📚 Year 11 Edexcel Maths: Vocabulary & Terminology Quick Recall Guide | Year 11 Edexcel 数学：词汇术语速记指南
A solid command of mathematical vocabulary is the foundation of success in Edexcel GCSE Maths. When you can speak the language of mathematics fluently, exam questions become clearer, problem-solving pathways open up, and you avoid the common pitfalls caused by misreading key terms. This guide provides a structured, bilingual quick-recall reference covering the essential terminology across all six content domains, complete with memory tips and side-by-side English-Chinese explanations.
牢固掌握数学术语词汇是攻克 Edexcel GCSE 数学的基础。当你能够流利地运用数学语言时，考试题目会变得更清晰，解题思路会自然展开，你也能避免因误解关键词而掉入常见陷阱。这份指南提供一个结构化的双语速记参考，覆盖全部六个内容领域的核心术语，并附有记忆技巧和逐条英中对照解释。
1. Number Terms | 数字术语
Integer: A whole number that can be positive, negative or zero, with no fractional or decimal part. Examples: –5, 0, 12.
整数：可以是正数、负数或零的整数，不带分数或小数部分。例如 –5, 0, 12。
Rational number integers and b ≠ 0. This includes terminating and recurring decimals, e.g. 0.75 = ¾, 0.333… = ⅓.
有理数：任何可以写成分数 a/b 形式的数，其中 a 和 b 是整数且 b ≠ 0。包括有限小数和循环小数，例如 0.75 = ¾、0.333… = ⅓。
Irrational number: A number that cannot be expressed as a simple fraction. Its decimal form is non-terminating and non-recurring; examples include π and √2. A common exam hint is that surds are irrational.
无理数：不能表示为简单分数的数，其小数形式无限不循环。例子有 π 和 √2。考试中常给出提示：根式（surd）是无理数。
Prime number: A number greater than 1 that has exactly two distinct factors — 1 and itself. 2 is the only even prime. Learn the first few primes: 2, 3, 5, 7, 11, 13, 17, 19.
质数（素数）：大于 1 且只有两个不同因数的数——1 和它本身。2 是唯一的偶质数。请熟记前几个质数：2, 3, 5, 7, 11, 13, 17, 19。
Factor and Multiple: A factor of a number divides it exactly with no remainder. A multiple is the product of that number and any integer. 3 is a factor of 12; 12 is a multiple of 3.
因数与倍数：一个数的因数能够整除该数且无余数。倍数则是该数与任意整数的乘积。3 是 12 的因数；12 是 3 的倍数。
Highest Common Factor (HCF) and Lowest Common Multiple (LCM): HCF is the largest factor shared by two or more numbers; LCM is the smallest multiple they share. For 8 and 12, HCF is 4, LCM is 24.
最大公因数（HCF）与最小公倍数（LCM）：HCF 是两个或多个数共有的最大因数；LCM 是它们共有的最小倍数。对于 8 和 12，HCF = 4，LCM = 24。
Standard form s as a × 10ⁿ where 1 ≤ a < 10 and n is an integer. 4500 = 4.5 × 10³; 0.00032 = 3.2 × 10⁻⁴.
标准形式：将很大或很小的数写成 a × 10ⁿ 的形式，其中 1 ≤ a < 10, n 为整数。4500 = 4.5 × 10³；0.00032 = 3.2 × 10⁻⁴。
Surd: An expression containing an irrational root, often a square root that cannot be simplified to an integer. √8 can be simplified to 2√2. Always leave answers in exact surd form unless told otherwise.
根式：含有无理根的表达式，通常为无法化简为整数的平方根。√8 可化简为 2√2。除非另有说明，答案须保留精确根式。
2. Algebraic Expressions | 代数表达式
Variable, Term and Coefficient: A variable is a symbol, usually a letter, representing an unknown number. A term is a single number, variable or product of numbers and variables (e.g. 5x²). The coefficient is the numerical factor of a term; in 5x², 5 is the coefficient.
变量、项与系数：变量是代表未知数的符号，常用字母表示。项是单个的数、变量或数与变量的乘积（如 5x²）。系数是项中数字因数；在 5x² 中，5 是系数。
Expression, Equation, Identity and Formula s (3x+2=11). An identity is true for all values of the variable, written with an identity sign ≡ (x+x ≡ 2x). A formula is an equation showing the relationship between variables (A=πr²).
表达式、方程、恒等式与公式：表达式是若干项的组合，不含等号（3x+2）。方程指出两个表达式相等，且仅对特定值成立（3x+2=11）。恒等式对所有变量取值均成立，用恒等号 ≡ 表示（x+x ≡ 2x）。公式是表示变量之间关系的方程（A=πr²）。
Simplify: Collect like terms and carry out any arithmetic to write an expression in its most compact form. 4x+2y–x+3y simplifies to 3x+5y.
化简：合并同类项并进行运算，将表达式写成最简形式。4x+2y–x+3y 化简为 3x+5y。
Expand: Remove brackets by multiplying each term inside by the factor outside. 3(2x+5) expands to 6x+15. For two brackets, use FOIL (First, Outer, Inner, Last).
展开：将括号外的因数乘以括号内的每一项以去除括号。3(2x+5) 展开得 6x+15。对于两个括号相乘，使用 FOIL （首、外、内、末）。
Factorise: The reverse of expanding; rewrite an expression as a product of its factors. 6x+15 factorises to 3(2x+5). Factorising quadratics into double brackets is a core skill.
因式分解：展开的逆运算；将表达式改写为因数的乘积。6x+15 分解为 3(2x+5)。将二次式分解为两个括号是因式分解的核心技能。
3. Equations and Inequalities | 方程与不等式
Solve d : Find the value(s) of the unknown that make the equation true. The solution to 2x+5=13 is x=4.
求解：找出使方程成立的未知数的值。方程 2x+5=13 的解为 x=4。
Linear and Quadratic Equations x is 1). A quadratic equation has an x² term, e.g. ax²+bx+c=0, and can have two solutions.
线性方程与二次方程：线性方程形式为 ax+b=0（x 的最高次幂为 1）。二次方程含有 x² 项，如 ax²+bx+c=0，可能有两个解。
Simultaneous equations: Two or more equations with the same variables. Solve by elimination, substitution or graphically to find the pair of values that satisfies both.
联立方程组：两个或以上含有相同变量的方程。可通过消元法、代入法或图像法求解，找出同时满足所有方程的一对值。
Inequality ring two expressions using signs <, >, ≤ or ≥. x+4 > 7 means x is greater than 3.
不等式：使用符号 <、>、≤ 或 ≥ 连接两个表达式的数学语句。x+4 > 7 表示 x 大于 3。
Solution set and region ph. A dashed line is used for strict inequalities (< or >), a solid line for ≤ or ≥.
解集与区域：不等式可在数轴上表示（空心/实心原点），也可在坐标图上表示为阴影区域。严格不等式（< 或 >）画虚线，≤ 或 ≥ 则画实线。
4. Sequences | 数列
Sequence and Term: A sequence is an ordered list of numbers governed by a rule. Each number is called a term. The first term is often labelled u₁, the second u₂, etc.
数列与项：数列是按照某种规则排列的一列数。每个数称为项。第一项常标记为 u₁，第二项 u₂，依此类推。
Term-to-term rule: Describes how to move from one term to the next. In 3, 7, 11, 15, … the rule is 'add 4'.
逐项规则：描述如何从一项得到下一项。在 3, 7, 11, 15, … 中，规则是 '加 4'。
nth term rule (position-to-term): Gives a formula for any term based on its position n. For the sequence 5, 8, 11, 14, … the nth term is 3n+2.
第 n 项规则（位置生成项）：根据项的位置 n 给出该值的公式。数列 5, 8, 11, 14, … 的第 n 项公式为 3n+2。
Arithmetic and Geometric sequences .g. 2, 5, 8, 11, d=3). A geometric sequence has a constant ratio (e.g. 2, 6, 18, 54, r=3).
等差数列与等比数列：等差数列相邻两项的差为常数（如 2, 5, 8, 11, 公差 d=3）。等比数列相邻两项的比为常数（如 2, 6, 18, 54, 公比 r=3）。
Quadratic sequence: The second differences between terms are constant. The nth term is of the form an²+bn+c. Spot by checking first and second differences.
二次数列：项之间的二阶差分为常数。第 n 项公式形式为 an²+bn+c。可通过检查一阶差和二阶差来识别。
5. Graphs | 图形
Coordinates and axes: The x-axis is horizontal, y-axis vertical. A point is written (x, y). The origin is (0,0).
坐标与坐标轴：x 轴为水平轴，y 轴为垂直轴。一个点记为 (x, y)。原点为 (0,0)。
Gradient and intercept ative slopes downward. The y-intercept is where the line crosses the y-axis (c in y=mx+c).
斜率与截距：斜率 (m) 衡量倾斜度：y 变化量 ÷ x 变化量。正斜率向右上方倾斜，负斜率向右下方倾斜。y 截距是直线与 y 轴交点的 y 坐标（即 y=mx+c 中的 c）。
Linear, Quadratic, Cubic, Reciprocal and Exponential graphs: Recognise the shapes. Linear: straight line; Quadratic: ∪ or ∩ bic: S-shaped or reverse; Reciprocal y = k/x: hyperbola with asymptotes; Exponential y = aˣ: rapid growth or decay with a horizontal asymptote.
一次、二次、三次、反比例和指数图形：辨别形状。一次：直线；二次：∪ 或 ∩ 形抛物线；三次：S 形或反 S 形；反比例 y = k/x：有渐近线的双曲线；指数 y = aˣ：带有水平渐近线的快速增长或衰减曲线。
Turning point and roots r minimum. Roots (or solutions) are the x-values where the graph crosses the x-axis (y=0).
转折点与根：在二次图形上，转折点是最大值或最小值。根（或解）是图形与 x 轴相交处的 x 值（y=0 时的值）。
Transformations of graphs: f(x)+a moves the graph up/down; f(x+a) moves left/right; – x-axis; af(x) stretches vertically. Learn the effect on coordinates: (x, y) → (x, y+a), (x–a, y), (x, –y), (x, ay).
图形变换：f(x)+a 上下平移；f(x+a) 左右平移；–f(x) 关于 x 轴反射；af(x) 纵向拉伸。记住对坐标的影响：(x, y) → (x, y+a), (x–a, y), (x, –y), (x, ay)。
6. Ratio, Proportion and Rates of Change | 比率、比例与变化率
Ratio and Proportion: Ratio compares the size of two or more parts, often written as a:b. For a recipe using 2 parts flour to 3 parts sugar, the ratio is 2:3. Proportion describes a part-whole relationship; flour makes up 2/5 of the total mixture.
比与比例：比用于比较两个或多个部分的大小，通常写作 a:b。某食谱用 2 份面粉与 3 份糖，面粉与糖的比为 2:3。比例描述部分与整体的关系；面粉占总混合物的 2/5。
Direct proportion: Two quantities are directly proportional if y ∝ x or y = kx, where k is a constant. Graph is a straight line through the origin.
正比例：若两个量满足 y ∝ x 即 y = kx（k 为常数），则它们成正比。图形为一条过原点的直线。
Inverse proportion: y is inversely proportional to x when y ∝ 1/x or y = k/x. The graph is a rectangular hyperbola. Doubling x halves y.
反比例：若 y ∝ 1/x 即 y = k/x，则 y 与 x 成反比。图形为等轴双曲线。x 加倍使 y 减半。
Percentage change, compound interest the multiplier (1 + r/100)ⁿ. Repeated percentage changes are multiplicative, not additive.
百分比变化、复利：百分比变化 = (变化量 ÷ 原来量)×100。复利使用乘数 (1 + r/100)ⁿ。重复的百分比变化是相乘关系而非相加。
Compound measures: speed, density, pressure e ÷ area. Use triangle diagrams to rearrange. Units are essential: e.g. km/h, kg/m³, N/m².
复合量度：速度、密度、压强：速度 = 距离 ÷ 时间；密度 = 质量 ÷ 体积；压强 = 力 ÷ 面积。可利用三角形图示进行公式变形。注意单位，如 km/h、kg/m³、N/m²。
7. Geometry and Measures | 几何与测量
Angles and parallel lines: Vertically opposite angles are equal. On parallel lines: corresponding angles are equal (F-shape), alternate angles are equal (Z-shape), co-interior angles sum to 180° (C-shape).
角与平行线：对顶角相等。平行线上：同位角相等（F 形），内错角相等（Z 形），同旁内角之和为 180°（C 形）。
Polygons: interior and exterior angles: Exterior angles of any convex polygon sum to 360°. Interior angle = 180° – exterior angle. Sum of interior angles = (n–2)×180° for an n-sided polygon.
多边形：内角与外角：任何凸多边形的外角和为 360°。内角 = 180° – 外角。n 边形内角和 = (n–2)×180°。
Circle theorems: Key facts: angle at centre is twice angle at circumference; angle in a semicircle is 90°; angles in the same segment are equal; opposite angles of a cyclic quadrilateral sum to 180°; tangent meets radius at 90°; alternate segment theorem.
圆定理：核心定理：圆心角等于两倍圆周角；半圆上的圆周角为 90°；同弧上的圆周角相等；圆内接四边形对焦互补（和为 180°）；切线与半径垂直；弦切角定理。
Pythagoras' theorem c², where c is the hypotenuse. Use to find a missing side or to prove a triangle is right-angled.
勾股定理：直角三角形中，a² + b² = c²，c 为斜边。用于求边长或证明三角形为直角三角形。
Trigonometry: SOHCAHTOA te/Adjacent. Use for right-angled triangles to find missing sides or angles. Non-right triangles require sine rule or cosine rule.
三角函数：SOHCAHTOA：Sin θ = 对边/斜边；Cos θ = 邻边/斜边；Tan θ = 对边/邻边。用于解直角三角形求边或角。非直角三角形需用正弦定理或余弦定理。
Sine rule and Cosine rule: Sine rule: a/sin A = b/sin B = c/sin C. Cosine rule: a² = b² + c² – 2bc cos A. Area of triangle = ½ab sin C. Label sides and angles carefully.
正弦定理与余弦定理：正弦定理：a/sin A = b/sin B = c/sin C。余弦定理：a² = b² + c² – 2bc cos A。三角形面积 = ½ab sin C。注意正确标出边和角。
Vectors: A vector has magnitude and direction. Written as a column vector (³/₋₂) or with i, j notation. Add vectors tip-to-tail. Scalar multiples stretch or shrink
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