📚 Year 9 SQA Advanced Mathematics: Rapid Glossary Memorisation Guide | Year 9 SQA 进阶数学：词汇术语速记指南
Mastering key mathematical vocabulary is essential for success in the Year 9 SQA Advanced Mathematics course. This guide provides effective memorisation techniques and bilingual explanations to help you recall terms quickly and accurately.
掌握关键数学词汇是Year 9 SQA进阶数学课程成功的基础。本指南提供有效的速记技巧和中英双语解释，帮助你快速准确地回忆术语。
1. Algebraic Expressions | 代数表达式
A term is a single number, variable, or product of numbers and variables separated by + or − signs. In 3x² + 5x − 7, the terms are 3x², 5x, and −7. A coefficient is the numerical part of a term, like 3 in 3x². A constant is a term without a variable. Like terms have exactly the same variable part and can be combined, for instance 2x and 4x.
项是由加号或减号分隔的单个数字、变量或乘积。在3x²+5x−7中，项分别为3x²、5x和−7。系数是项的数值因子，例如3x²中的3。常数是不含变量的项。同类项拥有完全相同的变量部分，可以合并，比如2x和4x。
A memorable trick: picture an expression as a fruit bowl. Each term is a different type of fruit, the coefficient tells you how many pieces you have, and constants are plain sugar cubes. Only fruits of the same kind can be mixed together.
记忆窍门：将表达式想象成一个果盘。每一项是一种水果，系数就是这种水果的数量，常数则是方糖。只有同种水果才能混合。
2. Factorisation Strategies | 因式分解策略
the largest factor shared by all terms. The difference of two squares follows the pattern a² − b² = (a + b)(a − b). Quadratic trinomials of the form x² + bx + c can be factorised into (x + p)(x + q) where p+q = b and p×q = c.
因式分解是展开的逆过程。公因式是能整除每一项的数或变量。最高公因式（HCF）是所有项共有的最大因式。平方差遵循模式a² − b² = (a + b)(a − b)。形如x²+bx+c的二次三项式可分解为(x+p)(x+q)，其中p+q=b且p×q=c。
To memorise, think of pulling out the HCF like unpacking a suitcase: you take out what is common. For the difference of squares, remember 'two terms, one plus, one minus' – it is like a mirror image split by opposites.
记忆方法：提取公因式就像打开行李箱，取出共同的东西。平方差记住“两项，一加一减”——它像一面被相反符号分开的镜子。
3. Solving Quadratic Equations | 解二次方程
ines the nature of the roots. The solutions (or roots) are given by the quadratic formula:
x = [−b ± √b² − 4ac] / 2a
二次方程的标准形式为ax²+bx+c=0，a≠0。判别式Δ=b²−4ac决定根的性质。求根公式如上。
Sing the formula to the tune of 'Pop Goes the Weasel': 'x equals minus b, plus or minus the square root, of b squared minus four a c, all over two a!' This rhythm sticks instantly.
用《Pop Goes the Weasel》的曲调唱求根公式：“x等于负b，加减根号下，b方减4ac，除以2a！”这个节奏立刻就能记住。
4. Simultaneous Equations | 联立方程
Simultaneous equations require finding values that satisfy two or more equations at the same time. Elimination involves adding or subtracting equations to cancel one variable. Substitution means replacing one variable with an equivalent expression from the other equation.
联立方程需要找出同时满足两个或多个方程的解。消元法是通过加减方程约去一个变量。代入法是用另一个方程中的等价表达式替换一个变量。
Visualise elimination as balancing a seesaw: remove identical weights from both sides. Substitution is like swapping a mystery gift with its known equivalent. The goal is to reduce to one unknown.
将消元法想象成平衡跷跷板：从两边拿走相同重量。代入法则像用已知物品换掉神秘礼物。目的是化为一元一次方程。
5. Pythagoras and Right-Angled Triangles | 勾股定理与直角三角形
se is the longest side, opposite the right angle. The other two sides are legs. Pythagoras' tenuse equals the sum of the squares of the legs: a² + b² = c², where c is the hypotenuse.
在直角三角形中，斜边是最长边，对着直角。另两边为直角边。勾股定理（毕达哥拉斯定理）指出：斜边的平方等于两直角边的平方和：a² + b² = c²，c为斜边。
To remember which side is c: c stands for 'crowded' — the largest square. Also, 3-4-5 triangles are classic examples: 3²+4²=5². Use the mnemonic 'A squared plus B squared equals C squared'.
记住哪边是c：c代表“拥挤”，它的平方最大。3-4-5三角形是经典例子。口诀“勾股弦”或"A square plus B square equals C square"都能帮助记忆。
6. Trigonometric Ratios | 三角比
For any acute angle θ in a right triangle, the sides are named relative to θ: opposite (O), adjacent (A), and hypotenuse (H). The three main ratios are:
| Ratio | Formula | Mnemonic |
|---|---|---|
| Sine (sin θ) | opposite / hypotenuse | SOH |
| Cosine (cos θ) | adjacent / hypotenuse | CAH |
| Tangent (tan θ) | opposite / adjacent | TOA |
The acronym SOH CAH TOA is a world-famous memory aid. You can also create a phrase: 'Silly Old Harry Caught A Herring Trawling Off America'.
缩写SOH CAH TOA是世界闻名的记忆法。也可自创中文口诀：“正弦对边比斜边，余弦邻边比斜边，正切对边比邻边。”反复念几遍就能记住。
7. Statistical Averages | 统计平均值
The mean is found by summing all values and dividing by the count. The median is the middle value when data is ordered. The mode is the value that appears most frequently. The range measures spread: maximum minus minimum.
平均数（均值）是总和除以个数。中位数是排序后位于中间的值。众数是出现频率最高的值。极差描述分散程度：最大值减最小值。
Link each term to its personality: Mean is the 'fair share' everyone gets; Median is the 'middle line' at a finish; Mode is the most 'popular' celebrity. Range tells how wide the couch is!
联想每个术语的性格：平均数是“人人有份”的公平分配；中位数是队伍中间那人；众数是人气最高明星。极差则告诉你沙发有多宽！
8. Basic Probability | 基础概率
of an event = number of favourable outcomes / total number of outcomes, expressed as a fraction, decimal, or percentage between 0 and 1.
结果是一次试验可能发生的情况。事件是一个或多个结果的集合。样本空间列出所有可能结果。概率 = 有利结果数 / 总结果数，用分数、小数或百分数表示，在0和1之间。
Think of probability as a weather forecast. A probability of 0 means it will never rain, 1 means it definitely will. The sample space is like the menu of all possible meals.
把概率看作天气预报。0表示绝不会下雨，1表示肯定会下。样本空间就像包含所有菜式的菜单。
9. Indices and Surds | 指数与根式
An index (or power) shows repeated multiplication. Base^exponent: an = a × a × ... (n times). Key laws: am × an = am+n; am / an = am−n; (am)n = amn; a0 = 1; a−n = 1/an. A surd is an irrational root, e.g., √2. √ab = √a × √b. Rationalising the denominator means removing surds from the bottom of a fraction.
指数表示重复相乘，an是a自乘n次。基本法则：am×an=am+n；am÷an=am−n；(am)n=amn；a0=1；a−n=1/an。根式是无法开尽的方根，比如√2。√ab=√a×√b。分母有理化即去掉分母中的根号。
Visualise indices as stacking blocks: multiplication adds layers, division removes layers, a power of a power stacks new blocks. Negatives flip to the basement (reciprocal). Surds are like unbreakable bricks, but √a × √a = a smashes them.
将指数想象为叠积木：乘法增加层数，除法减少层数，幂的幂再叠新积木。负指数则翻到地下室（倒数）。根式像打不碎的砖，但√a×√a=a瞬间砸碎它。
10. Sequences and the nth Term | 序列与第n项
An arithmetic sequence has a common difference (d) between consecutive terms. The nth term formula is un a + (n−1)d, where a is the first term. A geometric sequence has a common ratio (r), with un = arn−1.
等差数列相邻项之差为公差d。第n项公式un = a + (n−1)d，a为首项。等比数列相邻项之比为公比r，un = arn−1。
To memorise: arithmetic is like climbing stairs with equal height (d). Geometric is like photocopy enlargements — each step multiplies by r. The formula simply starts at a and adds (n−1) steps, or multiplies by r (n−1) times.
记忆：等差数列像等高的楼梯（d），等比数列像复印机逐次放大（r）。公式就是从首项a开始，添加n−1个台阶，或乘以n−1次r。
11. Linear Graphs and Gradient | 线性图与斜率
(y₂ − y₁)/(x₂ − x₁). The constant c is the y-intercept, where the line crosses the y-axis.
直线标准方程为y=mx+c。m是斜率（坡度），等于纵差/横差=(y₂−y₁)/(x₂−x₁)。常数c是y轴截距，即直线与y轴交点的纵坐标。
Think 'm for mountain' — how steep the hill is. 'c for cutting' — where the line cuts the y-axis. A positive m goes uphill, negative downhill. Parallel lines have equal m, perpendicular lines have gradients that multiply to −1.
联想“m像山”表示坡度，c是直线切割y轴的位置。正斜率上坡，负斜率下坡。平行线斜率相等
Published by TutorHao | Year 9 进阶数学 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图