📚 Year 12 Edexcel Geography: Formulas & Theorems Quick Reference Handbook | 爱德思 Year 12 地理：公式定理速查手册
This quick-reference handbook collates the essential quantitative formulas, statistical equations, and key geographic theorems you need to master for the Year 12 Edexcel Geography specification. Whether you are analysing population change, calculating river discharge, testing field data or unpacking urban hierarchy, having these tools at your fingertips will sharpen your data-response skills and boost your confidence for both Paper 1 (Dynamic Landscapes) and Paper 2 (Dynamic Places). Use it alongside your case studies for rapid revision.
这本速查手册汇总了 Year 12 Edexcel 地理考试必须掌握的核心定量公式、统计方程与关键地理学定理。无论你正在分析人口变化、计算河流流量、检验野外数据还是解读城市等级体系，这些工具都能帮你提升数据应答能力，让你在面对 Paper 1（动态景观）和 Paper 2（动态场所）时更加从容。请将它作为案例研究的伴侣，高效备考。
1. Demographic Formulas | 人口统计公式
Crude Birth Rate (CBR) = (Number of live births / Mid-year total population) × 1000. This expresses births per 1000 people per year and is a raw measure unaffected by age structure.
粗出生率 (CBR) = (活产数量 / 年中总人口) × 1000。该指标按每年每千人出生数表示，是不受年龄结构影响的原始度量。
Crude Death Rate (CDR) = (Number of deaths / Mid-year total population) × 1000. Similarly, it is a simple mortality indicator but can be misleading when comparing populations with different age profiles.
粗死亡率 (CDR) = (死亡人数 / 年中总人口) × 1000。同样，它是一个简单的死亡指标，但在比较年龄结构不同的人口时可能产生误导。
Natural Increase Rate (per 1000) = CBR − CDR. To convert to a percentage, divide by 10; thus Natural Increase (%) = (CBR − CDR) / 10. The annual population growth rate then incorporates net migration: Growth Rate (%) = ((CBR − CDR)/10) + Net Migration Rate (%).
自然增长率（每千人）= CBR − CDR。转换为百分比时除以 10，即自然增长 (%) = (CBR − CDR) / 10。年人口增长率还需纳入净迁移：增长率 (%) = ((CBR − CDR)/10) + 净迁移率 (%)。
Doubling time (years) = 70 / Annual growth rate (%). This rule of thumb tells you how many years it takes for a population to double if the current growth rate remains constant.
倍增时间（年）= 70 / 年增长率 (%)。这条经验法则告诉你，若当前增长率保持不变，人口翻一番所需的年数。
| Indicator | Formula | Unit |
|---|---|---|
| Crude Birth Rate | (B ÷ P) × 1000 | per 1000 |
| Crude Death Rate | (D ÷ P) × 1000 | per 1000 |
| Natural Increase (%) | (CBR − CDR) ÷ 10 | % |
| Population Growth Rate (%) | [(B−D+NM) ÷ P] × 100 | % |
2. Urbanisation & Regeneration Indices | 城市化与再生指数
Level of urbanisation = (Urban population / Total population) × 100. This percentage describes how concentrated a country’s population is in urban areas at a given point in time.
城市化水平 = (城市人口 / 总人口) × 100。该百分比反映某一时刻一国人口在城市地区的集中程度。
Rate of urbanisation = [(Urban population at end − Urban population at start) / Number of years] / Total population? Often expressed as an average annual percentage-point change or as a growth rate of the urban population itself. For Edexcel, you may simply track the difference in urbanisation level over time divided by the period length.
城市化速度 = [(期末城市人口 − 期初城市人口) / 年数] / 总人口？通常用年均百分点变化或城市人口本身的增长率表示。在爱德思考试中，你可以简单地用城市化水平的变化量除以时间跨度。
Location Quotient (LQ) = (Local employment in sector / Total local employment) ÷ (National employment in sector / Total national employment). An LQ > 1 indicates a local specialisation in that sector, a key tool in Regenerating Places for diagnosing economic strengths and weaknesses.
位置商数 (LQ) = (地区某行业就业人数 / 地区总就业人数) ÷ (全国该行业就业人数 / 全国总就业人数)。LQ > 1 表明该地区在这一行业具有专业化优势，是“地方再生”主题中诊断经济优劣势的关键工具。
LQ = (li / Li) ÷ (ni / Ni)
3. Hydrological & Fluvial Formulas | 水文与河流公式
Discharge (Q) = Cross-sectional area (A) × Mean velocity (v). Where A = average width × average depth. Discharge is measured in cumecs (m³/s) and is fundamental to flood risk analysis.
流量 (Q) = 横截面积 (A) × 平均流速 (v)。其中 A = 平均宽度 × 平均深度。流量以每秒立方米 (cumecs) 计量，是洪水风险分析的基础。
Q = A × v
Drainage density = Total stream length (km) / Drainage basin area (km²). High drainage density implies rapid storm runoff and a flashy hydrograph; low density suggests permeable geology.
河网密度 = 河流总长度 (km) / 流域面积 (km²)。高河网密度意味着暴雨汇流快、流量过程线陡涨陡落；低密度则暗示渗透性良好的地质。
Stream frequency = Total number of streams / Drainage basin area (km²). Used together with drainage density, it reveals the texture of the drainage network.
河流频数 = 河流总条数 / 流域面积 (km²)。与河网密度结合使用，可揭示水系网络的纹理特征。
Sediment budget equation (fluvial reach): Input (I) − Output (O) = Change in storage (ΔS). A positive ΔS means aggradation; a negative ΔS indicates erosion or scour.
沉积物收支方程（河段）：输入量 (I) − 输出量 (O) = 储存变化量 (ΔS)。ΔS 为正值代表淤积，负值则指示侵蚀或下切。
I − O = ΔS
4. Coastal Sediment Budget Equations | 海岸沉积物收支方程
Coastal systems are driven by the balance of sediment inputs (from rivers, cliff erosion, longshore drift) and outputs (to offshore sinks, dunes, dredging). The fundamental mass-balance equation is:
海岸系统由沉积物输入（来自河流、悬崖侵蚀、沿岸漂沙）与输出（向离岸汇、沙丘、疏浚）的平衡驱动。其基本的物质平衡方程为：
ΣInputs − ΣOutputs = ΔV (change in sediment volume)
Often simplified as Qin − Qout = ΔS, where S represents the store of sediment within a littoral cell. Understanding this budget helps predict shoreline advance or retreat.
常简化为 Qin − Qout = ΔS，其中 S 代表沿岸单元内的沉积物储积量。理解这一收支有助于预测岸线的前进或退蚀。
5. The Universal Soil Loss Equation (USLE) | 通用土壤流失方程
The USLE is a widely used model to estimate average annual soil loss from sheet and rill erosion on agricultural land. Its general form is:
USLE 是广泛用于估算农地片蚀与细沟侵蚀年均土壤流失量的模型，其一般形式为：
A = R × K × LS × C × P
where: R = rainfall erosivity factor, K = soil erodibility factor, LS = slope length and steepness factor, C = cover-management factor, and P = support practice factor. The output A is typically expressed in tonnes per hectare per year.
式中：R 为降雨侵蚀力因子，K 为土壤可蚀性因子，LS 为坡长坡度因子，C 为覆盖管理因子，P 为水土保持措施因子。结果 A 通常以吨/公顷/年表示。
- R captures the energy of rainfall; higher in tropical storms.
- R 捕捉降雨能量，热带风暴区数值较高。
- K reflects how prone the soil is to detachment; silty soils have high K-values.
- K 反映土壤易蚀程度，粉砂质土壤 K 值较高。
- LS accounts for slope length and angle; steeper, longer slopes generate more erosion.
- LS 考量坡长与坡度，越陡越长则侵蚀越强。
- C measures the effect of cropping and mulching; bare ground has C ≈ 1, forest near 0.
- C 衡量耕作与覆盖效应，裸地 C≈1，森林接近 0。
- P reduces erosion through contour ploughing and terracing.
- P 通过等高耕作与梯田减少侵蚀。
6. Measures of Central Tendency & Dispersion | 集中趋势与离散度公式
Mean (x̄) = Σx / n. The arithmetic average of the data set. Sensitive to outliers.
算术平均值 x̄ = Σx / n。数据集的算术平均，对异常值敏感。
Median is the middle value when data are ordered; robust against skew. Mode is the most frequent value.
中位数是将数据排序后居中的值，抗偏态；众数是出现频次最高的值。
Range = Maximum − Minimum. Interquartile Range (IQR) = Q₃ − Q₁, covering the middle 50% of data and ignoring extremes.
极差 = 最大值 − 最小值。四分位距 (IQR) = 上四分位数 Q₃ − 下四分位数 Q₁，涵盖中间 50% 的数据，忽略极端值。
Standard deviation measures the spread around the mean. The sample standard deviation (s) is:
标准差衡量数据围绕均值的离散程度。样本标准差 (s) 公式为：
s = √ [ Σ(x − x̄)² / (n − 1) ]
For a population standard deviation (σ), divide by N instead of n−1. Use s when analysing fieldwork samples.
如果计算总体标准差 (σ)，则分母用 N。分析野外抽样数据时使用 s。
Coefficient of Variation (CV) = (Standard deviation / Mean) × 100%. CV allows comparison of dispersion between data sets with different units or means.
变异系数 (CV) = (标准差 / 平均值) × 100%。CV 可在单位或均值不同的数据集之间比较离散程度。
CV = (s / x̄) × 100%
7. Spearman’s Rank Correlation | 斯皮尔曼等级相关
Spearman’s rank correlation coefficient (rs) tests the strength and direction of a monotonic relationship between two ranked variables. It is commonly used in geography fieldwork to link environmental gradients with human activity.
斯皮尔曼等级相关系数 (rs) 用于检验两个排序变量之间单调关系的强度与方向，常用于地理野外考察中将环境梯度与人类活动关联。
rs = 1 − [ 6 Σd² / (n(n² − 1)) ]
where d = difference between the ranks of each pair, n = number of paired observations. rs ranges from −1 (perfect negative) to +1 (perfect positive), with 0 indicating no correlation. Always compare with a critical value table at the 0.05 significance level.
式中 d = 每对数据的等级差，n = 成对观测个数。rs 取值从 −1（完全负相关）到 +1（完全正相关），0 表示无相关。必须与 0.05 显著性水平下的临界值表对比。
8. Chi-Squared Test | 卡方检验
The chi-squared test (χ²) determines whether there is a significant association between two categorical variables, e.g. land-use type and distance from CBD. It compares observed frequencies (O) with expected frequencies (E).
卡方检验 (χ²) 判定两个分类变量之间是否存在显著关联，例如土地利用类型与距市中心距离。它比较观测频数 (O) 与期望频数 (E)。
χ² = Σ [ (O − E)² / E ]
Expected frequency E = (Row total × Column total) / Grand total. Degrees of freedom (df) = (Number of rows − 1) × (Number of columns − 1). If χ² calculated > χ² critical (from table), reject the null hypothesis.
期望频数 E = (行合计 ×
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