
BIDMAS（或 BODMAS）运算顺序：规定计算的正确顺序。B – 括号，I – 指数（幂，如 2³），D – 除法，M – 乘法，A – 加法，S – 减法。除法和乘法优先级相同，从左到右计算；加法和减法也是如此。常用的记忆口诀是“括号指数先算好，乘除加减从左扫”。
Commutative on are commutative: 5+3 = 3+5 and 4×6 = 6×4. Subtraction and division are not commutative.
交换律：如果改变运算顺序而不改变结果，则这种运算满足交换律。加法和乘法满足交换律：5+3 = 3+5，4×6 = 6×4。减法和除法不满足交换律。
Inverse Operations: Operations that undo each other. Addition and subtraction are inverses; multiplication and division are inverses. Use inverses to check answers or solve simple equations.
逆运算：可以互相抵消的运算。加法与减法互为逆运算；乘法与除法互为逆运算。可以用逆运算来验算或解简单方程。
3. Fractions, Decimals and Percentages | 分数、小数与百分比
Numerator and Denominator: In a fraction, the top number is the numerator (how many parts you have), and the bottom number is the denominator (how many equal parts the whole is divided into). Remember: 'Denominator' starts with D for 'down'.
分子与分母：在分数中，上面的数是分子（表示取了多少份），下面的数是分母（表示整体被平均分成多少份）。记忆技巧：分母的“母”是底部，就像大地（Down）。
Proper Fraction, Improper Fraction, Mixed Number: A proper fraction has a numerator smaller than the denominator (e.g., 3/5). An improper fraction has a numerator larger than the denominator (e.g., 7/4). A mixed number has a whole part and a fraction part (e.g., 1 ½).
真分数、假分数、带分数：真分数的分子小于分母（如 3/5）。假分数的分子大于分母（如 7/4）。带分数由整数部分和分数部分组成（如 1½）。
Equivalent Fractions and Simplifying . To simplify a fraction, divide numerator and denominator by their highest common factor. 'Make it as simple as possible, like packing a bag tightly.'
等值分数与约分：等值分数数值相同但形式不同（如 1/2 = 2/4 = 3/6）。约分时，用分子和分母的最大公因数同时去除。就像把行李压缩到最小。
Decimal Places and Percentages: A decimal point separates the whole number part from the fractional part. The first place is tenths, second is hundredths. A percentage means 'out of 100' (%). To find 1% of a quantity, divide by 100. Think 'cent' as in century (100 years).
小数位与百分比：小数点把整数部分和小数部分分开。第一位是十分位，第二位是百分位。百分比表示“每一百份中的份数”（%）。求一个数的1%就除以100。联想“百分”就是100，和百岁（century）一样。
4. Ratio and Proportion | 比与比例
Ratio: A way of comparing two or more quantities, showing how many times one value contains another. Written as a:b or a to b. For example, if a recipe uses 2 cups of flour to 1 cup of sugar, the ratio is 2:1. Simplify ratios by dividing both sides by their highest common factor.
比：用来比较两个或多个数量，显示一个量是另一个量的几倍。写作 a:b 或 a 比 b。例如，食谱中用 2 杯面粉配 1 杯糖，比就是 2:1。通过两边同除最大公因数可以简化比。
Proportion: A statement that two ratios are equal. For instance, if the ratio of apples to oranges is 2:1, then having 4 apples and 2 oranges is in the same proportion. Direct proportion means as one quantity increases, the other increases at the same rate.
比例：表示两个比相等的式子。例如，苹果和橙子的比是 2:1，那么 4 个苹果和 2 个橙子就成比例。正比例意味着一个量增加，另一个量以相同速率增加。
Part-to-Part and Part-to-Whole: A ratio can compare one part to another part (3:2) or one part to the whole total (3 out of 5 total). Understanding the difference helps with solving word problems.
部分比部分和部分比整体：比可以比较部分与部分（3:2），也可以比较部分与整体（3/5）。理解这种区别有助于解决应用题。
5. Algebra Basics | 代数基础
Variable and Constant: A variable is a symbol, often a letter like x or y, that represents an unknown or changing number. A constant is a fixed numerical value, like 5 or -3. Think of 'variable' as 'able to vary'.
变量与常量：变量是表示未知数或会变化的数的符号，通常是字母，如 x 或 y。常量是固定的数值，如 5 或 -3。可以联想“变量”就是“可以变化的量”。
Term, Expression, and Coefficient: A term is a single number, variable, or product of numbers and variables (e.g., 4x, -2, y²). An expression is a combination of terms joined by + or − (e.g., 3a + 2b - 5). The coefficient is the number part multiplying the variable; in 4x, 4 is the coefficient.
项、表达式与系数：项是单个数字、变量或数字与变量的乘积（如 4x、-2、y²）。表达式是由加号或减号连接起来的多个项（如 3a + 2b - 5）。系数是乘以变量的数字部分；在 4x 中，4 是系数。
Like Terms and Simplifying: Like terms have exactly the same variable parts (e.g., 3x and -7x are like terms, but 3x and 5x² are not). You can collect like terms by adding or subtracting their coefficients. This is like grouping similar fruits.
同类项与化简：同类项具有完全相同的变量部分（例如 3x 和 -7x 是同类项，但 3x 和 5x² 不是）。通过加减同类项的系数来合并项，就像把同类的水果归在一起。
Substitution = 4, substitute 4 in place of a to work out y. Always use the correct order of operations.
代入：将变量替换为给定的数字。如果公式是 y = 2a + 3，而 a = 4，就把 a 换成 4 计算 y。代入时一定要遵循正确的运算顺序。
6. Expressions and Equations | 表达式与方程
Equation x + 2 = 11. Solving an equation means finding the value of the unknown that makes it true.
方程：用等号（=）表示两个表达式相等的数学语句。例如 3x + 2 = 11。解方程就是找出使方程成立的未知数的值。
Inequality equal to). For example, x > 5 means x can be any number greater than 5. The open circle on a number line shows the endpoint is not included.
不等式：用 <、>、≤（小于或等于）、≥（大于或等于）等符号比较两个表达式的语句。例如 x > 5 表示 x 可以是任何大于 5 的数。在数轴上，空心圆圈表示端点不包括在内。
Balance Method: A technique for solving equations by keeping both sides balanced. Whatever operation you perform on one side, you must do to the other. Imagine a see-saw that must stay level.
天平法：解方程的一种方法，要保持等号两边平衡。你对一边做什么运算，另一边也必须做同样的运算。想象一个跷跷板必须保持水平。
7. Sequences and Patterns | 数列与规律
Sequence and Term: A sequence is an ordered list of numbers following a rule. Each number in the sequence is called a term. For example, in 3, 6, 9, 12..., the first term is 3, the third term is 9.
数列与项：数列是按照某种规律排列的一列数。数列中的每个数称为项。例如在 3, 6, 9, 12... 中，第一项是 3，第三项是 9。
Term-to-Term Rule: This rule tells you how to get from one term to the next. In the sequence 5, 8, 11, 14..., the rule is 'add 3'. You can find it by subtracting any term from the next.
项对项法则：告诉你如何从一项得到下一项的法则。在数列 5, 8, 11, 14... 中，法则是“加 3”。通过相邻两项做减法可以找到这个规律。
Position-to-Term Rule (nth term): This rule allows you to find any term based on its position n. For a linear sequence, the nth term often looks like an + b, where a is the common difference and b is a constant. For 4, 7, 10, 13..., the nth term is 3n + 1.
位置法则（第 n 项）：根据位置 n 求出任意一项的法则。对于线性数列，第 n 项通常写作 an + b，其中 a 是公差，b 是常数。例如 4, 7, 10, 13... 的第 n 项是 3n + 1。
Arithmetic Sequence: A sequence where the difference between consecutive terms is constant (the common difference). Example: 2, 5, 8, 11... has a common difference of +3.
等差数列：相邻项之差为常数的数列（
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