📚 IGCSE Maths: Formula Summary Handbook | IGCSE 数学：公式汇总手册
This comprehensive handbook covers the essential formulas needed for the IGCSE Mathematics syllabus. Mastering these formulas will help you solve problems efficiently and build a strong foundation for further study.
这份综合手册涵盖了 IGCSE 数学课程所需的基本公式。掌握这些公式将帮助你高效解题，为进一步学习打下坚实基础。
1. Number and Arithmetic | 数与算术
Percentage change = (New − Original) / Original × 100%
The percentage change formula quantifies the relative increase or decrease from an original amount. It is widely used in real‑life contexts such as discounts and population growth.
百分比变化公式量化了相对于原始数量的相对增加或减少。它广泛用于折扣、人口增长等实际情境。
Simple Interest I = PRT / 100
Simple interest is calculated on the principal amount. P is the principal, R the annual interest rate, and T the time in years.
单利根据本金计算。P 为本金，R 为年利率，T 为时间（年）。
Compound Amount A = P(1 + r/100)ⁿ
Compound interest adds interest to the principal each period. The formula gives the total amount after n compounding periods.
复利每期将利息加入本金。该公式给出 n 个复利周期后的总金额。
Speed = Distance / Time
This relationship links distance, speed and time. It can be rearranged to find any of the three quantities.
该关系式关联距离、速度和时间。可变形以求解三者中任一量。
Standard Form: a × 10ⁿ, where 1 ≤ a < 10 and n is an integer
Standard form is used to write very large or very small numbers compactly. The exponent n indicates how many places the decimal point has moved.
标准形式用于简洁书写极大或极小的数字。指数 n 表示小数点移动的位数。
2. Algebra and Equations | 代数与方程
(a ± b)² = a² ± 2ab + b²
These perfect square expansions are fundamental for simplifying expressions and solving quadratic equations.
这两个完全平方展开式是化简表达式和求解二次方程的基础。
(a + b)(a − b) = a² − b²
The difference of two squares factorisation appears frequently in algebraic manipulation and equation solving.
平方差因式分解在代数运算和方程求解中经常出现。
x = (−b ± √b² − 4ac) / 2a
lutions of ax² + bx + c = 0. The discriminant b² − 4ac determines the nature of the roots.
二次公式给出 ax² + bx + c = 0 的解。判别式 b² − 4ac 决定根的性质。
Completing the square: x² + bx = (x + b/2)² − (b/2)²
This method rewrites a quadratic expression in vertex form, revealing the coordinates of the turning point.
这种方法将二次表达式写成顶点式，揭示拐点坐标。
3. Inequalities and Sequences | 不等式与数列
Arithmetic nth term: Tₙ = a + (n − 1)d
For an arithmetic sequence, each term is found by adding the common difference d to the previous term. a is the first term.
在等差数列中，每一项由前一项加上公差 d 得到。a 为首项。
Arithmetic series sum: Sₙ = n/2 [2a + (n − 1)d]
This sum formula combines the first and last term approach. It is useful for finding the total of the first n terms.
该求和公式结合了首项与末项方法，可用于求前 n 项的总和。
Geometric nth term: Tₙ = arⁿ⁻¹
In a geometric sequence, each term is multiplied by the common ratio r. The exponent is one less than the term number.
在等比数列中，每一项乘以公比 r。指数比项数少 1。
Solving inequalities: if a > b, then a + c > b + c; if c > 0, ac > bc
Inequality signs follow similar rules to equations except that multiplying or dividing by a negative number reverses the inequality.
不等式符号遵循与方程类似的规则，但乘以或除以负数时不等号方向反转。
4. Functions and Graphs | 函数与图像
Linear function: y = mx + c
m represents the gradient (slope) and c is the y‑intercept. Every straight line can be written in this form.
m 表示斜率，c 是 y 轴截距。每条直线均可写为此形式。
Gradient m = (y₂ − y₁) / (x₂ − x₁)
The gradient measures the steepness of a line between two points (x₁, y₁) and (x₂, y₂).
梯度衡量两点 (x₁, y₁) 和 (x₂, y₂) 之间直线的倾斜程度。
Midpoint M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
The midpoint is the average of the x‑coordinates and the y‑coordinates of the two endpoints.
中点坐标为两端点 x 坐标和 y 坐标的平均值。
Distance d = √((x₂ − x₁)² + (y₂ − y₁)²)
This formula derives from Pythagoras' theorem and gives the straight‑line distance between two points.
该公式源自勾股定理，给出两点之间的直线距离。
Quadratic vertex form: y = a(x − h)² + k
The turning point of the parabola is at (h, k). The sign of a determines whether the parabola opens upwards or downwards.
抛物线的顶点为 (h, k)。a 的符号决定抛物线开口向上还是向下。
5. Geometry: Angles and Polygons | 几何：角与多边形
Sum of interior angles = (n − 2) × 180°
For any polygon with n sides, the total of its interior angles is given by this expression. Each exterior angle of a regular polygon is 360°/n.
对于任意 n 边形，其内角总和由此式给出。正多边形的每个外角为 360°/n。
Angles on a straight line sum to 180°, around a point sum to 360°
These angle facts are fundamental when solving problems involving intersecting lines and supplementary angles.
这些角度性质是求解相交直线和补角问题的基础。
Vertically opposite angles are equal
When two lines intersect, the opposite angles formed are congruent. This property is often used to find missing angles.
两条直线相交时，形成的对顶角相等。该性质常用于求未知角。
Parallel line angles: corresponding equal, alternate equal, co‑interior sum to 180°
When a transversal crosses parallel lines, these angle relationships hold and are key to geometric reasoning.
截线穿过平行线时，这些角度关系成立，是几何推理的关键。
6. Mensuration: Perimeter, Area, Volume | 测量：周长、面积、体积
Triangle area = ½ × base × height
The area is half the product of a side and the perpendicular height to that side. This applies to all triangles.
面积是边长与对应垂直高度乘积的一半。适用于所有三角形。
Circle circumference C = 2πr, area A
Published by TutorHao | IGCSE 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