📚 Year 7 AQA History: Formula & Theorem Cheat Sheet | 公式定理速查手册
History may not have mathematical equations, but it does demand logical thinking and clear structures. This cheat sheet gathers the most important ‘formulas’ and ‘theorems’ that will help you think, write and argue like a real historian. Use these tools every time you analyse a source, explain causation or write a paragraph for your AQA Year 7 studies.
历史或许没有数学公式，但它确实需要逻辑思维和清晰的框架。本速查手册收集了最重要的“公式”和“定理”，助你像真正的历史学家一样思考、写作和论证。在你分析史料、解释因果关系或为AQA七年级课程撰写段落时，请随时使用这些工具。
1. The Causation Equation | 因果关系方程
Historians use a simple equation to understand why events happen: Long-term cause + Short-term trigger + Context → Historical Event. Long-term causes are deep-rooted reasons that build up over time, such as social tensions or economic problems. A trigger is the immediate spark that sets off the event, and context refers to the circumstances already in place.
历史学家使用一个简单方程来理解事件为何发生：长期原因 + 短期导火索 + 背景 → 历史事件。长期原因是随时间积累的深层原因，例如社会矛盾或经济问题。导火索是引发事件的直接火花，背景则指现有的整体环境。
Example: The Norman Conquest of England (1066). Long-term cause: Edward the Confessor had no clear heir. Trigger: Harold Godwinson was crowned king. Context: Viking threats and rival claims to the English throne. Equation: Succession crisis + Harold’s coronation → William’s invasion and the Battle of Hastings.
示例：诺曼征服英格兰（1066年）。长期原因：忏悔者爱德华没有明确的继承人。导火索：哈罗德·戈德温森加冕为王。背景：维京人的威胁以及对英格兰王位的多方竞争。方程：继承危机 + 哈罗德加冕 → 威廉入侵与黑斯廷斯战役。
2. The Consequence Theorem | 后果定理
Events rarely have a single outcome. The Consequence Theorem says: Historical Event → Intended outcomes + Unintended outcomes. Some results were planned by people at the time, but many consequences were accidental or took decades to appear.
事件极少只有单一结果。后果定理指出：历史事件 → 预期结果 + 非预期结果。有些结果是当时人们计划好的，但还有许多后果是偶然发生的，或者历经数十年才显现。
Example: The Black Death (1348–49). Intended outcome: people tried to flee cities to escape. Unintended outcomes: massive population decline, labour shortages, and the weakening of the feudal system because peasants could demand higher wages.
示例：黑死病（1348–49年）。预期结果：人们试图逃离城市以躲避瘟疫。非预期结果：人口锐减、劳动力短缺，以及因农民可以要求更高工资而导致封建制度的削弱。
3. Change and Continuity Formula | 变迁与延续公式
To decide how much a period really changed society, think of this logical check: Change = (New conditions after the period – Old conditions before the period) / Time span. This is not a number but a way of forcing you to compare before and after. If many things stayed the same, continuity was strong.
要判断一段时期究竟在多大程度上改变了社会，思考这一逻辑检验：变迁 = （时期后的新状况 – 时期前的旧状况）/ 时间跨度。这不是一个数字，而是迫使你去比较前后的思维方式。如果许多事物保持不变，那么延续性就很强。
Example: The Norman Conquest brought change (new rulers, castles, Domesday Book) but also continuity (most Anglo-Saxon villagers continued farming the same land). So the formula shows a mix of change and continuity.
示例：诺曼征服带来了变迁（新统治者、城堡、土地清账册），但也带来了延续（大多数盎格鲁-撒克逊村民继续耕种同一片土地）。因此这一公式显示出变迁与延续并存。
4. The PEEL Paragraph Theorem | PEEL段落定理
A strong historical paragraph follows the PEEL structure: Point + Evidence + Explain + Link. Theorem: Quality paragraph = Clear Point + Specific Evidence + Detailed Explanation + Link back to the question. Without this formula, your writing can become a simple story instead of an argument.
一个有力的历史段落要遵循PEEL结构：论点 + 证据 + 解释 + 联系。定理：优质段落 = 清晰论点 + 具体证据 + 详细解释 + 回扣问题。没有这个公式，你的写作可能变成简单的故事，而非论证。
Example: Point: ‘The Black Death weakened feudalism.’ Evidence: ‘Wages rose because there were fewer workers.’ Explain: ‘Peasants could now sell their labour for more money, which shifted power away from lords.’ Link: ‘This shows how disease could transform an entire social system.’
示例：论点：“黑死病削弱了封建制度。”证据：“工资上涨，因为工人减少了。”解释：“农民此时可以靠出卖劳动赚取更多金钱，这使权力从领主手中转移走。”联系：“这说明疾病如何能改变整个社会体系。”
5. Source Evaluation Triangle | 史料评估三角形
When you examine a source, remember the NOP triangle: Nature, Origin, Purpose. Theorem: Source Utility = (Nature + Origin + Purpose) × Context. A text is more useful if you know what type of source it is (a letter, a chronicle, a drawing), who made it, when and why.
当你审查一份史料时，请记住NOP三角形：性质、来源、目的。定理：史料效用 =（性质 + 来源 + 目的）× 背景。如果你知道史料的类型（信件、编年史、图画），是谁、何时、为何制作的，那么这份史料就更有用。
Example: A Bayeux Tapestry scene. Nature: embroidered cloth. Origin: made by Norman supporters soon after 1066. Purpose: to justify William’s invasion. With context of Norman bias, it is still useful for showing Norman viewpoint and arms and armour, but it must be treated carefully as propaganda.
示例：贝叶挂毯的一个场景。性质：刺绣纺织品。来源：1066年后不久由诺曼支持者制作。目的：论证威廉入侵的正当性。考虑到诺曼偏见这一背景，它在展示诺曼观点与武器装备方面仍然有用，但必须小心将其视为宣传品。
6. Evidence-Reasoning-Conclusion Chain | 证据-推理-结论链
Historians never make claims without support. The logical chain is: Evidence → Reasoning → Conclusion. Begin with something you can see in a source or fact, then use reasoning to explain what it means, and finally draw a conclusion.
历史学家从不提出没有根据的主张。其逻辑链条为：证据 → 推理 → 结论。从你能在史料或事实中看到的东西开始，然后利用推理来解释其含义，最后得出结论。
Example: Evidence: The Domesday Book records that only 5% of land was held by English lords in 1086. Reasoning: William had replaced the English nobility with Normans. Conclusion: The Norman Conquest caused a near-total transfer of land and power.
示例：证据：据《土地清账册》记载，1086年仅有5%的土地由英格兰领主持有。推理：威廉用诺曼人取代了英格兰贵族。结论：诺曼征服导致了近乎彻底的土地和权力转移。
7. Chronology Logic Rule | 年代逻辑规则
Timelines are the historian’s compass. Rule: If Event A happened before Event B, then Event A may have contributed to causing Event B. But the reverse is impossible. Always check dates to establish cause and effect correctly.
时间线是历史学家的指南针。规则：若事件A发生在事件B之前，则事件A可能促成了事件B的发生。但反向影响是不可能的。务必核查日期以正确建立因果关系。
Example: The Peasants’ Revolt (1381) came after the Black Death and the Statute of Labourers (1351). Chronology shows that anger over frozen wages built up over decades before exploding into rebellion. You cannot say the revolt caused the Black Death.
示例：农民起义（1381年）发生在黑死病和《劳工法令》（1351年）之后。年代顺序表明，对冻结工资的愤怒积累了数十年才爆发为起义。你不可能说起义导致了黑死病。
8. Significance Scale | 重要性量表
Not all events matter equally. To weigh significance, think: Significance = (Scale of impact + Duration of effects + Number of lives touched) / Contemporary expectation. An event that affected millions for centuries scores high; a local skirmish scores low.
并非所有事件都同等重要。要衡量重要性，请思考：重要性 =（影响规模 + 影响持续时长 + 触及的生命数量）/ 当代期望值。一个影响了数百万人并持续数世纪的事件得分很高；一次地方性小冲突则得分很低。
Example: The signing of Magna Carta (1215) had limited immediate impact but its ideas about the king being subject to the law resonated for centuries. Its significance grew over time, making it highly significant on this scale.
示例：《大宪章》的签署（1215年）在当时的直接影响有限，但其“国王须受法律约束”的理念却回响了数世纪。其重要性随时间增长，按此量表评分极高。
9. Interpretation Theorem | 解释性定理
The same event can be told in different ways. Interpretation = Evidence + Historian’s perspective + Purpose. Every account is shaped by who is telling the story and what they want to prove. There is rarely one single ‘true’ version.
同一事件可以有不同的讲述方式。解释 = 证据 + 历史学家的视角 + 目的。每一段叙述都会受到讲述者及其想要证明之事的影响。极少有唯一“真实”的版本。
Example: Historian A, writing after the British Empire, may explain the Norman Conquest as bringing ‘civilisation’ to England. Historian B, focusing on Anglo-Saxon culture, may highlight the destruction and cultural loss. Both have evidence, but their interpretations differ.
示例：历史学家甲在英帝国时期后写作，可能将诺曼征服解释为给英格兰带来了“文明”。历史学家乙专注盎格鲁-撒克逊文化，可能会强调毁灭与文化丧失。双方都有证据，但解释不同。
10. Historical Argument Formula | 历史论证公式
A balanced historical answer includes more than one viewpoint. Formula: Thesis (your main argument) + Supporting evidence + Counterargument + Rebuttal → Well-rounded Conclusion. This shows you can think critically and acknowledge other interpretations before defending your own.
一个平衡的历史答案包含不止一种观点。公式：论点（你的主要论证）+ 支持证据 + 反方论点 + 反驳 → 周全的结论。这表明你能够批判性思考，在捍卫自己的观点前承认其他解释。
Example: Thesis: ‘The Black Death was the main cause of the Peasants’ Revolt.’ Counterargument: ‘Some historians argue the Poll Tax was the true trigger.’ Rebuttal: ‘The tax was resented because wages had already been squeezed after the plague, so the disease remains the root cause.’
示例：论点：“黑死病是农民起义的主要原因。”反方论点：“一些历史学家认为人头税才是真正的导火索。”反驳：“人头税之所以招致怨恨，是因为瘟疫后工资早已被压缩，因此疾病仍是根本原因。”
11. Empathy and Perspective Formula | 同理心与视角公式
To understand people in the past, avoid judging them by today’s standards. Formula: Empathetic understanding = (Their beliefs + Their circumstances + Their available knowledge) – Modern hindsight. This helps you explain why people acted as they did, even if we now think differently.
要理解过去的人，避免用今天的标准去评判他们。公式：同理心理解 =（他们的信仰 + 他们的境况 + 他们可获的知识）– 现代后见之明。这有助于解释他们为何如此行动，即便我们今天持有不同看法。
Example: When studying medieval medicine, it is easy to dismiss bloodletting as foolish. But apply the formula: their belief in the four humours, limited technology and no knowledge of germs made bleeding seem logical. Empathy does not mean agreement, it means understanding their world.
示例：在学习中世纪医学时，很容易将放血疗法视为愚蠢。但运用这一公式：他们对四体液说的信仰、有限的技术以及对病菌的无知，使得放血在当时看似合乎逻辑。同理心不意味着认同，而是理解他们的世界。
12. Revision Memory Theorem | 复习记忆定理
History is full of names and dates. To make them stick: Memory = (Active recall + Story connection + Spaced repetition) / Passive rereading. Turning events into a story with causes and consequences builds a web of meaning, not just a list.
历史充满了人名和日期。要让它们记牢：记忆 =（主动回忆 + 故事联系 + 间隔重复）/ 被动重读。将事件串联为一个有因果的故事，构建的是一张意义之网，而非一张清单。
Example: Instead of learning ‘1066, Hastings’, link it to the story: ‘Edward died without an heir, Harold took the crown, William crossed the Channel, Harold was killed – this chain changed England.’ Then quiz yourself after a day and a week.
示例：与其学习“1066年，黑斯廷斯”，不如将其与故事联系起来：“爱德华去世无嗣，哈罗德夺取王冠，威廉横渡海峡，哈罗德被杀——这一链条改变了英格兰。”然后在一天、一周后自我提问。
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