📚 AS Edexcel Geography: Quick Reference Formula and Theorem Handbook | AS Edexcel 地理：公式定理速查手册
This quick reference guide brings together the essential formulas, indices and quantitative relationships examined in AS Edexcel Geography. From drainage basin hydrology to population change, urbanisation and ecological diversity, mastering these tools is crucial for data-response questions, fieldwork and case-study evaluation.
本速查手册汇集了 AS Edexcel 地理考试中必考的核心公式、指数与定量关系。从流域水文学到人口变动、城市化及生态多样性，掌握这些工具对数据应答、田野调查和案例评估至关重要。
1. Velocity and Discharge in River Channels | 河流流速与流量
Discharge (Q) is the volume of water flowing past a point in a given time. It is calculated by multiplying the cross-sectional area of the channel by the mean velocity of the water.
流量（Q）是单位时间内流过某一点的河水体积。它由河道横截面积乘以水流平均速度得出。
Q = A × v
Where A = cross-sectional area (width × mean depth) measured in m², v = mean velocity in m s⁻¹, and Q is given in m³ s⁻¹ (cumecs).
其中 A = 横截面积（宽度 × 平均水深），单位为 m²；v = 平均流速，单位为 m s⁻¹；Q 的单位为 m³ s⁻¹（立米每秒）。
To estimate A in a field study, measure channel width and a series of depths at regular intervals, then calculate the average depth. The area approximates width × mean depth. Float methods or flow meters can determine v.
在野外研究中，测量河道宽度和等间距的多个水深，计算平均深度即可。截面面积约等于宽度 × 平均水深。浮标法或流速仪可测定 v。
2. Rainfall–Runoff Relationship | 降雨–径流关系
The runoff coefficient expresses the proportion of rainfall that becomes surface runoff. It is a key concept for storm hydrographs and water budget analysis.
径流系数表示降雨转化为地表径流的比例。这是暴雨洪水过程和水量平衡分析的关键概念。
Runoff coefficient C = Runoff (mm) / Rainfall (mm)
A C value close to 1 indicates high runoff, typical on impermeable surfaces or saturated soils. A low C value indicates high infiltration and storage, common in forested catchments with permeable bedrock.
C 值接近 1 表示径流多，常见于不透水地面或饱和土壤；低 C 值表示下渗和蓄水多，常见于透水性基岩的森林流域。
Runoff depth can also be derived from river discharge: Runoff depth = (Total discharge volume / Catchment area).
径流深度也可由河流流量导出：径流深度 =（总排水量 / 流域面积）。
3. Natural Population Change | 人口自然变动
Crude Birth Rate (CBR) and Crude Death Rate (CDR) are fundamental demographic indicators expressed per 1000 population. The rate of natural increase (RNI) follows directly from them.
粗出生率和粗死亡率是基本的人口指标，以每千人表示。自然增长率直接由二者计算。
CBR = (Number of live births / Total population) × 1000
CDR = (Number of deaths / Total population) × 1000
RNI = CBR – CDR
RNI is often given per 1000 people; to express as a percentage divide by 10. For example, a CBR of 25 and CDR of 15 give an RNI of 10 per 1000, or 1.0 %.
RNI 常以每千人表示；转为百分比则除以 10。例如，CBR 为 25，CDR 为 15，则 RNI 为每千人 10，或 1.0 %。
Doubling time can be estimated using the ‘Rule of 70’: Doubling time (years) = 70 / annual RNI (%). This helps assess future population pressures.
人口倍增时间可用“70 法则”估算：倍增时间（年）= 70 / 年 RNI（%），用于评估未来人口压力。
4. Net Migration and Total Population Equation | 净迁移与人口变化方程
Population change in an area is the result of both natural change and net migration. The basic demographic balancing equation is:
一个地区的人口变化是自然变动和净迁移共同作用的结果。基本人口平衡方程如下：
ΔP = (B – D) + (I – E)
Where ΔP = population change, B = births, D = deaths, I = immigration, E = emigration. Net migration = I – E.
其中 ΔP 为人口变化，B 为出生人数，D 为死亡人数，I 为迁入人数，E 为迁出人数。净迁移 = I – E。
Net migration rate (per 1000): NMR = [(I – E) / Total population] × 1000. Together with RNI it completes the total growth rate.
净迁移率（每千人）：NMR = [(I – E) / 总人口] × 1000。与 RNI 相加即得总增长率。
5. Dependency Ratio | 依赖比率
The dependency ratio measures the pressure on the productive population. It is a crucial tool for evaluating ageing populations and youth-dependent structures.
依赖比率衡量生产性人口负担的压力，是评价老龄化社会和年轻型人口结构的重要工具。
Dependency Ratio = [(P₀₋₁₄ + P₆₅₊) / P₁₅₋₆₄] × 100
P₀₋₁₄ denotes population aged 0–14, P₆₅₊ denotes population aged 65 and over, and P₁₅₋₆₄ is the working-age group (15–64). The result is expressed as a number of dependents per 100 working-age people.
P₀₋₁₄ 指 0–14 岁人口，P₆₅₊ 指 65 岁及以上人口，P₁₅₋₆₄ 为劳动年龄人口（15–64 岁）。结果表示为每 100 名劳动年龄人口抚养的人口数。
A high dependency ratio (above 60) suggests a heavy economic burden; very low ratios are rare and can indicate an overheated labour market.
高依赖比率（超过 60）意味着沉重的经济负担；极低的依赖比率少见，可能反映劳动力市场过热。
6. Level of Urbanisation | 城市化水平
Urbanisation level measures the share of a country’s population that resides in urban areas. It is central to the study of global cities and regeneration.
城市化水平衡量一个国家人口居住在城市地区的比例，是全球城市与再生研究的核心。
Urbanisation level (%) = (Urban population / Total population) × 100
The pace of urbanisation is the annual change in this percentage. For rapidly urbanising LIDCs and EDCs, such rates can exceed 1% per year.
城市化速度即此百分比的年变化率。在快速城市化的低收入和发展中国家，年增长率可超过 1 个百分点。
Counter-urbanisation and re-urbanisation are measured by tracking changes in the absolute and relative urban population. Use the same formula to compare different census years.
反城市化与再城市化通过追踪城市人口绝对数和相对比例的变化来测量。同样使用该公式比较不同普查年份。
7. Location Quotient | 区位商
The Location Quotient (LQ) identifies the concentration of a particular industry or occupation in a local area compared with a larger reference region, usually the nation.
区位商（LQ）用来识别某一地区特定产业或职业与全国等大范围参考区域相比的集中程度。
LQ = (Local employment in sector / Total local employment) ÷ (National employment in sector / Total national employment)
An LQ of 1 means the local area has the same share as the nation. An LQ > 1 indicates specialisation; LQ < 1 shows under-representation. This is widely used in regeneration studies and economic geography.
LQ = 1 表示该地区与全国份额相同；LQ > 1 表明专业化集聚；LQ < 1 显示该部门占比不足。该指数广泛应用于再生研究和经济地理。
8. Simpson’s Diversity Index | 辛普森多样性指数
Simpson’s Diversity Index is used to quantify biodiversity in ecosystem fieldwork. It considers both species richness and evenness.
辛普森多样性指数用于在生态系统田野调查中量化生物多样性，同时考虑物种丰富度和均匀度。
D = 1 – Σ (n / N)²
Where n = number of individuals of a particular species, N = total number of individuals of all species. The sum is taken over all species in the sample.
其中 n 为某一物种的个体数，N 为所有物种的总个体数。对所有物种的 (n/N)² 求和。
The index ranges from 0 (no diversity) to almost 1 (infinite diversity). Higher D indicates a more diverse and stable ecosystem. The reciprocal form 1/D is also used to express ‘effective number of species’.
指数范围从 0（无多样性）到接近 1（极高多样性）。D 值越高，生态系统越多样和稳定。其倒数形式 1/D 可表示“有效物种数”。
9. Measures of Central Tendency and Dispersion | 集中趋势与离散量数
In data analysis, the mean and median describe central tendency, while range and interquartile range (IQR) summarise spread. These are vital for comparing climate data, economic indicators and census variables.
数据分析中，平均值和中位数描述集中趋势，而全距和四分位距概括离散程度。这对于比较气候数据、经济指标和人口普查变量至关重要。
Mean = Σx / n
Range = Max value – Min value
IQR = Q₃ – Q₁
Where Q₁ is the lower quartile (25th percentile) and Q₃ is the upper quartile (75th percentile). IQR is robust against outliers and preferred when reporting skewed distributions.
Q₁ 为下四分位数（第 25 百分位），Q₃ 为上四分位数（第 75 百分位）。IQR 不受异常值影响，适合偏态分布。
Standard deviation is another key measure but is less commonly hand-calculated at AS. Remember always to state units and recognise that large IQR signals high variability – important when comparing rainfall reliability or income inequality.
标准差是另一个重要量数，但在 AS 阶段较少手算。务必注明单位，并记住 IQR 大意味着变率大——在比较降水可靠性或收入不平等时十分重要。
10. Economic Multiplier Effect | 经济乘数效应
The multiplier concept explains how an initial injection of spending leads to a larger final increase in income or employment. It underpins regeneration strategies and local economy studies.
乘数效应解释一笔初始支出如何带来更大的最终收入或就业增长，是再生策略和地方经济研究的基础。
Multiplier k = 1 / (1 – MPC)
where MPC = marginal propensity to consume locally. A larger MPC (e.g. 0.8) gives k = 5, meaning each £1 injection generates £5 of local income.
其中 MPC 为本地边际消费倾向。MPC 越大（如 0.8），乘数 k 越大（k = 5），即每注入 1 英镑能产生 5 英镑本地收入。
The total change is calculated as: total change = k × initial injection. Negative multipliers can occur with factory closures.
总变化 = k × 初始注入量。工厂倒闭时甚至会出现负乘数效应。
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