📚 Year 13 WJEC German: Formula and Theorem Quick Reference Handbook | WJEC 13年级德语：公式定理速查手册
This handbook distils the core grammar of A-level German into precise "formulas" and "theorems" that govern word order, verb conjugation, case endings and clause construction. Internalising these patterns will sharpen accuracy in written and spoken tasks for the WJEC examination, helping you to manipulate language fluently rather than guessing rules.
这本速查手册将A-level德语的核心语法提炼为精准的“公式”和“定理”，涵盖词序、动词变位、格词尾以及从句构造等规则。内化这些模式有助于提升你在WJEC考试中书面与口语任务的准确性，让你流畅地驾驭语言，而非依赖猜测。
1. Regular Verb Present Tense Formula | 规则动词现在时公式
The present tense of a regular German verb is formed by removing the -en or -n from the infinitive and attaching the appropriate ending. The formula is: stem + -e (ich), -st (du), -t (er/sie/es), -en (wir), -t (ihr), -en (sie/Sie). For machen, this yields: ich mache, du machst, er macht, wir machen, ihr macht, sie machen. Stem changes never appear in regular verbs; this constancy makes it a reliable "theorem" for hundreds of verbs.
德语规则动词的现在时由不定式去掉 -en 或 -n 后附加相应词尾构成。公式为：词干 + -e（ich）、-st（du）、-t（er/sie/es）、-en（wir）、-t（ihr）、-en（sie/Sie）。以 machen 为例：ich mache, du machst, er macht, wir machen, ihr macht, sie machen。规则动词从不发生词干元音变化，这种恒定性使之成为适用于数百个动词的可靠“定理”。
Present = stem + ending (e, st, t, en, t, en)
2. Irregular Verb Stem-Vowel Change Theorem | 强变化动词词干元音定理
terns are e → i (geben → du gibst, er gibt), e → ie (sehen → du siehst, er sieht), and a → ä (fahren → du fährst, er fä esent ending. This is not random: it follows historical sound shifts that now function as a dependable pattern across A-level texts.
许多强变化动词在第二、第三人称单数中遵循可预测的元音变换规则：词干元音发生特定变化。常见模式为 e → i（geben → du gibst, er gibt）、e → ie（sehen → du siehst, er sieht）以及 a → ä（fahren → du fährst, er fährt）。一旦记住词干元音，词尾仍然采用标准现在时词尾，因此公式为：变化后的词干 + 标准现在时词尾。这并非随机现象，而是源于历史音变，如今已成为A-level文本中可靠的规律。
3. Perfect Tense Construction Formulas | 现在完成时构成公式
The Perfekt is a two-part formula: auxiliary verb (haben or sein in conjugated present form) + past participle (Partizip II). The choice of auxiliary follows a clear theorem: sein is used for verbs indicating movement from A to B or a change of state (gehen, fahren, aufwachen, sterben); haben applies to all other verbs, including all transitive verbs. The participle formula for regular verbs is ge + stem + t (machen → gemacht), while many strong verbs use ge + modified stem + en (gehen → gegangen). Separable verbs insert -ge- between prefix and stem, as in aufmachen → aufgemacht; inseparable verbs drop the ge-, as in verstehen → verstanden.
现在完成时由两部分构成：助动词（haben 或 sein 的现在时变位形式）+ 过去分词（Partizip II）。助动词的选择遵循明确定理：表示从某处移动到另一处或状态变化的动词用 sein（gehen, fahren, aufwachen, sterben）；其他所有动词（包括所有及物动词）用 haben。规则动词的分词公式为 ge + 词干 + t（machen → gemacht），而许多强变化动词使用 ge + 变化词干 + en（gehen → gegangen）。可分动词将 -ge- 插在前缀与词干之间，例如 aufmachen → aufgemacht；不可分动词则省略 ge-，如 verstehen → verstanden。
Perfekt = haben/sein (present) + Partizip II
4. Noun Declension and Case Formula | 名词变格与格公式
le is: der, die, das (nominative) → den, die, das (accusative) → dem, der, dem (dative) → des, der, des (genitive). Plural forms simplify: die, die, den, der. Masculine and neuter nouns often add -s or -es in the genitive singular (des Mannes, des Buchs); weak masculine nouns add -n or -en in all cases except nominative (der Junge → den Jungen, dem Jungen, des Jungen). Treat these as a "declension theorem" that applies consistently across A-level written expression.
德语名词依据格、性和数的不同，冠词会发生变化，有时名词本身也需添加词尾。定冠词的基本公式为：der, die, das（第一格）→ den, die, das（第四格）→ dem, der, dem（第三格）→ des, der, des（第二格）。复数形式则简化为：die, die, den, der。阳性和中性名词单数第二格常加 -s 或 -es（des Mannes, des Buchs）；阳性弱变化名词在除第一格以外的所有格需加 -n 或 -en（der Junge → den Jungen, dem Jungen, des Jungen）。可将这些视作一条贯穿A-level书面表达的“变格定理”。
5. Adjective Ending Formulas (Three Tables) | 形容词词尾公式（三表定理）
Adjective endings follow three distinct patterns determined by the preceding article. All can be expressed as compact formulas.
形容词词尾根据前置冠词的类型遵循三种不同模式，均可表示为紧凑的公式。
| Case/Gender | Definite Article (der-Word) Ending | Indefinite Article (ein-Word) Ending | No Article (Strong) Ending |
|---|---|---|---|
| Nominative M | -e | -er | -er |
| Nominative F | -e | -e | -e |
| Nominative N | -e | -es | -es |
| Accusative M | -en | -en | -en |
| Accusative F/Pl | -e / -en | -e / -en | -e / -e |
| Dative (all) | -en | -en | -em (M/N), -er (F), -en (Pl) |
| Genitive M/N | -en | -en | -en |
The theorem: after a definite article the ending is mostly -e or -en; after an indefinite article the ending carries the strong signal where the article lacks it; without an article the adjective takes over the full strong ending of the definite article (except neuter/adjective genitive -en). This three-table logic governs nearly all attributive adjective usage.
其定理为：定冠词后词尾多为 -e 或 -en；不定冠词后，在冠词缺少强变化信号之处由形容词词尾承担；无冠词时，形容词几乎完全承担定冠词的强变化词尾（仅中性/形容词第二格 -en 为例外）。这三张表基本上支配了所有定语形容词的用法。
6. Modal Verb Construction and Double Infinitive Theorem | 情态动词结构及双不定式定理
Modal verbs (koennen, duerfen, muessen, wollen, sollen, moegen) follow a strict formula in the present and imperfect: the modal verb is conjugated and takes the second position, while the main verb appears in the infinitive at the end of the clause. In the perfect tense, however, a double infinitive construction occurs: when the modal is combined with another infinitive, the past participle of the modal reverts to its infinitive form. Formula: haben + infinitive of main verb + infinitive of modal (‘Ich habe das machen muessen.’). This "double infinitive theorem" overrides the expected participle, and the finite verb (haben) appears before the two infinitives.
情态动词（koennen, duerfen, muessen, wollen, sollen, moegen）在现在时和过去时中遵循严格公式：情态动词变位后置于第二位，而主动词以不定式形式位于句末。但在现在完成时中会出现双不定式结构：当情态动词与另一不定式连用时，情态动词的过去分词会还原为不定式。公式：haben + 主动词不定式 + 情态动词不定式（‘Ich habe das machen muessen.’）。这条“双不定式定理”替代了预期的过去分词，且限定动词 haben 置于两个不定式之前。
Perfect modal = haben + infinitive + infinitive modal
7. Passive Voice Formulas (Vorgangs- und Zustandspassiv) | 被动语态公式（过程被动与状态被动）
The passive transforms the focus from the agent to the action or state. The process passive (Vorgangspassiv) formula is werden + Partizip II. In the perfect tense, the participle of werden shortens to worden without ge-: ist/war + Partizip II + worden. The state passive (Zustandspassiv) describes the result and uses sein + Partizip II tasks, you also need the passive with modal verbs: modal + Partizip II + werden (infinitive). E.g., ‘Das Problem kann geloest werden.’ Treat this as a combined formula.
被动语态将焦点从施事者转移到动作或状态。过程被动（Vorgangspassiv）的公式为 werden + Partizip II。在完成时中，werden 的过去分词省去 ge- 变为 worden：ist/war + Partizip II + worden。状态被动（Zustandspassiv）描述结果，使用 sein + Partizip II。由此我们得到两条定理：动态被动 = werden + Partizip II，静态被动 = sein + Partizip II。在考题中，还需掌握情态动词与被动结合的公式：情态动词 + Partizip II + werden（不定式），如 ‘Das Problem kann geloest werden.’，可视作一条组合公式。
8. Subjunctive (Konjunktiv) Formation Theorems | 虚拟式构成定理
Subjunctive II forms generally derive from the imperfect stem: if the imperfect is strong, it receives umlaut where possible plus subjunctive endings (-e, -est, -e, -en, -et, -en). Formula: imperfect stem (with umlaut if applicable) + subjunctive ending. For weak verbs, the subjunctive II coincides with the imperfect, so the wuerde + infinitive formula is preferred. Subjunctive I, crucial for reported speech in formal texts, uses the present stem + subjunctive I endings: stem + -e, -est, -e, -en, -et, -en. The only consistent exception is sein, which has distinct stems. The focal theorem: Subjunctive I (stem + specific endings) signals indirect speech; Subjunctive II (imperfect stem + umlaut + endings) expresses unreality, condition and politeness.
第二虚拟式通常由过去时词干衍生：若过去时为强变化，则尽可能加上变元音，再附加虚拟式词尾（-e, -est, -e, -en, -et, -en）。公式：过去时词干（可能加变元音）+ 虚拟式词尾。弱变化动词的第二虚拟式与过去时形式重合，因此更常使用 wuerde + 不定式公式。第一虚拟式在正式文本的间接引语中至关重要，采用现在时词干 + 第一虚拟式词尾：词干 + -e, -est, -e, -en, -et, -en。唯一一致的例外是 sein，有其独特词干。核心定理为：第一虚拟式（词干+特定词尾）标示间接引语；第二虚拟式（过去时词干+变元音+词尾）表达非现实、条件和礼貌。
Subjunctive II = imperfect stem (+Umlaut) + e/est/e/en/et/en
9. Word Order Theorems: Verb Position and Satzklammer | 词序定理：动词位置与句框结构
Main clause theorem: the conjugated verb occupies position 2, while other elements (subject, object, adverbial) cluster around it. The Satzklammer (sentence bracket) arises with separable prefixes, modals and perfects: the prefix or infinitive/participle closes the bracket at the end. Subordinate clause theorem: the conjugated verb is catapulted to the final position, preceded by the conjunction that introduces the clause. Thus, ‘weil ich das Buch lese’ obeys the formula conjunction + S + O + ... + verb. When multiple verbs appear at the end, the finite verb (often the auxiliary) comes last in a reverse order compared to English. This extended word-order law ensures that all non-finite elements precede the finite verb in subordinate clauses.
主句定理：变位动词占据第二位，而其他成分（主语、宾语、状语）围绕其分布。句框结构（Satzklammer）出现在可分前缀、情态动词以及完成时中：前缀或不定式/分词在句末关闭句框。从句定理：变位动词被推至句末，并由连词引导。因此，‘weil ich das Buch lese’ 遵循公式 连词 + 主语 + 宾语 + ... + 动词。当句末出现多个动词时，限定动词（常为助动词）通常置于最后，顺序与英语相反。这条扩展词序定律确保所有非限定成分在从句中都位于限定动词之前。
10. Relative Pronoun and Relative Clause Theorem | 关系代词与关系从句定理
The relative pronoun mirrors the definite article, carrying the gender and number of its antecedent but the case determined by its function within the relative clause. The formula is: definite article-like pronoun + relative clause with verb at the end. Prepositions preceding the relative pronoun force the dative or accusative as required. The relative genitive (dessen/deren) agrees with the antecedent in gender and number. When a whole clause is referred to, the neuter was is used. This "relative theorem" ensures that every relative clause meets the A-level requirement for complex sentences, e.g., ‘Der Autor, dessen Buch ich lese, ist bekannt.’
关系代词形如定冠词，性、数与先行词一致，格则取决于其在关系从句中的功能。公式为：定冠词式代词 + 动词位于句末的关系从句。介词置于关系代词前时，需根据习惯要求支配第三格或第四格。关系第二格（dessen/deren）与先行词保持性数一致。当指代整个从句时，使用中性代词 was。这条“关系定理”确保每条关系从句都能满足A-level复杂句型要求，例如 ‘Der Autor, dessen Buch ich lese, ist bekannt.’。
11. Preposition Case Governance Theorem | 介词格支配定理
Each preposition dictates a fixed case or a dual case contingent on motion versus location. Formula for two-way prepositions (an, auf, hinter, in, neben, ueber, unter, vor, zwischen): if movement towards a destination (Wohin?), use accusative; if indicating a static location (Wo?), use dative. Fixed prepositions are memorised in sets: dative-only (aus, bei, mit, nach, seit, von, zu) and accusative-only (bis, durch, fuer, gegen, ohne, um). The genitive prepositions (trotz, waehrend, wegen, innnerhalb) are increasingly used with the dative in speech, but exam writing still rewards the genitive. This case governance theorem is the scaffolding for prepositional phrase accuracy.
每个介词支配固定的格，或依据运动与位置在两者之间选择。两用介词（an, auf, hinter, in, neben, ueber, unter, vor, zwischen）的公式为：若表达朝向目的地的运动（Wohin?），用第四格；若指示静止位置（Wo?），用第三格。固定介词按组记忆：仅支配第三格的（aus, bei, mit, nach, seit, von, zu）和仅支配第四格的（bis, durch, fuer, gegen, ohne, um）。第二格介词（trotz, waehrend, wegen, innnerhalb）在口语中越来越常接第三格，但考试书面表达仍以第二格为佳。这一格支配定理是介词短语准确性的支架。
12. Participial Construction Formulas | 分词结构公式
cede the participle (present or past), and the whole block acts like an adjective before the noun. For example, ‘der die Sprache lernende Student’ is equivalent to ‘der Student, der die Sprache lernt’. The past participle with a passive sense follows a similar pattern: ‘das viel gelobte Buch’ = the book that has been much praised. In the WJEC reading and writing tasks, deconstructing and deploying these forms shows advanced grammatical control. The theorem: participial phrase = (object/complement) + participle, placed before the noun with adjectival ending agreement.
扩展分词短语是正式学术德语的标志，充当名词前的修饰语。公式为：所有补足语和状语置于分词（现在分词或过去分词）之前，整个板块如同一个形容词置于名词前。例如，‘der die Sprache lernende Student’ 等同于 ‘der Student, der die Sprache lernt’。带有被动意味的过去分词遵循相似模式：‘das viel gelobte Buch’ 即备受赞誉的书。在WJEC阅读与写作任务中，解构并运用这些形式能展现高级语法驾驭能力。其定理为：分词短语 =（宾语/补足语）+ 分词，置于名词前，并保持形容词词尾一致性。
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