IGCSE AQA Maths: Last-Minute Revision Notes | IGCSE AQA 数学：考前冲刺笔记

📚 IGCSE AQA Maths: Last-Minute Revision Notes | IGCSE AQA 数学：考前冲刺笔记

This article is a fast-paced revision guide for the IGCSE AQA Mathematics exam, covering key topics and essential techniques to help you maximise your marks in the final hours before the test. Use these concise notes to refresh your memory on formulas, methods and common pitfalls.

本文是一份快节奏的IGCSE AQA数学考试复习指南，涵盖关键主题和核心技巧，助你在考前最后冲刺中争取最高分。借助这些简明笔记，快速重温公式、解题方法和常见陷阱。

1. Number Fundamentals | 数字基础

Ensure you can confidently convert between fractions, decimals and percentages. Remember that 1/2 = 0.5 = 50%, and to change a fraction to a decimal, divide the numerator by the denominator.

确保能熟练地在分数、小数和百分数之间转换。记住 1/2 = 0.5 = 50%，要将分数化为小数，用分子除以分母即可。

When adding or subtracting fractions, always find a common denominator: a/b + c/d = (ad + bc) / bd. For multiplication, multiply numerators together and denominators together: a/b × c/d = ac / bd. Division is the same as multiplying by the reciprocal: a/b ÷ c/d = a/b × d/c.

分数加减时，务必先通分：a/b + c/d = (ad + bc) / bd。乘法时分子相乘、分母相乘：a/b × c/d = ac / bd。除法等于乘以倒数：a/b ÷ c/d = a/b × d/c。

Use standard form to write very large or very small numbers: N × 10ⁿ, where 1 ≤ N < 10 and n is an integer. E.g. 3.2 × 10⁵ = 320 000. For calculations, multiply the Ns and add the exponents when multiplying numbers in standard form.

使用标准形式表示极大或极小的数：N × 10ⁿ，其中 1 ≤ N < 10，n 为整数。例如 3.2 × 10⁵ = 320 000。标准形式下的乘法运算，将 N 部分相乘，指数相加。

Rounding and estimation can save time. Round to a given number of significant figures or decimal places. In an exam, estimate calculations first to check your answers are sensible.

四舍五入和估算可节省时间。按要求保留有效数字或小数位数。考试中先估算，以检验答案是否合理。

2. Algebraic Manipulation | 代数运算

Expanding brackets: a(b + c) = ab + ac. For double brackets, use FOIL (First, Outer, Inner, Last): (x + a)(x + b) = x² + (a+b)x + ab. Always simplify by collecting like terms.

展开括号：a(b + c) = ab + ac。对于双括号，使用 FOIL 法则（首、外、内、末）：(x + a)(x + b) = x² + (a+b)x + ab。记得合并同类项简化。

Factorising reverses expanding. Look for common factors first: 6x + 9 = 3(2x + 3). For quadratic expressions x² + bx + c, find two numbers that multiply to c and add to b: x² + 5x + 6 = (x + 2)(x + 3).

因式分解是展开的逆运算。先提取公因数：6x + 9 = 3(2x + 3)。对于二次式 x² + bx + c，找出两个数使其乘积为 c，和为 b：x² + 5x + 6 = (x + 2)(x + 3)。

Solving linear equations: isolate the variable by performing the same operation on both sides. E.g. 2x – 3 = 7 → 2x = 10 → x = 5. For equations with unknowns on both sides, collect all x terms on one side first.

解线性方程：通过在等式两边进行相同运算来分离变量。如 2x – 3 = 7 → 2x = 10 → x = 5。若未知数在等式两边，先把含 x 的项移到同一边。

Solving quadratic equations: when factorised to zero, set each bracket equal to zero. For (x + 2)(x – 4) = 0, the solutions are x = -2 and x = 4. If not factorisable, use the quadratic formula: x = [-b ± √(b² – 4ac)] / (2a) for ax² + bx + c = 0.

解二次方程：如果能因式分解使之等于零，则令每个括号为零。例如 (x + 2)(x – 4) = 0，解为 x = -2 和 x = 4。若无法分解，使用求根公式：对 ax² + bx + c = 0，x = [-b ± √(b² – 4ac)] / (2a)。

3. Linear Graphs & Equations | 线性图与方程

The equation of a straight line is y = mx + c, where m is the gradient and c is the y-intercept. To find the gradient between two points (x₁,

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