📚 Formula & Theorem Quick Reference Handbook for Year 8 Cambridge Chinese | 剑桥Year 8中文公式定理速查手册
This handbook compiles essential rules, formulas, and theorems for Year 8 Cambridge Chinese learners. Treat these as your quick lookup for pinyin, characters, grammar, and sentence patterns to strengthen your Mandarin foundation.
本手册为剑桥Year 8中文学习者汇编了核心规则、公式和定理。将这些视为拼音、汉字、语法和句型速查宝典，助你夯实中文基础。
1. Pinyin Spelling Rules | 拼音拼写规则公式
Rule 1: When the finals 'i', 'u', 'ü' stand alone as syllables, they are written as 'yi', 'wu', 'yu' respectively.
规则1：韵母 i, u, ü 自成音节时，分别写作 yi, wu, yu。
Rule 2: The umlaut (ü) is omitted after the initials j, q, x, so 'ju' is actually jü, but after n, l the umlaut remains, e.g., nü, lü.
规则2：ü 在声母 j, q, x 后省略两点，因此 'ju' 实际发音是 jü；但在 n, l 后两点保留，如 nü, lü。
Rule 3: The compound finals 'iou', 'uei', 'uen' are abbreviated to 'iu', 'ui', 'un' when preceded by an initial. (e.g., liu from liou, dui from duei, lun from luen).
规则3：复韵母 iou, uei, uen 在前面有声母时，缩写为 iu, ui, un（如 liou → liu，duei → dui，luen → lun）。
Rule 4: Tone marks are placed on the main vowel following the sequence: a, o, e, i, u, ü. If 'i' and 'u' occur together, the mark goes on the second one.
规则4：声调标在主要元音上，顺序为 a, o, e, i, u, ü。若 i 和 u 并列，则标在后一个元音上。
2. Tone Sandhi Theorems | 变调定理
tone syllables are consecutive, the first one changes to second tone in natural speech. (nǐ hǎo → ní hǎo in pronunciation).
定理1：两个三声相连时，前一个三声变读为二声（如 nǐ hǎo 实际读成 ní hǎo）。
Theorem 2: The character '一' (yī) changes: it is fourth tone before a first, second, or third tone (yì tiān); but second tone before a fourth tone (yí dìng).
定理2：“一”的变调：在一、二、三声前读四声（如 yì tiān）；在四声前读二声（如 yí dìng）。
Theorem 3: The character '不' (bù) is fourth tone except when followed by another fourth tone, where it becomes second tone (bù hǎo but bú duì).
定理3：“不”本调是四声，但在另一个四声前变为二声（bù hǎo 但 bú duì）。
Theorem 4: In certain adjectives in reduplicated form (AA or AABB), the second syllable often takes the first tone and may add an -r sound in northern speech.
定理4：重叠形容词（如 AA、AABB 式）中，第二个音节常变为一声并可儿化。
3. Stroke Order Formulas | 笔画顺序公式
Formula 1: Horizontal before vertical (e.g., 十: 一, 丨).
公式1：先横后竖（如“十”：先写一，再写丨）。
Formula 2: Left-falling before right-falling (e.g., 人: 丿, 乀).
公式2：先撇后捺（如“人”：先写丿，再写乀）。
Formula 3: From top to bottom (e.g., 三: top stroke first).
公式3：从上到下（如“三”：从上边一笔开始）。
Formula 4: From left to right (e.g., 川: leftmost stroke first).
公式4：从左到右（如“川”：从左边的笔画开始）。
Formula 5: Outside before inside (e.g., 月: outer frame, then inner strokes).
公式5：先外后内（如“月”：先写外框，再写内部）。
Formula 6: Inside before bottom enclosing (e.g., 这: write the inner component first, then the bottom radical 辶).
公式6：先内后外（如“这”：先写内部“文”，再写走之底）。
Formula 7: Middle before two sides (e.g., 小: central hook first, then left and right dots).
公式7：先中间后两边（如“小”：先写中间竖钩，再写左、右点）。
4. Radical-Recognition Law | 部首识别定理
Law: Most Chinese characters consist of a semantic radical that hints at meaning. Recognising common radicals speeds up character learning.
定理：大多汉字包含表意部首。识别常见部首能加速汉字学习。
Examples: 口 (mouth) relates to eating/speaking: 吃、喝、唱；扌 (hand) relates to actions: 打、拍、拉；氵 (water) relates to liquids: 河、海、洗。
例如：口字旁与吃、说相关：吃、喝、唱；提手旁与手部动作相关：打、拍、拉；三点水与液体相关：河、海、洗。
Other key radicals: 木 (wood/trees), 火 (fire), 女 (female), 心/忄 (heart/emotions), 日 (sun/time), 月 (moon/flesh), 足 (foot).
其他关键部首：木（树木）、火、女、心/忄（情感）、日（太阳/时间）、月（肉/身体）、足。
5. Word Formation Patterns | 构词法公式
Pattern 1 (Coordinative): Two characters with similar meanings combine, e.g.,
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