📚 IGCSE Maths: Which Formulas Are Provided in the Exam? | IGCSE数学：考试中会提供哪些公式？
One of the most common questions asked by IGCSE Maths students is whether they will be given a formula sheet in the exam. The answer depends on the examination board you are sitting. Some boards, such as Edexcel, provide a formula sheet at the front or back of the question paper, while others, such as Cambridge International, expect you to memorise all the necessary formulas yourself.
IGCSE 数学考生最常见的问题之一是考试中会不会提供公式表。答案取决于你所在的考试局。有些考试局如 Edexcel 会在试卷前或后附上公式表，而其他如 Cambridge International 则希望你自己记住所有必要公式。
1. Does IGCSE Maths Provide a Formula Sheet? | IGCSE 数学考试会提供公式表吗？
For Edexcel IGCSE Mathematics (both Specification A, 4MA1, and Specification B, 4MB1), a formula sheet is indeed included in the question paper. This sheet lists many of the key formulas you may need, especially for geometry and algebra. However, it does not contain every formula, so you still need a solid memory for many routine rules.
对于 Edexcel IGCSE 数学（A 类 4MA1 和 B 类 4MB1），试卷中确实附有公式表。该表列出了许多你可能需要的关键公式，尤其是几何和代数方面。但公式表并未包含全部公式，因此你仍然需要牢记许多常用规则。
For Cambridge IGCSE Mathematics (0580 and 0607), there is no such formula sheet. You are expected to recall all formulas from memory, including area, volume, trigonometric and algebraic formulas. This makes preparation very different from Edexcel.
对于 Cambridge IGCSE 数学（0580 和 0607），则没有这样的公式表。你需要凭记忆写出所有公式，包括面积、体积、三角学和代数公式。这使得备考方式与 Edexcel 很不一样。
In this article, we will first examine the formulas commonly provided in Edexcel's sheet, and then highlight the important formulas you must memorise, especially if you are taking Cambridge papers. You can also use the list as a quick revision checklist.
在本文中，我们先来看看 Edexcel 公式表中常见的公式，然后强调你必须记住的重要公式，尤其是如果你参加剑桥试卷。你也可以把这份列表当作快速复习清单。
2. Algebra: The Quadratic Formula | 代数：二次方程求根公式
The quadratic formula is almost always included on any formula sheet. It is used to solve equations of the form ax² + bx + c = 0. Even if the formula is provided, you must know how to substitute a, b and c correctly.
二次方程求根公式几乎总是出现在任何公式表中。它用于求解 ax² + bx + c = 0 形式的方程。即使公式已给出，你也必须知道如何正确代入 a、b 和 c 的值。
x = (-b ± √b² - 4ac) / (2a)
Remember that the discriminant, b² - 4ac, tells you about the nature of the roots. If it is positive, there are two real roots; if zero, one repeated root; if negative, no real roots.
记住判别式 b² - 4ac 能告诉你根的性质。若为正，则有两个实数根；若为零，则有一个重根；若为负，则没有实数根。
3. Geometry: Area and Perimeter | 几何：面积与周长
Formula sheets usually provide formulas for the area and circumference of a circle, as well as the area of a rectangle, triangle and parallelogram. You should still know how to calculate the area of composite shapes by breaking them into simpler parts.
公式表通常提供圆的面积和周长、矩形、三角形和平行四边形的面积公式。你仍需知道如何将复合图形分解为简单部分来求面积。
Here are the most common formulas that may appear on a formula sheet:
以下是公式表中可能出现的最常见公式：
Area of a rectangle: A = l × w
矩形面积：A = l × w
Area of a triangle: A = ½ × b × h
三角形面积：A = ½ × b × h
Area of a circle: A = πr²
圆的面积：A = πr²
Circumference of a circle: C = 2πr
圆的周长：C = 2πr
Area of a trapezium: A = ½(a + b) × h
梯形面积：A = ½(a + b) × h
If your board provides these on the sheet, you can save time remembering them. But for Cambridge, you must recall them instantly.
如果你的考试局在公式表中提供这些，你就能节省记忆时间。但剑桥考生必须瞬间回忆出来。
4. Volume and Surface Area | 体积与表面积
Volume and surface area formulas are common on formula sheets, especially for prisms, cylinders, cones and spheres. These formulas are frequently tested in IGCSE papers, so practice applying them to word problems.
体积和表面积公式常见于公式表中，特别是棱柱、圆柱、圆锥和球。这些公式在 IGCSE 试卷中频繁出现，所以要多练习应用它们解答文字题。
Volume of a cylinder = πr²h
Volume of a cone = ⅓πr²h
Volume of a sphere = ⁴⁄₃πr³
For surface area, the sheet may give:
对于表面积，公式表可能给出：
Surface area of a cylinder: 2πr² + 2πrh
圆柱表面积：2πr² + 2πrh
Surface area of a cone: πr² + πrl (where l is slant height)
圆锥表面积：πr² + πrl（l 为母线长）
Surface area of a sphere: 4πr²
球表面积：4πr²
Remember that units for volume are cubic (e.g. cm³), and for area are square (e.g. cm²).
记住体积单位是立方（如 cm³），面积单位是平方（如 cm²）。
5. Trigonometry: Sine and Cosine Rule | 三角学：正弦定理与余弦定理
For non-right-angled triangles, the sine rule and cosine rule are essential. These are often printed on formula sheets, but you must know when to use each one.
对于非直角三角形，正弦定理和余弦定理至关重要。它们常常印在公式表上，但你必须知道什么时候用哪一个。
Sine rule: a / sin A = b / sin B = c / sin C
Cosine rule: a² = b² + c² - 2bc cos A
The sine rule is useful when you know two angles and one side, or two sides and a non-included angle. The cosine rule is useful when you know two sides and the included angle, or all three sides.
正弦定理适用于已知两角一边，或两边及其中一边的对角。余弦定理适用于已知两边及其夹角，或已知三边的情况。
In addition, the formula sheet may also provide the angle version of the cosine rule:
此外，公式表还可能提供余弦定理的角度形式：
cos A = (b² + c² - a²) / (2bc)
6. Trigonometry: Area of a Triangle and Identities | 三角学：三角形面积与恒等式
The area of a triangle using trigonometry is another formula frequently given:
使用三角学的三角形面积公式也经常给出：
Area = ½ ab sin C
Here a and b are two sides and C is the included angle between them. This formula works for any triangle, not just right-angled ones.
其中 a 和 b 是两边，C 是它们的夹角。此公式适用于任意三角形，而不仅仅是直角三角形。
Additionally, some formula sheets include basic trigonometric identities:
此外，一些公式表还包括基本三角恒等式：
sin² θ + cos² θ = 1
tan θ = sin θ / cos θ
These identities are useful for simplifying expressions and solving equations. Even if they are not printed, you must remember them.
这些恒等式可用于简化表达式和解方程。即使没有印出，你也必须记住。
7. Statistics and Probability | 统计与概率
Statistics and probability formulas are rarely printed on IGCSE formula sheets. You are expected to know the basic measures and how to calculate them.
统计与概率公式很少印在 IGCSE 公式表上。你需要知道基本统计量及其计算方法。
Key ideas you must memorise include:
你必须记住的关键概念包括：
Mean = sum of all values ÷ number of values
平均值 = 所有数值之和 ÷ 数值个数
Median: the middle value when data is ordered
中位数：数据有序排列后的中间值
Mode: the most frequent value
众数：出现次数最多的值
Range = largest value - smallest value
极差 = 最大值 - 最小值
Probability of an event = favourable outcomes ÷ total outcomes
事件概率 = 有利结果数 ÷ 总结果数
For grouped data, you may need to use mid-interval values to estimate the mean or median.
对于分组数据，你可能需要使用组中值来估计平均值或中位数。
8. Formulas NOT Provided: What You Must Memorise | 不会提供的公式：必须牢记的内容
Even if your board provides a formula sheet, many essential formulas are still not printed. You must know them by heart. Below is a checklist of critical formulas that usually never appear on the sheet.
即使你的考试局提供公式表，许多必要公式也仍不会印出。你必须牢记它们。下面是一份通常不会出现在公式表上的关键公式清单。
Algebraic expansions: (a + b)² = a² + 2ab + b², (a - b)² = a² - 2ab + b², (a + b)(a - b) = a² - b²
代数展开： (a + b)² = a² + 2ab + b², (a - b)² = a² - 2ab + b², (a + b)(a - b) = a² - b²
Laws of indices: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁻ⁿ = 1/aⁿ
指数法则： aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁻ⁿ = 1/aⁿ
Equation of a straight line: y = mx + c, where m is gradient and c is y-intercept
直线方程：y = mx + c，其中 m 为斜率，c 为 y 轴截距
Gradient formula: m = (y₂ - y₁) / (x₂ - x₁)
斜率公式： m = (y₂ - y₁) / (x₂ - x₁)
Distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²)
距离公式：d = √((x₂ - x₁)² + (y₂ - y₁)²)
Percentage change = (new value - original value) / original value × 100%
百分变化率 = (新值 - 原值) / 原值 × 100%
Simple interest: I = PRT / 100
单利： I = PRT / 100
These formulas appear repeatedly in exams, so practise using them until they become second nature.
这些公式在考试中反复出现，所以请反复练习，直到它们成为你的本能。
9. How to Use the Formula Sheet Effectively | 如何有效使用公式表
If you are given a formula sheet in the exam, do not assume it will solve every problem. You must still understand how and when to apply each formula. Here are some practical tips.
如果你在考试中得到公式表，不要以为它能解决所有问题。你仍然需要理解每个公式如何应用以及何时应用。以下是一些实用技巧。
Familiarise yourself with the formula sheet before the exam. Know exactly where each formula is located so you can find it quickly.
考试前熟悉公式表。准确知道每个公式的位置，以便快速查找。
Do not stop to read the whole sheet during the exam. Only look up a formula when you are sure you need it.
考试时不要停下来通读整张表。只在确定需要时查阅。
Practise past papers using the same formula sheet you will receive, so you become comfortable with its layout.
使用你考试时会收到的同款公式表练习真题，以便熟悉其排版。
For Cambridge students, create your own formula book and review it weekly. Write out formulas from memory without looking.
对于剑桥考生，请创建自己的公式手册并每周复习。尝试默写公式，不要看答案。
Remember that a formula sheet does not replace understanding. Always check units and rearrange formulas correctly.
记住公式表不能代替理解。始终检查单位并正确变形公式。
10. Conclusion | 结论
Whether or not your IGCSE Maths exam provides a formula sheet depends entirely on your examination board. Edexcel gives a helpful formula sheet, while Cambridge requires you to memorise everything. In both cases, a strong command of core formulas is essential for success.
你的 IGCSE 数学考试是否提供公式表完全取决于你的考试局。Edexcel 会提供有用的公式表，而剑桥则要求你记住一切。无论哪种情况，熟练掌握核心公式都是成功的关键。
Use the lists in this article as a revision
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