Flashcards 公式 定义 间隔重复 提取练习
做完一套 past paper，很多学生才发现公式记不住：不是没看过，而是看过四遍的那种眼熟，经不起合上书复述一遍。Flashcards 的作用不在于反复看，而在于它逼你在没有任何提示的情况下，把答案从记忆里重新拉出来。下面按卡片正反面怎么写、哪些公式根本不用背、间隔怎么排、错卡怎么处理四件事往下讲，每一节都能当天动手改你手里那叠卡。
Most students revise formulas by reading them again, then discover in the exam that reading never built the path back to the answer. A flashcard is useful because it removes every clue and asks you to produce the answer from nothing. The four parts below cover what goes on each side, which formulas the paper already prints, how to space the reviews, and what to do with the cards you keep failing.
卡面只写一个问题，不写关键词
卡面只写「光合作用」这样的词，翻开时你只会觉得眼熟，却说不清到底要答什么。把课程标题改成疑问句，比如光反应在类囊体薄膜上生成哪三种产物，答案就有了边界。一张卡只对应一个可判分的点，卡面越短，复习时越难糊过去。很多学生以为卡面多写提示更好记，其实提示越多，考场上没有提示就越接不上。卡面用铅笔写编号，方便以后按章节重排。问题里带上考试局与主题词，比如 AQA GCSE 生物 光反应，混科复习时不会看错。写不出问题的知识点，说明你还没读懂那一页教材，先回去看完再制卡。
A prompt such as photosynthesis only confirms that the topic exists, and that kind of familiarity cannot survive a blank page. Turn the heading into a question with a defined answer, tag the card with the board and the topic so decks from different subjects do not get mixed up, and number the back corner so the cards can be re-sorted by chapter later. If you cannot phrase the question at all, the weakness sits in your reading rather than in your memory, and going back to the textbook page is faster than adding another card to a pile you cannot use.
卡背只放评分点，不放解释
卡背写的是阅卷人能打勾的那几个词，不是你的理解过程。比如定义酶的作用，卡背只写生物催化剂、降低活化能、不被反应消耗这三点，多一个字都不写。用自己的话解释一遍属于下一步，先背评分点的措辞。考纲里的小标题往往就是评分点的来源，照抄比改写更省事。卡背留一行空位，专门记你每次都漏掉的那一点。常见的错误是把卡背写成一整段笔记，复习时读起来很顺，合上却复述不出来。卡背超过三行，就把这张卡拆成两张。
The back of a card should carry only the points an examiner ticks, not your explanation of them. For enzyme action, three short phrases such as biological catalyst, lowers activation energy and not used up are enough to earn the mark, while a longer account slows the review without adding anything. Leave the last line blank and use it to record the single point you keep missing, and split the card in two as soon as the back runs past three lines, because a card you can read smoothly is not the same as a card you can reproduce.
公式卡把条件与单位写在同一面
公式写对了但适用条件漏掉，是 GCSE 物理与 A-level 数学里最常见的失分方式之一。匀速、恒加速度、小角度、理想气体，这些前提不写在卡上，考场上就会硬套。单位也一起写在卡背，比如电阻率用欧姆米，密度用千克每立方米。写条件时顺手添一个反例，比如动能定理不适用于有摩擦生热的系统。卡背再留一个数量级，方便你判断计算器算出来的答案是否离谱。阅卷时经常见到公式正确、代入错误的卷面，问题多半出在条件那一行。一张公式卡的信息量，应该刚好够你判断它能不能用。
A formula copied without its conditions is a trap, because the mark is lost when the assumption fails rather than when the algebra fails. Write the conditions on the same side as the equation, add the unit attached to each symbol, and note one case where the formula does not apply, such as a system with friction heating. A quick order-of-magnitude estimate on the back also tells you within seconds whether the number on your calculator is plausible.
定义卡照抄评分标准里的措辞
考试局在 mark scheme 里给的措辞通常比教材更省字，也更容易被判分。把考纲那一条的原文抄到卡背，比你自己改写一遍稳得多。比如经济学与生物学的定义题，评分点常按关键词给分，同义改写有时拿不到分。抄的时候保留术语的英文原词，中文解释放在第二行。考纲里的条款一旦调整，旧卡的措辞就要跟着更新，这一条最常被忽略。错得最多的是把教材整段话缩成一句，关键词反而丢了。一张卡片只放一个定义，同一术语的不同语境分开放。
Mark schemes are written in a compressed register, and copying that register is safer than paraphrasing it. Keep the technical term in English, put the Chinese gloss underneath, and update the card whenever the specification is revised, because an outdated phrase is marked as a missing point rather than a near miss. Where a definition carries several keywords, list them in the order the scheme uses them, since a sentence that sounds complete can still score nothing if the keyword itself never appears.
考卷给定哪些公式，先去考试局官网查
该背哪些公式，取决于你那张卷子会印什么。OCR 官网在 2026 年 9 月的说明里写明，GCSE 数学、物理与综合科学的公式与方程表在 2025 至 2027 年照发，并在现行大纲有效期内继续提供。Edexcel 的 A-level 数学在每场考试提供 Mathematical Formulae and Statistical Tables，等差与等比数列的通项公式、二倍角公式、乘积法则与链式法则都不在册，商法则在册。也就是说，链式法则要自己背，商法则可以不背。把考试局官网的公式表下载下来，逐行对照你手里的卡片，划掉已经给定的。很多学生以为所有公式都要硬背，结果把时间花在考卷会印出来的那几行上。这一步做完，卡片通常能少三分之一。
The first job is to find out what your paper actually prints. OCR states on its website that formulae and equation sheets are issued for GCSE mathematics, physics and combined science in 2025 to 2027 and continue for the life of the current specifications, while Edexcel supplies its formulae and statistical tables booklet in every A-level mathematics paper. Download the sheet, compare it line by line with your deck, and remove what is given: on Edexcel 9MA0 the chain rule stays on a card, the quotient rule does not.
一张卡只考一个点，复合知识要拆开
一张卡同时考定义、公式和单位，答错时你根本判断不出是哪一步忘了。拆成三张，错哪张就补哪张，复习节奏立刻不一样。判断标准很简单：卡背能不能用一句话说完。两句话就是两张卡，不用心软。章节里的因果链可以拆成前后两张，中间用编号连起来。常见的错误是把一整节的要点压在一张卡上，考前翻起来很有成就感，考场上还是空白。卡片数量变多不是坏事，重复次数会自己筛掉你已经会的那部分。拆卡时保留原来的编号顺序，重排一叠卡的代价比你想的高。
If one card tests a definition, a formula and a unit at once, a wrong answer tells you nothing about which part failed. Split it until the back can be said in one sentence, and link the resulting cards by number so that the reasoning still runs in order when you meet them again. A longer deck feels worse for a week and works better for a term, and repetition quietly removes the cards you have already mastered.
间隔重复：三次接触比每天翻更有效
同一张卡连着看五遍，效果不如隔三天看五次。Cepeda 等人在 2008 年发表于 Psychological Science 的研究给出一个可用的经验值：复习间隔取目标记忆期限的一成到两成比较合适，考前一个月的材料，间隔大约是三天到六天。照这个比例排，今天、第三天、第七天、第十四天各一次，就能覆盖到期末。每次复习只保留答不出的卡，答对的往后推。很多学生以为天天过一遍更保险，其实间隔太密，短期看着熟，长期留不住。排期写在卡盒的隔板上，比记在手机提醒里更容易执行。考纲范围大的科目按章节分盒，避免一盒几百张拖慢每一次复习。
Cramming one card five times in an evening is weaker than meeting it five times across a fortnight. Work backwards from the retention interval: Cepeda and colleagues, writing in Psychological Science in 2008, put the useful gap at roughly ten to twenty per cent of the period you need to remember the material, which for a summer exam means spacing of about three days to a week. Keep only the failures in rotation, push the rest further back, and write the schedule on the dividers rather than in a reminder you will dismiss without reading.
先合上再想：提取比重读管用
Dunlosky 等人在 2013 年发表于 Psychological Science in the Public Interest 的综述评了十种学习法，只有练习测试与分散练习被评为高效用，重读与划重点被列为低效用。这篇综述正好解释了为什么翻卡时不能先看答案。操作上就是先合上卡背，把答案完整说一遍，再翻面对照。说不出来时不要马上翻，先给自己十秒，卡住的地方才是要补的地方。翻面后不要只判对错，用铅笔在卡角点一下，表示这次没答全。同一张卡连续三次全对，就可以移到后面的盒子里。说实话，翻卡时最容易骗自己的动作，就是扫一眼答案然后点头。
Dunlosky and colleagues reviewed ten common techniques in Psychological Science in the Public Interest in 2013 and rated only practice testing and distributed practice as high utility, placing rereading and highlighting at the bottom of the list. That ranking is the argument for covering the back of the card before you attempt an answer. Say the whole answer aloud, wait ten seconds before turning the card, and mark the corner when a point was missing instead of grading yourself generously.
交错练习：把不同题型混在一叠里
同一题型的十道题连着做，你会越来越顺，但那只是记住了顺序。把不同章节、不同题型的卡混在一叠，逼自己先判断考什么，再想答案。数学可以混函数、数列与概率，物理可以混力学与电学。交错会让正确率下降，别把这个下降当成退步。考场上题目本来就是混着出的，平时混着练，临场才不慌。常见的错误是按章节从头翻到尾，翻到第三章已经忘了第一章。混合比例从三成开始，考前一个月提到一半。混着练的前两周会明显难受，撑过去之后判断题型只要几秒。
Ten questions of the same type in a row feel productive because the method is already loaded in your head. Shuffle the topics instead, so that choosing the method becomes part of the exercise, and accept a lower hit rate as the cost of that practice. Start with about a third of the deck interleaved and raise it towards the exam, since the paper itself will never arrive sorted by chapter.
判断会没会：不看卡背能复原评分点
会不会的标准不是眼熟，而是能不能不看卡背把评分点说出来。自测时给自己三个判据：关键词齐不齐、单位带没带、条件写没写。三条都过才算这张卡毕业，缺一条就留在当前盒里。有些卡你每次都差同一个词，把它单独抄一张放在最前面。用手机录一段复述再回听，比凭感觉判断准得多。这一步最容易偷懒，因为翻卡比复述轻松太多。每周留一次完整的口头复述，把一叠卡从头讲到尾。
Knowing a card is not the same as recognising it, and the only fair test is whether the marking points come back without a prompt. Check three things every time: the keywords, the units and the conditions, and keep the card in the current box until all three arrive unprompted. Recording yourself and listening back is a cheap way to catch the gaps that silent nodding hides.
错卡单独一叠，并把错因写下来
答错的卡不要放回原位，放进单独的错卡盒。卡背下方留两行，写清这次错在哪里：是条件漏了、单位漏了，还是关键词换了说法。错因要写具体，别只写粗心两个字。下次复习先过错卡盒，再动主线。同一张卡错三次，说明它需要重新读那一页教材，而不是继续硬背。错卡盒里的卡连续两次全对，就可以回到主线。考前一周只过错卡盒，能把有限的注意力放在真正的漏洞上。盒子上写明日期，你才知道这张是这周新错的，还是三个月前的老问题。
Wrong cards belong in their own box, with the cause written on the back in two lines. Name the specific failure, such as a missing condition or a unit left off, rather than writing careless, and review that box before the main deck in every session. A card that fails three times needs the textbook page again rather than another repetition in the same format.
考前两周：停用已过的卡，只留薄弱环节
考前两周继续从头翻整盒卡，性价比最低。把连续三次全对的卡收起来，只留错卡、公式条件卡与高频定义卡。每天固定二十分钟，比考前熬夜三小时更稳。考前三天不要再加新卡，新卡只会制造焦虑。最后一遍按考试顺序过：先公式与单位，再定义，最后错题卡。很多学生以为卡片要一路看到进考场，其实最后一天该做的是休息。一叠卡从三百张减到五十张，是正常状态，不是偷懒。
In the last fortnight the useful question is which cards still fail, not how many you own. Retire the ones answered correctly three times running, keep the formula conditions, the high-frequency definitions and the error box, and hold a fixed twenty minutes rather than a long session on the night before. Adding new cards in the final days creates anxiety without adding marks, and a deck that shrinks from three hundred cards to fifty is working as intended.
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