📚 Year 13 Edexcel Geography: Formula & Theorem Quick-Reference Handbook | Edexcel A Level 地理公式定理速查手册
Mastering the quantitative skills in Year 13 Edexcel Geography requires fluent recall of essential equations, statistical tests, and model parameters. This handbook presents each formula in a clear, paired English–Chinese format, with worked-style explanations and structured tables to support your revision for both physical and human geography topics.
在 Year 13 Edexcel 地理中熟练掌握量化技能，需要对核心方程、统计检验和模型参数能够自如回忆。本手册以清晰的中英配对形式呈现每一条公式，并配有表格和解释，帮助你为自然地理和人文地理的复习提供支撑。
1. Water Balance Equation | 水量平衡方程
The water balance equation quantifies the hydrological relationship between precipitation, evapotranspiration, runoff, and changes in storage within a drainage basin over a given period.
水量平衡方程量化了给定时期内流域内降水、蒸散、径流及储存量变化之间的水文关系。
P = Q + E + ΔS
- P = precipitation (mm) – 降水量（毫米）
- Q = runoff / stream discharge (mm) – 径流/河流流量（毫米）
- E = actual evapotranspiration (mm) – 实际蒸散量（毫米）
- ΔS = change in storage (soil water, groundwater, lakes) (mm) – 储存量变化（土壤水、地下水、湖泊）（毫米）
This equation underpins river regime analysis, flood forecasting, and water resource management. It is typically applied over a water year to close the basin budget.
该方程是分析河流情势、洪水预报和水资源管理的基础。通常在一个水文年内应用，以使流域水量收支闭合。
| Term | When P > Q+E | When P < Q+E |
|---|---|---|
| ΔS | positive (surplus stored) – 正（盈余储存） | negative (deficit from storage) – 负（储存亏损） |
2. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s rank tests the strength and direction of a monotonic relationship between two sets of ranked data. It is often used in geographical fieldwork to examine associations such as distance from source and river depth.
斯皮尔曼等级相关系数检验两组排序数据之间单调关系的强度和方向。常用在地理实地考察中，比如分析距源头距离与河流深度的关联。
rₛ = 1 − [ 6 Σ d² / (n³ − n) ]
- d = difference between ranks for each pair – 每配对等级的差值
- n = number of pairs of data – 数据对数量
When |rₛ| approaches 1, a strong correlation exists. A critical values table must then be used to assess statistical significance at p = 0.05 or 0.01.
当 |rₛ| 接近 1 时，相关性较强。之后需使用临界值表，在 p = 0.05 或 0.01 水平上判断统计显著性。
| rₛ value | Interpretation – 解释 |
|---|---|
| +1.0 | Perfect positive monotonic – 完全正单调 |
| 0 | No monotonic relationship – 无单调关系 |
| −1.0 | Perfect negative monotonic – 完全负单调 |
3. Chi-Squared Test (χ²) | 卡方检验
The chi-squared test determines whether there is a significant difference between observed and expected frequencies in categorical data, such as land use changes or migration flows across regions.
卡方检验用于判断分类数据（如土地利用变化或区域间迁移流）中观测频率与期望频率之间是否存在显著差异。
χ² = Σ [ (O − E)² / E ]
- O = observed frequency – 观测频数
- E = expected frequency – 期望频数
Degrees of freedom: df = (rows − 1) × (columns − 1).
自由度：df = (行数 − 1) × (列数 − 1)。
If χ² calculated exceeds the critical value at the chosen significance level, the null hypothesis (no difference) is rejected. This test is frequently applied in human geography when comparing land use or settlement patterns.
若计算得到的 χ² 值大于选定显著性水平下的临界值，则拒绝原假设（无差异）。该检验常用于人文地理中对比土地利用或聚落格局。
4. Gini Coefficient & Lorenz Curve | 基尼系数与洛伦兹曲线
The Lorenz curve plots the cumulative share of income (or other resource) against the cumulative share of population. The Gini coefficient measures the degree of inequality.
洛伦兹曲线描画收入（或其他资源）的累计份额与人口累计份额之间的关系。基尼系数衡量不平等程度。
Gini = A / (A + B)
- A = area between line of perfect equality and Lorenz curve – 完全平等线与洛伦兹曲线之间的面积
- B = area under the Lorenz curve – 洛伦兹曲线下方的面积
A Gini of 0 indicates perfect equality; 1 (or 100%) represents maximum inequality. In Edexcel Geography, this tool is used for evaluating development disparities, urban segregation, and resource distribution.
基尼系数为 0 表示完全平等；1（或 100%）表示最大不平等。在 Edexcel 地理中，该工具用于评估发展差距、城市隔离和资源分配。
5. Population & Demographic Indices | 人口统计指标
Accurate demographic calculations are needed when analysing census data, population pyramids, or the Demographic Transition Model.
在分析人口普查数据、人口金字塔或人口转变模型时，需要准确的人口统计计算。
Crude Birth Rate (CBR) = (Births / Total population) × 1000
粗出生率 (CBR) = (出生人数 / 总人口) × 1000
Crude Death Rate (CDR) = (Deaths / Total population) × 1000
粗死亡率 (CDR) = (死亡人数 / 总人口) × 1000
Natural Increase Rate (%) = [(CBR − CDR) / 10] %
自然增长率 (%) = [(CBR − CDR) / 10]%
Dependency Ratio = [(Population aged 0–14 + Population aged 65+) / Population aged 15–64] × 100
抚养比 = [(0–14 岁人口 + 65 岁以上人口) / 15–64 岁人口] × 100
These indices allow comparison of population structure and economic pressures between countries. Be careful to express rates per 1 000 or as percentages according to the question context.
这些指标便于比较各国人口结构和经济压力。注意根据题目背景，将比率表示为每千人值或百分比。
6. Gravity Model (Spatial Interaction) | 重力模型（空间相互作用）
The gravity model estimates the interaction between two places based on their masses (e.g., population, GDP) and the distance between them. It is used to explain migration, trade flows, or retail catchment areas.
重力模型根据两地规模（如人口、GDP）和它们之间的距离来估算相互作用。用来解释迁移、贸易流或零售辐射范围。
Iᵢⱼ = k (Mᵢ × Mⱼ) / dᵢⱼ²
- Iᵢⱼ = interaction between places i and j – 两地 i 与 j 之间的相互作用
- Mᵢ, Mⱼ = mass (e.g., population) of i and j – 两地规模（如人口）
- dᵢⱼ = distance between i and j – 两地距离
- k = constant – 常数
Often the exponent on distance is allowed to vary; in basic school-level applications it is taken as 2. The model can be inverted to predict retail store patronage or to understand the breaking point of a market.
距离的指数常可变化；在学校基础应用中常取 2。该模型可逆向预测零售商店客流或理解市场断裂点。
7. Simpson’s Diversity Index | 辛普森多样性指数
Simpson’s Diversity Index measures the biodiversity of an area or heterogeneity of land use. It considers both the number of categories and their relative abundance.
辛普森多样性指数衡量一个地区的生物多样性或土地利用的异质性，既考虑类别数量也考虑相对丰度。
D = 1 − [ Σ n(n−1) / N(N−1) ]
- n = number of individuals (or area units) of a single category – 某一类别的个体数（或面积单位）
- N = total number of individuals of all categories – 所有类别的总个体数
The index ranges from 0 (no diversity) to 1 (infinite diversity). It is used in coastal sand dune succession studies, urban function analysis, or assessing habitat fragmentation.
指数值从 0（无多样性）到 1（极高多样性）。常用于海岸沙丘演替研究、城市功能分析或评估栖息地破碎化。
8. Drainage Basin Morphometry Ratios | 流域形态计量比率
Morphometric analysis describes the shape and network characteristics of a drainage basin, essential for flood risk assessment and hydrograph prediction.
形态计量分析描述流域的形状和河网特征，这对洪水风险评估和过程线预测至关重要。
Drainage Density (Dd) = Total stream length (km) / Basin area (km²)
河网密度 (Dd) = 河流总长度 (公里) / 流域面积 (平方公里)
Bifurcation Ratio (Rᵦ) = Number of streams of a given order / Number of streams of next higher order
分叉比 (Rᵦ) = 某一级河流数目 / 下一级河流数目
Elongation Ratio (Rₑ) = Diameter of circle with same area as basin / Maximum basin length
伸长比 (Rₑ) = 与流域等面积圆的直径 / 流域最大长度
- High Dd → rapid runoff, steep slopes – 高河网密度→径流快、坡度陡
- Low Rₑ → elongated basin, longer lag time – 伸长比低→狭长流域、滞后时间长
- Rᵦ typically 3–5 for natural river networks – 天然河网分叉比通常为 3–5
These ratios link drainage basin form to hydrological response and can be calculated from topographic maps or GIS.
这些比率将流域形态与水文响应联系起来，可通过地形图或 GIS 计算。
9. Carbon Sequestration & Net Primary Productivity (NPP) | 碳封存与净初级生产力
In the carbon cycle and climate change topics, students must understand the balance of photosynthesis and respiration in ecosystems.
在碳循环和气候变化主题中，学生需要理解生态系统中光合作用与呼吸作用的平衡。
NPP = GPP − Rₐ
- GPP = gross primary productivity (total carbon fixed by photosynthesis) – 总初级生产力（光合作用固定的总碳量）
- Rₐ = autotrophic respiration (carbon lost by plants) – 自养呼吸（植物消耗的碳）
NPP is usually expressed in gC/m²/yr. In tropical rainforests, NPP is high because warm, wet conditions maximise photosynthesis, while in tundra it is low due to temperature constraints.
NPP 通常以克碳/平方米/年表示。热带雨林 NPP 高，因为温暖湿润的条件最大化光合作用；而冻原 NPP 低，受温度限制。
Carbon storage or sequestration potential can be estimated for different biomes and linked to management strategies such as REDD+.
不同生物群系的碳储存或封存潜力可以估算，并与 REDD+ 等管理策略相联系。
10. Statistical Significance: Critical Values & Degrees of Freedom Review | 统计显著性：临界值与自由度回顾
For any inferential test, knowing how to determine degrees of freedom and use critical value tables is essential. The following is a quick reference.
对于任何推断性检验，知晓如何确定自由度并使用临界值表至关重要。以下为速查。
| Test – 检验 | Degrees of freedom – 自由度 | Example critical values (p=0.05) – 示例临界值 (p=0.05) |
|---|---|---|
| Spearman’s rank | n (number of pairs) | n=10 → 0.564; n=20 → 0.377 |
| Chi-squared (χ²) | (rows−1)×(cols−1) | df=1 → 3.84; df=2 → 5.99 |
| Mann-Whitney U (for two independent samples) | n₁, n₂ (sample sizes) | n₁=5, n₂=5 → U ≤ 2 |
In your geographical investigation (NEA), always state the null hypothesis, confirm the test used, calculate the statistic, then compare with the critical value at the 95% or 99% confidence level.
在地理调查（NEA）中，务必陈述原假设、确认所用检验、计算统计量，然后与 95% 或 99% 置信水平的临界值进行比较。
Published by TutorHao | Geography Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导