📚 Year 10 SQA Maths: Key Terms Quick Memorisation Guide | 十年级 SQA 数学：词汇术语速记指南
Mastering the vocabulary of mathematics is like learning the language of a new country – once you know the words, everything becomes easier to understand. This guide uses pairing, mnemonics, and short memory hacks to help you lock in the essential terms for Year 10 SQA maths and walk into the exam with confidence.
掌握数学词汇就像学习一个新国家的语言一样——一旦你认识了这些词，一切都会变得更容易理解。本指南运用配对、助记口诀和短小记忆技巧，帮助你牢牢记住十年级 SQA 数学的关键术语，自信地走进考场。
1. Number & Arithmetic Terms | 数字与算术术语
These terms form the foundation of all number work – make sure you can recall them instantly.
这些术语是所有数字运算的基础——确保你能立刻想起它们。
Integer: A whole number that can be positive, negative, or zero, with no fractional or decimal part. Memory: think "intact" – nothing broken off.
整数：不带分数或小数部分的整数，可以是正数、负数或零。记忆：联想“完整的”——没有任何部分被打破。
Prime number: A number greater than 1 that has exactly two distinct factors: 1 and itself. Tip: "Prime" like a prime minister – unique and cannot be split evenly by others.
质数（素数）：大于 1 且恰好只有两个互异因数（1 和自身）的数。提示：像“首相”一样独一无二，不能被其他数整除。
Composite number: A whole number greater than 1 that has more than two factors. Think "composition" – made of several parts.
合数：大于 1 且拥有两个以上因数的整数。联想“组合”——由多个部分构成。
Factor: A number that divides another number exactly, leaving no remainder. Mnemonic: "Factor" sounds like "factory" – producing equal chunks.
因数：能够整除另一个数而不留余数的数。助记：“因数”像“工厂”一样，把数字分成等份。
Multiple: The result of multiplying a number by an integer. Image: "multiple" = "multiply" + "cycle" – it keeps repeating.
倍数：一个数乘以整数得到的结果。形象：倍数是“乘”的“循环”再现。
Square number: The product of a number multiplied by itself (e.g. 4, 9, 16). Visual: a square array of dots.
平方数：一个数自乘的积（如 4, 9, 16）。视觉化：点阵排成的正方形。
Cube number: The product of a number used three times in multiplication (e.g. 8, 27). Picture a cube made of unit blocks.
立方数：一个数自乘三次的积（如 8, 27）。想象由单位立方体搭成的立方体。
Standard form (scientific notation) s a × 10ⁿ where 1 ≤ a < 10 and n is an integer. Remember: move the decimal point n places.
标准式（科学记数法）：把很大或很小的数写成 a × 10ⁿ 的形式，其中 1 ≤ a < 10，n 为整数。记住：把小数点移动 n 位。
Significant figures: The digits in a number that carry meaningful accuracy. Handy rule: start counting from the first non-zero digit.
有效数字：数值中具有实际精确意义的数字。简易规则：从第一个非零数字开始数。
2. Fractions, Decimals & Percentages | 分数、小数与百分数
These three representations of parts of a whole appear everywhere – memorise the associated words to avoid confusion.
这三种表示整体之一部分的方式随处可见——记住相关词汇以避免混淆。
Numerator: The top number in a fraction; it tells how many parts we have. Think "North" – up in the North.
分子：分数中上面的数；它告诉你有多少份。联想“北”——在上方的北方。
Denominator: The bottom number; shows how many equal parts the whole is divided into. "Down" in the basement.
分母：下面的数；表示整体被分成了多少等份。联想“地下室”——在下方。
Equivalent fractions the same value, e.g. ½ = ²/₄. Imagine two different pizza slicings giving the same amount.
等值分数：表示相同值的分数，例如 ½ = ²/₄。想象同一张披萨切成不同份数，仍给出相同分量。
Reciprocal: The multiplicative inverse: flip the fraction; product is 1. Quick rhyme: "reciprocal, flip the cycle".
倒数：乘法逆元：把分数上下颠倒；乘积为 1。口诀：“倒数倒数，翻转就好”。
Terminating decimal: A decimal that comes to an end, e.g. 0.25. "Terminate" = ending like a terminus station.
有限小数：会结束的小数，如 0.25。“Terminate”像终点站一样结束。
Recurring decimal: A decimal with a repeating pattern, shown with a dot or bar. "Recur" means to come back again and again.
循环小数：具有重复模式的小数，用点或上划线表示。“Recur”意为一次又一次地返回。
Percentage change: (change ÷ original) × 100%. Tip: always divide by original, not new.
百分比变化：(变化量 ÷ 原值) × 100%。提示：永远除以原值，不是新值。
Simple interest: Interest calculated only on the initial principal. Formula: I = PRT. Remember "Simple" – it doesn't compound.
单利：仅根据初始本金计算的利息。公式：I = PRT。记住“Simple”就是不再生息。
3. Algebra Essentials | 代数基础
Algebraic language describes patterns and relationships. Lock in these door-openers early.
代数语言用于描述模式和关系。尽早锁定这些开门钥匙。
Term: A single number, variable, or numbers and variables multiplied together, separated by + or −. Picture a "term" as one word in a sentence.
项：一个单独的数字、变量，或由乘号连接的数字与变量，由 + 或 − 隔开。把“项”想象成句子中的一个单词。
Coefficient: The number multiplying a variable in a term (e.g. in 3x, 3 is the coefficient). "Co" means together, it works with x.
系数：项中乘以变量的数字（如在 3x 中，3 是系数）。“系”表示它与变量共同出现。
Constant: A term with a fixed value, no variable part. Think "constant = never changing".
常数：具有固定数值、不含变量部分的项。想象“恒定不变”。
Expression: A combination of terms with no equals sign, e.g. 4x + 2. It's like a phrase, not a full sentence.
表达式：由项组成的没有等号的式子，如 4x + 2。如同短语，不是完整句子。
Equation: A mathematical statement showing two expressions are equal, containing an = sign. Think "equate" = make equal.
方程：用等号表明两个表达式相等的数学陈述。联想“相等”。
Identity: An equation true for all values, symbol ≡. It means "exactly the same".
恒等式：对所有值都成立的等式，符号 ≡。意为“完全相同”。
Expand: Multiply out brackets, e.g. a(b + c) = ab + ac. Imagine spreading out a fan.
展开：乘开括号，如 a(b + c) = ab + ac。想象把扇子展开。
Factorise: The reverse of expanding; writing an expression as a product of factors. "Factor" + "ise" = make into factors.
因式分解：展开的逆过程；将式子写成因式乘积的形式。“因式”+“分解”= 变成因式。
Quadratic expression: An expression where the highest power of the variable is 2, e.g. x² + 3x + 2. "Quad" implies four, but think "square" (a square has four sides).
二次表达式：变量的最高次数为 2 的表达式，如 x² + 3x + 2。“Quad”暗示四，但联想为平方（正方形有四条边）。
4. Equations & Inequalities | 方程与不等式
Moving from equalities to comparisons – these words appear in almost every SQA question.
从等式到比较——这些词汇几乎出现在每道 SQA 试题中。
Solve: Find the value(s) of the variable that make the equation true. Remember: "Solve" = "Solution".
解（求解）：找出使方程成立的变量的值。记住：“Solve”得出“Solution”。
Root: Another word for solution of an equation. A plant's root anchors it; a root anchors the equation.
根：方程的解的另一种称呼。植物的根使植物固定；方程的根使方程成立。
Rearrange: Change the order of terms to isolate a variable using inverse operations. "Re-arrange" like moving furniture.
移项/重新整理：通过逆运算改变项的顺序来分离变量。像重新布置家具一样“重新安排”。
Substitution: Replacing variables with given numbers. "Sub" means under – you swap in numbers instead of letters.
代入：用给定的数字替换变量。“Sub”意为下面——你用数字替换字母。
Inequality s two expressions using <, >, ≤, ≥, ≠. The hungry alligator always eats the bigger number.
不等式：使用 <, >, ≤, ≥, ≠ 比较两个表达式的陈述。饥饿的鳄鱼总吃较大的数字。
Strict inequality: Uses < or >; does not include equality. The line is strict – no touching!
严格不等式：使用 < 或 >；不包括相等。界线严格——不能碰到！
Number line to show solutions, with open or closed circles. Open circle = strict; closed = inclusive.
数轴：用空心或实心圆圈表示解的视觉方式。空心圈 = 严格不等；实心圈 = 包含等号。
Simultaneous equations: A set of equations with multiple variables solved together. "Simultaneous" = happening at the same time – all equations must be satisfied at once.
联立方程：一组含多个变量并同时求解的方程。“Simultaneous”意为同时发生——所有方程必须同时成立。
5. Graphs & Functions | 图像与函数
Graphs give a visual story of relationships. Learn to describe them like a cartographer.
图像为关系提供了视觉叙述。像制图师一样学会描述它们。
Coordinate: A pair of numbers (x, y) that pinpoints a position on the grid. "Co-ordinate" – working together to locate.
坐标：一对在网格上确定位置的数字 (x, y)。“坐标”就是协同定位。
Origin: The point (0, 0) where the axes cross. "Origin" – where it all begins.
原点：坐标轴交叉的点 (0, 0)。“Origin”即一切的起点。
Gradient: The steepness or slope of a line; rise ÷ run. Think "grade" of a hill.
斜率/坡度：一条线的陡峭程度；垂直增量 ÷ 水平增量。联想山坡的“坡度”。
y-intercept: The point where a line crosses the y-axis (x = 0). "Intercept" = where the line "intercepts" the axis.
y 截距：直线与 y 轴的交点（此时 x = 0）。“截距”即直线“截”住坐标轴的地方。
Linear function: A function that graphs as a straight line, often in the form y = mx + c. "Line" in linear.
线性函数：图像为直线的函数，常表示为 y = mx + c 的形式。“Linear”中有“Line”。
Quadratic function: A function with x² causing a parabola. The "U" shape – like a roller coaster.
二次函数：含有 x² 从而产生抛物线的函数。形状像字母“U”——如过山车。
Turning point: The maximum or minimum point of a parabola. "Turn" – the graph changes direction.
转折点：抛物线的最大值或最小值点。“转折”即图像改变方向。
Asymptote: A line that a curve approaches but never touches. Think "asymptote" sounds like "a symptom" – it gets closer but never quite arrives.
渐近线：曲线无限靠近但永不触及的直线。联想“渐近”就是逐步接近却永不相交。
6. Geometry & Shapes | 几何与图形
Shape vocabulary pops up in angle problems, circles, and area questions – visualise each term.
图形词汇出现在角度问题、圆和面积题中——将每个术语形象化。
Acute angle: An angle less than 90°. "A cute" little angle.
锐角：小于 90° 的角。“A cute”（可爱的）小角。
Obtuse angle: An angle greater than 90° but less than 180°. "Obtuse" sounds like "obese" – a wider angle.
钝角：大于 90° 但小于 180° 的角。“Obtuse”听起来像“obese”（肥胖）——较宽的角。
Reflex angle: Greater than 180° but less than 360°. Think "reflex" – it stretches beyond a straight line.
优角/反角：大于 180° 但小于 360° 的角。联想“反射”——它越过了直线。
Perpendicular: Two lines that meet at a right angle (90°). "Perpendicular" has a 'p' like 'perfect corner'.
垂直：相交成直角（90°）的两条直线。“垂直”联想到立“直”。
Parallel: Lines that never meet, always the same distance apart. The two L's in parallel are like the two rails of a train track.
平行：永不相交、距离始终相等的直线。Parallel 中的两个“l”像铁轨的两条轨道。
Polygon: A closed 2D shape with straight sides. "Poly" = many, "gon" = angle; many-angled shape.
多边形：由直边围成的封闭二维图形。“Poly”多 + “gon”角 = 有很多角的图形。
Regular polygon: All sides and all angles are equal. "Regular" like a regimented row of soldiers – everything uniform.
正多边形：所有边和所有角都相等的多边形。“正”如排列整齐的士兵——全部一致。
Hypotenuse: The longest side of a right-angled triangle, opposite the right angle. "Hypo" = under tension, it stretches the longest – think "hippopotamus" is big.
斜边：直角三角形中最长的边，位于直角对面。联想“斜”就是最长的那条边，河马（hippo）也很大。
Circle circumference: The distance around a circle. "Circum" = around, "ference" = carry – carried around the circle.
圆的周长：围绕圆一周的距离。“圆周”就是绕一圈的长度。
Tangent: A straight line that touches a circle at exactly one point. "Tangent" like "touching" – only a light touch.
切线：只与圆交于恰好一点的直线。“切”就是轻轻触碰。
7. Trigonometry & Pythagoras | 三角学与毕达哥拉斯定理
These right-triangle relationships are indispensable – a solid vocabulary prevents mixing up ratios.
这些直角三角形的关系不可或缺——扎实的词汇能防止比例混淆。
Pythagoras' theorem the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². Memory: "Pythago-ras" sounds like "pie-thag-oras" – picture a square pie on each side.
毕达哥拉斯定理：直角三角形的斜边的平方等于另外两边平方之和：a² + b² = c²。记忆：想象每一边放着一块正方形的派。
Opposite side: In trigonometry, the side across from the angle of interest. It faces the angle, like an opponent.
对边：三角学中，与所关注的角相对的边。它正对着这个角，像对手一样。
Adjacent side: The side next to the angle (not the hypotenuse). "Ad-" means "towards" – it is next to.
邻边：与角相邻（但不是斜边）的边。“邻”就是旁边。
Sine (sin): Ratio of opposite / hypotenuse. Mnemonic: S O H – Some Old Horses.
正弦 (sin)：对边 / 斜边的比值。助记：S O H – Some Old Horses。
Cosine (cos): Ratio of adjacent / hypotenuse. C A H – Can Always Hear.
余弦 (cos)：邻边 / 斜边的比值。C A H – Can Always Hear。
Tangent (tan): Ratio of opposite / adjacent
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