📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
In IGCSE AQA German, mastering the language is like understanding a series of logical formulas. Grammar structures follow predictable patterns, and once you learn these “formulas,” you can construct accurate sentences with confidence. This quick reference handbook presents essential German grammar rules as clear formulas, complete with examples to help you revise efficiently.
在 IGCSE AQA 德语中，掌握语言就像理解一系列逻辑公式。语法结构遵循可预测的模式，一旦学会这些“公式”，你就能自信地构造正确的句子。本速查手册以清晰的公式形式呈现核心德语语法规则，并配有实例，助你高效复习。
1. The Basic Sentence Structure Formula | 基本句子结构公式
Every German main clause follows a formula: Subject + Verb + Other Elements. The conjugated verb is always the second idea in the sentence, even if the first element is not the subject. This is known as the V2 rule.
每个德语主句都遵循一个公式：主语 + 动词 + 其他成分。变位动词总是句子的第二个“意念”，即使第一个成分不是主语。这被称为 V2 规则。
Formula: (Topic) + Verb + Subject + ...
| Pattern | Example | Translation |
| Subject - Verb - Object | Ich spiele Fußball. | I play football. |
| Time - Verb - Subject - Object | Jeden Tag spiele ich Fußball. | Every day I play football. |
2. Present Tense Verb Conjugation Formula | 现在时动词变位公式
Regular verbs follow a stem + ending formula. Remove -en from the infinitive to find the stem, then add the appropriate endings. Irregular verbs may change the stem vowel for du and er/sie/es.
规则动词遵循词干 + 词尾的公式。去掉不定式的 -en 得到词干，然后加上相应的词尾。不规则动词在 du 和 er/sie/es 形式中可能改变词干元音。
Formula: stem + (e, st, t, en, t, en) – example: spiel-
| Person | Ending | spielen | Irregular: lesen (e→ie) |
| ich | -e | spiele | lese |
| du | -st | spielst | liest |
| er/sie/es | -t | spielt | liest |
| wir | -en | spielen | lesen |
| ihr | -t | spielt | lest |
| sie/Sie | -en | spielen | lesen |
3. The Perfect Tense Formula | 完成时公式
The perfect tense describes completed past actions. It uses an auxiliary verb (haben or sein) conjugated in the present tense plus the past participle of the main verb. The past participle usually begins with ge- and ends in -t (weak) or -en (strong).
完成时描述已完成的过去动作。它使用助动词 haben 或 sein 的现在时变位加上主要动词的过去分词。过去分词通常以 ge- 开头，以 -t（弱变化）或 -en（强变化）结尾。
Formula: haben/sein (present) + past participle (at end)
| Verb type | Auxiliary | Past participle | Example sentence |
| Weak (machen) | haben | ge-mach-t | Ich habe meine Hausaufgaben gemacht. |
| Strong (fahren) | sein | ge-fahr-en | Wir sind nach Berlin gefahren. |
| Mixed (bringen) | haben | ge-brach-t | Sie hat ein Geschenk gebracht. |
4. Future Tense Formula | 将来时公式
The future tense is formed with the present tense of werden plus an infinitive at the end of the clause. It expresses future intentions or predictions. In spoken German, the present tense is often used with a time expression instead.
将来时由 werden 的现在时加上位于句末的不定式构成。它表达未来的意图或预测。在口语中，通常用现在时配时间状语来代替将来时。
Formula: werden (conjugated) + ... + infinitive
| Person | werden | Example | Translation |
| ich | werde | Ich werde ins Kino gehen. | I will go to the cinema. |
| du | wirst | Du wirst es verstehen. | You will understand it. |
| er/sie/es | wird | Es wird regnen. | It will rain. |
5. Modal Verb Sentence Formula | 情态动词句公式
Modal verbs (können, müssen, dürfen, sollen, wollen, möchten) modify the action of a main verb. The modal verb is conjugated and occupies the V2 position, while the main verb appears as an infinitive at the very end of the clause.
情态动词（können, müssen, dürfen, sollen, wollen, möchten）修饰主要动词的动作。情态动词变位后占据 V2 位置，而主动词以不定式形式放在句末。
Formula: Subject + modal verb + ... + infinitive
| Modal verb | Meaning | Example | Translation |
| können (kann) | can / to be able to | Ich kann gut schwimmen. | I can swim well. |
| müssen (muss) | must / to have to | Du musst dein Zimmer aufräumen. | You must tidy your room. |
| wollen (will) | to want to | Er will Arzt werden. | He wants to become a doctor. |
6. The Case System Formula | 格系统公式
German has four cases that signal the function of nouns and pronouns. The definite and indefinite articles change according to case and gender. Think of case endings as a formula slot: article + (adjective) + noun.
德语有四个格，用来标示名词和代词的功能。定冠词和不定冠词根据格和性别变化。把格词尾看作公式插槽：冠词 +（形容词）+ 名词。
Formula: Case marker (article) + [adjective ending] + noun
| Case | Masc. | Fem. | Neut. | Plural |
| Nominative | der / ein | die / eine | das / ein | die / – |
| Accusative | den / einen | die / eine | das / ein | die / – |
| Dative | dem / einem | der / einer | dem / einem | den / – (+n on noun) |
| Genitive | des / eines (+s) | der / einer | des / eines (+s) | der / – |
7. Adjective Endings Formula | 形容词词尾公式
Adjective endings depend on three factors: the gender of the noun, the case, and whether a definite article, indefinite article, or no article precedes the adjective. This creates a grid-like formula that can be learned systematically.
形容词词尾取决于三个因素：名词的性、格，以及形容词前面是定冠词、不定冠词还是零冠词。这形成了一个网格式的公式，可以系统地学习。
Formula: article signal + adjective ending = correct form
| After der/die/das (Weak endings) | ||||
| Case | Masc. | Fem. | Neut. | Pl. |
| Nominative | -e | -e | -e | -en |
| Accusative | -en | -e | -e | -en |
| Dative | -en | -en | -en | -en |
| Genitive | -en | -en | -en | -en |
Example: der kleine Hund (the small dog), mit dem kleinen Hund (with the small dog).
8. Word Order After Conjunctions Formula | 连词后的语序公式
Subordinating conjunctions such as weil, dass, ob, wenn, als, bevor change word order. They send the conjugated verb to the end of the clause. Coordinating conjunctions like und, aber, oder, denn do not affect word order (position 0).
从属连词如 weil, dass, ob, wenn, als, bevor 改变语序。它们把变位动词送到从句末尾。并列连词如 und, aber, oder, denn 不影响语序（位置 0）。
Formula: Subordinating conjunction + Subject + ... + verb (at end)
| Conjunction | Example | Verb position |
| weil (because) | Ich bleibe zu Hause, weil ich krank bin. | bin at end |
| dass (that) | Ich denke, dass er recht hat. | hat at end |
| wenn (if/when) | Wenn ich Zeit habe, komme ich mit. | habe at end of clause |
9. The "Weil" Clause Formula | “weil”从句公式
'Weil' introduces a reason clause and always forces the verb to the end. This is one of the most frequently tested structures in IGCSE writing and speaking. Remember: weil + subject + other info + verb.
'Weil' 引出原因从句，并总是把动词推到句末。这是 IGCSE 写作和口语中最常考的结构之一。记住：weil + 主语 + 其他信息 + 动词。
Formula: Main clause, weil + subject + ... + verb.
| Correct | Incorrect (common mistake) | Translation |
| Ich esse viel Obst, weil es gesund ist. | weil es ist gesund. | I eat a lot of fruit because it is healthy. |
| Er kann nicht kommen, weil er arbeiten muss. | weil er muss arbeiten. | He can't come because he has to work. |
10. Preposition Case Triggers Formula | 介词支配格公式
Prepositions in German govern specific cases. Some always take accusative, some dative, and some can take either depending on movement vs. location (two-way prepositions). Treat each preposition as a case trigger in your sentence formula.
德语介词支配特定的格。有些总是接宾格，有些接与格，还有一些根据运动与位置的不同接第二格或第三格（双向介词）。在你的句子公式中，每个介词都是一个格的触发器。
Formula: Preposition + correct case article + noun
| Accusative only | Dative only | Two-way (Acc/Dat) |
| durch, für, gegen, ohne, um | aus, bei, mit, nach, seit, von, zu | an, auf, hinter, in, neben, über, unter, vor, zwischen |
| Für den Chef (for the boss) | mit dem Bus (by bus) | in die Schule (acc: movement) / in der Schule (dat: location) |
11. Relative Clause Formula | 关系从句公式
A relative clause gives more information about a noun. The relative pronoun (der, die, das, etc.) must match the gender and number of the antecedent but the case depends on its function inside the relative clause. The conjugated verb goes to the end.
关系从句提供关于名词的更多信息。关系代词（der, die, das 等）必须与先行词的性和数一致，但其格取决于它在从句中的功能。变位动词放在句末。
Formula: Main clause, relative pronoun + ... + verb (end)
| Antecedent | Relative pronoun (Nom.) | Example |
| der Mann (masc.) | der | Das ist der Mann, der hier wohnt. |
| die Frau (fem.) | die | Kennst du die Frau, die da steht? |
| das Kind (neut.) | das | Das Kind, das lacht, ist mein Bruder. |
12. The Imperative Formula | 祈使句公式
The imperative mood is used for commands and requests. It has three forms: du (informal singular), ihr (informal plural), and Sie (formal). The formula depends on the pronoun: du-imperative uses the stem (with optional -e), ihr-imperative uses the stem + t, and Sie-imperative uses the infinitive + Sie.
祈使语气用于命令和请求。它有三种形式：du（非正式单数）、ihr（非正式复数）和 Sie（正式）。公式取决于代词：du 祈使句使用词干（可选 -e），ihr 祈使句使用词干 + t，Sie 祈使句使用不定式 + Sie。
Formula: (Verb stem) + ... ! / (Verb stem + t) + ... ! / (Infinitive) + Sie + ... !
| Form | Pattern | Example (kommen) | Translation |
| du | stem (+ e) | Komm(e) hierher! | Come here! (to one friend) |
| ihr | stem + t | Kommt hierher! | Come here! (to several friends) |
| Sie | infinitive + Sie | Kommen Sie hierher! | Come here! (formal) |
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