GCSE数学物理 公式表 方程式表 2025至2027
从 2025 年夏季考试开始，英格兰的 GCSE 数学、物理与综合科学考生在考场里会拿到一份公式表或方程式表。这项安排不是某个考试局的临时好意，而是教育部在 2024 年 10 月 3 日作出决定、Ofqual 修改规则之后落到所有考试局的硬要求。正备考 2026 与 2027 年考试的学生，真正要弄清楚的不是表格会不会发，而是表上写了什么、哪些内容仍然要自己背、以及考试局在出题时被限制了什么。这篇文章把官方文件里的时间线、考试局官网公布的卷面安排和几处容易被忽略的考场细节梳理一遍。
From the summer 2025 exam series onwards, GCSE candidates in England taking mathematics, physics or combined science sit their papers with a formulae sheet or an equations sheet on the desk. The arrangement is not a favour granted by an individual board: the Department for Education confirmed it on 3 October 2024, Ofqual then changed its rules, and every board in England now has to comply. For candidates sitting exams in 2026 or 2027, the useful question is not whether the sheet will be handed out, but what it contains, which formulas still have to be memorised, and what Ofqual has forbidden boards from doing when they write the questions.
2024 年 10 月 3 日的决定与适用场次
教育部在 2024 年 10 月 3 日认定，参加 2025、2026 与 2027 年考试的考生不需要背诵 GCSE 数学的公式。物理与综合科学的大部分方程式也不用背。这项决定只管英格兰，威尔士、苏格兰与北爱尔兰各有自己的监管机构与考试安排。适用场次写得很具体。数学覆盖这三年的夏季考试，也覆盖同三年的 11 月重考。物理与综合科学只覆盖夏季考试。很多学生以为这项政策只管应届考生。实际上 11 月重考的学生一样会拿到公式表。原文可以在 gov.uk 的咨询结果页上核对。
The decision was taken by the Department for Education on 3 October 2024 and applies to candidates sitting GCSE mathematics, physics and combined science in 2025, 2026 and 2027. In mathematics the support also covers the November resit series in each of those years, while physics and combined science are summer only; Wales, Scotland and Northern Ireland set their own arrangements. Candidates sitting a November resit are therefore entitled to the same formulae sheet as summer candidates, which is a detail many students miss.
Ofqual 咨询收到的回复量与支持比例
Ofqual 在 2024 年 10 月 3 日到 17 日之间就这套安排公开征求意见。官方公布的回复总量是 15,796 份。支持给数学考生提供公式表的比例为 94%。支持给物理与综合科学考生提供方程式表的比例为 95%。Ofqual 在结论里写明，没有回复提出必须修改方案的实质问题。这些数字出自 gov.uk 上的咨询结果页，不是媒体的估算。原文还说明，Ofqual 此前检查过 2022 到 2024 年的做法，没有发现评估功能因此受损。
Ofqual ran the consultation from 3 to 17 October 2024 and published the outcome on gov.uk. Of the 15,796 responses, 94 per cent backed a formulae sheet for mathematics and 95 per cent backed an equations sheet for physics and combined science. The regulator also reviewed how the arrangement had worked in 2022, 2023 and 2024, found no evidence that assessment had been compromised, and carried the proposal forward without amendment.
公式表的公布时间与更新节奏
Ofqual 要求考试局分阶段把材料交给学生。2025 年考试用的表，考试局必须在 2024 年 12 月公布。2026 年考试用的表，公布截止日是 2025 年 9 月 1 日。2027 年考试用的表，截止日是 2026 年 9 月 1 日。这个提前量是为了让学生和老师在考试前就熟悉表格的排版。2025 年的表与 2024 年考试使用的那一份完全相同。Ofqual 预期 2026 与 2027 年的表与往年保持一致，各考试局之间也一致。考试局只能在不改变内容的前提下做轻微排版调整。OCR 已经在官网上放出了 2026 年考试使用的公式表与方程式表。
The publication rule is staggered. Boards had to release the 2025 sheets in December 2024, the 2026 sheets by 1 September 2025, and the 2027 sheets by 1 September 2026. That lead time lets candidates and teachers meet the layout long before the exam, and any change to the sheets is limited to presentation only.
数学公式表的两档分界与 Higher 额外公式
数学的公式表随试卷一起发到手上。Foundation 与 Higher 各自有一份表，不是同一份。Higher 的表在 Foundation 的基础上多列出一批公式。OCR 的官网页面写明了这一点。AQA 的 GCSE 数学 8300 与二级进阶数学证书 8365 也各有一份表。数学的公式表一般以插入页的形式随每一份试卷提供，不贴在试卷正文里。表里列出的是在普通年份学生需要记忆的那批公式，现在由考试局提供。具体的公式名单以考试局官网那一份表为准，不要凭记忆复述。三家考试局的表在实际内容上保持一致。
For mathematics each tier gets its own sheet rather than a shared one, and the Higher version carries a longer list of formulae on top of the Foundation content. The sheet is normally supplied as an insert with every question paper, so candidates should practise flicking to it under timed conditions. What appears on it is the set of formulae students would have had to memorise in a normal year, and the exact list is defined by the board's published sheet rather than by memory.
物理与综合科学的方程式表随卷发放
物理与综合科学的方程式表同样以插入页的形式随试卷提供。OCR 说明，这张表包含规范里的全部物理方程式，不再区分哪些要背、哪些要给。AQA 的安排是：物理 8463 的两份试卷、综合科学三科学 8464 的两份物理卷，以及综合科学协同 8465 的四份试卷都会附上物理方程式表。考查公式回忆与应用的题目沿用 2025 年的指令口径，卷面上直接指向方程式表。考试局官网会把当年的方程式表单独挂在科学科目的页面上，下载后就是考场上那一张。不同考试局给的公式范围因此并不完全一样。很多学生以为所有物理卷的表都是同一张，实际上要看自己考试局的官方版本。
The equations sheet arrives as an insert as well. For OCR it covers every physics equation in the specification rather than a subset. AQA attaches its Physics Equations Sheet to both Physics 8463 papers, the physics papers of Combined Science Trilogy 8464, and all four Combined Science Synergy 8465 papers. Questions that test recall and application still carry the same instruction as in 2025, pointing candidates at the sheet instead of asking them to reproduce it from memory.
Ofqual 对出题设下的红线
提供公式表并不等于题目变简单。Ofqual 在修改条件时加了一条限制：考试局不得命制只靠搬运表上信息就能作答的题目。这条限制把表格当成辅助工具，而不是答案来源。出题人仍然可以要求考生选择公式、重排公式、换算单位，或者把两个公式串起来用。很多学生以为看到表就不用练计算，这个想法会在方法分上吃亏。物理计算题的分值通常拆成公式、代入、结果三部分，写不出式子就拿不到前面的分。阅卷时最容易丢的正是没有写出来的那一步。
Handing out a sheet does not make the questions easier. When Ofqual changed its conditions it also barred boards from setting questions that can be answered solely by copying information off the sheet, so candidates are still expected to select and rearrange formulas, and to convert units before substituting. In practice, markers watch method marks disappear when a candidate jumps straight to a number without writing the equation first.
三大考试局的卷面安排对照
AQA 的数学 8300 分 Foundation 与 Higher 两份公式表，2026 年的表随每份试卷以插入页提供。二级进阶数学证书 8365 也有一份。物理 8463、综合科学三科学 8464 与协同 8465 都附物理方程式表，考查公式的题目沿用 2025 年的指令。OCR 的数学 J560 在 2025 至 2027 年的 6 月与 11 月考试里，每一份试卷都发公式表。物理 J249 与 J259、综合科学 J250 与 J260 发方程式表或数据表。Pearson 把数学的表叫 Exam Aid，Foundation 与 Higher 各一份，公告日期是 2024 年 11 月 18 日。三家都要求表和试卷一起交到考生手上，考试结束后随试卷收回。
The three boards publish the same kind of material under different names. AQA gives maths candidates two tiers of formulae sheet as an insert, and attaches its Physics Equations Sheet to Physics, Trilogy and Synergy papers. OCR supplies a formulae sheet with every mathematics paper in the June and November series through 2027, plus equation or data sheets for its physics and combined science suites, while Pearson calls its maths sheets Exam Aids and issued them for both tiers on 18 November 2024. In every case the sheet travels with the question paper and is collected at the end of the exam.
数学卷里仍然要自己掌握的内容
公式表不等于把整本教材搬到考场。数学卷里仍有一批内容不在表上，需要学生自己掌握。勾股定理、三角函数的三条比值、扇形面积与弧长公式通常都不在表内。阅卷时常见的错误是公式用对了但计算顺序错，或者在百分比题里把乘数与除数写反。反向百分比题的做法是除以乘数，而不是再乘一次。非精确答案默认保留三位有效数字，提前约掉小数会让答案超出容差。这些判分口径写在考试局的评分方案里，不是考生的猜测。
A formulae sheet does not carry the whole syllabus. Pythagoras' theorem, the three trigonometric ratios and the sector formulae sit outside the sheet, so they still have to be learned. A common mistake is choosing the right formula but doing the arithmetic in the wrong order; another is multiplying again in a reverse percentage question, when the correct move is to divide by the multiplier. Non-exact answers are expected to three significant figures, which is why rounding early costs marks.
物理计算题的单位与有效数字
物理计算题的失分点集中在单位与进位。考试局的考官报告连续几年提到，替换数字时没有换算单位是最高频的错误。厘米不换成米、克不换成千克，结果就会差出好几个数量级。进位方式错误排在第二位，把中间步骤提前取整会让最终答案落在容差之外。另一个常见问题是只写答案不写过程，考官报告明确鼓励写出过程以争取方法分。动能的单位是焦耳，功率的单位是瓦特，比热容的单位是焦耳每千克摄氏度。做题时先把单位统一，再代入公式，最后检查数量级是否合理。
Physics calculations are lost mostly on units and rounding. Examiner reports mention year after year that candidates substitute numbers without converting them first, so centimetres stay as centimetres and grams as grams. Rounding comes next, because tidying up a middle step pushes the final answer outside the tolerance, and a bare answer with no working cannot pick up the method marks that examiners are told to award.
2026 年 2 月与 5 月的政策延续
2026 年 2 月 26 日，教育部的学校标准部长致函 Ofqual，要求把这项支持维持到现行规范生命周期结束。Ofqual 在回信里确认，会就继续提供公式表与方程式表征求意见。征求意见在 2026 年 3 月 23 日截止。到了 2026 年 5 月 5 日，Ofqual 确认 2028 年起的考试继续提供这两类表格，覆盖现行规范的全部剩余场次，也包括重考机会。新要求同时写明，考试局要在每个考试系列前一年的 9 月 1 日之前公布当年的表，并在试卷里附上干净副本。这条口径把原先只管到 2027 年的安排往后延了一整批场次。相关文件都在 gov.uk 与考试局官网上公开。
The arrangement was extended during 2026. On 26 February the schools minister wrote to Ofqual asking it to keep the support for the lifetime of the current specifications. Ofqual closed a further consultation on 23 March, and on 5 May 2026 it confirmed that formulae and equations sheets will continue for exams from 2028 onwards, including any resit opportunities.
课程与评估评审与 2029 年之后的改革时间线
2025 年 11 月，课程与评估评审发布最终报告。报告建议政府评估一件事：学生是否应该既会使用公式，又能回忆公式。教育部在回应中说明，这件事会放到重新制定科目内容的流程里一并考虑。按现有计划，这些科目的新 GCSE 在 2029 年或 2030 年首次施教。Ofqual 预计现行规范下的那套安排，会一直适用到 2030 年或 2031 年及之前的考试以及随后的重考系列。新资格的科目内容与准确启用年份，要等教育部确认后才算定案。眼下这批考生的备考方式不会因此改变。学校的教学安排仍然以现行规范与当年公布的表格为准。
The Curriculum and Assessment Review published its final report in November 2025 and recommended that government look again at whether students should be required to recall formulas as well as apply them. DfE folded that question into its work on revised subject content, with new GCSEs in these subjects planned for first teaching in 2029 or 2030. Until then the current arrangements stand, and Ofqual expects them to run through exams taken in 2030 or 2031 and any resit series after that.
用公式表复习的三周做法与考场细节
公式表发到手之后，复习方式要跟着调整。第一周把表按模块抄成自己的清单，数学按数与代数、比与比例、几何与测度、概率与统计分组，物理按力学、电学、波、能量分组。第二周做真题时把每次查阅的公式在表上做记号，被反复查的那几行就是薄弱项。第三周按限时条件练查表速度，目标是先判断题干需要哪个公式，再动笔。考场上有几个细节值得提前练。表通常随试卷发下，考完和试卷一起收回。不要在表上写字或做标记。公式表不会替你换算单位，也不会替你保留有效数字。
Once the sheet is in your hands the revision plan changes shape. Copy it into your own topic-ordered list in the first week, mark the formulas you keep looking up while working through past papers in the second week, and spend the third week training yourself to find the right formula under timed conditions. A few exam-room habits are worth rehearsing: the sheet comes with the paper and is collected with it, writing on it is not allowed, and it will not convert your units or choose your significant figures for you.
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