AS Cambridge Geography: Quick Reference Handbook of Formulas & Theorems | AS 剑桥地理：公式定理速查手册

📚 AS Cambridge Geography: Quick Reference Handbook of Formulas & Theorems | AS 剑桥地理：公式定理速查手册

This compact revision guide collates the essential quantitative formulas and key theoretical theorems you need to master for the AS Cambridge Geography syllabus. Each entry presents the core idea in a simple, paired English–Chinese statement, followed by worked examples or explanatory notes where useful. Keep this handbook close for quick in-class reference and last-minute exam revision.

这份精简的复习手册汇集了你在 AS 剑桥地理课程中必须掌握的核心定量公式与关键理论定理。每个条目都以简单的英中对照陈述呈现核心思想，适当时附有计算示例或解释说明。将本手册放在手边，便于课堂快速查阅和考前最后冲刺复习。

---

1. Population Growth Rate Formula | 人口增长率公式

The annual population growth rate (%) is calculated as: (Crude Birth Rate – Crude Death Rate + Net Migration Rate) / 10. The result is expressed as a percentage change per year, but careful attention must be paid to whether rates are given per 1,000 or as percentages.

年人口增长率(%)的计算公式为：(粗出生率 – 粗死亡率 + 净迁移率) / 10。结果表示为年百分比变化，但需注意所给比率是千分比还是百分比。

Example: If CBR = 35 per 1,000, CDR = 12 per 1,000, and net migration rate = –3 per 1,000, then growth rate = (35 – 12 – 3)/10 = 20/10 = 2.0%.

示例：若粗出生率为 35‰，粗死亡率为 12‰，净迁移率为 –3‰，则增长率 = (35 – 12 – 3)/10 = 20/10 = 2.0%。

For longer periods, use the instantaneous growth rate r = (ln(P₂/P₁))/t, but for AS the basic arithmetic formula suffices.

对于较长时间段，可使用瞬时增长率 r = (ln(P₂/P₁))/t，但 AS 阶段用基本算术公式即可。

---

2. Natural Increase and Net Migration | 自然增长与净迁移

Natural Increase = Crude Birth Rate – Crude Death Rate (both per 1,000 population). A positive value means births exceed deaths; a negative value signals natural decrease. Net Migration = Immigration – Emigration, often expressed per 1,000 population to standardise comparisons.

自然增长 = 粗出生率 – 粗死亡率（两者均按每千人计算）。正值表示出生数超过死亡数；负值表示自然减少。净迁移 = 迁入 – 迁出，通常以每千人为单位以便标准化比较。

Always check whether data is absolute or per 1,000: 350,000 net migrants into a population of 70 million yields a net migration rate of (350,000 / 70,000,000) × 1,000 = 5 per 1,000.

务必检查数据是绝对数还是千分比：例如 3.5 亿人口的国家净迁入 35 万人，净迁移率 = (350,000 / 70,000,000) × 1,000 = 5‰。

---

3. Dependency Ratio | 抚养比

Dependency Ratio = ((Population aged 0–14 + Population aged 65+) / Population aged 15–64) × 100. The result is a dimensionless number (often treated as a percentage) showing how many dependents there are for every 100 working‑age people.

抚养比 = ((0–14 岁人口 + 65 岁及以上人口) / 15–64 岁人口) × 100。结果为无量纲数（常视作百分比），表示每 100 名劳动适龄人口需抚养多少名非劳动人口。

Youth dependency ratio and old‑age dependency ratio can be computed separately to reveal different demographic pressures.

少儿抚养比和老年抚养比可分别计算，以揭示不同的人口压力。

Example: country with 28% under 15, 8% over 64, and 64% working age: (28+8)/64 × 100 = 56.25. That means 56 dependents per 100 workers.

示例：某国 15 岁以下占 28%，65 岁以上占 8%，劳动年龄占 64%：(28+8)/64 × 100 = 56.25。即每 100 名劳动者抚养 56 人。

---

4. Urbanisation Level and Rate of Urbanisation | 城市化水平与城市化速率

Urbanisation Level = (Urban population / Total population) × 100%. Rate of Urbanisation = ((Urban population in year 2 – Urban population in year 1) / Urban population in year 1) × 100 / number of years. The level is a snapshot; the rate is a measure of change.

城市化水平 =（城镇人口 / 总人口）× 100%。城市化速率 = [(第 2 年城镇人口 – 第 1 年城镇人口) / 第 1 年城镇人口] × 100 / 年数。水平是横截面指标；速率衡量变化快慢。

Note that the rate of urbanisation is not simply the difference in levels. It reflects the growth speed of the urban population itself and can exceed the total population growth rate due to rural‑urban migration.

注意城市化速率不是简单的水平之差。它反映了城镇人口本身的增长速度，且因城乡迁移可能快于总人口增长率。

---

5. Rank–Size Rule | 位序—规模法则

The rank‑size rule states that the population of a city is inversely proportional to its rank in the urban hierarchy: Pₙ = P₁ / n, where P₁ is the population of the largest city and n is the rank of the city. This is an empirical regularity, not a law.

位序—规模法则认为，城市人口与其在城市体系中的位序成反比：Pₙ = P₁ / n，其中 P₁ 为最大城市的人口，n 为该城市的位序。这是经验规律，而非自然定律。

A country that follows the rule displays a log‑linear pattern on a graph of log rank against log population. Deviations suggest primacy or a fragmented urban system.

符合该法则的国家在对数秩序—对数人口图上呈对数线性模式。偏离该模式则表明存在首位城市或破碎的城市体系。

Example: If the largest city has 10 million, the 4th‑ranked city is expected to have about 10/4 = 2.5 million.

示例：若最大城市有 1000 万人口，第 4 大城市预计约为 1000/4 = 250 万。

---

6. Primacy Index | 城市首位度指数

The two‑city primacy index is calculated as Population of the largest city / Population of the second‑largest city. A value above 2.0 is often taken as evidence of a primate city. The four‑city index (P₁/(P₂+P₃+P₄)) is also widely used.

二城市首位度 = 最大城市人口 / 第二大城市人口。比值大于 2.0 通常视为存在首位城市的证据。四城市指数 P₁/(P₂+P₃+P₄) 也广泛使用。

Primate cities dominate their national urban network, concentrating political, economic, and cultural functions.

首位城市在国家城市网络中占主导地位，集中了政治、经济和文化功能。

---

7. River Discharge (Q) | 河流径流量 (Q)

Discharge (Q) is the volume of water passing a given cross‑section per unit time: Q = A × v, where A is cross‑sectional area (width × mean depth, in m²) and v is mean flow velocity (m/s). Units are cubic metres per second (cumecs).

径流量 (Q) 是单位时间内通过某断面的水体积：Q = A × v，其中 A 为过水断面面积（宽度 × 平均水深，单位 m²），v 为平均流速（m/s）。单位是立方米/秒 (cumecs)。

Field measurements: width measured with tape, depth with wading rod or sounding line, and velocity with a flow meter at 0.6 of depth from the surface.

野外测量：用卷尺测宽度，涉水杆或测深绳测水深，流速仪在水面以下 0.6 倍水深的位置测速。

Example: Stream width 8 m, mean depth 1.2 m, mean velocity 0.5 m/s: Q = (8 × 1.2) × 0.5 = 4.8 cumecs.

示例：河宽 8 m，平均水深 1.2 m，平均流速 0.5 m/s：Q = (8 × 1.2) × 0.5 = 4.8 m³/s。

---

8. Hydraulic Radius and Wetted Perimeter | 水力半径与湿周

Hydraulic Radius (R) = Cross‑sectional area (A) / Wetted Perimeter (P). A higher R indicates a more efficient channel for conveying water, as less energy is lost overcoming friction.

水力半径 (R) = 过水断面面积 (A) / 湿周 (P)。R 值越大，表示河道输水效率越高，因为克服摩擦损失的能量较少。

Wetted perimeter is the total length of the bed and banks in contact with water. For a rectangular channel, P = width + 2 × depth.

湿周是与水接触的河床和河岸总长度。对于矩形河道，P = 宽度 + 2 × 水深。

Used in the Manning formula for open channel flow, though AS primarily requires conceptual understanding.

用于曼宁明渠流公式，但 AS 阶段主要要求概念理解。

---

9. Catchment Water Balance | 流域水量平衡

The hydrological water balance equation: P = Q + ET + ΔS, where P = precipitation, Q = stream discharge, ET = evapotranspiration, and ΔS = change in storage (soil moisture, groundwater). All terms in mm over a given period.

水文水量平衡方程：P = Q + ET + ΔS，其中 P 为降水量，Q 为河川径流，ET 为蒸散发量，ΔS 为储水变化量（土壤水、地下水）。各项均以某时期毫米数表示。

In the long term, ΔS ≈ 0, so P ≈ Q + ET. This relationship helps explain regional water availability.

长期来看，ΔS ≈ 0，所以 P ≈ Q + ET。此关系有助于解释区域水资源可利用量。

Example: A catchment receives 1,200 mm rainfall, records 500 mm runoff, and storage increases by 100 mm; then ET = 1,200 – 500 – 100 = 600 mm.

示例：某流域降水 1200 mm，径流 500 mm，储水增加 100 mm；则 ET = 1200 – 500 – 100 = 600 mm。

---

10. Malthusian Theory of Population | 马尔萨斯人口理论

Thomas Malthus argued that population grows geometrically (1, 2, 4, 8…) while food supply grows arithmetically (1, 2, 3, 4…). This imbalance inevitably leads to ‘positive checks’ (famine, disease) or ‘preventive checks’ (moral restraint, later marriage) to re‑establish equilibrium.

马尔萨斯认为，人口呈几何级数增长（1, 2, 4, 8…），而食物供应仅呈算术级数增长（1, 2, 3, 4…）。这种不平衡必然导致“积极抑制”（饥荒、疾病）或“预防性抑制”（道德约束、晚婚）以恢复平衡。

The theory is often criticised for underestimating technological progress, but it provides a foundation for understanding carrying capacity and sustainability debates.

该理论常因低估技术进步而受到批评，但它为理解环境承载力与可持续发展辩论奠定了基础。

---

11. Demographic Transition Model (DTM) Theorem | 人口转变模型定理

The DTM proposes that as countries develop, they pass through stages of high fluctuating births and deaths (Stage 1), declining death rates (Stage 2), declining birth rates (Stage 3), low fluctuating rates (Stage 4), and a possible Stage 5 with natural decrease. The theorem links demographic change to socioeconomic development.

人口转变模型提出，随着国家发展，会经历高出生高死亡波动阶段（第一阶段）、死亡率下降（第二阶段）、出生率下降（第三阶段）、低出生低死亡波动（第四阶段）以及可能出现的自然减少阶段（第五阶段）。该定理将人口变化与经济社会发展联系起来。

Key transitions: Stage 2 is triggered by improved healthcare, Stage 3 by urbanisation and changing attitudes towards family size.

关键转变：第二阶段由医疗改善触发，第三阶段由城市化及家庭规模观念变化引发。

---

12. Central Place Theorem (Christaller) | 中心地理论（克里斯泰勒）

Christaller’s central place theorem states that settlements provide goods and services to surrounding market areas (complementary regions) and are hierarchically arranged. High‑order goods have large threshold populations and range, whereas low‑order goods require small thresholds. The ideal arrangement follows a hexagonal lattice under uniform plain assumptions.

克里斯泰勒的中心地理论认为，聚落向周边市场区（补充区域）提供商品和服务，并呈层级排列。高级商品有较大的门槛人口和范围，低级商品则门槛较低。在均质平原假设下，理想排列遵循六边形网格。

The theory introduces the concepts of threshold (minimum population needed to sustain a service) and range (maximum distance consumers will travel). K = 3, 4, 7 networks describe different organising principles.

该理论引入了门槛（维持一项服务所需最小人口）和范围（消费者愿意出行的最大距离）的概念。K=3、4、7 网络描述了不同的组织原则。

---

13. Core–Periphery Model (Friedmann) | 核心—边缘模型（弗里德曼）

Friedmann’s core–periphery theorem describes how economic growth concentrates in a core region, which dominates the periphery through resource flows, migration, and political control. Over time, spread effects may reduce disparities, but backwash effects often strengthen the core.

弗里德曼的核心—边缘模型定理描述经济增长如何集中在一个核心区域，该核心通过资源流动、人口迁移和政治控制主导边缘区。随着时间推移，扩散效应可能缩小差距，但回波效应往往会强化核心。

The model is applied at national scales (e.g. Southeast England vs. rest of UK) and global scales (Global North vs. South), and is essential for explaining spatial inequality.

该模型适用于国家尺度（如英格兰东南部与英国其他地区）和全球尺度（全球北方与南方），对于解释空间不平等至关重要。

---

Published by TutorHao | Geography Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）