📚 A-Level CCEA German: Formula & Theorem Quick Reference Handbook | A-Level CCEA 德语：公式定理速查手册
While German is a language, not a natural science, mastering its grammatical structures often feels like applying a set of reliable formulas. From the way articles decline across four cases to the precise word order in subordinate clauses, each rule functions like a theorem that unlocks confident communication. This quick reference handbook compiles the essential ‘formulas’ of A-Level CCEA German — article and adjective endings, verb conjugation patterns, tense structures, subjunctive forms, and clause-building principles — so you can revise systematically and perform with precision in your exams.
德语虽是一门语言而非自然科学，但掌握其语法结构常常像是在应用一套可靠的公式。从冠词在四个格中的变格到从句中精确的语序，每一条规则都如同一个定理，帮你自信地表达。这本速查手册汇集了 A-Level CCEA 德语的核心“公式”——冠词与形容词词尾变化、动词变位模式、时态结构、虚拟式形式以及句子构成原则——让你能够系统复习，在考试中精准答题。
1. Noun Genders & Definite Articles | 名词的性与定冠词
Every German noun has one of three genders: masculine, feminine, or neuter. The definite article (the) must agree with the gender, case, and number of the noun. This is the first ‘formula’ you need to memorise.
每个德语名词都有三种性之一：阳性、阴性或中性。定冠词（相当于英语的 the）必须与名词的性、格和数保持一致。这是你需要记住的第一个“公式”。
The table below shows the definite article forms for all cases and genders. Treat it as a declension matrix.
下表显示了所有格和性的定冠词形式，把它当作变格矩阵来掌握。
| Case | Masculine | Feminine | Neuter | Plural |
|---|---|---|---|---|
| Nominative | der | die | das | die |
| Accusative | den | die | das | die |
| Dative | dem | der | dem | den (+n on noun) |
| Genitive | des (+s on noun) | der | des (+s on noun) | der |
Like a formula, the definite article depends on the input ‘variables’ of gender and case. For example, ‘der Mann’ (the man) becomes ‘den Mann’ in the accusative, and ‘dem Mann’ in the dative. Note how the plural dative adds an -n to the noun if possible: ‘die Kinder’ → ‘den Kindern’.
就像公式一样，定冠词取决于性和格这两个输入“变量”。例如，’der Mann’（这个男人）在宾格中变为’den Mann’，在与格中变为’dem Mann’。注意复数与格在可能的情况下会为名词添加 -n：’die Kinder’ → ‘den Kindern’。
2. The Indefinite Article & Negation | 不定冠词与否定词
The indefinite article ‘ein’ (a/an) and the negation ‘kein’ (no/not a) follow a very similar declension formula. They have no plural forms as articles, but ‘kein’ can be used in the plural to mean ‘no’ (e.g. keine Kinder). The endings largely mirror the definite article, with a few missing forms where the stem is bare.
不定冠词 ‘ein’ 和否定词 ‘kein’ 遵循极为相似的变格公式。作为冠词它们没有复数形式，但 ‘kein’ 可用于复数表示“没有”（如 keine Kinder）。其词尾大部分与定冠词呼应，只是在某些位置词干不带词尾。
| Case | Masculine | Feminine | Neuter |
|---|---|---|---|
| Nominative | ein / kein | eine / keine | ein / kein |
| Accusative | einen / keinen | eine / keine | ein / kein |
| Dative | einem / keinem | einer / keiner | einem / keinem |
| Genitive | eines / keines (+s) | einer / keiner | eines / keines (+s) |
Remember the formula: the masculine nominative and neuter nominative/accusative have no ending; all other forms carry an ending that signals gender and case, just like the definite article endings you already know. ‘Kein’ is essential for negation: ‘Ich habe kein Geld’ (I have no money).
记住这条公式：阳性主格以及中性主格/宾格没有词尾；其他所有形式都带有标示性和格的词尾，正如你已经熟知的定冠词词尾一样。’Kein’ 对于否定至关重要：’Ich habe kein Geld’（我没有钱）。
3. Adjective Endings: The Three Declension Formulas | 形容词词尾：三种变格公式
Adjective endings in German depend on three factors: the preceding article (definite, indefinite, or no article), the gender of the noun, and the case. This yields three distinct declension patterns — think of them as Formula A, Formula B, and Formula C.
德语中的形容词词尾取决于三个因素：前面的冠词（定冠词、不定冠词或无冠词）、名词的性和格。这产生了三种不同的变格模式——你可以把它们看作公式 A、公式 B 和公式 C。
Formula A: After the definite article (der-words)
公式 A：定冠词（der 词）之后
After a definite article, the adjective takes weak endings: -e for nominative singular (all genders) and accusative feminine/neuter; -en for all other cases. This is the most predictable formula.
在定冠词后，形容词采用弱变化词尾：主格单数（所有性）以及宾格阴性和中性为 -e；其余所有格为 -en。这是最可预测的公式。
- der gute Wein → den guten Wein | the good wine (acc.)
- die schöne Frau → der schönen Frau | the beautiful woman (dat.)
- das kleine Kind → dem kleinen Kind | the small child (dat.)
Formula B: After the indefinite article (ein-words) and kein
公式 B：不定冠词（ein 词）和 kein 之后
Here the adjective takes strong endings where the article has no ending, and weak endings elsewhere. So masculine nominative and neuter nominative/accusative get strong endings (-er, -es); all other forms take -en.
在这种情况下，当冠词没有词尾时形容词用强变化词尾，其余用弱变化词尾。因此阳性主格和中性主格/宾格获得强变化词尾（-er, -es）；所有其他形式用 -en。
- ein guter Wein, einen guten Wein | a good wine (nom./acc.)
- eine schöne Frau, einer schönen Frau | a beautiful woman (nom./dat.)
- ein kleines Kind, einem kleinen Kind | a small child (nom./dat.)
Formula C: No article (strong declension)
公式 C：无冠词（强变化）
When there is no article at all, the adjective must carry the full burden of signalling gender and case, so it uses strong endings that closely mirror the definite article endings.
当完全没有冠词时，形容词必须完全承担标示性和格的任务，因此它使用强变化词尾，这些词尾与定冠词词尾非常相似。
- guter Wein, guten Wein, gutem Wein | good wine
- schöne Frau, schöner Frau | beautiful woman
- kleines Kind, kleinem Kind | small child
4. Present Tense Conjugation: The Stem + Ending Formula | 现在时变位：词干+词尾公式
Regular German verbs in the present tense follow a clean formula: verb stem + personal ending. The stem is obtained by removing -en or -n from the infinitive. The endings are -e, -st, -t, -en, -t, -en for ich, du, er/sie/es, wir, ihr, sie/Sie respectively.
规律德语动词的现在时遵循一个清楚的公式：动词词干 + 人称词尾。词干通过去掉不定式的 -en 或 -n 获得。词尾分别为 ich -e, du -st, er/sie/es -t, wir -en, ihr -t, sie/Sie -en。
machen → mach- + e, st, t, en, t, en
Some spelling modifications occur when the stem ends in -t, -d, or a sibilant like -s, -ß, -z. In the du and er/sie/es forms, an extra -e- is often inserted for pronunciation: du arbeitest (not arbeitst), er reist (from reisen, du reist).
当词干以 -t、-d 或咝音如 -s、-ß、-z 结尾时，会发生一些拼写调整。在 du 和 er/sie/es 形式中，通常会插入一个 -e- 以便发音：du arbeitest（而非 arbeitst），er reist（来自 reisen，du reist）。
Irregular, or strong, verbs change their stem vowel in the du and er/sie/es forms. These vowel changes are not formulas but must be memorised: e → i (e.g. sprechen → du sprichst), e → ie (sehen → du siehst), a → ä (fahren → du fährst). Treat these as ‘exception rules’ that override the standard formula.
不规则动词或强变化动词在 du 和 er/sie/es 形式中会改变词干元音。这些元音变化并非公式，必须单独记忆：e → i（如 sprechen → du sprichst），e → ie（sehen → du siehst），a → ä（fahren → du fährst）。将这些视为覆盖标准公式的“例外规则”。
5. Perfect Tense: The haben/sein + Past Participle Formula | 现在完成时：haben/sein + 过去分词公式
The Perfekt tense is the main past tense in spoken German. Its structure is a two-part formula: auxiliary verb (haben or sein) conjugated in the present tense + past participle of the main verb placed at the end of the clause.
现在完成时是德语口语中的主要过去时态。其结构是一个两部分公式：助动词（haben 或 sein）在现在时变位 + 主要动词的过去分词置于从句末尾。
Ich habe ein Buch gelesen. (I have read a book.)
Er ist nach Berlin gefahren. (He went to Berlin.)
The choice between haben and sein follows a reliable logic: sein is used with verbs indicating a change of location or state, and with a few exceptions like sein and bleiben. Most other verbs take haben.
选择 haben 还是 sein 遵循可靠的逻辑：sein 用于表示位置变化或状态变化的动词，以及少数例外如 sein 和 bleiben。大多数其他动词用 haben。
Past participles are formed with the formula: ge + verb stem + (e)t for weak verbs, and ge + (often altered) stem + en for strong verbs. Separable verbs insert -ge- between the prefix and stem: aufgemacht (opened). Verbs ending in -ieren do not add ge-: studiert.
过去分词的构成公式为：弱变化动词 ge + 词干 + (e)t；强变化动词 ge +（常有变化的）词干 + en。可分动词将 -ge- 插入前缀和词干之间：aufgemacht。以 -ieren 结尾的动词不加 ge-：studiert。
6. Modal Verbs: The ‘Verb-At-The-End’ Formula | 情态动词：“动词置末”公式
Modal verbs (können, müssen, dürfen, sollen, wollen, mögen) combine with a main verb in the infinitive. The formula in a main clause places the conjugated modal verb in the second position, while the infinitive moves to the very end of the clause.
情态动词（können, müssen, dürfen, sollen, wollen, mögen）与主要动词的不定式搭配。在主句中的公式是将变位的情态动词放在第二位，而不定式移至句末。
Ich kann sehr gut schwimmen. (I can swim very well.)
Wir müssen morgen früh aufstehen. (We must get up early tomorrow.)
In a subordinate clause, the modal verb moves to the end along with the infinitive, following the standard rule that the conjugated verb goes to the end. The formula becomes: …, dass ich schwimmen kann.
在从句中，情态动词和不定式一同移至句末，遵循变位动词置末的标准规则。公式变为：…, dass ich schwimmen kann。
Modal verbs in the present tense are irregular and follow their own stem-vowel pattern. For example, können: ich kann, du kannst, er kann, wir können, ihr könnt, sie können. Notice the singular takes a different stem vowel from the plural — a pattern shared by several modals.
情态动词的现在时不规则，遵循自己的词干元音模式。例如 können：ich kann, du kannst, er kann, wir können, ihr könnt, sie können。注意单数使用与复数不同的词干元音——这也是多个情态动词共有的模式。
7. Subjunctive II (Konjunktiv II): The Würde-Formula & Past Subjunctive | 第二虚拟式：würde 公式与过去式虚拟
The Subjunctive II is used for hypothetical situations, polite requests, and reported speech when the speaker expresses detachment. The most versatile formula for forming Subjunctive II is ‘würde + infinitive’, which parallels the English ‘would + verb’.
第二虚拟式用于假设情况、礼貌请求以及表达说话者疏远态度的间接引语。构成第二虚拟式最通用的公式是 ‘würde + 不定式’，相当于英语的 ‘would + 动词’。
Wenn ich Zeit hätte, würde ich ins Kino gehen. (If I had time, I would go to the cinema.)
For many strong verbs, a distinctive past subjunctive form exists (without würde), created by taking the simple past stem, adding Umlaut where possible, and attaching subjunctive endings (-e, -est, -e, -en, -et, -en). This is the ‘original formula’, still common for high-frequency verbs.
许多强变化动词存在独特的不使用 würde 的过去式虚拟形式，由普通过去时词干添加可能的变音再加虚拟式词尾（-e, -est, -e, -en, -et, -en）构成。这是“原始公式”，在高频动词中仍常见。
- haben → hätte, hätten (I would have)
- sein → wäre, wären (I would be)
- können → könnte, könnten (I could)
- gehen → ginge, gingen (less common, often replaced by würde gehen)
The exam often tests the ability to recognise and form both the würde-construction and the simple subjunctive forms of the key verbs. Remember that ‘wäre’ and ‘hätte’ are practically mandatory in certain fixed expressions: ‘Ich hätte gern …’ (I would like …).
考试常常考查识别和使用 würde-结构以及关键词的简单虚拟形式的能力。记住在特定固定表达中，’wäre’ 和 ‘hätte’ 几乎是强制性的：’Ich hätte gern …’（我想要……）。
8. The Passive Voice: werden + Past Participle | 被动语态：werden + 过去分词
The German passive uses the formula: a form of the auxiliary ‘werden’ + past participle of the main verb. The past participle stays at the end, and ‘werden’ carries the tense and subject agreement. In the perfect passive, the past participle of ‘werden’ (worden) is used without the usual ‘ge-‘.
德语被动语态使用这一公式：助动词 ‘werden’ 的某种形式 + 主要动词的过去分词。过去分词留在句子末尾，’werden’ 承载时态和主谓一致的标记。在完成时被动语态中，使用 ‘werden’ 的过去分词 worden，而不加常见的 ‘ge-‘。
Das Buch wird gelesen. (The book is being read. – Present passive)
Das Buch wurde gelesen. (The book was read. – Simple past passive)
Das Buch ist gelesen worden. (The book has been read. – Perfect passive)
When an agent is expressed, the preposition ‘von’ + dative is used, though often the passive is employed precisely to omit the agent. The formula with agent: subject + werden + (von + agent) + past participle.
当需要表达动作的执行者时，使用介词 ‘von’ + 与格，但被动语态常常正是为了省略执行者。带执行者的公式：主语 + werden +（von + 执行者）+ 过去分词。
A variation is the ‘dative passive’ with verbs that take a dative object, where the dative object becomes the subject in the passive: ‘Man hilft ihm.’ → ‘Ihm wird geholfen.’ The subject remains in the dative, and the verb is always in the 3rd person singular.
一种变体是“与格被动”，适用于接与格宾语的动词，其中与格宾语变为被动语态的主语：’Man hilft ihm.’ → ‘Ihm wird geholfen.’ 主语仍保持与格，动词永远使用第三人称单数。
9. Relative Clauses: The ‘Relativpronomen’ Formula | 关系从句：关系代词公式
Relative pronouns in German bridge two clauses and agree in gender and number with the antecedent, but their case is determined by the role they play within the relative clause. The forms are almost identical to the definite article, with the exception of the genitive (dessen, deren) and dative plural (denen).
德语关系代词连接两个从句，在性和数上与先行词一致，但其格由它在关系从句中扮演的角色决定。其形式几乎与定冠词相同，只有属格（dessen, deren）和与格复数（denen）是例外。
| Case | Masculine | Feminine | Neuter | Plural |
|---|---|---|---|---|
| Nominative | der | die | das | die |
| Accusative | den | die | das | die |
| Dative | dem | der | dem | denen |
| Genitive | dessen | deren | dessen | deren |
After the relative pronoun, the conjugated verb is sent to the end of the clause — the hallmark of a subordinate clause. Example: ‘Der Mann, der dort steht, ist mein Onkel.’ (The man who is standing there is my uncle.) If the relative pronoun is in the dative: ‘Die Frau, der ich das Buch gab, lächelt.’ (The woman to whom I gave the book is smiling.)
在关系代词之后，变位动词被送至从句末尾——这是从句的标志。例如：’Der Mann, der dort steht, ist mein Onkel.’（站在那里的男人是我叔叔。）如果关系代词是与格：’Die Frau, der ich das Buch gab, lächelt.’（我给书的那个女人在微笑。）
10. Prepositions & Their Case Formulas | 介词及其格的公式
German prepositions are not random; they govern fixed cases. The most reliable formulas are: prepositions of location with the dative (aus, bei, mit, nach, seit, von, zu) and prepositions of motion with the accusative (durch, für, gegen, ohne, um). Then there are two-way prepositions that take either dative (location) or accusative (direction) depending on the verb and context: an, auf, hinter, in, neben, über, unter, vor, zwischen.
德语介词不是随机的；它们支配固定格。最可靠的公式是：表示位置的介词接与格（aus, bei, mit, nach, seit, von, zu），表示运动的介词接宾格（durch, für, gegen, ohne, um
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