📚 Edexcel A-Level Maths Appendix: Formula Booklet & Statistical Tables | 爱德思A-Level数学附录：公式手册与统计表
In the Edexcel A-Level Mathematics examination, the appendix is not just an extra page at the back of a textbook. It is the official Mathematical Formulae and Statistical Tables booklet that every candidate receives in the exam hall. Used well, it can save you from memorising dozens of results and can help you check your work under pressure. Used badly, it can waste valuable minutes and lead to careless errors.
在爱德思 A-Level 数学考试中，附录不只是课本末尾的额外页面。它是每位考生在考场中都会拿到的官方《数学公式和统计表》手册。用得好，它可以免去你背诵几十个结论的负担，并帮助你在压力下检查解题过程。用得不好，它会浪费宝贵时间并导致粗心错误。
1. What Is the Appendix in Edexcel A-Level Maths? | 什么是 Edexcel A-Level 数学附录？
Every candidate sitting Edexcel A-Level Mathematics (9MA0) or Further Mathematics (9FM0) is given the same printed booklet in the examination room. It is produced by Pearson Edexcel and its official name is the Mathematical Formulae and Statistical Tables booklet. Students call it the appendix, the formula book or the formulae sheet, but whatever name you use, it is the only printed reference material you are allowed to consult during the exam.
每位参加爱德思 A-Level 数学（9MA0）或进阶数学（9FM0）考试的考生，都会在考场中拿到同一份印刷手册。它由培生爱德思出版，正式名称是《数学公式和统计表》手册。学生们把它叫作附录、公式本或公式表，但无论你怎么称呼它，它都是考试期间唯一允许查阅的印刷参考资料。
The appendix is divided into three main sections: Pure Mathematics, Statistics and Mechanics. The Pure section collects results from algebra, sequences and series, trigonometry, calculus, vectors and numerical methods. The Statistics section covers probability, distributions and the standard normal table. The Mechanics section gathers the kinematics and force results you need for the mechanics questions.
附录分为三个主要部分：纯数学、统计和力学。纯数学部分汇集了代数、数列与级数、三角、微积分、向量和数值方法中的结论；统计部分涵盖概率、分布以及标准正态分布表；力学部分则收录力学题目所需的运动学和力的结论。
It is important to understand what the appendix is not. It is not a textbook, not a revision guide and not a collection of worked examples. The booklet gives concise results without detailed explanations. Therefore, you must know when and how to apply each formula.
重要的是要明白附录不是什么。它不是教材，不是复习指南，也不是例题集。手册只给出简明结论，没有详细解释。因此，你必须知道何时以及如何应用每个公式。
A common mistake is to treat the booklet as a substitute for understanding. If you do not recognise the notation or the conditions, having the formula in front of you will not help. For example, the geometric series formula for infinite sum only applies when |r| < 1.
一个常见错误是把手册当作理解的替代品。如果你不认识符号或条件，即使公式摆在面前也无济于事。例如，无穷几何级数求和公式只在 |r| < 1 时成立。
2. Structure of the Booklet: Three Sections | 手册的结构：三大部分
Before you revise, spend twenty minutes reading the booklet from cover to cover. Most students only ever look at the pages they happen to need, which means they never discover the tables that could save them time in the statistics paper.
开始复习前，先花二十分钟把手册从头到尾读一遍。大多数学生只翻自己碰巧需要的那几页，结果从来没有发现那些能在统计卷中省下大量时间的表格。
| Section | 部分 | Typical content | 通常包含 | Examples | 示例 |
|---|---|---|
| Pure Mathematics | 纯数学 | Algebra, series, trigonometry, calculus, vectors, numerical methods | 代数、数列、三角、微积分、向量、数值方法 | Geometric series, binomial expansion, trapezium rule, Newton-Raphson | 等比级数、二项式展开、梯形法则、牛顿-拉夫逊法 |
| Statistics | 统计 | Probability, discrete and continuous distributions, standard normal table | 概率、离散与连续分布、标准正态分布表 | Standardising z = (x − μ) ÷ σ, normal distribution tables | 标准化 z = (x − μ) ÷ σ、正态分布表 |
| Mechanics | 力学 | Kinematics with constant acceleration, forces, Newton's laws | 匀加速运动学、力、牛顿定律 | v = u + at, s = ut + ½at² | v = u + at，s = ut + ½at² |
Notice that the booklet uses the same symbols as the specification. If you have never seen the notation for a vector line or for a cumulative probability, the entry is useless to you. Learning the notation is part of learning the formula.
注意，手册使用的符号与考纲一致。如果你从没见过向量直线方程或累积概率的记号，这条公式对你毫无用处。学习符号本身就是学习公式的一部分。
3. What the Appendix Gives You and What It Does Not | 附录给你什么、不给你什么
The appendix gives you standard results, definitions in condensed form, and statistical tables. It does not give you derivations, it does not tell you when a result is valid, and it does not give you the proofs that appear in "show that" questions.
附录提供标准结论、浓缩形式的定义以及统计表。它不提供推导过程，不会告诉你结论在什么条件下成立，也不会给出"证明题"所需的证明。
- Given: standard derivatives and integrals, series formulas, trigonometric identities, the trapezium rule and the standard normal table. | 提供：常用导数与积分、级数公式、三角恒等式、梯形法则和标准正态分布表。
- Not given: the sine rule and cosine rule, most algebraic manipulation skills, and the reasoning that turns a worded problem into an equation. | 不提供：正弦定理和余弦定理、大部分代数变形技巧，以及把文字应用题转化为方程式的推理过程。
- Not given: the meaning of a symbol, the units, or the rounding convention expected in the final answer. | 不提供：符号的含义、单位，以及最终答案所要求的取整规则。
This is why examiners can still ask difficult questions even though the formula is printed. The mark scheme rewards selection and application, not transcription.
这就是为什么即使公式印在手册上，考官依然能出难题。评分标准奖励的是选择和运用，而不是照抄。
4. Pure Mathematics: Key Formulas You Must Recognise | 纯数学：必须识别的关键公式
The Pure Mathematics section covers algebra, trigonometry, calculus, vectors and numerical methods. You should be able to point to each formula and say in one sentence what problem it solves. Below are the entries that appear in almost every paper.
纯数学部分涵盖代数、三角、微积分、向量和数值方法。你应该能指着每一条公式，用一句话说出它解决什么问题。以下是几乎每份试卷都会用到的条目。
(1 + x)ⁿ = 1 + nx + n(n − 1)x² ÷ 2! + n(n − 1)(n − 2)x³ ÷ 3! + …
This is the binomial expansion for rational n, valid when |x| < 1. It appears in approximation questions and in partial fractions work.
这是 n 为有理数时的二项式展开，在 |x| < 1 时成立。它常出现在近似值问题和部分分式题目中。
aₙ = arⁿ⁻¹ Sₙ = a(1 − rⁿ) ÷ (1 − r) S∞ = a ÷ (1 − r), |r| < 1
seful entries in the booklet. Remember that S∞ exists only when the common ratio satisfies |r| < 1, and that the arithmetic series sum Sₙ = ½n[2a + (n − 1)d] is also printed nearby.
等比级数公式是整本手册中最常用的条目。记住：只有当公比满足 |r| < 1 时 S∞ 才存在；紧邻的等差级数求和公式 Sₙ = ½n[2a + (n − 1)d] 也印在同一区域。
sin(A ± B) = sin A cos B ± cos A sin B
cos 2θ = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ
a sin θ + b cos θ = R sin(θ + α), R = √a² + b², tan α = b ÷ a
sin(θ + α), and the arc length and sector area results s = rθ and A = ½r²θ (θ in radians).
三角部分是一整块印出的：平方恒等式、和角公式、倍角公式、辅助角形式 R sin(θ + α)，以及弧长与扇形面积公式 s = rθ 和 A = ½r²θ（θ 以弧度计）。
∫ y dx ≈ ½h [ y₀ + yₙ + 2(y₁ + y₂ + … + yₙ₋₁) ]
xₙ) support the numerical methods questions. You must still decide how many strips to use and whether the estimate is an overestimate or underestimate.
梯形法则与牛顿-拉夫逊迭代式 xₙ₊₁ = xₙ − f(xₙ) ÷ f′(xₙ) 服务于数值方法题目。你仍然需要自己判断该分多少条、估计值是偏大还是偏小。
r and b is a direction vector. Recognising that the same booklet entry covers both two-dimensional and three-dimensional problems saves time.
向量题使用直线方程 r = a + tb，其中 a 是位置向量，b 是方向向量。意识到同一条公式既适用于二维问题也适用于三维问题，可以节省时间。
5. Statistics: Probability, Distributions and Tables | 统计：概率、分布与统计表
The Statistics section of the appendix is where careless candidates lose the most marks, because it contains tables that must be read correctly. The standard normal table is the most heavily used entry in the whole booklet.
附录的统计部分是粗心考生失分最多的地方，因为它包含必须正确读取的表格。标准正态分布表是
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