📚 Year 12 OCR German: Formula & Theorem Quick Reference Guide | Year 12 OCR 德语：公式定理速查手册
Mastering German at Year 12 level requires more than memorising vocabulary – it demands a systematic grasp of grammatical “formulas” that govern how the language operates. This quick reference guide treats key grammar rules as theorems, providing you with clear, equation-like structures to simplify revision. From verb conjugations to adjective endings, these “formulas” will sharpen your accuracy and confidence for the OCR exams.
掌握 Year 12 阶段的德语，不仅是背单词那么简单——更需要系统掌握支配语言运作的语法“公式”。这份速查手册将核心语法规则视作定理，为你提供像方程式一样清晰的结构，助力复习。从动词变位到形容词词尾变化，这些“公式”将提升你答题的准确性与信心，从容应对 OCR 考试。
1. Present Tense Conjugation Formulas | 现在时变位公式
The present tense in German follows a stem + ending model. For regular verbs, drop the -en from the infinitive to obtain the stem, then apply the endings: -e, -st, -t, -en, -t, -en.
德语现在时遵循“词干 + 词尾”的模式。对于规则动词，去掉不定式的 -en 得到词干，然后加上词尾：-e, -st, -t, -en, -t, -en。
Formula: stem + { -e, -st, -t, -en, -t, -en }
| Person | machen (to make/do) | spielen (to play) |
|---|---|---|
| ich | mache | spiele |
| du | machst | spielst |
| er/sie/es | macht | spielt |
| wir | machen | spielen |
| ihr | macht | spielt |
| sie/Sie | machen | spielen |
For stem-changing verbs like fahren (du fährst) or lesen (du liest), the vowel change applies only to du and er/sie/es forms.
对于词干元音变化的动词，如 fahren（du fährst）或 lesen（du liest），元音变化仅出现在 du 和 er/sie/es 人称上。
2. Perfect Tense (Perfekt) Formula | 完成时公式
The Perfekt is the main past tense used in spoken German. It is formed with an auxiliary verb (haben or sein) conjugated in the present, plus the past participle (Partizip II) at the end of the clause.
完成时是德语口语中主要使用的过去时态。它由在现在时变位的助动词（haben 或 sein）加上位于句末的过去分词（Partizip II）构成。
Formula: Subject + auxiliary (haben/sein) + ... + Partizip II
Most verbs use haben; verbs of movement or change of state (e.g., gehen, fahren, aufwachen) use sein. Weak verbs form the participle with ge + stem + t (e.g., gespielt). Strong verbs often have ge + stem + en with a possible vowel change (e.g., gefahren, geschrieben).
大多数动词用 haben；表示位置移动或状态变化的动词（如 gehen, fahren, aufwachen）用 sein。弱变化动词构成过去分词：ge + 词干 + t（如 gespielt）。强变化动词常有 ge + 词干 + en，并可能发生元音变化（如 gefahren, geschrieben）。
3. Future Tense and the Verb werden | 将来时与动词 werden
The future tense in German is formed using the conjugated form of werden (to become) plus the infinitive of the main verb placed at the end. The formula is straightforward.
德语将来时由变位后的 werden 加上位于句末的主要动词不定式构成。公式十分直接。
Formula: Subject + werden (conjugated) + ... + infinitive
| Person | werden |
|---|---|
| ich | werde |
| du | wirst |
| er/sie/es | wird |
| wir | werden |
| ihr | werdet |
| sie/Sie | werden |
Example: Ich werde morgen ins Kino gehen. (I will go to the cinema tomorrow.) Notice how the infinitive gehen is at the very end.
例句：Ich werde morgen ins Kino gehen.（我明天要去电影院。）注意不定式 gehen 位于句末。
4. Modal Verb Formulas | 情态动词公式
Modal verbs (können, müssen, dürfen, sollen, wollen, mögen) modify the meaning of a main verb. The conjugated modal occupies the second position in a main clause, and the main verb keeps its infinitive form at the end.
情态动词（können, müssen, dürfen, sollen, wollen, mögen）修饰主要动词的含义。变位后的情态动词在主句中占据第二位，而主要动词以不定式形式留在句末。
Formula: Subject + modal verb (conjugated, 2nd position) + ... + infinitive
Each modal verb has its own irregular present tense conjugation, often with a different vowel in the singular:
每个情态动词均有不规则现在时变位，单数人称中元音常与不定式不同：
- können: ich kann, du kannst, er kann
- müssen: ich muss, du musst, er muss
- dürfen: ich darf, du darfst, er darf
- sollen: ich soll, du sollst, er soll
- wollen: ich will, du willst, er will
- mögen: ich mag, du magst, er mag
Example: Er muss seine Hausaufgaben machen. (He must do his homework.) The main verb machen appears at the end.
例句：Er muss seine Hausaufgaben machen.（他必须做作业。）主要动词 machen 出现在句末。
5. Cases and Article Declension Formula | 格与冠词变格公式
German has four cases (Nominative, Accusative, Dative, Genitive) that signal the grammatical function of a noun. Definite and indefinite articles change according to case, gender, and number. Below are the “formulas” for the definite article (the).
德语有四个格（主格、宾格、与格、属格），标示名词的语法功能。定冠词和不定冠词根据格、性和数变化。以下是定冠词（英语 the）的“公式”。
| Case | Masculine | Neuter | Feminine | Plural |
|---|---|---|---|---|
| Nominative | der | das | die | die |
| Accusative | den | das | die | die |
| Dative | dem | dem | der | den (+n on noun) |
| Genitive | des (+(e)s on noun) | des (+(e)s on noun) | der | der |
A similar pattern applies to indefinite articles (ein, kein) and possessive adjectives. The accusative case is used for the direct object, the dative for the indirect object, and after certain prepositions.
不定冠词（ein, kein）和物主形容词遵循类似模式。宾格用于直接宾语，与格用于间接宾语，以及某些介词后。
6. Adjective Endings: The Three Tables Theorem | 形容词词尾：三表定理
Adjective endings depend on the preceding article and the case/gender. They follow a strict “formula” based on whether the article is definite, indefinite, or missing altogether.
形容词词尾取决于其前的冠词以及格和性。它们按照一套严格的“公式”变化，取决于冠词是定冠词、不定冠词还是无冠词。
With definite article (der/die/das): The adjective takes the weak ending -e or -en.
定冠词后： 形容词用弱变化词尾 -e 或 -en。
| Case | Masculine | Neuter | Feminine | Plural |
|---|---|---|---|---|
| Nom | -e | -e | -e | -en |
| Acc | -en | -e | -e | -en |
| Dat | -en | -en | -en | -en |
| Gen | -en | -en | -en | -en |
With indefinite article (ein): The adjective endings are strong except in the nominative masculine/neuter and accusative neuter, where they are -er and -es respectively.
不定冠词后： 形容词词尾多为强变化，除主格阳/中性及宾格中性使用 -er, -es。
No article (strong declension): The adjective takes the full strong endings, which closely resemble the definite article endings but with -en in genitive masculine/neuter.
无冠词（强变化）： 形容词采用强变化词尾，与定冠词词尾接近，但属格阳/中性为 -en。
7. Word Order: Main Clause Formula | 语序：主句公式
German main clauses follow the V2 (verb second) rule: the conjugated verb must be the second element in the sentence. The first element can be the subject, a time expression, an object, or any other constituent.
德语主句遵循 V2（动词第二位）原则：变位动词必须是句子中的第二个成分。第一位可以是主语、时间状语、宾语或任何其他成分。
Formula: Element X + verb (conjugated) + subject + ... + rest
If the subject is not in first position, it must appear immediately after the verb, a rule often called the “Vorfeld” and “Mittelfeld” structure. Example: Heute gehe ich ins Kino. (Today I am going to the cinema.)
如果主语不在第一位，它必须紧跟在动词后出现，这条规则常被称作“前域”和“中域”结构。例句：Heute gehe ich ins Kino.（今天我去了电影院。）
8. Subordinate Clause Word Order Formula | 从句语序公式
In subordinate clauses, the conjugated verb moves to the very end of the clause. The clause is introduced by a subordinating conjunction (e.g., dass, weil, obwohl, wenn).
在从句中，变位动词移至从句最末尾。从句由从属连词（如 dass, weil, obwohl, wenn）引导。
Formula: conjunction + subject + ... + rest + verb (conjugated)
If there is a modal verb or Perfekt auxiliary, the finite verb goes to the end, and any infinitive or past participle comes before it. Example: Ich weiß, dass er heute ins Kino geht. (I know that he is going to the cinema today.)
如果有情态动词或完成时助动词，限定动词移至句末，而任何不定式或过去分词在其之前。例句：Ich weiß, dass er heute ins Kino geht.（我知道他今天去电影院。）
This “verb-final” rule is a key differentiator and must be applied consistently in OCR exam writing tasks.
这条“动词结尾”规则是关键区别，必须在 OCR 考试的写作任务中始终遵守。
9. Passive Voice Formula | 被动语态公式
The passive voice in German is formed with the auxiliary verb werden (conjugated) and the past participle of the main verb. The perfect passive uses sein + Partizip II + worden.
德语被动语态由助动词 werden（变位）和主要动词的过去分词构成。完成时被动式使用 sein + Partizip II + worden。
Present passive: Subject + werden (conjugated) + ... + Partizip II
Perfect passive: Subject + sein (conjugated) + ... + Partizip II + worden
Example: Das Buch wird gelesen. (The book is being read.) Das Buch ist gelesen worden. (The book has been read.)
例句：Das Buch wird gelesen.（这本书正在被阅读。）Das Buch ist gelesen worden.（这本书已被阅读。）
10. Subjunctive II (Konjunktiv II) Formulas | 虚拟式第二式公式
Konjunktiv II is used for hypothetical situations, polite requests, and wishes. It is formed from the simple past stem of the verb with umlaut (if possible) plus personal endings.
虚拟式第二式用于假设情况、礼貌请求和愿望。它由动词的过去时词干加上变音符号（如可能）和人称词尾构成。
Formula: past stem (with umlaut) + { -e, -est, -e, -en, -et, -en }
For regular verbs, the Konjunktiv II looks like the simple past, so the würde + infinitive construction is often used instead. For strong verbs: haben → hätte, sein → wäre, können → könnte, müssen → müsste, etc.
对于规则动词，虚拟式第二式看起来与过去时相同，因此常使用 würde + 不定式结构替代。强变化动词如：haben → hätte，sein → wäre，können → könnte，müssen → müsste 等等。
Example: Wenn ich mehr Zeit hätte, würde ich reisen. (If I had more time, I would travel.)
例句：Wenn ich mehr Zeit hätte, würde ich reisen.（如果我有更多时间，我就会去旅行。）
11. Prepositions and Case Governance Formulas | 介词与格的支配公式
German prepositions dictate which case the following noun phrase must take. They fall into three groups: accusative-only, dative-only, and two-way prepositions (accusative for movement, dative for location).
德语介词决定其后名词短语的格。它们分为三类：只支配宾格的、只支配与格的，以及交替介词（表移动用宾格，表位置用与格）。
- Accusative prepositions: durch, für, gegen, ohne, um
- Dative prepositions: aus, bei, mit, nach, seit, von, zu
- Two-way prepositions: an, auf, hinter, in, neben, über, unter, vor, zwischen
For the two-way prepositions, use accusative with verbs of direction (wohin?) and dative with verbs of location (wo?).
对于交替介词，与方向动词（wohin?）连用时用宾格，与位置动词（wo?）连用时用与格。
Movement → Accusative; Location → Dative
12. Relative Clause Construction Formula | 关系从句构建公式
Relative clauses provide additional information about a noun and are introduced by relative pronouns that match the antecedent in gender and number, but take their case from their role within the clause.
关系从句提供关于名词的附加信息，由关系代词引导；关系代词的性和数与先行词一致，但格由其从句内的角色决定。
Formula: antecedent + , + relative pronoun (der/die/das etc., case-governed) + ... + verb-final
| 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: Der Mann, den ich gesehen habe, ist freundlich. (The man whom I saw is friendly.) Here den is accusative masculine because it is the direct object of the relative clause verb.
例句：Der Mann, den ich gesehen habe, ist freundlich.（我看到的那位男士很友善。）这里 den 是阳性宾格，因为它在关系从句中是动词的直接宾语。
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