📚 Year 10 Eduqas Geography Formula and Theorem Quick Reference Handbook | Year 10 Eduqas 地理：公式定理速查手册
This quick reference handbook brings together the key formulas, models, and 'geographic theorems' you need for Year 10 Eduqas Geography. Whether you are revising population, urban patterns, river processes, or development indicators, having a compact list of the essential quantitative tools and conceptual models will sharpen your exam skills and help you apply them correctly in data response and essay questions.
这本速查手册汇集了Year 10 Eduqas地理课程中必须掌握的关键公式、模型和'地理定理'。无论你正在复习人口、城市模式、河流过程还是发展指标，拥有这些核心定量工具和概念模型的简洁清单，都能提升你的考试技巧，并帮助你在数据分析题和论述题中准确运用它们。
1. Crude Birth and Death Rates | 粗出生率和粗死亡率
The crude birth rate (CBR) is the number of live births per 1000 people per year. The crude death rate (CDR) is the number of deaths per 1000 people per year. Both are expressed as CBR = (Total live births ÷ Total population) × 1000 and CDR = (Total deaths ÷ Total population) × 1000.
粗出生率指一年中每千人的活产数，粗死亡率指每千人的死亡数。两者均以千分比表示：CBR = (活产总数 ÷ 总人口) × 1000，CDR = (死亡总数 ÷ 总人口) × 1000。
2. Natural Increase and Population Growth Rate | 自然增长率与人口增长率
The rate of natural increase (RNI) ignores migration and is calculated as RNI = CBR − CDR, usually given per 1000. The total population growth rate adds net migration: Growth rate (%) = [(CBR − CDR) + (Immigration − Emigration)] ÷ 10. Remember to align units when moving between per 1000 and percentages.
自然增长率不考虑迁移，计算公式为RNI = CBR − CDR，通常以每千人表示。总人口增长率则需加入净迁移：增长率(%) = [(CBR − CDR) + (迁入 − 迁出)] ÷ 10。注意在千分比与百分比之间换算时要统一单位。
3. Population Density and Physiological Density | 人口密度与生理密度
Arithmetic population density shows overall pressure per unit of land: Density = Total population ÷ Total land area (km²). Physiological density refines this by considering only arable land: Physiological density = Total population ÷ Arable land area (km²). It helps indicate the strain a population places on productive farmland.
算术人口密度反映每单位土地的人口压力：密度 = 总人口 ÷ 土地总面积 (km²)。生理密度进一步聚焦于耕地面积：生理密度 = 总人口 ÷ 耕地面积 (km²)。它能更好地说明人口对可用耕地的依赖程度。
4. Dependency Ratio | 依赖比率
The dependency ratio compares the economically dependent population (young 0–14 and old 65+) to the working-age population (15–64). The formula is Dependency Ratio = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100. A high ratio signals a greater financial burden on the working population.
依赖比率将受抚养人口（0–14岁和65岁以上）与劳动年龄人口（15–64岁）进行比较。公式为依赖比率 = [(0–14岁人口 + 65岁以上人口) ÷ 15–64岁人口] × 100。比率越高，劳动人口的抚养负担越重。
5. Demographic Transition Model (DTM) | 人口转变模型定理
The DTM is a conceptual framework tracing population change through five stages. It links birth and death rates to economic development. Key stages: Stage 1 (high fluctuating), Stage 2 (early expanding, death rate falls), Stage 3 (late expanding, birth rate falls), Stage 4 (low fluctuating), and Stage 5 (natural decrease). The model helps explain historical population booms and current decline patterns.
人口转变模型是一种将人口变化与经济发展联系起来的概念框架，分为五个阶段：第一阶段高出生高死亡、第二阶段死亡率先降、第三阶段出生率下降、第四阶段低出生低死亡、第五阶段自然减少。这一'定理'有助于解释历史上的人口爆发和当前某些国家的人口缩减。
6. Urban Land Use Models | 城市土地利用模型定理
Three classic urban models appear in the Eduqas specification. The Burgess Concentric Zone Model (1925) organises cities in rings around the CBD. The Hoyt Sector Model (1939) proposes sectors extending along transport routes. The Harris–Ullman Multiple Nuclei Model (1945) shows several growth centres. Although they are simplifications, these 'theorems' help analyse land value gradients, social segregation, and industrial location in real cities.
Eduqas考试涉及三个经典城市模型。伯吉斯同心圆模型以CBD为中心呈圈层分布；霍伊特扇形模型强调沿交通线形成扇状功能区；哈里斯–乌尔曼多核心模型则提出多个增长中心。尽管这些'定理'是简化的，它们仍有助于分析真实城市的地租梯度、社会隔离和产业选址。
7. Distance Decay and the Gravity Model | 距离衰减与重力模型
Distance decay states that interaction between two places decreases as the distance between them increases. The gravity model gives this a mathematical form: Interaction (I) ∝ (Population₁ × Population₂) ÷ Distance². Larger centres attract more flows, but friction of distance reduces them. Apply this when explaining retail catchment areas, migration flows, or transport demand.
距离衰减定理指出两地间的相互作用随距离增加而减弱。重力模型用数学形式表达：相互作用(I) ∝ (人口₁ × 人口₂) ÷ 距离²。规模越大的中心吸引力越强，但距离的摩擦效应会削弱流量。在解释零售辐射区、人口迁移和交通需求时均可运用这一'定理'。
8. River Discharge and Hydraulic Radius | 河流流量与水力半径
Discharge is the volume of water flowing past a point per second. The fundamental formula is Q = A × V, where Q is discharge (m³/s or cumecs), A is cross-sectional area (m²), and V is mean velocity (m/s). Hydraulic radius measures channel efficiency and is given by R = A ÷ P, with P being the wetted perimeter. A larger hydraulic radius generally means less friction and higher velocity.
流量指单位时间内通过河流断面的水量，基本公式为Q = A × V，Q为流量(m³/s)，A为横截面积(m²)，V为平均流速(m/s)。水力半径反映河道的输水效率，公式为R = A ÷ P，P为湿周。水力半径越大，通常摩擦越小，流速越高。
9. Bradshaw Model of River Characteristics | 河流特征的Bradshaw模型定理
The Bradshaw model summarises how a river’s properties change from source to mouth. Discharge, average velocity, hydraulic radius, and channel depth increase downstream, while particle size, channel roughness, and gradient decrease. Use it as a checklist to describe or predict changes along a long profile.
Bradshaw模型总结了河流从上游到河口特征的变化趋势：流量、平均流速、水力半径和河道深度向下游增大，而颗粒粒径、河道糙率和坡度则减小。可将其作为描述或预测河流纵剖面变化的速查清单。
10. GDP per Capita and the Human Development Index | 人均GDP与人类发展指数
Gross Domestic Product per capita is a simple measure: GDP per capita = Total GDP ÷ Population. It reflects average income but ignores inequality and quality of life. The Human Development Index (HDI) combines three dimensions: A long and healthy life (life expectancy at birth), knowledge (mean and expected years of schooling), and a decent standard of living (GNI per capita, PPP$). HDI = (Ihealth × I_education × Iincome)1/3. In exams, you mainly need to explain the components and their limitations.
人均国内生产总值是一个简单指标：人均GDP = 国内生产总值 ÷ 人口。它反映平均收入，但忽略了不平等和生活质量。人类发展指数综合了三个维度：健康长寿（预期寿命）、知识（平均受教育年限和预期受教育年限）、体面的生活水平（人均国民总收入，按购买力平价计）。HDI = (I_健康 × I_教育 × I_收入)1/3。考试中主要需解释其构成及局限性。
11. The Multiplier Effect and Cumulative Causation | 乘数效应与累积因果定理
The multiplier effect describes how an initial injection of investment or jobs can trigger secondary and tertiary rounds of economic activity. For instance, a new factory creates direct employment, which increases local spending, leading to more shops and services, and in turn attracts further business. Cumulative causation (Myrdal) extends this idea over time, showing how successful regions can keep attracting investment while peripheral areas decline – a core concept in explaining regional inequality.
乘数效应描述一次初始投资或就业注入如何引发第二、第三轮经济活动。例如，新工厂创造直接就业，增加本地消费，催生更多商店和服务，进而吸引更多企业。累积因果理论则将其延伸到长期过程，说明成功地区如何持续吸引投资，而边缘地区则不断衰退，这是解释区域不平等的核心'定理'。
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