📚 Year 12 Cambridge German: Formulas & Theorems Quick Reference | 12年级剑桥德语：公式定理速查手册
In A‑Level German, grammar often feels like a set of rigid equations. Just as in mathematics, mastering the core formulas enables you to generate countless correct sentences. This handbook collects the essential ‘formulas’ and ‘theorems’ of Year 12 Cambridge German – from word‑order rules to case endings, tense formations, and clause‑linking patterns. Keep it by your side for quick revision and accurate production in both writing and speaking.
在A‑Level德语中，语法常常像一套严格的方程式。如同数学一样，掌握核心公式就能生成无数正确的句子。这本手册汇集了12年级剑桥德语的基础“公式”和“定理”——从词序规则到格尾变化，从时态构成到从句连接模式。把它放在手边，便于快速复习，在写作和口语中准确输出。
1. The V2 Formula (Verb Second Rule) | 动词第二位公式
In a standard German main clause, the finite verb occupies the second position. The first position can be the subject, an adverb, an object, or even a whole clause – but the conjugated verb must follow immediately. This is the most fundamental theorem of German syntax.
在标准德语主句中，限定动词占据第二位。第一位可以是主语、副词、宾语甚至一个从句——但变位动词必须紧随其后。这是德语语法最基本的定理。
POS1 + finite verb + …
位置1 + 限定动词 + …
Consider the sentence I am going to the cinema tomorrow. In German, no matter whether you start with ich or morgen, the verb stays in second place.
以句子“我明天去电影院”为例。无论你以“我”还是“明天”开头，动词始终在第二位。
Ich gehe morgen ins Kino.
Morgen gehe ich ins Kino.
When a separable prefix verb is used, the conjugated stem takes V2, while the prefix moves to the end of the clause. This is the ‘prefix bracket’ corollary.
当使用可分动词时，变位词干占据V2位，而前缀移至句末。这称为“前缀括号”推论。
Ich stehe um 7 Uhr auf. (aufstehen)
Um 7 Uhr stehe ich auf.
2. Inversion Theorem (Questions & Subordinating Conjunctions) | 倒置定理（疑问句与从属连词）
Questions without a question word (yes/no questions) place the finite verb in position 1, followed immediately by the subject. This is often taught as ‘inverted V2’.
不带疑问词的问句（一般疑问句）将限定动词放在第一位，主语紧随其后。这常被教为“倒置V2”。
Finite verb + subject + …?
限定动词 + 主语 + …?
Kommst du heute? (Are you coming today?)
Hat er das Buch gelesen? (Has he read the book?)
When a subordinating conjunction (weil, dass, obwohl, wenn, etc.) is introduced, the finite verb is pushed to the very end of the clause. This is a ‘verb‑final’ formula.
当引入从属连词（weil, dass, obwohl, wenn 等）时，限定动词被推到从句的末端。这是“动词末位”公式。
Conjunction + subject + … + finite verb.
连词 + 主语 + … + 限定动词。
Ich bleibe zu Hause, weil ich krank bin.
Er sagt, dass er morgen kommt.
3. The Case System Formula | 格系统公式
German operates with four cases: Nominative, Accusative, Dative, and Genitive. Each case signals a specific syntactic function. Think of the article and pronoun forms as variables that change according to the case formula.
德语有四个格：主格、宾格、与格和属格。每个格标记特定的句法功能。把冠词和代词形式想象成根据格公式变化的变量。
| Case / 格 | Function / 功能 | Example Question / 提问 |
|---|---|---|
| Nominative | Subject / 主语 | Wer? / 谁? |
| Accusative | Direct object / 直接宾语 | Wen? / 谁? (宾) |
| Dative | Indirect object / 间接宾语 | Wem? / 谁? (与) |
| Genitive | Possession / 所属 | Wessen? / 谁的? |
The definite article formula changes predictably across cases. For masculine ‘der’ it becomes ‘den’ in accusative and ‘dem’ in dative, while neuter ‘das’ remains ‘das’ in accusative but also ‘dem’ in dative. Feminine ‘die’ shifts to ‘die’ (acc.) and ‘der’ (dat.). Plural follows a similar pattern.
定冠词公式在格之间可预测地变化。阳性 der 在宾格变为 den，在与格为 dem；中性 das 在宾格保持 das，与格同样变为 dem；阴性 die 在宾格保持 die，与格变为 der。复数遵循类似模式。
Der Hund beißt den Mann. (Nominative → Accusative)
Ich gebe dem Mann den Ball. (Dative + Accusative)
4. Adjective Endings Algorithm | 形容词词尾算法
Adjective endings depend on three factors: gender, case, and whether a determiner (definite article, indefinite article, or no article) precedes the adjective. This can be seen as a three‑branch decision tree.
形容词词尾取决于三个因素：性、格，以及形容词前是否有限定词（定冠词、不定冠词或无冠词）。这可以视为一个三分支决策树。
When preceded by a definite article, the adjective takes weak endings: -e (nominative) or -en in most other cases, because the article already carries the strong case signal.
当前面有定冠词时，形容词采取弱变化词尾：主格用 -e，大多数其他格用 -en，因为冠词已经携带了强格信号。
| Gender/Case | Weak Ending (def. art.) | Strong Ending (no art.) | Mixed (ein-) Ending |
|---|---|---|---|
| Masc. Nom. | -e (der gute Mann) | -er (guter Mann) | -er (ein guter Mann) |
| Masc. Acc. | -en (den guten Mann) | -en (guten Mann) | -en (einen guten Mann) |
| Neut. Nom. | -e (das gute Kind) | -es (gutes Kind) | -es (ein gutes Kind) |
| Fem. Dat. | -en (der guten Frau) | -er (guter Frau) | -en (einer guten Frau) |
The algorithm: Check the determiner. If it’s a definite article, use weak endings; if no determiner, use strong endings (showing the case clearly); if it’s ein, kein, or possessive, the endings mix – strong in nominative and neuter accusative, weak elsewhere.
算法：检查限定词。如果是定冠词，用弱变化词尾；如果无限定词，用强变化词尾（清楚地显示格）；如果是 ein、kein 或物主代词，词尾混合——主格及中性宾格用强变化，其他地方用弱变化。
5. Tense Formation Formulas | 时态构成公式
Each tense can be expressed as a fixed construction formula. The present tense uses conjugated verb alone; the perfect tense combines a present‑tense auxiliary (haben/sein) with a past participle; the future uses werden + infinitive; the simple past (imperfect) is often used in written narrative; the pluperfect pairs the simple past auxiliary with a past participle.
每一种时态都可以表示为固定的构成公式。现在时单用变位动词；现在完成时把助动词 haben/sein 的现在时与过去分词结合；将来时使用 werden + 不定式；一般过去时（imperfect）常用于书面叙事；过去完成时则将助动词的过去式与过去分词配对。
Perfect = haben/sein (present) + past participle (ge‑…‑t/en)
现在完成时 = haben/sein (现在时) + 过去分词 (ge‑…‑t/en)
Ich habe ein Buch gelesen. (read)
Er ist nach Berlin gefahren. (travelled, motion → sein)
Future = werden (present) + infinitive (at the end)
将来时 = werden (现在时) + 不定式 (句末)
Ich werde morgen kommen.
Wir werden das Problem lösen.
The passive voice in various tenses simply inserts the passive auxiliary werden in the appropriate form together with the past participle. The formula becomes werden + past participle, and the agent is often introduced by von + dative.
各个时态的被动语态只是在合适的时态形式中插入被动助动词 werden 以及过去分词。公式变为 werden + 过去分词，施动者常用 von + 与格引入。
6. The Time‑Manner‑Place Ordering Theorem | 时间—方式—地点顺序定理
When multiple adverbial phrases appear in a German clause, they tend to follow a fixed sequence: Time (wann?), Manner (wie?), Place (wo/wohin?). This TeMPo ordering ensures natural‑sounding German.
当多个副词短语出现在德语句子中时，它们倾向于遵循一个固定顺序：时间（何时？）、方式（怎样？）、地点（哪里/去哪里？）。这个 TeMPo 顺序保证德语听起来自然。
Time – Manner – Place (TeMPo)
时间 – 方式 – 地点
Ich fahre morgen (time) mit dem Zug (manner) nach Hamburg (place).
Ich bin gestern (time) zufällig (manner) im Park (place) gelaufen.
If the place phrase is a pronoun or very short, it can move earlier. However, the default theorem remains TeMPo, especially for A‑Level writing tasks where precision is rewarded.
如果地点短语是代词或非常短，它可以提前。但默认定理仍是 TeMPo，尤其是在 A‑Level 写作中，精准度会加分。
7. The Passive Voice Transformation Formula | 被动语态转换公式
To transform an active sentence into the passive, move the accusative object to the subject position (nominative), conjugate werden in the original tense, and use the past participle of the main verb. The original subject becomes an optional ‘von + dative’ phrase.
将主动句转换为被动句时，把宾格宾语移到主语位置（主格），在原时态下变位 werden，并使用主要动词的过去分词。原主语变为可选的“von + 与格”短语。
Active: Subject (nom.) – verb – object (acc.)
Passive: Object → Subject (nom.) – werden (conj.) – … – past participle
Der Lehrer erklärt die Regel. (Active)
Die Regel wird (von dem Lehrer) erklärt. (Passive present)
Die Regel wurde erklärt. (Passive simple past)
Die Regel ist erklärt worden. (Passive perfect – note ‘worden’ not ‘geworden’)
In the perfect passive, the auxiliary sein combines with the participle worden (short for geworden). This is a special theorem: sein … worden never geworden in the passive perfect.
在完成时被动中，助动词 sein 与过去分词 worden（geworden 的缩写）连用。这是一个特殊定理：sein … worden，被动完成时中绝不使用 geworden。
8. Subjunctive II (Konjunktiv II) Formula | 第二虚拟式公式
Konjunktiv II expresses hypothetical situations, politeness, or reported speech when the speaker distances themselves from the statement. The modern default formula is würde + infinitive, but common verbs retain special Konjunktiv II stems.
第二虚拟式用于表达假设情况、礼貌，或在转述时拉开说话人与陈述的距离。现代默认公式是 würde + 不定式，但常见动词保留特殊的第二虚拟式词干。
würde + infinitive (end of clause)
werden 的虚拟式 + 不定式（句末）
Wenn ich viel Geld hätte, würde ich eine Weltreise machen.
For the modals and a few high‑frequency verbs, the pure Konjunktiv II form is preferred: könnte, müsste, dürfte, möchte; hätte, wäre, wüsste, brächte (from bringen), etc.
对于情态动词和一些高频动词，纯第二虚拟式更常用：könnte, müsste, dürfte, möchte；hätte, wäre, wüsste, brächte（来自 bringen）等。
Ich wünschte, ich wäre zu Hause.
Das könnte gefährlich sein.
In reported speech (Konjunktiv I often replaced by II in spoken German), the same form is used to indicate that the statement is not the speaker’s own claim.
在间接引语中（口语常用第二虚拟式替代第一虚拟式），同一形式用来表明陈述并非说话者本人的断言。
9. Relative Clause Connector Rule | 关系从句连接规则
Relative clauses in German are introduced by relative pronouns that agree in gender and number with the antecedent, but their case depends on the function inside the relative clause. The finite verb is pushed to the end, following the subordinate clause formula.
德语的关系从句由关系代词引导，关系代词的性和数与前述词一致，但其格取决于在从句内的句法功能。限定动词遵循从句公式，被推到句末。
Main clause + comma + relative pronoun (case‑dependent) + … + finite verb.
主句 + 逗号 + 关系代词（依格而定） + … + 限定动词。
| Case | Masc. | Neut. | Fem./Plural |
|---|---|---|---|
| Nom. | der | das | die |
| Acc. | den | das | die |
| Dat. | dem | dem | der / denen (pl.) |
| Gen. | dessen | dessen | deren |
Der Mann, der dort steht, ist mein Onkel. (Nom., masc.)
Die Frau, deren Hund bellt, wohnt nebenan. (Gen., fem.)
Das Buch, das ich lese, ist spannend. (Acc., neut.)
If a preposition is involved, it comes before the relative pronoun, and the pronoun takes the case required by that preposition.
如果涉及介词，介词置于关系代词之前，代词取该介词要求的格。
Der Freund, mit dem ich gesprochen habe, kommt aus Spanien.
10. Preposition Cases Quick Reference Table | 介词格速查表
German prepositions govern specific cases. Learning them as formula sets will drastically reduce case errors. The most frequent prepositions are grouped below.
德语介词支配特定的格。把它们作为公式组来学习，将大大减少格错误。下面分组列出了最常用的介词。
| Prepositions with Accusative | Prepositions with Dative | Two‑way (Acc.→motion, Dat.→location) |
|---|---|---|
| durch, für, gegen, ohne, um, bis, entlang | aus, außer, bei, mit, nach, seit, von, zu, gegenüber | an, auf, hinter, in, neben, über, unter, vor, zwischen |
The two‑way prepositions follow a clear theorem: if the verb expresses direction or movement towards a destination, use accusative; if it describes a static location, use dative.
双格介词遵循明确的定理：如果动词表达朝向某一目的地的方向或移动，用宾格；如果描述静态位置，用与格。
Ich gehe in die Stadt. (motion → Acc.)
Ich bin in der Stadt. (location → Dat.)
Some verbs inherently combine with a fixed preposition and case. These ‘verb + preposition’ formulas must be memorised as chunks (e.g., warten auf + Acc., sich interessieren für + Acc., träumen von + Dat.).
有些动词固有地与固定介词和格搭配。这些“动词 + 介词”公式必须作为语块记忆（例如 warten auf + 宾格，sich interessieren für + 宾格，träumen von + 与格）。
11. Irregular Verb Conjugation Patterns | 不规则动词变位模式
Strong verbs change the stem vowel in the present tense for du/er/sie/es (e → i, a → ä, etc.) and follow ablaut series in the past tense and past participle. Treat the principal parts as mini‑formulas to derive all forms.
强变化动词在现在时 du/er/sie/es 人称作词干元音变化（e → i, a → ä 等），并在过去时和过去分词中遵循元音交替系列。将三个基本形式视为微型公式，推导所有形式。
Infinitive – past stem – past participle (ge‑…‑en)
不定式 – 过去词干 – 过去分词 (ge‑…‑en)
| Pattern / 模式 | Example / 例子 |
|---|---|
| ei – i – i | bleiben – blieb – geblieben |
| ie – o – o | fliegen – flog – geflogen |
| i – a – u | finden – fand – gefunden |
| e – a – o | sprechen – sprach – gesprochen |
Mixed verbs combine strong stem changes with weak weak‑verb endings (‑te, ‑t). These include kennen, nennen, brennen, rennen, wissen and modals. Their formula is: infinitive stem change + ‑te + ge‑…‑t.
混合动词将强变化词干变化与弱动词词尾（‑te, ‑t）结合在一起。包括 kennen, nennen, brennen, rennen, wissen 和情态动词。它们的公式是：不定式词干变化 + ‑te + ge‑…‑t。
kennen – kannte – gekannt
denken – dachte – gedacht
12. Summary: Applying the Formulas | 总结：应用公式
When faced with a German sentence, you can run the following checks: ensure verb position (V2 or final), apply the correct case after the main verb or preposition, adjust adjective endings according to the determiner, sequence adverbials TeMPo, and select the right tense formula. Treat each decision as a theorem application, and you will eliminate most structural mistakes.
面对德语句子时，你可以进行以下检查：确保动词位置（V2 或末位），在主要动词或介词后使用正确的格，根据限定词调整形容词词尾，按 TeMPo 排列状语，以及选择正确的时态公式。把每个决定当作一次定理应用，你将消除大部分结构错误。
Keep this reference close when writing essays or preparing for the speaking exam. The formulas work like a safety net: even under pressure, you can fall
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