📚 Year 13 Edexcel Geography: Formula & Theorem Quick Reference Handbook | Year 13 Edexcel 地理：公式定理速查手册
This quick reference handbook compiles the essential formulas, indices and statistical tools required for the Year 13 Edexcel Geography course. From demographic rates to river discharge, carbon cycle productivity and Spearman’s Rank, each entry is presented with a clear formula, worked symbol explanations and a paired Chinese translation to support bilingual revision. Use this guide alongside your class notes and past papers to build confidence in data-response questions and synoptic investigations.
本速查手册汇编了 Year 13 Edexcel 地理课程必备的公式、指数和统计工具。从人口统计率、河流流量、碳循环生产力到斯皮尔曼等级相关，每个条目都配有清晰的公式、符号说明和中文翻译，支持双语复习。请将本指南与课堂笔记和历年真题结合使用，增强在数据分析题和综合探究中的信心。
1. Demographic Rates | 人口统计率
The Crude Birth Rate (CBR) measures the number of live births per 1,000 people in a year: CBR = (B / P) × 1000, where B is total live births and P is the mid‑year population.
粗出生率（CBR）衡量每年每千人口中的活产数：CBR = (B / P) × 1000，其中 B 为活产总数，P 为年中人口。
The Crude Death Rate (CDR) is calculated similarly: CDR = (D / P) × 1000, with D representing the number of deaths in a year.
粗死亡率（CDR）计算类似：CDR = (D / P) × 1000，D 代表年内死亡人数。
Infant Mortality Rate (IMR) focuses on deaths under one year of age: IMR = (Deaths under 1 / Total live births) × 1000.
婴儿死亡率（IMR）指一岁以下婴儿的死亡情况：IMR =（一岁以下死亡数 / 活产总数）× 1000。
2. Natural Increase & Doubling Time | 自然增长与人口倍增时间
Rate of Natural Increase (RNI) can be expressed per 1,000: RNI = CBR – CDR. To convert to a percentage, divide by 10: RNI (%) = (CBR – CDR) / 10.
自然增长率（RNI）可用千分比表示：RNI = CBR – CDR。转换为百分比时除以 10：RNI (%) = (CBR – CDR) / 10。
Doubling time estimates how many years it takes for a population to double at a constant growth rate, using the Rule of 70: Doubling time (years) = 70 / annual growth rate (%).
人口倍增时间用于估算在恒定增长率下人口翻一番所需的年数，采用 70 法则：倍增时间（年）= 70 / 年增长率（%）。
3. Net Migration & Migration Rate | 净迁移与迁移率
Net migration is the difference between in‑migration and out‑migration: Net migration = I – E, where I is immigrants and E is emigrants.
净迁移是迁入与迁出人数之差：净迁移 = I – E，I 为迁入人数，E 为迁出人数。
Net migration rate expresses this movement relative to population size: Net migration rate = (Net migration / P) × 1000.
净迁移率将人口移动与总人口规模相联系：净迁移率 =（净迁移 / P）× 1000。
4. Dependency & Age‑Sex Ratios | 抚养比与年龄性别比
The total dependency ratio shows the pressure on the productive population: Dependency ratio = ((Pop₀₋₁₄ + Pop₆₅₊) / Pop₁₅₋₆₄) × 100. Each age group is the population in that bracket.
总抚养比反映劳动年龄人口承受的负担：抚养比 =（（0-14岁人口 + 65岁及以上人口）/ 15-64岁人口）× 100。各组为对应年龄段人口。
Youth dependency ratio isolates the young: Youth ratio = (Pop₀₋₁₄ / Pop₁₅₋₆₄) × 100. Old‑age dependency ratio is (Pop₆₅₊ / Pop₁₅₋₆₄) × 100.
少儿抚养比仅考虑儿童：少儿抚养比 =（0-14岁人口 / 15-64岁人口）× 100。老年抚养比为 （65+人口 / 15-64岁人口）× 100。
5. Location Quotient & Economic Specialisation | 区位商与经济专门化
The Location Quotient (LQ) identifies whether a region has a higher concentration of a certain industry than the national average: LQ = (eᵢ/E) / (Eᵢ/N), where eᵢ is regional employment in industry i, E is total regional employment, Eᵢ is national employment in industry i, and N is total national employment.
区位商（LQ）用于判断某地区特定产业的集中度是否高于全国平均水平：LQ = (eᵢ/E) / (Eᵢ/N)，eᵢ 为区域 i 产业就业人数，E 为区域总就业，Eᵢ 为全国 i 产业就业，N 为全国总就业。
If LQ > 1, the region specialises in that sector and may export its goods or services. If LQ < 1, the sector is under‑represented.
若 LQ > 1，该地区专门化于该产业，可能输出商品或服务。若 LQ < 1，则产业集中度不足。
6. Gini Coefficient & Index of Dissimilarity | 基尼系数与相异指数
The Gini coefficient measures income or wealth inequality on a scale from 0 (perfect equality) to 1 (perfect inequality). It is derived from the Lorenz curve: G = A / (A + B), where A is the area between the line of equality and the Lorenz curve, and B is the area under the Lorenz curve.
基尼系数衡量收入或财富不平等程度，范围从 0（完全平等）到 1（完全不平等）。由洛伦兹曲线推导：G = A / (A + B)，A 为平等线与洛伦兹曲线之间的面积，B 为洛伦兹曲线下方面积。
A numerical approximation using deciles is: G = (2 / (n-1)) × Σ (i × yᵢ) – (n+1)/(n-1), but in exams interpretation is more common than computation.
用十分位数近似计算为：G = (2 / (n-1)) × Σ (i × yᵢ) – (n+1)/(n-1)，但考试中更常考解读而非计算。
The Index of Dissimilarity (ID) measures residential segregation between two groups: ID = 0.5 × Σ |aᵢ/A – bᵢ/B|, where aᵢ and bᵢ are the numbers of two groups in sub‑area i, and A and B are their total numbers in the whole city.
相异指数（ID）衡量两个群体在居住上的隔离程度：ID = 0.5 × Σ |aᵢ/A – bᵢ/B|，aᵢ 和 bᵢ 为子区域 i 中两群体的人数，A 和 B 为全市总数。
7. Hydrological & Fluvial Calculations | 水文与河流计算
River discharge is the volume of water passing a cross‑section per unit time: Q = A × v, where A is the cross‑sectional area (m²) and v is the mean velocity (m s⁻¹).
河流流量指单位时间通过断面的水体体积：Q = A × v，A 为横截面积（m²），v 为平均流速（m s⁻¹）。
Cross‑sectional area can be calculated from width and mean depth: A = w × d. For irregular channels, sum the areas of vertical sections.
横截面积可通过宽度和平均水深计算：A = w × d。不规则河槽可将多个垂直段面积求和。
Hydraulic radius describes the efficiency of a channel: R = A / P, where P is the wetted perimeter. A larger R indicates less resistance.
水力半径描述河道的输水效率：R = A / P，P 为湿周。R 越大，阻力越小。
Manning’s equation estimates velocity in open channels: v = (R^(2/3) × S^(1/2)) / n, where S is the water surface slope and n is Manning’s roughness coefficient.
曼宁公式估算明渠流速：v = (R^(2/3) × S^(1/2)) / n，S 为水面坡降，n 为曼宁粗糙系数。
8. Coastal Sediment Budget & Longshore Drift | 海岸沉积物预算与沿岸漂沙
A sediment budget expresses the balance between inputs and outputs in a coastal cell: Net change = Σ Inputs – Σ Outputs. Inputs may include river sediment, cliff erosion and longshore drift into the cell; outputs include sediment transported offshore, dredging and drift out of the cell.
沉积物预算表示海岸单元内输入与输出的平衡：净变化 = Σ 输入 – Σ 输出。输入可包括河流来沙、崖壁侵蚀和漂入沙量；输出包括离岸输送、疏浚和漂出沙量。
Longshore drift volume can be estimated practically by measuring the depth of closure and beach sediment movement, but a simplified conceptual formula is: Drift rate = K × (wave energy component alongshore). In Edexcel questions, you are more likely to interpret beach profiles and sediment budgets.
沿岸漂沙量可通过闭合深度和海滩沉积物移动估算，简化概念公式为：漂沙率 = K ×（沿岸波能分量）。在 Edexcel 试题中，更常见的是解读海滩剖面和沉积物预算。
9. Carbon Cycle & Ecological Productivity | 碳循环与生态生产力
Net Primary Productivity (NPP) is the amount of carbon fixed by photosynthesis minus plant respiration: NPP = GPP – R, where GPP is Gross Primary Productivity and R is autotrophic respiration.
净初级生产力（NPP）是光合作用固定的碳减去植物自身呼吸消耗后的剩余量：NPP = GPP – R，GPP 为总初级生产力，R 为自养呼吸。
NPP is usually expressed in grams of carbon per square metre per year (gC m⁻² yr⁻¹) and reflects the energy available to consumers.
NPP 通常以每年每平方米碳克数（gC m⁻² yr⁻¹）表示，反映可供消费者利用的能量。
Net Ecosystem Exchange (NEE) can be thought of as the balance between carbon uptake and release: NEE = – NPP + R_hetero; a negative NEE indicates a carbon sink.
净生态系统交换（NEE）可视为碳吸收与释放的平衡：NEE = -NPP + R_hetero；负 NEE 表示碳汇。
10. Risk & Vulnerability Assessment | 风险与脆弱性评估
The disaster risk equation commonly used is: Risk = (Hazard × Vulnerability) / Capacity to cope. Hazard refers to the physical event, vulnerability to the social and economic factors that increase susceptibility, and capacity to resources that reduce impacts.
常用灾害风险公式为：风险 =（致灾因子 × 脆弱性）/ 应对能力。致灾因子指物理事件，脆弱性指增加易损性的社会经济因素，应对能力指减轻影响的资源。
An alternative expression focusing on exposure is: Risk = f (Hazard, Exposure, Vulnerability). This highlights that people and assets must be present for a hazard to become a risk.
另一种强调暴露度的表达为：风险 = f（致灾因子，暴露度，脆弱性）。这强调只有存在人员和资产时，致灾因子才会转化为风险。
11. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s Rank tests the strength and direction of association between two ranked variables. The formula is: rₛ = 1 – (6 Σ d²) / (n(n² – 1)), where d is the difference between the ranks of each pair, and n is the number of paired observations.
斯皮尔曼等级相关系数检验两个排序变量之间的相关强度和方向。公式为：rₛ = 1 – (6 Σ d²) / (n(n² – 1))，d 为每对观测值的等级差，n 为配对观测数。
The result rₛ ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation). A critical values table must be used to determine statistical significance at the 95% or 99% confidence level. Remember to check for tied ranks and apply corrections if necessary.
结果 rₛ 介于 -1（完全负相关）到 +1（完全正相关）之间。必须查临界值表，判断在 95% 或 99% 置信水平下的统计显著性。注意检查相同等级，必要时进行校正。
12. Chi‑Squared Test & Standard Deviation | 卡方检验与标准差
The chi‑squared test compares observed frequencies with expected frequencies in categorical data: χ² = Σ ( (O – E)² / E ), where O is the observed value and E is the expected value. Degrees of freedom (df) must be calculated, usually (rows – 1) × (columns – 1) for contingency tables.
卡方检验比较分类数据中的观测频数与期望频数：χ² = Σ ( (O – E)² / E )，O 为观测值，E 为期望值。需计算自由度（df），列联表通常为（行数 – 1）×（列数 – 1）。
Standard deviation measures the spread of data around the mean. For a sample: s = √( Σ (x – x̄)² / (n – 1) ). A small s indicates data are clustered near the mean; a large s shows wide dispersion.
标准差衡量数据围绕均值的分散程度。样本标准差：s = √( Σ (x – x̄)² / (n – 1) )。s 小说明数据聚集在均值附近，s 大表示离散度大。
Coefficient of Variation (CV) allows comparison of dispersion across different units: CV = (s / x̄) ×
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