📚 Year 13 CAIE German: Formula & Theorem Quick Reference Handbook | 德语公式定理速查手册
Welcome to your ultimate A-Level German quick reference. This handbook reframes high‑yield grammar rules as ‘formulas’ and ‘theorems’ – structured building blocks you can apply with precision. Keep it close while tackling translations, essays and speaking tasks on the CAIE syllabus. Mastering these patterns will give your written and spoken German the accuracy examiners look for.
欢迎使用这份 A‑Level 德语终极速查手册。我们把高频语法规则重新打造成“公式”和“定理”——结构清晰、拿来即用的积木。翻译、作文和口语任务中遇到难题时，随时翻阅。拿下这些模式，你的书面语和口语就能达到考官期待的那种准确性。
1. The Noun Gender & Case System | 名词性与格系统
German nouns belong to one of three genders: masculine (der), feminine (die) or neuter (das). Every noun also appears in four cases – Nominative, Accusative, Dative and Genitive – which signal its role in a sentence. Think of gender × case as a 3‑by‑4 grid that determines the form of articles, adjectives and pronouns around the noun.
德语名词分属三种词性：阳性 (der)、阴性 (die) 和中性 (das)。每个名词还会以四种格出现——主格、宾格、与格和属格——标明它在句中的功能。可以把“性 × 格”看成一张 3×4 的网格，决定了名词周围冠词、形容词和代词的形式。
Theorem of Suffix Hints: Certain endings strongly predict gender. For example, nouns ending in -ung, -heit, -keit, -schaft are feminine (die). Endings -chen and -lein make a noun neuter (das). Many nouns ending in -er (referring to people or tools) are masculine (der). This is a powerful shortcut, but remember to learn the article as a chunk for every new noun.
词尾暗示定理： 某些词尾强烈暗示性别。比如以 -ung, -heit, -keit, -schaft 结尾的名词是阴性 (die)。-chen 和 -lein 让名词变成中性 (das)。许多指人或工具的 -er 结尾名词是阳性 (der)。这是一条强大的捷径，但每个新名词仍要连同冠词一起记忆。
2. Definite and Indefinite Articles | 定冠词与不定冠词
The definite article (the) and indefinite article (a/an) change across case, gender and number. The pattern resembles a formula: take the stem d‑ (for definite) or ein‑ (for indefinite), then add the case‑gender ending. Plural indefinite articles have no form – instead use the bare noun or pronouns like ‘welche’.
定冠词（the）和不定冠词（a/an）随格、性、数变化。模式像一个公式：取词干 d‑（定冠词）或 ein‑（不定冠词），再跟上格性词尾。复数不定冠词没有形式——可以直接用名词原型或代词如 welche。
| Case | Masculine | Neuter | Feminine | Plural |
|---|---|---|---|---|
| Nominative | der / ein | das / ein | die / eine | die / – |
| Accusative | den / einen | das / ein | die / eine | die / – |
| Dative | dem / einem | dem / einem | der / einer | den / – |
| Genitive | des / eines | des / eines | der / einer | der / – |
Notice how dative and genitive masculine/neuter add ‑m and ‑s respectively. This is a core ‘declension micro‑formula’ that also appears in adjective endings.
注意阳性/中性在第三格和第二格分别添加 ‑m 和 ‑s。这是一个核心的变格微公式，同样会出现在形容词词尾中。
3. Adjective Endings ‘Formula’ | 形容词词尾“公式”
German adjective endings depend on three parameters: the article type (definite, indefinite, zero article), case and gender/number. You can memorise three tables as if they were formula sheets. Once you internalise the logic, you can fire them off automatically in any sentence.
德语形容词词尾取决于三个参数：冠词类型（定冠词、不定冠词、零冠词）、格和性/数。可以把三张表格当成公式表一样记熟。一旦内化了这套逻辑，就能在任意句子中自动调用。
Weak endings (after definite article): The der‑word already shows case, so the adjective adds only ‑e or ‑en.
弱变化词尾（定冠词后）： 定冠词已经体现格，形容词只需加 ‑e 或 ‑en。
| Case | Masculine | Neuter | Feminine | Plural |
|---|---|---|---|---|
| Nominative | -e | -e | -e | -en |
| Accusative | -en | -e | -e | -en |
| Dative | -en | -en | -en | -en |
| Genitive | -en | -en | -en | -en |
Mixed endings (after indefinite article): ein has no ending in nominative masculine/neuter, so the adjective takes on the strong ending. Elsewhere it follows the weak pattern.
混合变化词尾（不定冠词后）： 不定冠词在阳性/中性第一格没有词尾，所以形容词必须带上强变化词尾。其他情况下则遵循弱变化模式。
| Case | Masculine | Neuter | Feminine | Plural (no article) |
|---|---|---|---|---|
| Nominative | -er | -es | -e | -en |
| Accusative | -en | -es | -e | -en |
| Dative | -en | -en | -en | -en |
| Genitive | -en | -en | -en | -en |
Strong endings (no article): The adjective must carry the full case signal, effectively copying the missing determiner’s ending, except in genitive masculine/neuter where it is ‑en.
强变化词尾（零冠词）： 形容词必须完全承担格标识，实际上就是复制缺失的限定词词尾，只是阳性/中性属格用 ‑en。
| Case | Masculine | Neuter | Feminine | Plural |
|---|---|---|---|---|
| Nominative | -er | -es | -e | -e |
| Accusative | -en | -es | -e | -e |
| Dative | -em | -em | -er | -en |
| Genitive | -en | -en | -er | -er |
4. Personal Pronouns in Cases | 人称代词的格变化
Personal pronouns shift dramatically across cases. The ‘formula’ is a roster: ich → mich → mir, du → dich → dir, er → ihn → ihm, sie → sie → ihr, es → es → ihm, wir → uns → uns, ihr → euch → euch, sie/Sie → sie/Sie → ihnen/Ihnen. Reflexive pronouns in the dative often differ from accusative only in the 3rd person (sich → sich).
人称代词在不同格中变化强烈。公式就是一张清单：ich → mich → mir, du → dich → dir, er → ihn → ihm, sie → sie → ihr, es → es → ihm, wir → uns → uns, ihr → euch → euch, sie/Sie → sie/Sie → ihnen/Ihnen。第三格反身代词与第四格的区别通常只出现在第三人称 (sich → sich)。
- Nominative: ich, du, er, sie, es, wir, ihr, sie, Sie
- Accusative: mich, dich, ihn, sie, es, uns, euch, sie, Sie
- Dative: mir, dir, ihm, ihr, ihm, uns, euch, ihnen, Ihnen
Pronouns in the genitive (meiner, deiner, seiner, ihrer etc.) appear mainly after prepositions or in formal written register. Keep these as your ‘at‑a‑glance’ substitution spreadsheet.
属格代词 (meiner, deiner, seiner, ihrer 等) 主要出现在介词后或正式书面语中。把这张表当成你的即时代入电子表格。
5. Relative Pronouns and Clause Link | 关系代词与从句连接
Relative pronouns in German essentially look like the definite article, except in the dative plural (denen) and genitive (dessen, deren). They introduce a relative clause where the conjugated verb goes to the end. This ‘relay’ structure merges two main clauses into one elegant sentence.
德语中的关系代词基本形似定冠词，区别在于复数第三格 (denen) 和属格 (dessen, deren)。关系代词引导从句，其中变位动词置于末尾。这种“接转”结构把两个主句揉成一句优雅的复合句。
| Case | Masculine | Neuter | Feminine | Plural |
|---|---|---|---|---|
| Nominative | der | das | die | die |
| Accusative | den | das | die | die |
| Dative | dem | dem | der | denen |
| Genitive | dessen | dessen | deren | deren |
Example: Das ist der Mann, dem ich das Buch gegeben habe. (That is the man to whom I gave the book.) Note the verb ‘gegeben habe’ at the end – a classic relative‑clause footprint.
例：Das ist der Mann, dem ich das Buch gegeben habe.（这就是我给了他书的那个人。）注意末尾的动词 gegeben habe——关系从句的经典脚印。
6. Verb Conjugation Master Keys | 动词变位万能钥匙
Regular verbs obey a predictable framework: stem + personal ending. The present‑tense template is: ich ‑e, du ‑st, er/sie/es ‑t, wir ‑en, ihr ‑t, sie/Sie ‑en. Separable prefixes (auf‑, an‑, mit‑ etc.) split off to the end in main clauses but remain attached in subordinate clauses – a crucial word‑order theorem.
规则动词遵循可预测的框架：词干 + 人称词尾。现在时模板是：ich ‑e, du ‑st, er/sie/es ‑t, wir ‑en, ihr ‑t, sie/Sie ‑en。可分前缀 (auf‑, an‑, mit‑ 等) 在主句中拆分到句末，在从句中仍紧附动词——这是一条至关重要的词序定理。
Irregular verb alert: Stem‑vowel changes occur in du and er/sie/es forms. Common patterns include e → i (geben → gibt), e → ie (lesen → liest), a → ä (fahren → fährt). Treat these as exceptions to the ‘regular formula’ that must be memorised individually.
不规则动词提醒： 词干元音变化发生在 du 和 er/sie/es 形式中。常见模式包括 e → i (geben → gibt)，e → ie (lesen → liest)，a → ä (fahren → fährt)。把它们看作“规则公式”的例外，需要单独记忆。
The perfect tense relies on haben/sein + past participle. Past participles usually follow the pattern ge‑ + stem + ‑t (weak) or ge‑ + stem + ‑en (strong). Mixed verbs like ‘bringen’ → ‘gebracht’ combine features of both.
现在完成时依靠 haben/sein + 过去分词。过去分词通常遵循 ge‑ + 词干 + ‑t（弱变化）或 ge‑ + 词干 + ‑en（强变化）的模式。混合动词如 bringen → gebracht 融合了两者特征。
7. The Framework: Verb-Second & Verb-Final Rules | 句框结构：动词二位与动词末位规则
German word order is governed by the ‘Verb‑Second’ principle in main clauses: the conjugated verb must occupy position 2. The first position can be the subject, an adverb, an object, or even a subordinate clause. Everything else fills the ‘Mittelfeld’ before non‑finite verb parts occupy the final slot (Satzklammer).
德语词序受主句“动词二位”原则支配：变位动词必须占据第二位。第一位可以是主语、副词、宾语，甚至是一个从句。其余成分填充中间场，非限定动词部分则占据末尾位（句框）。
Example: Heute Morgen hat der Student das Buch gelesen. (This morning the student read the book.) ‘hat’ is position 2, ‘gelesen’ closes the bracket. In subordinating clauses, the conjugated verb goes to the very end: weil der Student das Buch gelesen hat.
例：Heute Morgen hat der Student das Buch gelesen.（今天早上学生读了那本书。）hat 在第 2 位，gelesen 关闭句框。在从句中，变位动词移至最末：weil der Student das Buch gelesen hat.
This flexible bracket structure is one of the most powerful ‘generative formulas’ of German syntax – learn to move elements in and out of it like a jigsaw puzzle.
这种弹性句框结构是德语语法最具威力的“生成公式”之一——学会像玩拼图一样自由调度其中的成分。
8. The Passive Voice Recipe | 被动语态食谱
The German passive is built with a simple recipe: werden + past participle. The agent (von + dative) is optional. In perfect and past perfect tenses, ‘worden’ replaces ‘geworden’: ist/war + past participle + worden. Remember the ‘micro‑formula’: werden (conjugated) + Partizip II (end of clause).
德语被动语态用一道简单食谱即可烹得：werden + 过去分词。施事者 (von + 第三格) 可省。在现在完成时和过去完成时中，worden 取代 geworden：ist/war + 过去分词 + worden。记住这条微公式：werden (变位) + Partizip II（从句末）。
- Present: Der Brief wird geschrieben. (The letter is being written.)
- Perfect: Der Brief ist geschrieben worden. (The letter has been written.)
- Future: Der Brief wird geschrieben werden. (The letter will be written.)
In impersonal passives, ‘es’ acts as a placeholder in position 1: Es wird heute getanzt. / Heute wird getanzt. (There is dancing today.) This holds true for any verb without an accusative object.
无主动式中，es 充当第一位占位符：Es wird heute getanzt. / Heute wird getanzt.（今天有舞会。）任何不带第四格宾语的动词都适用这一规则。
9. Subjunctive II (Konjunktiv II) Formula | 第二虚拟式公式
Subjunctive II expresses hypotheses, wishes, politeness and reported speech when events are unlikely or unreal. The go‑to contemporary formula is: würde + infinitive. However, for common auxiliary and modal verbs, use their genuine Konjunktiv II forms: hätte, wäre, könnte, dürfte, müsste, wollte, sollte.
第二虚拟式表达假设、愿望、客套以及在非真实情况下的间接引语。当代最常用的公式是：würde + 不定式。但对于常用的助动词和情态动词，要用它们真正的第二虚拟式形式：hätte, wäre, könnte, dürfte, müsste, wollte, sollte。
- Wenn ich mehr Zeit hätte, würde ich reisen. (If I had more time, I would travel.)
- Er sagte, er sei krank gewesen. (He said he had been ill – Subjunctive I in reported speech, common in formal German.)
Formal written German often prefers Konjunktiv I for indirect speech: er komme, er habe. In Year 13, knowing both registers will impress examiners, but the würde + infinitive pattern is the safest ‘default theorem’ for hypothetical contexts.
正式书面语中常用第一虚拟式表达间接引语：er komme, er habe。在 Year 13，熟悉两种语体会让考官眼前一亮，而 würde + 不定式则是假设情境下最稳妥的“默认定理”。
10. Preposition Case Triggers | 介词格触发定理
Every German preposition governs a specific case. You can visualise them as three ‘trigger’ groups. Once the preposition appears, the following noun phrase must wear the correct case – no exceptions. This is a pure theorem: preposition ⇒ case.
每一个德语介词都支配特定的格。你可以把它们形象化为三个“触发”组。介词一出，后面名词短语就必须穿上正确的格——没有例外。这是一条纯定理：介词 ⇒ 格。
Accusative-only triggers: durch, für, gegen, ohne, um, bis, entlang
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