📚 GCSE Maths: Formula Sheet Policy for Exams until 2027 and Its Impact | GCSE 数学：至2027年考试提供公式表的政策与影响
Beginning in 2022 as a pandemic recovery measure, the UK's Ofqual and the Department for Education announced that GCSE Mathematics students would be provided with a formula sheet in their exams. This temporary support was initially set to expire, but in a significant update, the measure has been extended to cover the 2025, 2026, and 2027 examination series. The decision aims to ensure a smooth transition back to normal grading standards while recognising ongoing disruptions to learning. This article examines the background of this policy, the exact content of the formula sheet, and the multifaceted impact it is having on teaching, learning, and assessment in GCSE Mathematics.
从2022年开始，作为疫情恢复措施，英国资格考试监督办公室（Ofqual）和教育部宣布，GCSE数学考生将在考试中获得一张公式表。这一临时支持原定取消，但根据最新通知，该措施已延长至2025、2026和2027年的考试系列。这项决定旨在确保向正常评分标准的平稳过渡，同时承认学习上仍然存在的干扰。本文将探讨这一政策的背景、公式表的具体内容，以及它对GCSE数学教学、学习和评价产生的多方面影响。
1. Background of the Formula Sheet Policy | 公式表政策背景
In response to the significant disruption caused by the COVID-19 pandemic, Ofqual introduced a package of support for students taking GCSEs in 2022. The central feature for mathematics was the provision of a separate formulae sheet in the examination room, removing the requirement for candidates to memorise a long list of equations. This built on a similar approach used in 2020 and 2021 when teacher-assessed grades were awarded.
为应对新冠疫情造成的严重干扰，Ofqual为2022年参加GCSE考试的学生推出了一套支持措施。数学科的核心举措是在考场提供单独的公式表，从而不再要求考生记忆大量公式。这延续了2020和2021年教师评估成绩时采取的类似做法。
Initially planned as a one-year only concession for 2022, the formula sheet support was subsequently extended for the 2023 and 2024 cohorts, recognising that those students had also experienced significant disruption to their Key Stage 4 studies. In late 2023, Ofqual confirmed a further extension to cover the 2025, 2026, and 2027 examination series for all awarding bodies in England, such as AQA, Pearson Edexcel, and OCR. This signals an understanding that the return to pre-pandemic arrangements must be gradual and carefully managed.
该公式表最初仅计划作为2022年的一次性安排，但随后考虑到2023和2024届学生同样在关键阶段4学习中遭遇重大中断，这一支持措施得以延长。2023年底，Ofqual确认进一步延长至2025、2026和2027年的考试系列，适用于英格兰所有考试局，如AQA、爱德思和OCR。这表明决策者认识到，恢复至疫情前的安排必须循序渐进、谨慎管理。
The policy applies to all tiers of GCSE Mathematics (Foundation and Higher) and to the full suite of question papers. It ensures that all students, regardless of their background or individual challenges with memorisation, have equitable access to the core toolkit of mathematical formulae during their high-stakes exams.
该政策适用于GCSE数学的所有级别（基础层和进阶层）以及全部试卷。它确保所有学生，无论其背景或在记忆方面有何个体困难，都能在高风险考试中公平地获取核心数学公式这一工具包。
2. What's on the Formula Sheet | 公式表包含的内容
The exact layout varies slightly between awarding bodies, but all formula sheets for the 2025–2027 exams contain the same essential set of equations and expressions. Students receive a pre-printed insert alongside their question papers, and they are expected to know how and when to apply each formula.
尽管各考试局的排版略有不同，但2025至2027年考试的所有公式表都包含同一套核心方程和表达式。学生会随试卷收到一份预印的活页插页，他们需要知道如何以及何时使用每个公式。
and depreciation equations; trigonometric ratios (sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent); and the quadratic formula. Some boards also include the area and circumference of a circle, Pythagoras' theorem, and the equations for speed, density, and pressure.
基础层公式表通常涵盖：梯形面积 = ½(a + b)h；棱柱体积 = 横截面积 × 长；复利与折旧公式；三角比（sin θ = 对边/斜边，cos θ = 邻边/斜边，tan θ = 对边/邻边）；以及二次方程求根公式。部分考试局还包括圆面积和周长、毕达哥拉斯定理，以及速度、密度和压强公式。
− 2bc cos A); area of a triangle using ½ab sin C; the quadratic formula in full (x = (−b ± √b² − 4ac) / 2a); surface area and volume of a sphere and a cone; and the area of a sector and length of an arc. Crucially, it also includes the trigonometric exact values for 0°, 30°, 45°, 60°, and 90°, a notoriously memory-intensive part of the syllabus.
进阶层学生则会收到一份更详细的公式表。其中增加了：正弦定理 (a/sin A = b/sin B = c/sin C) 和余弦定理 (a² = b² + c² − 2bc cos A)；三角形面积公式 ½ab sin C；完整的二次方程求根公式 (x = (−b ± √b² − 4ac) / 2a)；球体和圆锥体的表面积与体积；以及扇形面积和弧长公式。更重要的是，它还包含了 0°、30°、45°、60° 和 90° 的精确三角值，这本是教学大纲中著名的记忆密集型部分。
Despite having these references, students must still understand the units and conventions, such as the distinction between the curved surface area and total surface area of a cone, or the correct substitution of values into the quadratic formula when a, b, or c are negative. The sheet does not provide worked examples or explain what each variable represents; that knowledge remains an essential learning outcome.
即使有了这些参考资料，学生仍需理解单位和常规表示，例如区分圆锥的侧面积与全面积，或当二次方程系数 a、b、c 为负数时如何进行正确的代入。公式表并不提供解题示例或解释每个变量的含义；这些知识仍然是关键的学习目标。
3. Reasons for Extending the Measure | 延长措施的原因
Ofqual's rationale for continuing the formula sheet into 2025–2027 rests on three pillars: ongoing impact of learning disruption, fairness for the cohort, and the principle of gradual return to pre-pandemic assessment. Although schools have returned to normal operations, the cumulative effect of missed learning during lockdowns has left subtle gaps in depth of understanding and procedural fluency for many students currently in year 10 and beyond.
Ofqual将公式表继续沿用到2025至2027年的理由基于三大支柱：学习干扰的持续影响、对相关年级学生的公平性，以及逐步回归疫情前评估的原则。尽管学校已恢复正常运作，但封锁期间缺失学习所造成的累积效应，使许多目前在10年级及以上的学生在深度理解与程序性熟练程度上存在不易察觉的薄弱点。
Statistical evidence from 2023 and 2024 exams showed that students made more errors in non-calculator papers when required to recall exact trigonometric values or the quadratic formula from memory. By retaining the sheet, the regulator aims to prevent an artificial spike in anxiety and failure rate, and to ensure that the measured attainment reflects genuine mathematical problem-solving rather than the capacity to memorise under pressure.
2023年和2024年考试的统计数据显示，当学生需要在非计算器试卷中凭记忆回忆精确三角值或求根公式时，会犯更多错误。通过保留公式表，监管机构旨在防止焦虑情绪和不及格率出现人为飙升，并确保所衡量的能力反映的是真实的数学问题解决本领，而非在压力下记忆的能力。
The decision also acknowledges that many students in this cohort moved from primary to secondary school during the pandemic, disrupting the foundational transition that builds number fluency and algebraic confidence. A full removal of the support in 2025 would have hit those students hardest, hence the extended timeline.
这一决定也承认，该年级群中有许多学生是在疫情期间从小学升入中学的，这打乱了培养数字流利度和代数信心的基础性过渡。如果在2025年完全取消支持，受影响最大的正是这批学生，因此才制定了延长的时间表。
4. Benefits for Students | 对学生的好处
The most immediate benefit is a significant reduction in cognitive load during revision and on exam day. Instead of spending countless hours drilling the exact trigonometric values for sin 30° and cos 45°, students can redirect their energy towards understanding why a particular ratio is used, or how to model a real-world scenario with a quadratic equation.
最直接的好处是显著减少了复习期间和考试当天的认知负担。学生不必花费大量时间死记 sin 30° 和 cos 45° 的精确三角值，而是可以将精力转移到理解为何使用某个特定比率，或如何用二次方程对现实世界情景建模。
For learners with dyscalculia, dyslexia, or memory-related difficulties, the formula sheet is a powerful equaliser. It removes a barrier that was never about mathematical reasoning but purely about retention and recall. This aligns with a broader movement in education towards inclusive assessment design that measures aptitude rather than a narrow recollection skill.
对于有计算障碍、阅读障碍或记忆困难的学生来说，公式表是一种强有力的平衡器。它所消除的障碍从来都与数学推理无关，而纯粹关乎记忆与回想。这与教育界推动包容性评估设计的大趋势相一致，即衡量的是能力，而非狭隘的记忆技巧。
Additionally, the sheet provides a psychological safety net. Knowing that the quadratic formula and sine rule will be available reduces test anxiety, which in turn can improve performance. Anxious students are more likely to complete questions and demonstrate their true ability when they are not panicked by a forgotten constant or sign.
此外，公式表还提供了一种心理安全网。知道二次方程求根公式和正弦定理就在手边，可以减轻考试焦虑，进而提升表现。当学生不因遗忘某个常数或负号而慌乱时，他们更有可能完成题目，展示出真实水平。
5. Impact on Teaching and Classroom Practice | 对课堂教学的影响
Many experienced mathematics teachers have adapted their pedagogy since 2022, and this extension solidifies a shift in emphasis from rote memorisation to deeper conceptual understanding and intelligent application. Lessons now place greater weight on exploring the derivation of the quadratic formula through completing the square, rather than simply chanting the final expression.
自2022年以来，许多经验丰富的数学教师已经调整了自己的教学方式，而这次延长则进一步巩固了从死记硬背向深度概念性理解和灵活应用的转变。如今的课堂更侧重于通过配方法来探究历次方程求根公式的推导过程，而非仅仅机械背诵最终表达式。
Teachers are also integrating regular formula-sheet literacy into their schemes of work. This involves teaching students how to navigate the insert efficiently, how to select the correct formula for a problem, and how to perform correct substitutions including handling negative numbers and multiple steps. It is becoming a skill in its own right, akin to interpreting a data table or a graph.
教师们还将公式表使用能力培训常态化地融入教学计划。这包括教会学生如何高效查阅活页插页，如何为问题选择正确的公式，以及如何进行正确的代入，包括处理负值和多步运算。这本身正逐渐成为一项技能，类似于解读数据表或图形。
Formative assessment has also evolved. Low-stakes quizzes now often include a 'which formula would you choose and why' segment, or require students to correct a deliberate misapplication straight from the sheet. This shifts classroom discussion towards justification and decision-making, key higher-order thinking skills promoted by the GCSE assessment objectives.
形成性评价方式也随之演变。低风险的课堂测验现在往往包含“你会选择哪个公式？为什么？”的环节，或要求学生直接根据公式表纠正一个故意误用的例子。这使得课堂讨论转向推理论证和决策，这正是GCSE评估目标所提倡的高阶思维技能。
6. Exam Design and Perceived Difficulty | 考试设计与难度感受
Contrary to the assumption that giving out a formula sheet makes exams easier, the evidence suggests that exam writers have adjusted the question style to compensate. There has been a noticeable rise in multi-step, synthesis-style problems where a candidate must combine a formula from the sheet with geometric reasoning or an algebraic manipulation not directly prompted by the printed reference.
与“发放公式表会使考试变简单”的假设相反，证据表明命题人员已相应调整了题目风格。多步骤、综合型问题明显增多，考生必须将公式表中的某个公式与几何推理或代数操作相结合，而后者并非印刷参考资料中直接提示的内容。
For instance, rather than asking a student to simply calculate the area of a sector, a question might provide the area and ask for the radius, requiring inverse operations and a careful use of the arc length relationship as well. The sheet supplies the toolkit, but the toolbox still needs a skilled craftsperson.
例如，题目可能不再是直接要求计算扇形面积，而是给出面积反求半径，需要逆向运算并同时审慎使用弧长关系。公式表提供了工具，但工具箱仍然需要娴熟的工匠。
Grade boundaries have remained broadly stable, which indicates that the overall standard required for a grade 4 or grade 7 has been preserved. The perceived difficulty has therefore shifted from 'what is the formula for the volume of a cone?' to 'given this partially filled cone, find the height when the volume is maximised' – a far richer and more authentic mathematical challenge.
分数线基本保持稳定，这表明达到4级或7级所要求的整体标准得以维持。因此，感受上的难度已从“圆锥体积公式是什么？”转变为“给定这个部分填充的圆锥，求体积最大时的高度”——这是一个更为丰富且贴近真实的数学挑战。
7. Fairness and Inclusivity | 公平性与包容性
One of the strongest arguments for retaining the formula sheet is its role in promoting equity. Disparities in home support, access to private tutoring, and the prevalence of high-quality revision materials mean that not all learners enter the exam hall with the same level of formula recall. The policy helps to level that playing field.
保留公式表最有说服力的理由之一在于其促进公平的作用。家庭支持、获取私人辅导和高品质复习资料的机会存在差异，这意味着并非所有考生都能以相同水平的公式记忆力步入考场。该政策有助于创造公平竞争的环境。
For students who speak English as an additional language, committing a long list of abstract symbols and technical vocabulary to memory can be an extra layer of barrier. The sheet allows them to focus on the numerical and logical reasoning that forms the heart of mathematics, without being penalised by a secondary memory test.
对于英语为第二语言的学生来说，把一长串抽象符号和专业术语塞进记忆可能构成额外障碍。公式表让他们能够专注于构成数学核心的数值与逻辑推理，而不至于被次要的记忆测验所惩罚。
Furthermore, the measure aligns with reasonable adjustments often recommended for students with specific learning difficulties. By extending the provision universally, the exam system avoids the administrative burden of individual applications while simultaneously destigmatising the support.
此外，该措施与通常为有特殊学习困难学生建议的合理调整相契合。通过普遍推广该支持，考试体系既避免了单独申请产生的行政负担，又同时去除了这项支持可能带来的污名化标签。
8. Concerns and Criticisms | 担忧与批评
Despite the broad support, the policy has not been without its critics. Some mathematicians and educationalists argue that a certain amount of memorisation is healthy for building mathematical fluency and automaticity. They express concern that students who never internalise the quadratic formula or the basic trigonometric ratios may struggle when they encounter more advanced topics at A-level, where the foundational tools are simply assumed.
尽管该政策获得广泛支持，但也不乏批评之声。一些数学家和教育人士认为，适度的记忆对于建立数学流畅度和自动化技能是有益的。他们担忧，从未将二次方程求根公式或基本三角比内化的学生，在遇到A-level更高级课题时可能会遇到困难，因为那时这些基础工具被视为默认已知。
There is also a fear of 'over-reliance', where pupils treat the formula sheet as a crutch rather than a reference. In some observed lessons, weaker students paused mid-problem merely to check the sheet, even for the simple area of a circle, delaying the development of instant recognition. Teachers have had to actively combat this by building deliberate recall practice into starters and retrieval tasks.
还有人担心会产生“过度依赖”，学生把公式表当成拐杖而非参考资料。在所观察到的一些课堂上，能力较弱的学生即使在面对简单的圆面积问题时也会中途停下来查阅公式表，从而延迟了瞬间识别能力的发展。教师不得不通过在课堂导入和知识检索任务中有意加入回忆练习来积极应对。
Finally, some parents and school leaders wonder whether a permanent formula sheet may eventually lead to a lowering of standards or to universities perceiving the qualification as less rigorous. However, Ofqual has firmly stated that the depth of mathematical reasoning assessed remains unchanged and that there is no intention to devalue the grade.
最后，一些家长和学校领导担心，永久性的公式表可能最终导致标准降低，或促使大学认为该资格证书不够严谨。然而，Ofqual明确表示，所评估的数学推理深度保持不变，没有贬低该成绩等级的意图。
9. How to Use the Formula Sheet Effectively | 如何有效利用公式表
Merely having the sheet in the exam is not enough; students must be trained to use it strategically. Teachers recommend a three-step approach: first, identify the topic and the variable you need to find; second, scan the sheet for the relevant formula; third, write down the formula, then substitute values carefully before reaching for the calculator or simplifying.
仅在考试中拥有公式表是不够的；学生必须经过训练以策略性地使用它。教师推荐三步法：第一，识别主题以及你需要求出的变量；第二，快速浏览公式表找到相关公式；第三，写下公式，然后仔细代入数值，之后再动计算器或进行简化。
A common pitfall is reading the wrong line from the sheet, such as using the surface area of a sphere formula when the question asks for volume. To avoid this, students should highlight or mentally underline key words in the question (e.g., 'curved surface' vs 'total surface') before checking the sheet. Annotating the insert with pencil in the exam, though not mandatory, can help with focus.
一个常见的陷阱是从公式表中读错行，例如题目要求体积却用了球的表面积公式。为避免这种情况，学生应在查表前先将题目中的关键词（如“侧面积”与“全面积”）高亮或在脑海中划线。考试时可以用铅笔在活页上做标记，虽非强制，但有助于集中注意力。
Revision should also involve timed practice with a copy of the exact same insert that will appear in the real exam. Familiarity breeds speed; a student who knows that the trigonometric exact values are located in the bottom-right corner can locate them instantly, saving precious minutes for problem-solving. Mock exams must replicate the condition of having the sheet from the start.
复习还应包括用与实际考试完全相同的公式表复制件进行计时练习。熟悉带来速度；一个知道精确三角值位于右下角的学生能瞬间找到它们，从而节省出宝贵的解题时间。模拟考试必须从开始就再现持有公式表的情景。
10. Progression to A-Level Mathematics | 与A-Level数学的衔接
The bridging from GCSE to A-level Mathematics has always been a significant step, and the formula sheet policy adds a new dimension to this transition. At A-level, no such formula sheet is provided for pure mathematics content; students are expected to know and fluently apply a much larger set of identities, derivatives, and integrals from memory. The worry is that students who have never committed the GCSE quadratic formula to long-term memory may find the first term of Year 12 particularly demanding.
从GCSE到A-level数学的衔接一直是一个重要台阶，而公式表政策为这一过渡增添了新的维度。在A-level中，纯数学内容并不提供类似的公式表；学生被期望凭记忆了解并流利应用一套庞大得多的恒等式、导数和积分公式。担忧之处在于，从未将GCSE二次方程求根公式存入长期记忆的学生，可能会在12年级的第一学期发现学习尤为吃力。
To mitigate this, many sixth-form colleges and schools have introduced early bridging units that explicitly teach the recollection of key GCSE formulae alongside algebraic fluency. Teachers are also encouraging current GCSE pupils to still learn the derivations and connections, so that even if they rely on the sheet in the exam, they are constructing meaningful mental schemas that will serve them later.
为缓解这一问题，许多高中和学校引入了早期的衔接单元，明确教导学生记忆关键的GCSE公式，同时培养代数流利度。教师也鼓励正在学习GCSE的学生继续学习公式推导与联系，这样即便他们在考试中依赖公式表，也能构建出对未来有益的有意义的心理图式。
Furthermore, A-level exam boards are aware of the change. They have begun to examine the first few waves of 'formula sheet' GCSE students and are monitoring whether foundational knowledge is weaker. Early indications suggest that the more conceptual approach at GCSE can be beneficial if the student is a strong reasoner, but additional independent formula practice remains essential.
此外，A-level考试局已意识到这一变化。他们开始对首批受益于“公式表”的GCSE学生进行考察，并监测其基础知识是否薄弱。早期迹象表明，如果学生推理能力强，GCSE中更注重概念的方法可能是有益的，但额外的自主公式练习仍然十分必要。
11. Beyond 2027: The Future Outlook | 2027年之后：未来展望
What happens after 2027 remains an open question. Ofqual has committed to a formal consultation before any further decision is made, gathering evidence from teachers, exam marker reports, and higher education stakeholders. The extension until 2027 effectively covers the cohort of students who were in reception and Year 1 during the first lockdowns, marking a symbolic closure of the pandemic-era adjustments.
2027年之后会发生什么仍是一个悬而未决的问题。Ofqual承诺在做出任何进一步决定之前将进行正式咨询，广泛收集来自教师、考官报告和高等教育利益相关方的证据。延至2027年，实质上涵盖了最初封控期间正处于学前和一年级的学生群体，标志着疫情时代调整的一个象征性结束。
Some commentators advocate for the permanent retention of a formula sheet, arguing that real-life mathematicians, scientists, and engineers constantly refer to reference materials and that the ability to look up and apply a formula is itself a crucial competency. They suggest the current 'extended temporary' model could evolve into a permanent, redesigned booklet that also includes conversion tables and common constants.
一些评论人士主张永久保留公式表，认为现实生活中的数学家、科学家和工程师始终需要查阅参考资料，查阅并应用公式本身就是一项关键能力。他们提议，目前“延长临时”的模式可以演变成一份永久性的、重新设计的小册子，其中还包含换算表和常见常数。
Opponents, however, warn that a permanent sheet could further embed a 'just-in-time' learning culture that undermines the depth of mathematical knowledge expected at the end of compulsory schooling. The eventual decision will likely need to balance inclusivity, global competitiveness, and the foundational needs of future mathematicians and physicists.
然而，反对者警告说，永久性的公式表可能进一步固化一种“即时”学习文化，削弱义务教育结束时理应具备的数学知识深度。最终的决策很可能需要在包容性、全球竞争力以及未来数学家和物理学家的基础需求之间取得平衡。
12. Revision Strategies for Students | 给学生的复习策略
With the formula sheet in hand, effective revision is not about sitting and staring at the paper. Students should adopt an active recall approach: cover the formula on the sheet, say or write it from memory, then check. This blends rote safety with the recognition that the sheet is available, and transfers the formula to memory gradually without pressure.
有了公式表在手，高效的复习并不是坐在那里盯着纸看。学生应采取主动回忆的方法：遮住公式表上的公式，凭记忆说出或写下它，然后再核对。这结合了死记硬背的安全感与公式表现成可用的认识，并能在无压力的情况下逐步将公式转入记忆。
Using a 'blank sheet' diagnostic test is also powerful. Start by trying to reconstruct as much of the formula sheet as possible from memory, then fill in the gaps in a different colour. Focus revision on the areas that consistently remain blank – these are the ones where conceptual understanding may also be weaker, so revisit the topic's underlying principles first.
使用“空白格式”诊断测验也十分有效。先尝试凭记忆尽可能重现公式表的内容，然后用不同颜色补上遗漏之处。集中复习那些始终留白的部分——这些地方相关的概念性理解通常也较弱，因此应首先重新回顾该主题的基本原理。
Past paper practice remains indispensable, but it must be done with the formula sheet on the desk from the outset, simulating the real environment. After finishing, students should reflect not only on what they got wrong but on how they used the sheet. Did they select the correct formula? Did they substitute accurately? This metacognitive review elevates the sheet from a passive aid to an active learning tool.
历年真题练习仍然不可或缺，但必须从一开始就将公式表置于桌上，模拟真实环境。完成后，学生不仅应反思做错了什么，还应反思自己是如何使用公式表的。他们选择了正确的公式吗？代入准确吗？这种元认知反思将公式表从被动的辅助工具提升为主动的学习工具。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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