📚 A-Level Cambridge Geography: Formula and Theorem Quick Reference Handbook | A-Level Cambridge 地理：公式定理速查手册
Welcome to this quick reference handbook designed for Cambridge International A-Level Geography (9696). It brings together the essential formulae, equations, and models that appear across both physical and human geography topics. Use this guide to reinforce your understanding of quantitative reasoning in population studies, urban systems, hydrology, land degradation, and inequality measurement. Each entry provides the mathematical expression alongside concise bilingual explanations, ensuring you can interpret and apply them accurately in exam contexts.
欢迎使用本手册，专为剑桥国际A-Level地理（9696）设计。手册汇集了自然地理与人文地理各专题中出现的关键公式、方程与模型。通过本指南，你可以强化人口研究、城市系统、水文、土壤侵蚀以及不平等度量等领域的定量推理能力。每一公式条目都配有简明的中英双语解释，帮助你在考试中准确理解和应用。
1. Population Change Formulae | 人口变化公式
These demographic formulae measure the fundamental components of population change: births, deaths, and migration. They form the basis for understanding population dynamics at national and regional scales.
以下人口统计公式衡量人口变化的基本组成部分：出生、死亡和迁移。这些是理解国家和地区人口动态的基础。
| Formula / 公式 | Description / 说明 |
|---|---|
| CBR = (B ÷ P) × 10³ |
Crude Birth Rate: number of live births per 1000 people in a year. 粗出生率：一年内平均每千人口中的活产婴儿数。 |
| CDR = (D ÷ P) × 10³ |
Crude Death Rate: number of deaths per 1000 people in a year. 粗死亡率：一年内平均每千人口中的死亡人数。 |
| RNI = (CBR − CDR) ÷ 10 |
Rate of Natural Increase (percentage). Converts per 1000 values into a percentage change. 自然增长率（百分比）。将千分比转换为百分比变化。 |
| P₂ = P₁ + (B − D) + (I − E) |
Total population change equation: adds natural change (births minus deaths) and net migration (immigration minus emigration) to the initial population. 总人口变化方程：将自然变动（出生减死亡）和净迁移（迁入减迁出）加到初始人口上。 |
2. Fertility and Mortality Measures | 生育与死亡指标
Beyond crude rates, geographers use age-specific measures to refine fertility and mortality analysis. These give more accurate insights into reproductive patterns and health conditions.
在粗率之外，地理学家使用分年龄指标来更精细地分析生育和死亡率，从而更准确地洞察生育模式和健康状况。
| Formula / 公式 | Description / 说明 |
|---|---|
| GFR = (B ÷ Pf,15–49) × 10³ |
General Fertility Rate: live births per 1000 females aged 15–49. 一般生育率：每千名15–49岁女性中的活产数。 |
| TFR = Σ (ASFRa × 5) ÷ 1000 |
Total Fertility Rate: average number of children a woman would have if she experienced current age-specific fertility rates throughout her reproductive life. ASFRs are per 1000; multiplying by age-group width (usually 5) and dividing by 1000 gives the TFR. 总和生育率：若一名妇女按照当前各年龄别生育率度过整个生育期，她平均将生育的子女数。年龄别生育率以千分比表示；乘以年龄组距（通常为5）再除以1000即得总和生育率。 |
| IMR = (D0–1 ÷ B) × 10³ |
Infant Mortality Rate: deaths of infants under one year per 1000 live births. 婴儿死亡率：每千名活产婴儿中一岁前死亡的人数。 |
3. Population Structure and Dependency | 人口结构与抚养比
Dependency ratios summarise the economic burden on the productive population. They are essential for comparing age structures and forecasting public service needs.
抚养比概括了生产性人口所承受的经济负担，对于比较年龄结构和预测公共服务需求至关重要。
| Formula / 公式 | Description / 说明 |
|---|---|
| TDR = ((P0–14 + P65+) ÷ P15–64) × 100 |
Total Dependency Ratio: number of dependents (young and old) per 100 working-age persons. 总抚养比：每百名劳动年龄人口对应的受抚养（少、老）人数。 |
| CDRyoung = (P0–14 ÷ P15–64) × 100 |
Child Dependency Ratio: young dependents per 100 working-age. 少儿抚养比：每百名劳动年龄人口对应的少年儿童人数。 |
| ODR = (P65+ ÷ P15–64) × 100 |
Old-Age Dependency Ratio: elderly dependents per 100 working-age. 老年抚养比：每百名劳动年龄人口对应的老年人数。 |
4. Urban Rank-Size Rule and Primate City | 城市位序-规模法则与首位城市
The rank-size rule is a key empirical regularity in urban geography, while the primacy index captures how dominant the largest city is in a national urban system.
位序-规模法则是城市地理学中一个重要的经验规律，而首位度指数衡量最大城市在一国城市体系中的主导程度。
| Formula / 公式 | Description / 说明 |
|---|---|
| Pr = P1 ÷ rq |
Rank-Size Rule: the population of the rth-ranked city is equal to the largest city’s population divided by rank raised to exponent q. When q = 1 (Zipf’s Law), the second city is half the size of the largest, the third is one-third, etc. 位序-规模法则：第r位城市的人口等于最大城市人口除以位序的q次方。当q=1（齐夫定律）时，第二大城市人口是最大城市的一半，第三大城市是三分之一，以此类推。 |
| Primacy Ratio = P1 ÷ P2 |
Two-city primacy index: ratio of the largest city’s population to that of the second-largest city. A value greater than 2 often indicates a primate city distribution. 双子首位度指数：最大城市与第二大城市人口之比。若比值大于2，通常意味着存在首位城市分布。 |
5. Gravity Model and Interaction | 重力模型与相互作用
Borrowing from Newtonian physics, the gravity model predicts the interaction between two places based on their mass (population) and the friction of distance. It is widely applied in retail, migration, and transport studies.
重力模型借鉴牛顿物理学，根据“质量”（人口）和距离摩擦预测两地之间的相互作用，广泛应用于零售、迁移和交通研究。
| Formula / 公式 | Description / 说明 |
|---|---|
| Iij = k × (Pi × Pj) ÷ dijβ |
General gravity model: interaction (flows) between place i and j is proportional to the product of their populations and inversely proportional to distance raised to the exponent β (often β=2). k is a scaling constant. 通用重力模型：地点i和j之间的相互作用（流量）与两地人口乘积成正比，与距离的β次方成反比（β常取2）。k为比例常数。 |
| Ba/Bb = (Pa/Pb) × (db/da)2 |
Reilly’s Law of Retail Gravitation: the ratio of retail trade attracted from an intermediate place to two competing centres a and b depends on their populations and the squared distances. 赖利零售引力定律：从中间地点吸引到两个竞争中心a和b的零售额之比，取决于各自人口和距离的平方。 |
6. Location Quotient and Specialisation | 区位商与专门化指数
The location quotient identifies regional specialisation by comparing local employment shares with a national benchmark. A value above 1 indicates that the region has a higher concentration in that sector than the national average.
区位商通过比较地方就业份额与全国基准来识别地区专业化。数值大于1表示该地区在该行业的集中度高于全国平均水平。
| Formula / 公式
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