📚 AS AQA Geography: Formula & Theorem Quick-Reference Handbook | AS AQA 地理：公式定理速查手册
This quick-reference handbook compiles the essential formulas, key equations, and fundamental theorems required for the AS AQA Geography specification. From hydrological calculations to demographic indicators, mastering these tools will enhance your data-response skills and strengthen your exam performance. Each entry includes a clear definition, the mathematical expression where applicable, and a contextual explanation to support your understanding of physical and human geography concepts.
本速查手册汇集了 AS AQA 地理课程所需的基本公式、关键方程和核心定理。从水文计算到人口统计指标，掌握这些工具将提升你处理数据题的能力并增强考试表现。每个条目都包含清晰的定义、适用的数学表达式以及情境解释，以帮助你理解自然地理和人文地理概念。
1. Water Budget Equation | 水收支方程
The water budget equation describes the balance of inputs and outputs within a drainage basin system over a given time period. It is fundamental to understanding how water is distributed between runoff, evaporation, and storage changes.
水收支方程描述了在给定时间段内流域系统输入与输出的平衡。它是理解水在径流、蒸发和储存变化之间如何分配的基础。
Equation:
P = Q + E + ΔS
Where P is precipitation, Q is runoff (streamflow), E is evapotranspiration, and ΔS is the change in water stored in soil, rock, and surface reservoirs. All terms are usually expressed in millimetres or cubic metres over the period.
其中 P 为降水量，Q 为径流量（河流流量），E 为蒸发蒸腾量，ΔS 为土壤、岩石和地表水库中储存水量的变化。所有项通常以毫米或立方米表示该时段内的数值。
In a closed system equilibrium, if precipitation increases and evapotranspiration remains constant, either runoff or storage must increase. This principle aids in flood prediction and water resource management.
在封闭系统的均衡状态下，如果降水量增加而蒸散量保持不变，那么径流量或储存量必然会增加。这一原理有助于洪水预报和水资源管理。
2. River Discharge and Velocity | 河流流量与流速
Discharge is the volume of water flowing past a given point in a river per unit time. It is one of the most frequently calculated values in fluvial field studies and links directly to flooding and channel morphology.
流量是指单位时间内流过河道某一点的浑水量。它是河流实地研究中最常计算的数值之一，并与洪水和河道形态直接相关。
Equation:
Q = A × V
Q is discharge (m³/s), A is the cross-sectional area of the channel (m²), and V is the mean flow velocity (m/s). To obtain A, measure the channel width and depth at regular intervals and integrate.
Q 为流量（立方米/秒），A 为河道横截面积（平方米），V 为平均流速（米/秒）。获得 A 需要在定间隔点测量河宽和水深并积分求得。
Velocity can be determined using a flowmeter or float method. Discharge data enable flood routing, pollution dilution modelling, and assessment of river regime changes over seasons.
流速可用流速仪或浮标法测定。流量数据可用于洪水演进、污染物稀释模拟以及评估河流季节变化规律。
3. Crude Birth Rate (CBR) and Crude Death Rate (CDR) | 粗出生率与粗死亡率
These two basic demographic indicators measure the number of births or deaths relative to the total population, standardised per 1000 individuals. They are crude because they do not account for the age or sex structure of the population.
这两个基本人口统计指标以每千人为单位衡量出生或死亡人数相对于总人口的比率。它们被称为“粗”是因为没有考虑人口的年龄和性别结构。
Formulas:
CBR = (Total live births / Mid-year population) × 1000
CDR = (Total deaths / Mid-year population) × 1000
For example, a country with 500,000 people and 10,000 births per year has a CBR of 20 per 1000. CBR above 30 typically indicates high fertility; below 10 suggests very low fertility. CDR can be affected by age structure and healthcare availability.
例如，某国人口50万，年出生1万人，则CBR为20‰。CBR高于30通常表示高生育率，低于10则表明生育率极低。CDR会受年龄结构和医疗条件影响。
Together they give a first impression of population dynamics before examining migration and age effects.
两者结合可在考虑迁移和年龄效应之前，初步了解人口动态。
4. Natural Increase Rate (NIR) | 自然增长率
NIR expresses the rate at which a population is growing (or declining) in a year due solely to births and deaths, excluding migration. It is a vital sign of demographic momentum.
NIR 表示一年中仅因出生和死亡（不包括迁移）而导致的人口增长（或减少）速率。它是衡量人口势能的重要标志。
Formula:
NIR = CBR – CDR (per 1000)
Alternatively, expressed as a percentage: NIR (%) = ((Births – Deaths) / Population) × 100. A rate of 15 per 1000 corresponds to a 1.5% annual increase. Many AS exam tasks ask students to calculate NIR from given birth and death totals.
或者以百分比表示：NIR (%) = ((出生数 – 死亡数) / 总人口) × 100。15‰的比率对应年增长率1.5%。许多AS考题要求根据给定的出生和死亡总数计算NIR。
Countries in Stage 2 of the Demographic Transition Model often exhibit high NIR due to falling death rates and sustained high birth rates.
处于人口转变模型第二阶段的的国家通常因死亡率下降而出生率仍高而表现出较高的NIR。
5. Total Fertility Rate (TFR) | 总和生育率
TFR is the average number of children a woman would have during her reproductive years (typically ages 15-49) if she experienced the current age-specific fertility rates. It is a more refined measure than CBR because it accounts for the age structure of women.
TFR 是指一名妇女如果按照当前的年龄别生育率度过其育龄期（通常为15-49岁），她一生平均生育的孩子数量。这是比CBR更精确的指标，因为它考虑了女性的年龄结构。
The calculation sums age-specific fertility rates: TFR ≈ 5 × Σ (ASFR_i / 1000) when using five-year age groups, where ASFR_i is the births per 1000 women in age group i. A TFR of 2.1 is considered replacement level for developed countries.
计算时累加年龄别生育率：若使用五岁年龄组，TFR ≈ 5 × Σ (ASFR_i / 1000)，其中ASFR_i为该年龄组每千名妇女的生育数。TFR为2.1被认为是发达国家的更替水平。
In exam data-response questions, TFR helps explain future population growth potential, dependency burdens, and pressure on services.
在考试的数据分析题中，TFR有助于解释未来人口增长潜力、抚养负担以及服务压力。
6. Infant Mortality Rate (IMR) | 婴儿死亡率
IMR measures the number of deaths of infants under one year of age per 1000 live births in a given year. It is a sensitive indicator of healthcare quality, nutrition, and socioeconomic development.
IMR 衡量给定年份每千名活产儿中一岁以下婴儿的死亡数。这是反映医疗质量、营养水平和社会经济发展的敏感指标。
Formula:
IMR = (Deaths under age 1 / Live births) × 1000
A high IMR (above 50) points to poor antenatal and postnatal care, while an IMR below 5 is typical for highly developed nations. The indicator is often used alongside life expectancy to gauge overall well-being.
高婴儿死亡率（高于50‰）表明产前和产后护理不良，而低于5‰则是高度发达国家的典型水平。该指标经常与预期寿命一起使用，以评估整体健康水平。
7. Dependency Ratio | 抚养比率
The dependency ratio compares the economically dependent part of the population (young and old) to the working-age population. It informs government policy on education, pensions, and healthcare spending.
抚养比率将经济依赖人口（年轻人和老年人）与劳动年龄人口进行比较。它为国家在教育、养老金和医疗支出方面的政策提供依据。
Formula:
Dependency Ratio (%) = [(Population 0-14 + Population 65+) / Population 15-64] × 100
Youth dependency and old-age dependency can be separated to show different pressures. A ratio above 60% is considered high and can strain economic resources.
少儿抚养比和老年抚养比可以分开，以显示不同的压力。60%以上的抚养比被认为是高水平，可能给经济资源带来压力。
For example, Japan’s old-age dependency is rising rapidly, whereas many sub-Saharan African countries have extremely high youth dependency ratios.
例如，日本的老年抚养比正在迅速上升，而许多撒哈拉以南的非洲国家则面临着极高的少儿抚养比。
8. Population Density | 人口密度
Population density quantifies the number of people living per unit area. It lays the groundwork for analysing spatial pressure, urbanisation, and resource allocation.
人口密度量化了单位面积上居住的人口数量。它为分析空间压力、城市化以及资源配置奠定了基础。
Formulas:
Arithmetic Density = Total Population / Total Land Area (per km²)
Physiological density, which divides population by arable land area, offers insight into potential food stress. Agricultural density relates farmers to arable land.
生理密度将人口除以可耕地面积，可提供有关潜在粮食压力的见解。农业密度则为农民数量与耕地面积之比。
Exam questions frequently present choropleth maps of density variations and ask candidates to link high densities with environmental and economic factors.
考试题目常给出密度变化的等值区域图，要求考生将高密度与环境和经济增长因素联系起来。
9. Percentage Change | 百分比变化
Percentage change is a universal tool for comparing growth or decline across time in any geographic variable: population, GDP, carbon emissions, or urban area.
百分比变化是跨时间比较任意地理变量（人口、GDP、碳排放或城市面积）增长或下降的通用工具。
Formula:
Percentage Change (%) = [(New value – Original value) / Original value] × 100
When interpreting results, a positive percentage indicates growth; a negative value indicates contraction. Be mindful of the base: a small original population can produce a deceptively high percentage change.
解读结果时，正值表示增长，负值表示收缩。需要注意基数问题：极小的原始人口可能产生误导性的高百分比变化。
This formula is applied in topics such as gentrification-led population shifts, industrial decline, and deforestation rates.
该公式可用于诸如绅士化带来的人口变动、产业衰退以及森林砍伐率等主题。
10. Location Quotient (LQ) | 区位商
Location Quotient measures the geographic concentration of a particular industry, occupation, or demographic group in a sub-region compared to a larger reference area, typically the nation.
区位商衡量某个特定产业、职业或人口群体在子区域相对于较大参考范围（通常是全国）的地理集中程度。
Formula:
LQ = (Local employment in industry / Total local employment) / (National employment in industry / Total national employment)
An LQ greater than 1.0 indicates a higher than average concentration, which may reveal a region’s economic specialisation. LQ is widely used in changing places analysis to examine shifting economic structure and identity.
LQ大于1.0表明集中程度高于平均，可能揭示区域的经济专门化。LQ在“变化的地方”分析中被广泛用于考察经济结构与地方的认同变化。
For instance, if financial services account for 12% of local jobs but only 6% nationally, the LQ is 2.0, highlighting a strong specialisation.
例如，若金融服务业占当地就业的12%，而全国仅为6%，则LQ为2.0，突显了较强的专业化特征。
11. Rank-Size Rule | 位序-规模法则
The rank-size rule describes a certain statistical regularity observed in many urban systems: the population of a city is inversely proportional to its rank in the urban hierarchy.
位序规模法则描述了在许多城市系统中观察到的一种统计规律：城市的人口与其在城市体系中的位序成反比。
Expression:
Pₙ = P₁ / n
Where Pₙ is the population of the nth largest city, P₁ is the population of the largest city, and n is the rank. The rule is best illustrated by cases such as the United States or Germany, whereas primate city patterns (e.g., France, Mexico) deviate markedly.
其中 Pₙ 为第n大城市人口，P₁ 为最大城市人口，n 为排名。美国或德国等案例最好地体现了该规则，而首位城市型分布（如法国、墨西哥）则出现明显偏离。
AS AQA questions might present a table of city sizes and require you to test whether the rank-size rule holds, explaining reasons for any deviation, such as political centralisation or colonial legacy.
AS AQA 题目可能给出一张城市规模表，要求你检验是否符合位序规模法则，并解释任何偏离的原因，例如政治集中化或殖民历史遗产。
12. Urbanisation Rate | 城市化率
Urbanisation rate measures the percentage of a country’s population living in areas classified as urban. It reflects the level of economic development and the pace of rural-to-urban migration.
城市化率衡量一国居住在划定为城市地区的人口百分比。它反映了经济发展水平和农村人口迁往城市的步伐。
Formula:
Urbanisation Rate (%) = (Urban population / Total population) × 100
In addition to this static measure, annual urban growth rate can be calculated using percentage change, distinguishing between urbanisation (increase in proportion) and urban growth (absolute increase).
除了这一静态指标，还可以利用百分比变化计算年度城市增长率，并区分城市化（比例增加）与城市增长（绝对增加）。
Over half the world’s population now lives in urban areas, but rates differ drastically between HICs and LICs, influencing planning for housing, transport, and sustainability.
目前全球超过一半人口居住在城市地区，但高收入国家和低收入国家之间城市化率差异巨大，影响了住房、交通和可持续发展的规划。
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