📚 Year 10 Edexcel Further Mathematics: Glossary and Quick Memorisation Guide | Year 10 Edexcel 进阶数学：词汇术语速记指南
Mastering the terminology of Year 10 Edexcel Further Mathematics is your first step towards solving complex problems with confidence. This guide breaks down the essential vocabulary into bite-sized definitions, paired with memory hacks and visual tips, so you can recall them swiftly during exams.
掌握 Year 10 Edexcel 进阶数学的术语是自信解决复杂问题的第一步。本指南将核心词汇拆解为易于消化的定义，并配以记忆技巧和视觉提示，帮助你在考试中快速回忆。
1. Algebraic Fundamentals and Functions | 代数基础与函数
A function a rule that assigns each input (x-value) to exactly one output (y-value). Think of it as a 'number machine' where an input enters, gets processed, and only one result comes out. Notation: f(x) = ...
函数是将每个输入（x值）对应到唯一输出（y值）的规则。可以把它想象成一台“数字机器”：一个输入进入后经过处理，只有一个结果输出。记作 f(x) = ...
The domain is the set of all possible input values (x), and the range is the set of possible output values (y). Mnemonic: 'D' for Domain points along the x-axis; 'R' for Range points along the y-axis.
定义域是所有可能输入值（x）的集合，值域是可能输出值（y）的集合。记忆法：“D”代表定义域对应x轴方向；“R”代表值域对应y轴方向。
A composite function fg(x) means apply g first, then f: f◦g(x) = f(g(x)). Work from inside out – like peeling an onion. The order matters: fg(x) is rarely the same as gf(x).
复合函数 fg(x) 表示先应用 g，再应用 f：f◦g(x)=f(g(x))。从内向外运算——像剥洋葱一样。顺序很重要：fg(x) 通常不等于 gf(x)。
The inverse function x and y and solve for y. A function must be one-to-one over its domain to have an inverse.
反函数 f⁻¹(x) 逆转原函数的效果。图像上是关于直线 y = x 的反射。求反函数时交换 x 和 y 并解出 y。函数在其定义域上必须是一一映射才有反函数。
The modulus function |x| returns the non-negative absolute value, the 'distance from zero' on the number line. Graphically it reflects any negative part of the graph in the x-axis to make it positive.
绝对值函数 |x| 返回非负的绝对值，即数轴上“到零的距离”。图像上它将图形的负值部分关于 x 轴反射，使其全部非负。
2. Quadratics and Inequalities | 二次型与不等式
A quadratic equation = 0 (a ≠ 0). Three main solving methods: factorising, completing the square, and using the quadratic formula x = [-b ± √b² − 4ac] / (2a).
二次方程具有形式 ax² + bx + c = 0（a ≠ 0）。三种主要解法：因式分解、配方法和使用求根公式 x = [-b ± √b² − 4ac] / (2a)。
The discriminant ; Δ = 0 → one repeated real root; Δ < 0 → no real roots (the roots are complex). Memorise: 'D high? two fly. D zero? one hero. D low? no show.'
判别式 Δ = b² − 4ac 揭示根的性质：Δ > 0 → 两个不等实根；Δ = 0 → 一个重根；Δ < 0 → 没有实根（复数根）。记忆法：判别式大，两个分叉；判别式零，一个就行；判别式负，实数止步。
Inequalities (less than or equal to). Solve them like equations, but remember the golden rule: when multiplying or dividing by a negative number, flip the inequality sign.
不等式使用符号 >（大于）、<（小于）、≥（大于等于）、≤（小于等于）。解法类似方程，但记住黄金法则：当乘以或除以一个负数时，必须反转不等号方向。
Set notation {x : x > 3} reads "the set of all x such that x is greater than 3" tation as (3, ∞). Square brackets [ ] include the endpoint; round brackets ( ) exclude it.
集合符号 {x : x > 3} 读作“所有使得 x > 3 的 x 的集合”。也可用区间符号 (3, ∞)。方括号 [ ] 表示包含端点；圆括号 ( ) 表示不包含端点。
3. Coordinate Geometry and Circles | 坐标几何与圆
Between points (x₁, y₁) and (x₂, y₂): gradient = (y₂ − y₁) / (x₂ − x₁); distance = √[(x₂ − x₁)² + (y₂ − y₁)²]; midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). Remember: 'difference in y over difference in x' for gradient.
两点 (x₁, y₁) 和 (x₂, y₂) 之间：斜率 = (y₂ − y₁) / (x₂ − x₁)；距离 = √[(x₂ − x₁)² + (y₂ − y₁)²]；中点 = ((x₁+x₂)/2, (y₁+y₂)/2)。记忆法：斜率就是“y的差除以x的差”。
The equation of a circle s (x − a)² + (y − b)² = r². If the centre is at the origin, it simplifies to x² + y² = r².
圆心为 (a, b) 半径为 r 的圆的方程是 (x − a)² + (y − b)² = r²。若圆心在原点，则简化为 x² + y² = r²。
A tangent to a circle touches it at exactly one point. The radius drawn to the point of tangency is perpendicular to the tangent. Use this fact to find tangent equations by equating gradients to −1/ m.
圆的切线与圆恰好交于一点。切点处的半径与切线垂直。利用这一事实，可通过斜率为 −1/m 的关系求切线方程。
A chord is a line segment joining two points on a circle. The perpendicular from the centre of the circle to a chord bisects the chord – a very handy property for solving coordinate problems.
弦是连接圆上两点的线段。从圆心到弦的垂直线平分该弦——这是解决坐标几何问题的一个非常实用的性质。
4. Trigonometry and Identities | 三角学与恒等式
Basic trigonometric ratios ypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Use the famous mnemonic SOH CAH TOA to lock them in.
直角三角形的基本三角比：sin θ = 对边/斜边，cos θ = 邻边/斜边，tan θ = 对边/邻边。用著名的记忆口诀 SOH CAH TOA 来牢牢记住。
For non-right triangles, use the sine rule: a/sin A = b/sin B = c/sin C, and the cosine rule: a² = b² + c² − 2bc cos A. The cosine rule is like Pythagoras' theorem with an extra '−2bc cos A' term.
对于非直角三角形，使用正弦定理：a/sin A = b/sin B = c/sin C，以及余弦定理：a² = b² + c² − 2bc cos A。余弦定理就像是毕达哥拉斯定理多了一项“−2bc cos A”。
The area of any triangle can be found using ½ ab sin C, where C is the angle between sides a and b. This is particularly useful when you know two sides and the included angle.
任意三角形的面积可用公式 ½ ab sin C 计算，其中 C 是边 a 和 b 的夹角。当已知两边及其夹角时，该公式尤为有用。
Radians (deg to rad) or 180/π (rad to deg). Arc length s = rθ, sector area = ½ r²θ (θ in radians).
弧度制是角度的另一种度量：π 弧度 = 180°。换算时，角度制转弧度制乘 π/180，反之乘 180/π。弧长 s = rθ，扇形面积 = ½ r²θ（θ 用弧度）。
Essential trigonometric identities θ = sin θ / cos θ. These are your tools for simplifying expressions and solving equations.
核心三角恒等式：sin²θ + cos²θ = 1（毕达哥拉斯恒等式），以及 tan θ = sin θ / cos θ。这些都是化简表达式和求解方程的工具。
5. Introduction to Calculus | 微积分初步
Differentiation from first principles gives the derivative as a limit: f'(x) = limₕ→₀ [f(x+h) − f(x)] / h. Though you won' always use this, it defines what a derivative truly is: the instantaneous rate of change.
从第一原理求导将导数定义为极限：f'(x) = limₕ→₀ [f(x+h)
Published by TutorHao | Year 10 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