Using the Formula Sheet in Maths Exams: Tips & Exam Preparation | 数学考试：公式表使用技巧与备考建议

📚 Using the Formula Sheet in Maths Exams: Tips & Exam Preparation | 数学考试：公式表使用技巧与备考建议

Many students believe that the formula sheet is a safety net — something to rely on only when memory fails. In reality, the formula sheet is a strategic tool that, when used correctly, can save time, reduce anxiety, and improve accuracy. This article explores how to use the formula sheet effectively in mathematics exams and how to prepare with it in mind.

许多学生认为公式表只是一个安全网——只有在记忆模糊时才需要依赖它。事实上，公式表是一个策略性工具，如果使用得当，可以节省时间、减少焦虑并提高准确性。本文将探讨如何在数学考试中有效使用公式表，以及如何围绕它进行备考。

1. Know Exactly What Is on the Sheet | 精确了解公式表内容

Before the exam, obtain the official formula sheet for your specific board and qualification. Every exam board publishes its own version, and the content varies significantly. Do not assume that Cambridge, Edexcel, AQA, or OCR provide the same formulas — they do not.

考前务必要获取你所参加考试局官方发布的公式表。每个考试局都会发布自己的版本，内容差异很大。不要想当然地认为剑桥、爱德思、AQA 或 OCR 提供的公式相同——它们并不相同。

Download the official PDF from the board’s website and print a copy.

从考试局官网下载官方 PDF 并打印一份。
Highlight the formulas you have never memorised or often forget.

标出那些你从未记住或经常忘记的公式。
Identify which formulas are not on the sheet — these must be memorised perfectly.

找出哪些公式不在公式表上——这些必须完美记住。

2. Categorise Formulas: Must-Memorise vs. Can-Reference | 公式分类：必须记忆 vs. 可查阅

Not every formula deserves the same level of attention. Make a two-column list: formulas you must know by heart, and formulas you can safely look up. This saves revision time and focuses your mental energy on what truly matters.

并非每个公式都值得同等程度的关注。制作一个两栏列表：必须熟记的公式，以及可以放心查阅的公式。这样可以节省复习时间，将精力集中在真正重要的内容上。

Must-Memorise \| 必须记忆	Can-Reference \| 可查阅
Quadratic formula: x = (-b ± √(b² – 4ac)) / 2a 二次方程求根公式：x = (-b ± √(b² – 4ac)) / 2a	Integration by parts formula 分部积分公式
Pythagorean theorem: a² + b² = c² 勾股定理：a² + b² = c²	Reduction formulae for trigonometric integrals 三角函数积分的递推公式
Simple differentiation rules: d/dx(xⁿ) = nxⁿ⁻¹ 基本求导法则：d/dx(xⁿ) = nxⁿ⁻¹	Sum of arithmetic/geometric series 等差/等比数列求和公式

3. Annotate Your Own Master Sheet | 制作你自己的标注版公式表

During revision, create an annotated version of the formula sheet. Add conditions, domain restrictions, and common pitfalls next to each formula. For example, the quadratic formula only applies when a ≠ 0, and the cosine rule has two forms depending on which side you are finding.

复习时，制作一份带标注的公式表版本。在每个公式旁边补充适用条件、定义域限制和常见陷阱。例如，二次方程求根公式仅适用于 a ≠ 0 的情况；余弦定理根据所求边不同有两种形式。

Write small reminders like “works for all real x” or “only if n is an integer”.

写下简短提醒，例如“对所有实数 x 成立”或“仅在 n 为整数时成立”。
Note the notation used by your board — for example, whether log means log₁₀ or ln.

记录考试局使用的符号规范——例如，log 表示 log₁₀ 还是 ln。
Add a worked example next to tricky formulas.

在易错公式旁边添加一个例题。

4. Use the Formula Sheet During Practice Papers | 在练习试卷时使用公式表

This is the most important piece of advice: always practise with the same formula sheet you will use in the real exam. This trains your brain to locate formulas quickly and builds confidence in navigating the document. If you only use the sheet once on exam day, you will waste precious minutes searching.

这是最重要的建议：务必使用与真实考试相同的公式表进行练习。这样可以训练大脑快速定位公式，并建立翻阅公式表的信心。如果你只在考试当天才第一次使用公式表，你会浪费宝贵的分钟去寻找。

Time yourself: how fast can you find the formula for the volume of a sphere or the standard deviation?

给自己计时：找到球体体积公式或标准差公式需要多长时间？
Practise flipping between the formula sheet and your working paper smoothly.

练习在公式表和答题纸之间平稳切换。
During timed mock exams, use the sheet exactly as you would on the day — no peeking at your own notes.

在限时模拟考试中，完全按照考试当天的方式使用公式表——不要偷看自己的笔记。

5. Do Not Over-Rely on the Sheet | 不要过度依赖公式表

The formula sheet is a reference, not a substitute for understanding. Students who rely on the sheet for every single formula often lose time and make errors because they copy symbols incorrectly. A balanced approach is to memorise core formulas and use the sheet only for lengthy or rarely used expressions.

公式表是参考资料，不能替代理解。每个公式都依赖公式表的学生，往往会浪费时间，并且可能因抄错符号而出错。平衡的做法是记住核心公式，仅在需要冗长或较少使用的表达式时才查阅公式表。

If you can derive it quickly, memorise it; if it is long and rarely used, reference it.

如果能快速推导，就记住它；如果冗长且不常用，就查阅它。

6. Understand the Hidden Information Behind Each Formula | 理解公式背后的隐藏信息

A formula is more than a string of symbols — it encodes conditions, assumptions, and relationships. When you look at a formula on the sheet, ask yourself: what does each symbol mean? What are the units? What happens at the boundaries? This deeper understanding helps you apply the formula correctly under exam pressure.

公式不仅仅是一串符号——它编码了条件、假设和关系。当你看到公式表上的一个公式时，问问自己：每个符号代表什么？单位是什么？在边界条件下会发生什么？这种更深层次的理解能帮助你在考试压力下正确应用公式。

For example, the formula for compound interest:

例如，复利公式：

A = P(1 + r/n)ⁿᵗ

Here, P is the principal, r the annual interest rate (as a decimal), n the number of compounding periods per year, and t the time in years. Knowing that r must be a decimal and n is the compounding frequency prevents careless mistakes.

其中，P 是本金，r 是年利率（以小数表示），n 是每年复利次数，t 是以年为单位的时间。知道 r 必须化为小数、n 是复利频率，可以避免粗心错误。

7. Use the Sheet to Diagnose Weak Topics | 利用公式表诊断薄弱知识点

Your formula sheet acts as a syllabus map. Flip through it and for each formula, ask: can I use this confidently in a problem? If not, that topic needs revision. This is a fast, structured way to identify gaps before exam day.

公式表就像一张教学大纲地图。翻阅公式表，对每个公式问自己：我能自信地在题目中使用它吗？如果不能，这个主题就需要复习。这是在考前快速、有条理地发现知识漏洞的方法。

Mark each formula with a colour: green for confident, yellow for shaky, red for unknown.

给每个公式标记颜色：绿色表示有把握，黄色表示不太确定，红色表示不会。
Focus your remaining revision time on the yellow and red areas.

将剩余复习时间集中在黄色和红色区域。
Re-test yourself one week later and see if the colours have improved.

一周后重新测试自己，看看颜色是否有改善。

8. Exam-Day Strategy for Using the Formula Sheet | 考试当天使用公式表的策略

On the day of the exam, the formula sheet should not be a page you flip through frantically. Instead, follow a calm, structured routine. First, read each question carefully. Then, identify which formula is needed. Only then open the sheet and locate the exact formula. Copy it accurately into your working area before substituting numbers.

考试当天，公式表不应是你慌乱翻找的页面。相反，应该遵循一套冷静、有条理的流程。首先，仔细阅读每道题目。然后，确定需要哪个公式。此时才打开公式表，定位确切公式。在代入数字之前，准确地将公式抄写到答题区域。

Read → Identify → Locate → Copy → Substitute → Check

读题 → 识别 → 定位 → 抄写 → 代入 → 检查

Do not copy the whole formula from memory — copy it from the sheet.

不要凭记忆抄写整个公式——要从公式表上抄。
Check that you have copied every symbol correctly, especially subscripts and superscripts.

检查每个符号是否抄写正确，尤其是下标和上标。
If a question gives you a formula, use that formula even if it differs from your memory.

如果题目提供了公式，即使与你记忆中的不同，也要使用题目给出的公式。

9. Common Mistakes When Using the Formula Sheet | 使用公式表的常见错误

Students often misuse the formula sheet in predictable ways. Recognising these pitfalls can help you avoid them. One common mistake is selecting the wrong formula because two formulas look similar — for instance, confusing the formula for arc length with that for sector area.

学生使用公式表时经常会犯一些可预见的错误。识别这些陷阱有助于避免。一个常见错误是选择了错误的公式，因为两个公式看起来相似——例如，将弧长公式与扇形面积公式混淆。

Mistake \| 错误	How to Avoid \| 如何避免
Reading the wrong row/column in a table 在表格中读错行或列	Trace with your finger or ruler 用手指或尺子辅助定位
Using a formula without checking conditions 使用公式时未检查适用条件	Annotate conditions next to each formula 在每个公式旁标注条件
Panicking and forgetting the sheet exists 慌张出错，忘记公式表的存在	Practise with it daily before the exam 考前每天用它练习
Overwriting the printed formula with own notation 用自己的符号覆盖印刷公式	Never write on the official sheet unless permitted 除非允许，绝不在官方公式表上写字

10. Integrate Formula-Sheet Familiarity into Your Revision Plan | 将公式表熟悉度融入复习计划

Formula-sheet mastery is not a one-day task. Build it into your revision schedule over several weeks. In the first week, simply read the sheet top to bottom. In the second week, cover the left side of each formula and test recall. By the fourth week, you should be able to close the sheet and list every formula from memory — even if you are allowed to use it in the exam.

公式表掌握不是一天能完成的任务。将其融入几周的复习计划中。第一周，从头到尾通读公式表。第二周，遮住每个公式的左侧，测试回忆能力。到第四周，你应该能够合上公式表，凭记忆列出每个公式——即使考试中允许使用公式表。

Weak 1: Read → Week 2: Cover & Recall → Week 3: Apply in Past Papers → Week 4: Full Mental Recall

第1周：通读 → 第2周：遮盖回忆 → 第3周：真题应用 → 第4周：完全默写

This progressive approach transforms the formula sheet from a passive reference into an active learning tool. By the time the exam arrives, you will know the sheet so well that even if it were taken away, you could still perform at your best.

这种循序渐进的方法将公式表从被动参考转变为主动学习工具。到考试来临时，你已经对公式表了如指掌，即使没有它，你也能发挥出最佳水平。

Conclusion | 结语

The formula sheet is a gift — but only for those who have prepared to use it well. Knowing exactly what is on it, practising with it, understanding the logic behind each formula, and diagnosing your weak areas are all essential steps. Treat the formula sheet as a revision checklist and an exam-day assistant, not a crutch.

公式表是一份礼物——但只属于那些做好充分准备去使用它的人。精确知道其内容、使用它练习、理解每个公式背后的逻辑、诊断自己的薄弱环节，这些都是至关重要的步骤。将公式表视为复习清单和考试当天的助手，而不是拐杖。

With consistent practice, you will walk into the exam room with confidence, knowing that the formula sheet is just one more tool in your well-equipped mathematical toolkit.

只要坚持练习，你将满怀信心走进考场，知道公式表只是你装备齐全的数学工具箱中又多了一件工具。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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Using the Formula Sheet in Maths Exams: Tips & Exam Preparation | 数学考试：公式表使用技巧与备考建议