📚 Year 7 CCEA Further Mathematics: Quick Vocabulary Memorisation Guide | Year 7 CCEA 进阶数学：词汇术语速记指南
Mastering the language of mathematics is the first step towards confident problem‑solving. In Year 7 CCEA Further Mathematics, you will encounter a core set of words and phrases that form the building blocks for everything from algebra to statistics. This guide groups those terms by topic and provides simple memory hooks, visual associations, and word origins to help the vocabulary stick — quickly and permanently.
掌握数学语言是自信解题的第一步。在 Year 7 CCEA 进阶数学中，你会遇到一批核心词汇和术语，它们构成了从代数到统计等所有内容的基础模块。本指南按主题将这些词汇分组，并提供简单的记忆钩子、视觉联想和词源说明，帮助你把单词牢牢记住——又快又牢固。
1. Number and Place Value | 数与位值
An integer is any whole number that is not a fraction or decimal. The word comes from the Latin integrum, meaning "whole". Integers can be positive, negative or zero. A negative integer sits to the left of zero on a number line; think of it as "below zero" or an overdraft.
整数 是任何不是分数或小数的完整数。这个词源自拉丁语 integrum，意为“完整”。整数可以是正数、负数或零。负数 在数轴上位于零的左边；可以把它想象成“零下”或银行透支。
Place value tells you the worth of a digit based on its position — for example, in 3047 the digit '3' really means 3000 (three thousands). Ascending order means going from smallest to largest, like climbing up a ladder; descending is the opposite. Remember "aScending = Small to big" (both start with S).
位值 告诉你一个数字根据其位置所代表的值——例如，在 3047 中，数字“3”实际代表的是 3000（三千）。升序 是从小到大排列，就像向上爬梯子；降序 则相反。可以这样记：“升序”的“升”就是往上，先小后大。
Use a mental number line to keep comparisons straight: greater than (>) means the wider end opens to the bigger number; less than (<) points the small end at the smaller one. Visualise the crocodile mouth eating the larger morsel.
用脑海中的数轴来理清比较关系：大于 (>) 表示开口对着较大的数；小于 (<) 表示尖角指向较小的数。想象鳄鱼的大嘴巴总是吞吃较大的那块食物。
2. Operations and BODMAS | 四则运算与运算顺序
The four basic operations are addition (joining), subtraction (taking away), multiplication (repeated addition) and division (splitting equally). To carry out calculations with several operations, we need a strict order — remembered by the acronym BODMAS.
四种基本运算是加法（合起来）、减法（拿走）、乘法（重复加）和除法（等分）。当一道算式包含多种运算时，我们需要一个严格的顺序——这个顺序可以用首字母缩略词 BODMAS 来记忆。
MAS = Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction
BODMAS = 括号、指数（乘方和根号）、除法、乘法、加法、减法
Work from left to right. Division and multiplication have equal priority, so do whichever comes first. The same rule applies to addition and subtraction. A helpful chant: "Brackets first, then powers perk, divide and multiply in the given work, add and subtract from left to right — your answers will be out of sight!"
计算时从左向右进行。除法和乘法具有相同的优先级，哪个先出现就先算哪个。加法和减法也遵循同样的规则。一个朗朗上口的口诀是：“有括号先算括号，有指数再算指数，乘除同级从左到右，加减同级从左到右——答案永远不出错！”
3. Factors, Multiples and Primes | 因数、倍数与质数
A factor of a number divides it exactly without leaving a remainder. Factor pairs multiply to give the number. A multiple is what you get when you multiply that number by any integer — think of skip‑counting. A prime number has exactly two distinct factors: 1 and itself. (Note: 1 is not prime.) Composite numbers have more than two factors.
一个数的因数 是指能整除该数而不留余数的数。因数成对相乘得到原数。倍数 是将这个数乘以任意整数后得到的结果——想象一下跳着数数。质数 恰有两个不同的因数：1 和它自身。（注意：1 不是质数。）合数 则有多于两个因数。
HCF (Highest Common Factor) is the largest factor shared by two or more numbers; LCM (Lowest Common Multiple) is the smallest multiple they share. Use a factor tree for prime factorisation — breaking a number into its building‑ ve of Eratosthenes is a classic way to spot primes: cross out multiples of 2, then 3, then 5…
HCF（最大公因数） 是两个或多个数共有的最大因数；LCM（最小公倍数） 是它们共有的最小倍数。用因数树 进行质因数分解——把一个数拆成基础质数的乘积，例如 12 = 2² × 3。埃拉托色尼筛法是寻找质数的经典方法：依次划掉 2 的倍数、3 的倍数、5 的倍数……
Square numbers result from multiplying a number by itself (e.g., 1, 4, 9, 16). Cube numbers come from multiplying three copies (e.g., 1, 8, 27). Visualise squares as area and cubes as volume to lock in their meanings.
平方数 是一个数自己乘自己的结果（如 1, 4, 9, 16）。立方数 是三个相同的数相乘的结果（如 1, 8, 27）。把平方想象成面积，立方想象成体积，就能牢牢记住它们的含义。
4. Fractions, Decimals and Percentages | 分数、小数与百分比
In a fraction, the numerator (top) counts how many parts we have; the denominator (bottom) names how many equal parts make a whole. Think "denominator = down‑naming". A proper fraction has a numerator smaller than its denominator; an improper fraction has a larger numerator. A mixed number combines a whole number with a proper fraction.
在分数中，分子（上方）表示我们有多少份；分母（下方）表示整体被等分成多少份。记法：“分母”就是“分”成多少份的数字。一个真分数 分子小于分母；一个假分数 分子大于分母。带分数 由一个整数和一个真分数组合而成。
Equivalent fractions are different ways of writing the same value; they are created by multiplying or dividing numerator and denominator by the same number. Simplifying a fraction means writing it in its lowest terms. A decimal uses a decimal point and place values of tenths, hundredths, thousandths. A percentage is a fraction out of 100 — the symbol % literally means "per cent" or "per hundred".
等价分数 是同一个值的不同写法；将分子和分母同时乘或除以相同的数就能得到。把分数化简 就是用最简单的形式表示它。小数 使用小数点以及十分位、百分位、千分位。一个百分比 是分母为 100 的分数——符号 % 的字面意思就是“每百”。
Memory chain: to convert a fraction to a decimal, divide; decimal to percentage, multiply by 100. The bridge between them is always a hundred‑square grid. Picture a chocolate bar with 100 pieces — each piece is 1%.
记忆链条：分数化小数，做除法；小数化百分数，乘 100。它们之间的桥梁总是一个百格图。想象一块有 100 小块的巧克力——每一小块就是 1%。
5. Algebraic Expressions | 代数表达式
A variable is a letter that stands for an unknown or changing number. A term is a single mathematical unit, such as 5x, -3y or 7. A coefficient is the number part of a term that multiplies the variable — in 4a, the coefficient is 4. An expression is a combination of terms linked by + or – signs, without an equals sign.
变量 是代表未知或变化数值的字母。项 是单个数学单位，如 5x、-3y 或 7。系数 是项中与变量相乘的数字部分——在 4a 中，系数为 4。表达式 是由加号和减号连接的多个项的组合，不带等号。
Like terms have exactly the same variable raised to the same power — for example, 2x and -5x can be added, but 2x and 3x² cannot. To simplify an expression, collect like terms: 3a + 2b + 5a = 8a + 2b. Substitution means replacing a variable with a given number and working out the value.
同类项 包含完全相同的变量，且变量的指数也相同——例如，2x 与 -5x 可以相加减，但 2x 与 3x² 不能。化简 表达式，就是合并同类项：3a + 2b + 5a = 8a + 2b。代入 是指用给定的数值替换变量并计算出结果。
Think of algebra as a mini zoo: each different type of animal (variable) must stay with its own kind. You can only group lions with lions and tigers with tigers — that is the rule for collecting like terms.
将代数想象成小动物园：不同种类的动物（变量）必须各归各群。只能将狮子与狮子归类，老虎与老虎归类——这就是合并同类项的法则。
6. Equations and Inequalities | 方程与不等式
An equation is a mathematical sentence with an equals sign that shows two expressions have the same value. The solution is the value of the variable that makes the equation true. To solve an equation, perform inverse operations on both sides, keeping the equation balanced like a set of scales.
方程 是带等号的数学句子，表示两个表达式具有相同的值。使方程成立的变量的值就是解。要解 方程，需在等式两边进行逆运算，就像保持天平平衡一样。
An inequality compares two values using signs: > (greater than), < (less than), ≥ (greater than or equal to) and ≤ (less than or equal to). The open side of the symbol always faces the larger amount — like the crocodile’s mouth. Inequalities are solved in much the same way as equations, but remember: multiplying or dividing by a negative number flips the sign.
不等式 用符号比较两个值：>（大于）、<（小于）、≥（大于或等于）和 ≤（小于或等于）。符号的开口始终朝向较大的量——就像鳄鱼的嘴巴。解不等式与解方程的方法大致相同，但要记住：乘以或除以负数时要将不等号方向反转。
Balance card: write an equation on one side of a card and the step‑by‑step solution on the other. Equate each algebraic move to a physical action on a scale.
平衡卡：在卡片一面写下方程，另一面写下逐步求解的过程。将每一步代数操作对应为天平上的一个物理动作。
7. Coordinates and Graphs | 坐标与图像
A coordinate pair (x, y) pinpoints a position on a grid. The x‑axis runs horizontally, the y‑axis runs vertically, and they meet at the origin (0, 0). To plot a point, start at the origin, move along the x‑axis first, then go up or down the y‑axis.
一个坐标 对 (x, y) 在网格上确定一个位置。x 轴 水平延伸，y 轴 垂直延伸，它们相交于原点 (0, 0)。要标点 时，从原点出发，先沿 x 轴移动，再沿 y 轴上下移动。
Picture yourself walking along a corridor (the x‑direction) before climbing the stairs (the y‑direction): "Along the corridor, up the stairs" is the classic rhyme. The grid is divided into four quadrants, numbered anticlockwise. A linear graph represents relationships that form a straight line, often written as y = mx + c.
想象自己沿走廊（x 方向）先走，然后再爬楼梯（y 方向）：“先横后纵，沿廊上楼”是经典顺口溜。网格分为四个象限，按逆时针编号。线性图像 表示形成一条直线的关系，常写作 y = mx + c。
Use the rhyme "X is a cross, it's horizontal first" to avoid mixing up the order. Many pupils draw a little man walking the corridor before climbing to reinforce the sequence.
用口诀“X 是叉，先横后纵不混淆”来避免顺序出错。很多学生画一个小人先顺走廊走，再爬楼，以强化顺序。
8. Properties of Shapes | 图形性质
A polygon is a closed 2D shape with straight sides. The name tells you the number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8). Regular polygons have all sides and all angles equal; irregular ones do not.
多边形 是由直边围成的封闭二维图形。名称本身就告诉你边数：三角形 (3)、四边形 (4)、五边形 (5)、六边形 (6)、七边形 (7)、八边形 (8)。正多边形 各边等长、各角相等；不规则多边形 则不然。
Learn the Greek prefixes: tri‑ (three wheels on a tricycle), quad‑ (four sides of a quad bike), pent‑ (penthouse, five‑sided in popular imagination), hex‑ (six sides in a honeycomb cell). Parallel lines are always the same distance apart and never meet; perpendicular lines meet at a right angle (90°). A line of symmetry splits a shape into two mirrored halves.
记牢希腊语前缀：tri‑（三轮车有三个轮子），quad‑（四轮摩托车有四个边），pent‑（顶层公寓，常联想为五边形），hex‑（蜂巢的六边形孔）。平行 线间距始终相等，永不相交；垂直 线以直角（90°）相交。对称轴 将图形分成两个镜像重合的部分。
Draw a quick sketch of each polygon and label the number of sides; add a tiny crow’s foot (>>) for parallel lines and a square corner for perpendicular ones. These geometric “stickers” make the vocabulary visual.
快速画出每个多边形的简图并标上边数；用箭头形的平行线符号标记平行，用方角符号标记垂直。这些几何“贴纸”能让词汇变得可视化。
9. Perimeter, Area and Volume | 周长、面积与体积
Perimeter is the total distance around the outside of a 2D shape — imagine fencing a garden. Area is the amount of space inside a shape, measured in square units such as cm² or m². Volume measures the space inside a 3D object, reported in cubic units like cm³.
周长 是二维图形外边界的总长度——想象给花园围篱笆。面积 是图形内部的空间大小，以平方单位如 cm² 或 m² 度量。体积 衡量三维物体内部的空间，以立方单位如 cm³ 表示。
A formula is a rule written with symbols. For a rectangle, area = length × width and perimeter = 2 × (length + width). For a compound shape, split it into simpler rectangles, calculate their areas separately, then add them together. Volume of a cuboid = length × width × height.
公式 是用符号写出的规则。对于矩形，面积 = 长 × 宽，周长 = 2 × (长 + 宽)。对于组合图形，先将其分割成多个简单的矩形
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