📚 Year 11 SQA German: Formulas & Theorems Quick Reference Handbook | 11年级 SQA 德语：公式定理速查手册
Mastering German grammar at Year 11 SQA level often feels like solving an equation — systems of rules that fit together like mathematical formulas. This handbook condenses those rules into simple formulas and theorems: from the V2 theorem that governs word order to the adjective ending agreement formulas. Use it as a quick revision tool before assessments.
掌握11年级SQA德语语法常常像是在解方程式——各种规则就像数学公式一样组合在一起。本手册将这些规则浓缩为简单的公式与定理：从主导语序的动词二位定理到形容词词尾一致公式。请在评估前用它快速复习。
1. Noun Case & Gender Formula | 名词的格与性公式
Every German noun has a gender (der, die, das) and must be used in the correct case. The case formula tells you which form of ‘the’ to use. Below is the definite article declension table — the foundation of all noun phrase formulas.
每个德语名词都有性（der, die, das），并必须用于正确格位。格公式告诉你该使用“the”的哪种形式。下表是定冠词变格表——所有名词短语公式的基础。
| Case | Masculine | Feminine | Neuter | Plural |
|---|---|---|---|---|
| Nominative (subject) | der | die | das | die |
| Accusative (direct object) | den | die | das | die |
| Dative (indirect object) | dem | der | dem | den |
| Genitive (possession) | des | der | des | der |
Remember this mnemonic formula: for masculine, ‘der’ becomes ‘den’ in accusative and ‘dem’ in dative; neuter mirrors masculine except nominative/accusative ‘das’. The accusative formula marks the direct object, dative the indirect object, genitive possession (often replaced by ‘von’ + dative).
记住这个记忆公式：阳性名词的一格der，四格变为den，三格变为dem；中性名词类似阳性但一格和四格为das。四格公式标记直接宾语，三格标记间接宾语，二格表示所有格（常用von+三格替代）。
2. Verb Conjugation Formulas | 动词变位公式
Regular (weak) verbs follow the stem + ending formula. Remove ‘-en’ from the infinitive to find the stem, then add the endings in the table.
规则（弱变化）动词遵循“词干+词尾”公式。从不定式去掉-en得到词干，然后加上表中的词尾。
| Pronoun | Ending | machen (to make/do) |
|---|---|---|
| ich | -e | mache |
| du | -st | machst |
| er/sie/es | -t | macht |
| wir | -en | machen |
| ihr | -t | macht |
| sie/Sie | -en | machen |
This is the ‘e-st-t-en-t-en’ formula. For stems ending in -d or -t (e.g. arbeiten), insert an extra -e before -st and -t: du arbeitest, er arbeitet. Irregular verbs like ‘sein’ and ‘haben’ must be memorised separately: sein (bin, bist, ist, sind, seid, sind); haben (habe, hast, hat, haben, habt, haben).
这就是“e-st-t-en-t-en”公式。对于词干以-d或-t结尾的动词（如arbeiten），在-st和-t前插入一个-e：du arbeitest, er arbeitet。像sein和haben这样的不规则动词需单独记忆：sein (bin, bist, ist, sind, seid, sind); haben (habe, hast, hat, haben, habt, haben)。
3. The V2 Theorem (Main Clause) | 动词二位定理（主句）
V2 Theorem: Subject/Phrase + Conjugated Verb + …
The ‘verb-second’ theorem states that in a German declarative main clause, the conjugated verb must be the second element. The first position can be the subject, an adverb of time, a prepositional phrase, or even an object. If you bring another element to the front, the subject moves directly after the verb.
“动词二位”定理指出，在德语陈述主句中，变位动词必须是第二个成分。第一位可以是主语、时间副词、介词短语甚至宾语。如果你把其他成分提到第一位，主语就必须紧跟在动词之后。
Example: ‘Ich spiele Tennis.’ (Subject first) vs ‘Morgen spiele ich Tennis.’ (Time first). The formula remains fixed: the verb never leaves second position.
例句：’Ich spiele Tennis.’（主语首位）对比 ‘Morgen spiele ich Tennis.’（时间首位）。公式固定不变：动词永远不离第二位。
4. The TMP Adverbial Formula | 时间-方式-地点状语公式
TMP Sequence: Time → Manner → Place
When a sentence contains multiple adverbials, they almost always follow the TMP formula: Time (when?), Manner (how?), Place (where?). This is a key word-order rule for SQA writing and speaking.
当句子含有多个状语时，它们几乎总是遵循TMP公式：时间（何时？）→ 方式（如何？）→ 地点（哪里？）。这是SQA写作和口语中的关键语序规则。
Example: ‘Ich fahre am Morgen mit dem Bus zur Schule.’ (Time: am Morgen, Manner: mit dem Bus, Place: zur Schule). Breaking the TMP order can sound unnatural, though it is not strictly ungrammatical.
例句：’Ich fahre am Morgen mit dem Bus zur Schule.’（时间：am Morgen，方式：mit dem Bus，地点：zur Schule）。打破TMP顺序会听起来不自然，尽管并非严格不合语法。
5. Modal Verb Sentence Frame | 情态动词语序框架
Modal + … + Infinitive (end)
Modal verbs (können, müssen, dürfen, sollen, wollen, mögen) work as a frame: the conjugated modal occupies the second position, and the main verb infinitive is pushed to the end of the clause. This is an essential formula for expressing ability, necessity, permission and desire.
情态动词（können, müssen, dürfen, sollen, wollen, mögen）形成一个框架：变位的情态动词占据第二位，而主要动词的不定式被推到句末。这是表达能力、必要性、许可和愿望的基本公式。
Example: ‘Ich kann gut schwimmen.’ (can swim well). ‘Du musst die Hausaufgaben machen.’ (must do homework). In questions: ‘Kannst du mir helfen?’ modal in first place, infinitive at end.
例句：’Ich kann gut schwimmen.’（游泳游得好）。’Du musst die Hausaufgaben machen.’（必须做作业）。疑问句中：’Kannst du mir helfen?’ 情态动词在第一位，不定式在末尾。
6. Perfect Tense Formula | 完成时公式
haben/sein (conjugated) + … + Past Participle (end)
The perfect tense is the most common past form in spoken German. Formula: choose the auxiliary (haben for most verbs, sein for motion/state-change intransitives), conjugate it in second position, and place the past participle at the end. The participle formula: ge + stem + t (weak) or ge + stem + en (strong). Separable prefixes wrap around ‘ge-‘: aufmachen → aufgemacht.
完成时是德语口语中最常用的过去时。公式：选择助动词（大多数动词用haben，表示移动或状态变化的不及物动词用sein），将其变位置于第二位，过去分词置于句末。分词公式：弱变化：ge + 词干 + t；强变化：ge + 词干 + en。可分离前缀包裹’ge-‘：aufmachen → aufgemacht。
Examples: ‘Ich habe einen Kuchen gebacken.’ (baked). ‘Er ist nach Berlin gefahren.’ (travelled). In subclauses, the auxiliary goes to the end, e.g. ‘…, weil ich gegessen habe’.
例句：’Ich habe einen Kuchen gebacken.’（烤了蛋糕）。’Er ist nach Berlin gefahren.’（去了柏林）。在从句中，助动词移到末尾，如’…, weil ich gegessen habe’。
7. Future Tense Formula | 将来时公式
werden (conjugated) + … + Infinitive (end)
The future tense is formed using ‘werden’ as an auxiliary. ‘Werden’ behaves exactly like a modal verb in word order: it takes the second position (or first in questions), and the main verb infinitive moves to the end. This formula is straightforward and frequently tested in SQA writing tasks.
将来时用werden作助动词构成。werden在语序上表现得和情态动词完全一样：它占据第二位（疑问句中第一位），主要动词不定式移到末尾。该公式简单明了，在SQA写作任务中经常考到。
Example: ‘Ich werde morgen ins Kino gehen.’ (I will go to the cinema). ‘Wirst du das machen?’ (Will you do that?). Remember, the infinitive cannot be separated from the auxiliary by a full stop.
例句：’Ich werde morgen ins Kino gehen.’（我明天将去看电影）。’Wirst du das machen?’（你会做那个吗？）。记住，不定式和助动词不能被句号分隔开来。
8. Adjective Ending Formulas | 形容词词尾公式
Adjective endings in German depend on the preceding article, gender, case, and number — a system of ‘agreement’. There are three main declension schemes. The tables below summarise the formulas for definite article, indefinite article, and no article (strong declension).
德语形容词词尾取决于前面的冠词、性、格和数——这是一个“一致”系统。主要有三种变格方案。下表总结了定冠词后、不定冠词后、零冠词（强变化）的公式。
After der/die/das (definite article):
定冠词der/die/das后：
| Case | Published by TutorHao | Year 11 德语 Revision Series | aleveler.com
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