Edexcel A-Level Maths Formula Booklet P54458A: Key Formulae and Exam Tips | Edexcel A-Level 数学公式手册 P54458A：核心公式与应试技巧

📚 Edexcel A-Level Maths Formula Booklet P54458A: Key Formulae and Exam Tips | Edexcel A-Level 数学公式手册 P54458A：核心公式与应试技巧

The Edexcel GCE Maths Formula Booklet, often printed with code P54458A and labelled as the 8th proof, is the official reference sheet provided in every AS and A-Level Mathematics paper. Knowing exactly what it contains, and just as importantly what it does not contain, can save time in exams and prevent careless mistakes across pure mathematics, statistics and mechanics.

Edexcel GCE 数学公式手册通常带有印刷代码 P54458A，并标注为第 8 次校对稿，是每份 AS 和 A-Level 数学试卷都会提供的官方公式表。清楚它包含哪些公式、不包含哪些公式，可以在纯数学、统计和力学的考试中节省时间，并减少粗心错误。

1. What the P54458A Booklet Is and How Exams Use It | 什么是 P54458A 公式手册以及考试如何使用

The booklet is printed as part of the Edexcel A-Level Mathematics examination materials. It is divided into Pure Mathematics, Statistics and Mechanics sections. It gives key results quickly, but it does not explain conditions, restrictions or worked examples.

该手册与 Edexcel A-Level 数学试卷一起印制，分为纯数学、统计学和力学三个部分。它能快速给出核心结论，但不会解释使用条件、限制或例题。

You should treat the booklet as a checking tool rather than a complete revision resource. Questions often require you to decide which formula applies, and several formulae look similar but have different validity ranges.

你应该把它当作检查工具，而不是完整的复习资料。题目经常要求你判断哪个公式适用，而很多公式看起来很相似，但有效范围不同。

2. Pure Mathematics: Arithmetic and Geometric Series | 纯数学：等差数列与等比数列

The arithmetic and geometric series results are grouped together in the pure section. For an arithmetic sequence with first term a and common difference d, the nth term is uₙ = a + (n − 1)d.

等差与等比级数的结果集中在纯数学部分。对于首项为 a、公差为 d 的等差数列，第 n 项是 uₙ = a + (n − 1)d。

Sₙ = ½ n [2a + (n − 1)d]

For a geometric sequence with first term a and common ratio r, the nth term is uₙ = arⁿ⁻¹. The sum of the first n terms is given below, with the infinite sum valid only for |r| < 1.

对于首项为 a、公比为 r 的等比数列，第 n 项是 uₙ = arⁿ⁻¹。前 n 项和如下所示，而无穷和公式仅在 |r| < 1 时成立。

Sₙ = a(1 − rⁿ)/(1 − r), S∞ = a/(1 − r) for |r| < 1

A common mistake is to use the infinite sum formula when the ratio is not between −1 and 1. The booklet states the condition, but many students ignore it under time pressure.

一个常见错误是在公比不在 −1 到 1 之间时仍然使用无穷和公式。公式手册写明了条件，但很多学生在时间压力下会忽略它。

3. Pure Mathematics: Binomial Expansion | 纯数学：二项式展开

The booklet gives two main binomial forms. For a positive integer n, the expansion of (a + b)ⁿ is finite.

该手册给出两种主要二项式形式。对于正整数 n，(a + b)ⁿ 的展开是有限项的。

(a + b)ⁿ = aⁿ + n aⁿ⁻¹ b + [n(n − 1)/2!] aⁿ⁻² b² + … + bⁿ

For rational n and |x| < 1, the expansion of (1 + x)ⁿ is an infinite series. The general term is [n(n − 1)…(n − r + 1)/r!] xʳ.

对于有理数 n 且 |x| < 1，(1 + x)ⁿ 的展开是一个无穷级数。其通项是 [n(n − 1)…(n − r + 1)/r!] xʳ。

(1 + x)ⁿ = 1 + n x + [n(n − 1)/2!] x² + … + [n(n − 1)…(n − r + 1)/r!] xʳ + …

In exam questions, you may be asked to state the validity range or to approximate using the first few terms. The condition |x| < 1 is usually required for the infinite expansion of (1 + x)ⁿ.

考试中可能会要求你写出有效范围，或者使用前几项进行近似计算。对于 (1 + x)ⁿ 的无穷展开，通常必须满足 |x| < 1。

4. Pure Mathematics: Trigonometric Identities | 纯数学：三角恒等式

The trigonometric section includes compound-angle, double-angle and Pythagorean identities. These are often used together in proofs and equation solving.

三角学部分包括复角、二倍角和毕达哥拉斯恒等式。这些公式经常在证明和解方程中组合使用。

sin(A ± B) = sin A cos B ± cos A sin B

cos(A ± B) = cos A cos B ∓ sin A sin B

tan(A ± B) = (tan A ± tan B)/(1 ∓ tan A tan B)

The double-angle forms for cosine appear in three equivalent versions. Choosing the right version often depends on whether you want the expression entirely in sine, entirely in cosine, or in terms of cos 2θ.

余弦的两倍角公式有三种等价形式。选择哪种形式通常取决于你希望表达式全部用正弦、全部用余弦，还是用 cos 2θ 表示。

sin 2θ = 2 sin θ cos θ

cos 2θ = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ

tan 2θ = 2 tan θ/(1 − tan²θ)

Also remember the small-angle approximations in radians: sin θ ≈ θ, cos θ ≈ 1 − ½ θ² and tan θ ≈ θ. These appear in the formula booklet and are useful in modelling or limiting behaviour questions.

此外还要记住弧度制下的小角近似：sin θ ≈ θ，cos θ ≈ 1 − ½ θ²，tan θ ≈ θ。这些公式出现在手册中，在建模或极限行为问题中很有用。

5. Pure Mathematics: Differentiation and Integration | 纯数学：微分与积分

The booklet lists basic derivatives and integrals, but it does not include the product rule, quotient rule or chain rule. You must memorise those separately and use them confidently.

该手册列出了基本导数和积分，但不包含乘法法则、除法法则或链式法则。你必须单独记忆并能熟练使用它们。

Common differentiation results in the booklet include:

手册中常见的微分公式包括：

f(x) = xⁿ → f'(x) = n xⁿ⁻¹

f(x) = sin kx → f'(x) = k cos kx

f(x) = cos kx → f'(x) = −k sin kx

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）