📚 IGCSE Cambridge History: Formula & Theorem Quick Revision Handbook | IGCSE 剑桥历史：公式定理速查手册
History is not a subject of mathematical formulas, but high marks in Cambridge IGCSE History depend on repeatable analytical formulas and theorems. This handbook converts key historical skills into quick revision formulas for causation, consequence, source evaluation, essay structure, comparison, change, and time management.
历史学科并不是一门使用数学公式的学科，但在剑桥 IGCSE 历史考试中取得高分，依赖于可反复使用的分析公式与定理。本手册将关键的史学技能转化为速查公式，覆盖原因分析、后果评估、史料评估、论文结构、比较、变化以及时间管理。
1. Cause Analysis Formula | 原因分析公式
The core causation formula for Cambridge IGCSE History is:
剑桥 IGCSE 历史中核心的原因分析公式是：
Cause = Trigger + Short-term cause + Long-term cause + Catalyst
原因 = 导火索 + 短期原因 + 长期原因 + 催化剂
A trigger is the immediate spark that sets events in motion. For example, the assassination of Archduke Franz Ferdinand at Sarajevo on 28 June 1914 was the trigger for the outbreak of the First World War.
导火索是直接引发事件的即时火花。例如，1914 年 6 月 28 日弗朗茨·斐迪南大公在萨拉热窝遇刺，就是第一次世界大战爆发的导火索。
Long-term causes operate over decades and create the underlying conditions. In the case of the First World War, these included militarism, the alliance system, imperialism, and nationalism.
长期原因在数十年间持续起作用，并创造了深层的爆发条件。就第一次世界大战而言，长期原因包括军国主义、联盟体系、帝国主义和民族主义。
Catalysts accelerate an existing process rather than start it. Germany’s ‘blank cheque’ to Austria-Hungary in July 1914 acted as a catalyst by promising unconditional support and encouraging Vienna to take a hard line against Serbia.
催化剂加快已经存在的进程，而不是开启这一进程。1914 年 7 月德国对奥匈帝国给出的“空白支票”就是一种催化剂，它承诺无条件支持，从而鼓励维也纳对塞尔维亚采取强硬立场。
2. Consequence Evaluation Formula | 后果评估公式
To evaluate consequences fully, use the impact formula below:
要全面地评估后果，可以使用下面的影响公式：
Impact = (Immediate + Long-term) × (Political + Economic + Social + Military)
影响 = (直接 + 长期) × (政治 + 经济 + 社会 + 军事)
This formula prevents one-sided answers by forcing you to combine time frames with different aspects of society. Many IGCSE questions ask ‘How far did X change Y?’ and require this multi-dimensional approach.
这个公式通过把时间框架与社会的不同方面结合起来，防止片面的答案。许多 IGCSE 题目会问“X 在多大程度上改变了 Y？”，这就需要使用这种多维度的分析方法。
For example, the Treaty of Versailles had immediate political effects such as the weakening of the new Weimar Republic, long-term economic effects through reparations and the 1923 hyperinflation, social effects in the form of popular resentment, and military effects through disarmament that created a sense of national humiliation.
例如，《凡尔赛条约》产生了直接的政治影响，如削弱了新成立的魏玛共和国；长期的经济影响，如赔款和 1923 年的恶性通货膨胀；社会影响表现为民众的怨恨情绪；军事影响则通过裁军造成了一种民族屈辱感。
3. Source Usefulness Formula | 史料有用性公式
For Paper 2 source questions, usefulness is not the same as reliability. Use the formula:
在 Paper 2 的史料题中，有用性并不等同于可靠性。请使用以下公式：
Usefulness = Provenance + Content + Context + Cross-reference
有用性 = 来源信息 + 内容 + 历史背景 + 交叉参照
Provenance means the origin, author, date, and type of source. A private diary written by a soldier in the trenches in 1916 may be useful for revealing personal feelings and daily conditions, even if it is not reliable for accurate casualty figures.
来源信息指的是史料的出处、作者、日期和类型。1916 年一名战壕士兵写下的私人日记，可能对揭示个人感受和日常生活状况很有用，尽管它在精确伤亡数字方面并不可靠。
Content must be linked to the specific question. Ask: what information or attitudes does this source provide that helps answer the question? Context means placing the source in wider events, such as knowing that a speech was made just after a military defeat.
内容必须与具体问题联系起来。要问：这份史料提供了哪些有助于回答问题信息或态度？历史背景则是把史料放在更宏观的事件之中，例如知道某次演说是在一次军事失败之后发表的。
4. Source Reliability Theorem | 史料可靠性定理
Reliability can be assessed with a parallel theorem:
可靠性可以用一个类似的定理来评估：
Reliability = Nature + Origin + Purpose + Emphasis
可靠性 = 史料性质 + 来源 + 目的 + 侧重
Nature means the type of source, such as an official report, cartoon, poster, memoir, or statistics. Origin includes who produced it and when. Purpose is about why the source was created: to persuade, inform, justify, or entertain.
史料性质指的是史料的类型，例如官方报告、漫画、海报、回忆录或统计数据。来源包括作者身份和制作时间。目的则是指史料为何被创作：是为了说服、告知、辩护还是娱乐。
Bias can be detected through a further formula:
偏见可以通过进一步的公式来检测：
Bias = Language + Omission + Emphasis + Source type
偏见 = 语言 + 省略 + 侧重 + 史料类型
A Nazi propaganda poster from 1936 may use emotive language, omit evidence about unemployment, emphasise military strength, and be an openly biased type of source. A British government report on the same period may appear more factual but can still be biased by what it chooses not to mention.
一张 1936 年的纳粹宣传海报可能使用情绪化的语言，省略失业问题的证据，强调军事力量，并且本身就是一种公开带有偏见的史料类型。同一时期的一份英国政府报告可能看起来更加客观，但它仍然可以通过选择不提某些内容而带有偏见。
5. Essay Structure Formula: PEEL | 论述题结构公式：PEEL
For extended writing, use the PEEL formula in every body paragraph:
在展开论述时，每个主体段落都应使用 PEEL 公式：
PEEL = Point + Evidence + Explanation + Link
PEEL = 观点 + 证据 + 解释 + 回扣
Point is a clear analytical statement that directly addresses the question. Evidence is specific factual material such as dates, names, statistics, or events. Explanation shows why the evidence supports the point, and Link connects the paragraph back to the question or forward to the next point.
观点是一个清晰的、直接回答问题的分析性陈述。证据是具体的史实材料，例如日期、人名、统计数据或事件。解释是说明证据为何支持观点，而回扣则把该段与问题连接起来，或过渡到下一个要点。
For example, in answer to ‘Why did the Cold War emerge?’, a PEEL paragraph might argue that Stalin’s actions in Eastern Europe convinced the West that the USSR was expansionist, use evidence from the 1946 Iron Curtain speech and the 1948 Berlin Blockade, explain how these actions broke wartime agreements, and link back to the question.
例如，在回答“冷战为何形成？”时，一个 PEEL 段落可以论证斯大林在东欧的行动使西方相信苏联具有扩张性，引用 1946 年铁幕演说和 1948 年柏林封锁为证据，解释这些行动如何破坏了战时协定，并回扣到问题。
6. Comparison and Contrast Formula | 比较与对照公式
For questions asking about similarities or differences, use the comparison formula:
对于询问相似点或不同点的问题，使用比较公式：
Similarity / Difference = Point + Evidence A + Evidence B + Explanation
相似点 / 不同点 = 观点 + 证据 A + 证据 B + 解释
A comparison is only effective when both sides of the comparison receive specific evidence. Do not write one paragraph on topic A and a separate paragraph on topic B without comparing them.
只有当比较的双方都有具体证据支撑时，比较才是有效的。不要先写一段关于主题 A 的内容，再单独写一段关于主题 B 的内容，却不进行任何比较。
For example, comparing Bismarck’s and Kaiser Wilhelm II’s foreign policy: a difference is that Bismarck aimed to keep France isolated through alliances such as the Dual Alliance, while Wilhelm II allowed the Reinsurance Treaty with Russia to lapse, pushing Russia towards France.
例如，比较俾斯麦与威廉二世的外交政策：一个不同点是俾斯麦旨在通过德奥同盟等联盟体系孤立法国，而威廉二世任由与俄国的《再保险条约》失效，从而把俄国推向了法国一边。
7. Change and Continuity Theorem | 变化与延续定理
Historical development is best understood as a combination of change and continuity:
历史发展最好被理解为变化与延续的结合：
Historical development = Change + Continuity
历史发展 = 变化 + 延续
Change can be measured by speed, direction, and scale. The Industrial Revolution brought a rapid change from rural hand production to urban factory production, but the direction of change was uneven across regions, and the scale affected working-class families most directly.
变化可以通过速度、方向和规模来衡量。工业革命带来了从乡村手工生产到城市工厂生产的迅速变化，但变化的方向在不同地区并不均衡，其规模则最直接地影响了工人阶级家庭。
Continuity means the institutions, attitudes, and structures that persisted. Despite industrial change, social hierarchy, gender roles, and private property remained largely intact in nineteenth-century Britain.
延续指的是持续存在的制度、观念和结构。尽管发生了工业变革，在 19 世纪的英国，社会等级、性别角色和私有财产制度仍然基本保持原状。
8. Multiple Causation Theorem | 历史解释多元定理
Strong historical explanations avoid single-cause determinism. Use the hierarchy of causes:
有力的历史解释会避免单因决定论。请使用原因的重要性层级：
Explanation = Trigger + Long-term causes + Context + Agency
解释 = 导火索 + 长期原因 + 背景 + 行动者作用
Agency refers to the choices and actions of individuals and groups. For example, the Russian Revolution of 1917 cannot be explained only by economic hardship; the decisions of Nicholas II, the impact of the First World War, and the organisation of the Bolshevik Party were all necessary parts of the explanation.
行动者作用指的是个人和群体的选择与行动。例如，1917 年俄国革命不能只用经济困难来解释；尼古拉二世的决策、第一次世界大战的影响以及布尔什维克党的组织，都是解释中必不可少的部分。
When a question asks ‘Which cause was most important?’, rank causes and justify the ranking. You can say that the First World War was the most important cause because it turned pre-existing discontent into revolutionary crisis, while other causes were necessary but not sufficient.
当问题问“哪一个原因最重要？”时，要对原因进行排序并说明排序依据。你可以说第一次世界大战是最重要的原因，因为它把原有的不满转化为革命危机，而其他原因虽然必要，但并不充分。
9. Chronology Analysis Formula | 时间线分析公式
Chronological reasoning requires more than memorising dates. Use the formula:
时序推理需要的不仅仅是记住日期。请使用以下公式：
Chronology = Sequence + Duration + Turning point + Pace
时序 = 先后顺序 + 持续时间 + 转折点 + 节奏
Sequence is the order of events; duration distinguishes long-term trends from short episodes; turning points mark moments when the direction of history changed; pace describes whether change was gradual or sudden.
先后顺序是事件发生的次序；持续时间把长期趋势与短期事件区分开来；转折点标志着历史方向发生改变的时刻；节奏则描述变化是渐进的还是突然的。
For the Cold War, a useful chronology identifies 1945-1947 as the breakdown of the Grand Alliance, 1948-1949 as the Berlin Blockade and NATO creation, and 1989-1991 as the collapse of Soviet control in Eastern Europe and the USSR itself.
对于冷战而言，一个有用的时间线把 1945—1947 年视为大同盟的破裂时期，把 1948—1949 年视为柏林封锁与北约成立的时期，把 1989—1991 年视为苏联对东欧控制以及苏联自身瓦解的时期。
10. Answer Time Management Formula | 答案时间管理公式
Marks are won by applying knowledge, not by writing everything you know. Use the time formula:
得分靠的是运用知识，而不是写出你所知道的一切。请使用时间管理公式：
Time per mark = Total minutes ÷ Total marks
每分时间 = 总分钟数 ÷ 总分值
For a 20-mark essay in roughly 25 minutes, allocate about 5 minutes to plan, 15 minutes to write, and 5 minutes to review. Each body paragraph should take about 5 minutes to produce one strong PEEL point.
对于大约 25 分钟内完成的一道 20 分论述题，可以分配约 5 分钟构思、15 分钟写作和 5 分钟检查。每个主体段落大约需要 5 分钟，用来完成一个有力的 PEEL 要点。
A common error is spending too long on the first paragraph and then rushing the judgement. The essay formula is:
一种常见错误是在第一个段落上花费太多时间，然后仓促得出结论。论文的时间公式是：
Answer = Plan + Write + Review
答案 = 构思 + 写作 + 检查
11. Paper 2 Source Question Formula | Paper 2 史料题答题公式
For Paper 2 questions such as ‘How useful is Source A to a historian studying…?’, use the formula:
对于 Paper 2 中的问题，例如“史料 A 对研究……的历史学家有多大用处？”，请使用以下公式：
Source answer = Judgement + Evidence from source + Provenance + Cross-reference
史料答案 = 判断 + 史料中的证据 + 来源信息 + 交叉参照
Begin with a clear judgement, for example ‘Source A is useful to a significant extent, but with limitations.’ Then support this with specific content from the source, analyse provenance, and if possible cross-reference with another source or your own knowledge.
开头要给出清晰的判断，例如“史料 A 在很大程度上是有用的，但也存在局限性”。然后用史料中的具体内容来支撑，分析来源信息，并在可能的情况下与另一则史料或自己的知识进行交叉参照。
For ‘What is the message of this cartoon?’ use a similar structure: point out symbols, identify the main idea, and link it to historical context. A cartoon showing Stalin as a giant eating Eastern Europe might have the message that Stalin was aggressively expanding Soviet power after 1945.
对于“这幅漫画传达了什么信息？”这类问题，也可以使用类似的结构：指出象征符号，识别核心观点，并将其与历史背景联系起来。一幅把斯大林描绘成吞食东欧的巨人的漫画，其主旨可能是斯大林在 1945 年后正在积极扩张苏联势力。
12. Depth Study Essay Formula | 深度研究答题公式
For Paper 4 or any depth study essay, structure your answer using the criteria formula:
对于 Paper 4 或任何深度研究论文，可以使用标准公式来组织答案：
Depth Study essay = Criteria + For + Against + Judgement
深度研究论文 = 评价标准 + 支持 + 反对 + 最终判断
In the introduction, define the criteria by which you will judge the question. For example, if the question is ‘How successful was Nazi economic policy?’, your criteria might include employment, rearmament, agricultural performance, and living standards.
在引言中，要明确你用来评判该问题的标准。例如，如果问题是“纳粹经济政策有多成功？”，你的标准可以包括就业、重整军备、农业表现和生活水平。
The body should then present evidence both for and against success, with each paragraph linked to the criteria. The conclusion must make an overall judgement, such as ‘Nazi economic policy was successful in reducing unemployment but failed to create genuine prosperity because much growth depended on rearmament.’
正文部分应呈现支持和反对成功两方面的证据，每一段都要与评价标准相联系。结论必须给出一个总体判断，例如“纳粹经济政策在降低失业率方面是成功的，但未能创造真正的繁荣，因为许多增长依赖于重整军备。”
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