📚 Year 8 SQA Advanced Maths: Vocabulary & Terminology Quick Memorization Guide | Year 8 SQA 进阶数学：词汇术语速记指南
Mastering the precise vocabulary of advanced mathematics is essential for success in the Year 8 SQA curriculum. This bilingual guide organises key terms into logical categories, offers clear definitions in English and Chinese, and provides clever memory tricks to help you recall them quickly in tests and homework. By linking each term to a visual or conceptual hook, you can transform abstract jargon into familiar, lasting knowledge.
掌握进阶数学的精确词汇是Year 8 SQA课程成功的关键。这本双语指南将关键术语按逻辑分类，提供清晰的中英文定义，并附上巧妙的记忆窍门，帮助你快速在考试和作业中回想起来。通过将每个术语与图像或概念挂钩，你可以把抽象的术语转化为熟悉且持久的知识。
1. Number Types and Fractions | 数字类型与分数
Integer: A whole number, positive, negative or zero (e.g. -3, 0, 17). Think of 'integer' as meaning 'intact' or 'complete' – no fractional bits.
整数：正、负或零的整数（如 -3, 0, 17）。记住 '整数' 就像是完整的数，没有小数或分数部分。
Fraction, numerator and denominator: A fraction is a part of a whole, written as a/b. The top number (numerator) names the part; the bottom (denominator) tells how many equal parts make the whole. In 3/4, 3 is the numerator, 4 the denominator.
分数、分子和分母：分数表示整体的一部分，写作 a/b。上面的数（分子）表示取了多少份；下面的数（分母）表示整体被分成了几等份。3/4 中，3是分子，4是分母。
Equivalent fractions and simplifying: Fractions that represent the same amount, like 1/2 and 2/4. To simplify, divide numerator and denominator by their highest common factor (HCF).
等值分数与化简：表示相同量的分数，比如 1/2 和 2/4。化简时将分子分母同时除以它们的最大公因数 (HCF)。
Terminating and recurring decimals inating decimal ends (e.g. 0.25), a recurring decimal repeats forever (e.g. 0.333... = 0.3̅). Remember: 'Terminating' terminates; 'recurring' repeats.
有限小数与循环小数：有限小数会结束（如 0.25），循环小数不断重复（如 0.333... = 0.3̅）。联想：'终止' 意味着结束，'循环' 意味着重复。
Memory trick:
- ture fractions as slices of pizza: denominator = total slices, numerator = slices you eat.
- 把分数想象成披萨块：分母 = 总块数，分子 = 你吃掉的块数。
Use the phrase 'Numerator – Number of parts; Denominator – Division of the whole' to keep them straight.
用口诀 '分子数份数，分母分整体' 来分清上下。
2. Algebraic Expressions | 代数表达式
Variable: A letter or symbol that stands for an unknown or changing number, like x or n. See it as a 'varying' value.
变量：用来代表未知或变化的数字的字母或符号，如 x 或 n。把它看作 '会变化的数量'。
Coefficient: The number multiplying the variable, e.g. in 5y, 5 is the coefficient. Think of the coefficient as the variable’s 'partner' that tells how many you have.
系数：乘在变量前面的数，如 5y 中，5 是系数。把系数想象成变量的 '搭档'，表明有多少个变量。
Constant: A fixed value that does not change, like 3 in x + 3. 'Constant' stays constant.
常数：固定不变的值，如 x + 3 中的 3。'常数' 就是永远不变的数。
Term: A single number, variable, or product of numbers and variables separated by + or – signs. Think of terms as 'chunks' of an expression.
项：单独的数、变量或数与变量的乘积，由 + 或 – 分隔。把项看作表达式的一个个 '块'。
Like terms s, e.g. 2x and -5x. Combine them like you combine objects: 2 apples + 3 apples = 5 apples.
同类项：变量部分完全相同的项，如 2x 和 -5x。像合并物品一样合并它们：2个苹果 + 3个苹果 = 5个苹果。
Expression vs. equation: An expression has no equal sign (2x + 5), an equation has one (2x + 5 = 11). Remember: 'Equation' has 'equal'.
表达式与方程：表达式没有等号（如 2x + 5），方程有等号（2x + 5 = 11）。记住：'方程' 含有 '等号'。
3. Equations and Inequalities | 方程与不等式
Solve: Find the value(s) that make an equation true. Goal: isolate the variable by inversing operations.
解方程：找到使方程成立的未知数值。目标：通过逆运算把变量单独留在一边。
Inverse operation: Opposite action: addition ↔ subtraction, multiplication ↔ division. Use the 'scale' model: do the same thing to both sides to keep balance.
逆运算：相反的运算：加法 ↔ 减法，乘法 ↔ 除法。用 '天平' 模型：两边做同样的操作才能保持平衡。
Inequality symbols (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to). 'The crocodile eats the bigger number' helps with direction.
不等式符号：< (小于)、> (大于)、≤ (小于等于)、≥ (大于等于)。用 '鳄鱼吃大数' 记住开口方向。
Solution set: The range of values satisfying an inequality, often shown on a number line with open or closed circles.
解集：满足不等式的数值范围，常用数轴表示，空心圈表示不含该点，实心圈表示包含。
x + 3 = 7 → x = 4
Memorise: 'Equations demand equality; inequalities show a spread.'
记忆口诀：'方程求相等，不等式看范围。'
4. Powers and Roots | 幂与根
Exponent (index, power) cation, e.g. 5³ = 5 × 5 × 5. The base is 5, exponent is 3. Think of the exponent as a tiny 'super-multiplier' sitting on the shoulder.
指数（幂）：表示重复相乘，如 5³ = 5 × 5 × 5。5 是底数，3 是指数。把指数想象成坐在肩膀上的超小 '乘数'。
Square and cube: a² is 'a squared' (area of a square side a), a³ is 'a cubed' (volume of a cube side a).
平方与立方：a² 读作 'a 的平方'（边长为 a 的正方形面积），a³ 读作 'a 的立方'（边长为 a 的立方体体积）。
Square root and cube root: √ is the inverse of squaring. √9 = 3 because 3² = 9. Cube root ∛ is inverse of cubing.
平方根与立方根：√ 是平方的逆运算。√9 = 3 因为 3² = 9。∛ 是立方的逆运算。
Index laws:
- Multiply same base: add exponents, a² × a³ = a²⁺³ = a⁵.
- Divide: subtract exponents, a⁵ ÷ a² = a⁵⁻² = a³.
- Power of power: multiply exponents, (a²)³ = a²×³ = a⁶.
指数定律：
- 同底数相乘：指数相加，a² × a³ = a²⁺³ = a⁵。
- 同底数相除：指数相减，a⁵ ÷ a² = a⁵⁻² = a³。
- 幂的乘方：指数相乘，(a²)³ = a²×³ = a⁶。
Visual trick: exponents 'climb' up when multiplying, 'slide' down when dividing.
形象记忆：相乘时指数'爬升'，相除时指数'下滑'。
5. Sequences | 数列
Sequence: An ordered list of numbers following a rule. The numbers are called terms, and the position number is n.
数列：按照一定规则排列的一列数。这些数称为项，位置序号用 n 表示。
Arithmetic (linear) sequence ncreases or decreases by a constant common difference d. Example: 3, 7, 11, 15... (d = 4). 'Arithmetic' makes you think of adding.
等差数列（线性数列）：按固定的公差 d 递增或递减。例子：3, 7, 11, 15... (d = 4)。'等差' 联想 '等距离差'，像走楼梯一样步步固定。
Geometric sequence: Multiplies by a common ratio r. Example: 2, 6, 18, 54... (r = 3). 'Geometric' grows by multiplying.
等比数列：按固定公比 r 相乘。例子：2, 6, 18, 54... (r = 3)。'等比' 联想 '成倍变化'，像放大镜一样放大。
nth term: The formula that gives any term from its position n. For arithmetic: a + (n-1)d. For geometric: arⁿ⁻¹. Focus on finding the pattern.
第 n 项（通项公式）：用位置 n 求任意项的公式。等差：a + (n-1)d。等比：arⁿ⁻¹。重点在于找规律。
Remember: 'Arithmetic – adding steps; Geometric – multiplying leaps.'
记忆：'等差步步加，等比跳跳乘。'
6. Angles and Shapes | 角与形状
Acute, obtuse, reflex: Acute angle < 90°, 'a cute little angle'. Obtuse between 90° and 180°, 'obtuse is obese, big and wide'. Reflex > 180°, 'reflex bends back'.
锐角、钝角、优角：锐角 < 90°，可以联想 '尖锐锋利'。钝角 90° 到 180° 之间，联想 '钝' 就是 '大'。优角 > 180°，像是向后弯折。
Complementary and supplementary: Complementary angles sum to 90° (it's 'complete' to a right angle). Supplementary sum to 180° (s as 'straight line').
互余与互补：两角之和为 90° 互余（'余' 指剩下到90°），和为 180° 互补（'补' 到平角）。
Parallel and transversal: Parallel lines never meet. A transversal cuts across them, creating angle families. Use Z for alternate angles (equal), F for corresponding (equal), C/U for co-interior (sum to 180°).
平行线与截线：平行线永不相交。截线穿过两条线，产生一系列角。用 Z 形记内错角（相等），F 形记同位角（相等），C/U 形记同旁内角（和为 180°）。
Polygons: Interior angle sum = (n – of sides. Exterior angles always sum to 360°. Regular polygon: all sides and angles equal.
多边形：内角和 = (n – 2) × 180°，n 为边数。外角和恒为 360°。正多边形：所有边和角都相等。
Angle sum = (n – 2) × 180°
Mnemonic: 'Interior = inside corners; exterior = outside turn.'
助记：'内角看里头，外角看转身。'
7. Area, Perimeter and Volume | 面积、周长与体积
Perimeter: Total distance around a shape. Add all side lengths. 'Peri' – around, 'meter' – measure. 'Rim' in perimeter.
周长：围绕形状一圈的总长度。把所有边长加起来。'周' 指围绕一圈。
Area D shape, measured in square units. Rectangle: length × width. Triangle: ½ × base × height. 'Area' sounds like 'area rug' covering the floor.
面积：二维图形内部的空间，单位用平方。矩形：长 × 宽。三角形：½ × 底 × 高。联想 '面' 就是铺满表面的意思。
Volume olid, cubic units. Cuboid: length × width × height. Prism: area of cross-section × length. 'Volume' like sound volume fills a room.
体积：三维立体内部空间，单位用立方。长方体：长 × 宽 × 高。棱柱：横截面面积 × 长。'体积' 像音量一样充满空间。
Circle terms: Circumference (perimeter of circle) = π × diameter or 2πr. Area = πr². Memorise: 'Cherry pie is delicious (C = πd); apple pie are round (A = πr²).'
圆的术语：周长 = π × 直径 或 2πr。面积 = πr²。记忆口诀：'周长派乘直径，面积派乘半径平方。'
Surface area: Sum of the areas of all faces of a 3D solid. Net helps visualise it.
表面积：立体所有面的面积之和。展开图有助于可视化。
8. Coordinates and Straight-line Graphs | 坐标与直线图
Coordinate: An ordered pair (x, y) showing a point’s position. x first 'along the corridor', y 'up the stairs'. Remember: 'x is a cross (horizontal), y to the sky'.
坐标：有序数对 (x, y) 表示点的位置。先沿 x 轴水平走，再沿 y 轴上下走。口诀：'x 横走，y 纵上'。
Quadrants: The four regions labelled I, II, III, IV. Sign of coordinates: (+,+), (–,+), (–,–), (+,–). 'All Students Take Calculus' (All, Sin, Tan, Cos) shows positive.
象限：四个区域按逆时针标记为 I, II, III, IV。坐标符号：(+,+), (–,+), (–,–), (+,–)。借助 'All Students Take Calculus' 记各象限正号。
Straight-line graph: Equation y = mx + c. m = gradient (steepness), c = y-intercept (where line cuts y-axis). 'm' as mountain slope, 'c' as crossing point.
直线图：方程 y = mx + c。m = 斜率（陡峭程度），c = 截距（与 y 轴交点）。'm' 像山的斜坡，'c' 像交叉点。
Plotting points: Choose x-values, substitute into equation, find y, plot (x,y).
描点画线：选取 x 值，代入方程求 y，描点连线。
y = mx + c
Say: 'm for the move, c for the cut.'
口诀：'m 管坡陡，c 管截距。'
9. Ratio, Proportion and Percentages | 比、比例与百分数
Ratio: Compares part-to-part, e.g. 3:2. The order matters. Simplest form: divide by HCF.
比：部分对部分的比较，如 3:2。顺序重要。化成最简形式除以最大公因数。
Proportion: Compares part-to-whole or the relationship between ratios. Direct proportion: as one quantity doubles, the other doubles. Inverse proportion: as one doubles, the other halves.
比例：部分与整体的比较，或比之间的关系。正比例：一个量翻倍，另一个也翻倍。反比例：一个量翻倍，另一个减半。
Percentage: A fraction out of 100. 'per cent' means per hundred. Use the formula: part/whole × 100%.
百分数：分母为 100 的分数。'percent' 意为每百。用公式：部分/整体 × 100%。
Unitary method: Find the value of 1 unit first, then scale. Great for shopping and best buy problems.
单位法：先求出 1 个单位的值，再放大。购物和最佳购买问题中非常实用。
Link: 'Ratio is sharing between friends; proportion is the recipe.'
联系：'比是朋友间分配，比例是菜谱配方。'
10. Statistics and Probability | 统计与概率
Mean, median, mode, range: Mean: sum of values ÷ number of values ('average' = fair share). Median: middle value when ordered. Mode: most frequent. Range: max – min.
平均数、中位数、众数、极差：平均数：总和 ÷ 个数（均摊概念）。中位数：排序后中间的数。众数：出现最多的数。极差：最大值减最小值。
Probability scale raction, decimal or percentage. P(event) = number of favourable outcomes / total outcomes.
概率尺度：0（不可能）到 1（必然）。可用分数、小数或百分数表示。P(事件) = 有利结果数 / 总结果数。
Sample space: All possible outcomes. A two-way table or list helps organise it. Tree diagram for multi-step experiments.
样本空间：所有可能的结果。用双向表或列表整理。树状图用于多步试验。
Theoretical vs. experimental probability: Theoretical is what should happen; experimental is what happens in an actual trial. More trials make experimental closer to theoretical.
理论概率与实验概率：理论概率是预期值；实验概率是真实试验结果。试验次数越多，实验概率越接近理论值。
Memory: 'Median – middle, Mode – most.'
记忆：'中位数中间站，众数最常看。'
11. Sets and Venn Diagrams | 集合与维恩图
Set: A collection of objects, usually shown inside curly braces { }. Each object is an element.
集合：一组对象的汇总，常用花括号 { } 表示。其中每个对象称为元素。
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