📚 Year 11 Eduqas Maths: Key Terminology Memorisation Guide | 11年级Eduqas数学：关键术语速记指南
Mastering mathematical vocabulary is a powerful shortcut to exam success. When you can precisely name concepts, your brain organises problem-solving strategies more quickly. This guide covers the essential terminology across every Eduqas GCSE topic taught in Year 11, pairing clear definitions with memory tricks that save revision time.
掌握数学词汇是通往考试成功的捷径。当你能够准确命名概念时，大脑能更快地组织解题策略。本指南涵盖 Year 11 每个 Eduqas GCSE 主题的核心术语，将清晰的定义与记忆技巧配对，帮你节省复习时间。
1. Number Essentials | 数的基础术语
Integer: A whole number that can be positive, negative, or zero (e.g., -7, 0, 36). Think of 'intact' – no fractional or decimal parts are allowed.
整数: 可以是正数、负数或零的完整数字（如 -7, 0, 36）。联想“完整”一词——不允许有分数或小数部分。
Prime number: A number greater than 1 whose only factors are 1 and itself. The first primes are 2, 3, 5, 7, 11, ... Remember that 2 is the only even prime – an 'odd one out' among evens.
质数: 大于 1 且只有 1 和自身两个因数的数。首个质数：2, 3, 5, 7, 11, ... 记住 2 是唯一的偶质数——偶数中的“异类”。
HCF and LCM: Highest Common Factor (largest number that divides into two or more numbers) and Lowest Common Multiple (smallest number that is a multiple of two or more numbers). Use a Venn diagram of prime factors: HCF is the product of numbers in the intersection, LCM is the product of all circled numbers.
最大公因数 (HCF) 与最小公倍数 (LCM): 最大公因数是能同时整除两个或多个数的最大数；最小公倍数是两个或多个数的倍数中最小的一个。画出质因数文氏图：HCF 是交集数字的乘积，LCM 是所有圈出数字的乘积。
Standard form: lt; 10 and n is an integer. Large numbers have positive n, small decimals have negative n. The memory hook: 'A' stays between 1 and 10, n counts the decimal move.
标准型: 写为 A × 10ⁿ 的形式，其中 1 ≤ A < 10，n 为整数。大数 n 为正，小数 n 为负。记忆锚点：“A 在 1 和 10 之间，n 计算小数点移动的位数”。
Surd: An irrational root, such as √2 or √3, that cannot be written exactly as a decimal or fraction. Keep surds in exact answers unless the question asks for a decimal approximation. 'Surd' rhymes with 'absurd' – they never end!
无理根 (Surd): 无法写成精确小数或分数的无理数根，如 √2 或 √3。除非题目要求近似值，否则答案保留无理根形式。“Surd”与“absurd（荒谬）”押韵——它们永远没完没了！
2. Algebraic Expressions and Manipulation | 代数表达式与运算
Expression, term and coefficient: An expression is a collection of terms joined by + or – (e.g., 3x² + 5x – A term is a single part (3x²), and its coefficient is the numerical factor (3). Memorise: 'term' = piece, 'coefficient' = number in front.
表达式、项与系数: 表达式是由加号或减号连接的若干项（如 3x² + 5x – 2）。项是单个部分（如 3x²），其系数是数值因数（3）。记住：“项”就是片段，“系数”是前面的数字。
Expand: Multiply out brackets using the distributive law. For (x + a)(x + b) the expanded form is x² + (a+b)x + ab. A quick check: FOIL – First, Outer, Inner, Last.
展开: 运用分配律将括号乘开。对于 (x + a)(x + b)，展开式为 x² + (a+b)x + ab。一个快捷检验法：FOIL——先乘首、外、内、尾。
Factorise: a² − b² = (a − b)(a + b). The backwards FOIL method turns x² + 5x + 6 into (x + 2)(x + 3).
因式分解: 把表达式写成因式的乘积。先提取公因式，再运用平方差公式：a² − b² = (a − b)(a + b)。逆向 FOIL 法可将 x² + 5x + 6 分解为 (x + 2)(x + 3)。
Quadratic expression: An algebraic expression with the term x², such as 2x² − 4x + 1. Quad means square, linking to the power of 2.
二次式: 含有 x² 项的代数表达式，如 2x² − 4x + 1。“Quad”意指平方，联系到 2 次幂。
Completing the square: Rewriting a quadratic in the form (x + p)² + q to find the vertex or solve. Halve the coefficient of x to get p, then adjust the constant. It is the bridge to the quadratic formula.
配方法: 将二次式写成 (x + p)² + q 的形式以寻找顶点或解方程。将 x 的系数减半得到 p，再调整常数项。它是通向二次公式的桥梁。
3. Equations and Inequalities | 方程与不等式
Equation vs. identity: ertain values (e.g., 2x = 10 gives x = 5). An identity is true for all values and uses the ≡ sign. Spot '≡' and you know you need to prove both sides are algebraically equivalent.
方程与恒等式: 方程只在特定值成立（如 2x = 10 得 x = 5）。恒等式对所有值成立并使用 ≡ 符号。看到“≡”就意味着需用代数证明两边等价。
Inequality symbols: al to), ≥ (greater than or equal to). The wider end faces the larger number. Memory trick: 'The alligator eats the bigger value.'
不等式符号: <（小于），>（大于），≤（小于等于），≥（大于等于）。宽开口朝向较大的数。记忆窍门：“鳄鱼吃大数”。
Solving inequalities: Treat like equations, but when multiplying or dividing by a negative, reverse the inequality sign. Highlight this with 'Flip the sign when the line goes negative!'
解不等式: 与解方程类似，但当乘或除以负数时，不等号方向反转。用“遇负就翻转”强调。
Quadratic formula: For ax² + bx + c = 0, x = ( −b ± √b² − 4ac ) / 2a. Sing the formula to a rhythm – many students remember it as 'minus b plus/minus square root, b squared minus four a c, all over two a'.
二次公式: 对于 ax² + bx + c = 0，x = ( −b ± √b² − 4ac ) / 2a。把公式谱上节奏——很多学生将其记作“负 b 加减根号，b 平方减四 a c，整体除以二 a”。
Simultaneous equations: A pair of equations with two unknowns. Solve by elimination (add/subtract to remove a variable) or substitution (replace one letter with an expression). The clue: the coordinates where two lines cross.
联立方程: 含有两个未知数的一组方程。可用消元法（加减消去一个变量）或代入法（将一个字母用表达式替换）求解。线索：两条直线交点的坐标。
4. Sequences and Straight-Line Graphs | 数列与直线图
nth term of a linear sequence: (n−1)d. In GCSE style, the formula simplifies to dn + (a − d). Check by substituting n = 1 – you must get the first term.
线性数列的第 n 项: 对于公差为 d 的数列，第 n 项 an = a₁ + (n−1)d。在 GCSE 中通常简化为 dn + (a − d)。用 n=1 代入检验——必须得到首项。
Gradient (m): The steepness of a line, calculated as rise over run: (change in y) ÷ (change in x). A positive gradient slopes upwards, negative slopes downwards. 'M' stands for 'how steep am I?'
梯度 (m): 直线的倾斜程度，用纵向变化除以横向变化计算：(y 的变化) ÷ (x 的变化)。正梯度向上倾斜，负梯度向下倾斜。“M”代表“我有多陡？”。
y-intercept (c): e the line crosses the y-axis, obtained by setting x = 0. Together, y = mx + c is the line's equation. 'c' is where you cut the y-axis.
y 轴截距 (c): 直线与 y 轴的交点，令 x=0 求得。y = mx + c 合在一起就是直线方程。“c”是切割 y 轴的位置。
Parallel lines: h : Lines with exactly the same gradient. If y = 2x + 3 and y = 2x − 7 are parallel (both m = 2). Think 'parallel paths never meet – same slope.'
平行线: 梯度完全相同的直线。若 y = 2x + 3 和 y = 2x − 7 是平行的（m 均为 2）。想象“平行的道路永不相交——相同的坡度”。
Perpendicular lines: Their gradients multiply to give −1. If one line has gradient 2, a perpendicular line has gradient −½. Memory aid: 'Flip and change sign for a perfect right angle.'
垂直线: 两条直线的梯度乘积为 −1。若一线梯度为 2，则与之垂直的线梯度为 −½。记忆辅助：“颠倒并变号，打造完美的直角”。
5. Angles and Circle Theorems | 角度与圆定理
Angle at the centre theorem: The angle formed at the centre of a circle by two radii is double the angle at the circumference subtended by the same arc. Imagine a 'central bow-tie' where the centre angle dominates.
圆心角定理: 由两条半径在圆心形成的角，是同一圆弧所对圆周角的两倍。想象一个“中心领结”，圆心角占据主导。
Angle in a semicircle: An angle inscribed in a semicircle is always a right angle (90°). 'Thales' theorem' – if the diameter is the base, the third point on the circle makes a right angle.
半圆上的圆周角: 内接于半圆的角始终为直角 (90°)。泰勒斯定理——如果直径作为底边，圆上第三点构成的角为直角。
Angles in the same segment: Angles subtended by the same chord on the same side of the chord are equal. Visualise two spiders hanging from the same web – they share the same arc.
同弧上的圆周角: 同弦同侧所对的圆周角相等。想象两只蜘蛛从同一张网上垂下——它们共享同一段弧。
Cyclic quadrilateral: A quadrilateral whose vertices all lie on a circle. Opposite angles sum to 180°, so if one is 70°, its opposite is 110°. 'Cyclic' reminds us the sum is supplementary.
圆内接四边形: 所有顶点都在圆上的四边形。对角之和为 180°，所以若一角为 70°，其对角为 110°。记住“cyclic”提示对角互补。
Alternate segment theorem: The angle between a tangent and a chord through the point of contact equals the angle in the alternate segment. Picture a 'tangent-chord sandwich' filling the same angle on the other side.
弦切角定理: 切线与经过切点的弦所夹的角，等于另一侧交替弧段内的圆周角。想象一个“切弦三明治”，在另一边填充等角。
6. Trigonometry and Pythagoras | 三角学与毕达哥拉斯定理
Pythagoras' Theorem: nly works for right triangles; identifying c is the longest side opposite the right angle.
毕达哥拉斯定理: 在直角三角形中，斜边的平方等于两直角边的平方和：a² + b² = c²。仅适用于直角三角形；识别 c 为直角对边的最长边。
SOH CAH TOA:
SOH CAH TOA:
SOH CAH TOA: e/Hypotenuse, Cos θ = Adjacent/Hypotenuse, Tan θ = Opposite/Adjacent. Chant it as a mantra – 'SOH CAH TOA' turns confusing ratios into a catchy phrase.
SOH CAH TOA: sin θ = 对边/斜边, cos θ = 邻边/斜边, tan θ = 对边/邻边。像口诀一样反复念——'SOH CAH TOA' 把容易混淆的比值变成朗朗上口的短语。
Sine rule: B = c/sin C. Useful when you have an angle and its opposite side. The ratio stays constant – 'side over sine stays fine.'
正弦定理: 对于任意三角形，a/sin A = b/sin B = c/sin C。当已知一角及其对边时特别有用。比值保持不变——“边除正弦很稳定”。
Cosine rule: Adapts Pythagoras for non-right triangles by including the −2bc cos A term. Remember it as 'the Pythagoras upgrade with an angle adjustment.'
余弦定理: a² = b² + c² − 2bc cos A。通过加入 −2bc cos A 这一项，将毕达哥拉斯定理扩展至非直角三角形。记住“带有角度修正的升级版毕达哥拉斯”。
Area of a triangle using sine: Area = ½ ab sin C, where a and b are two sides and C is the included angle. Think of it
Published by TutorHao | Year 11 Mathematics 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