📚 Year 12 SQA Geography: Formula and Theorem Quick Reference Guide | SQA地理公式定理速查手册
This quick reference guide brings together the key quantitative formulas, statistical tests, and geographical models required for the SQA Geography course at Year 12 (Higher and Advanced Higher). Whether you are analysing river discharge, calculating population indices, or applying Spearman’s rank correlation, having these equations at your fingertips will strengthen your exam technique and data-interpretation skills. Every formula is accompanied by a clear explanation of its components and context, so you can move from memory to application with confidence.
本速查手册汇总了Year 12 SQA地理（Higher 与 Advanced Higher）必备的定量公式、统计检验与地理模型。无论你在计算河流流量、人口指数，还是进行斯皮尔曼秩相关分析，掌握这些公式都将提升你的考试技巧与数据解读能力。每条公式都附有对各个变量及其应用场景的清晰说明，帮助你从记忆走向灵活运用。
1. River Discharge | 河流流量公式
River discharge is the volume of water passing a given cross-section per unit of time. It is a fundamental measure for understanding channel capacity, flood risk and the efficiency of a river in transporting material.
河流流量是单位时间内通过某一横断面的水体体积。它是理解河道容量、洪水风险以及河流输沙效率的基础指标。
Q = A × v
where Q is discharge (m3/s), A is cross-sectional area (m2), and v is mean velocity (m/s). Area is calculated from channel width and depth measurements taken at regular intervals across the stream.
其中 Q 为流量（m3/s），A 为横截面积（m2），v 为平均流速（m/s）。面积通常通过在河道中多点测量宽度与水深后加权计算得出。
2. Water Balance Equation | 水平衡方程
The water balance equation expresses the relationship between inputs, outputs and changes in storage within a drainage basin. It is essential for evaluating water availability and the impact of land-use change on the hydrological cycle.
水平衡方程表达了流域内输入、输出与蓄水量变化之间的关系。它是评估水资源可利用量以及土地利用变化对水循环影响的关键工具。
P = Q + E + ΔS
P = precipitation, Q = runoff (streamflow), E = evapotranspiration, ΔS = change in basin water storage (soil moisture, groundwater, etc.). The equation can be rearranged to isolate any single component, depending on the data available.
P 为降水量，Q 为径流量，E 为蒸散发量，ΔS 为流域蓄水量变化（土壤水、地下水等）。该方程可根据已知数据重新排列，以求解任一未知项。
3. Runoff Coefficient | 径流系数
The runoff coefficient indicates the proportion of rainfall that becomes direct runoff. It reflects the permeability of surfaces, vegetation cover and antecedent soil moisture, and is widely used in flood estimation and urban drainage design.
径流系数表示降水中转化为直接径流的比例。它反映了地表渗透性、植被覆盖和前期土壤湿度，广泛应用于洪水估算和城市排水设计中。
C = Q / P
where C is the runoff coefficient (dimensionless, often expressed as a percentage), Q is total runoff depth (mm) and P is total precipitation depth (mm) over the same period. A higher coefficient indicates more impermeable conditions and greater flood risk.
其中 C 为径流系数（无量纲，常以百分比表示），Q 为同期总径流深（mm），P 为总降水量（mm）。系数越高，表明下垫面越不透水，洪水风险也越大。
4. Population Growth Rate | 人口增长率
Population change is analysed using crude birth rate, crude death rate and the rate of natural increase. These metrics are fundamental in demography and feature frequently in SQA population geography questions.
人口变化通过粗出生率、粗死亡率和自然增长率进行分析。这些指标是人口学的基础，经常出现在SQA人口地理的考题中。
Rate of Natural Increase (%) = (CBR − CDR) / 10
CBR (crude birth rate) and CDR (crude death rate) are expressed per 1000 population per year. Dividing by 10 converts the net annual change from per thousand to a percentage. A related useful model is the ‘rule of 70’ for doubling time: Doubling Time (years) = 70 / growth rate (%).
CBR（粗出生率）和 CDR（粗死亡率）以每年每千人为单位。除以10可将净年变动从千分比转换为百分比。一个相关的常用模型是计算人口倍增时间的 “70法则”：倍增时间（年）= 70 / 增长率（%）。
5. Population Density & Dependency Ratio | 人口密度与抚养比
Population density illustrates the spatial concentration of people, while the dependency ratio quantifies the economic burden on the working-age population. Together they help explain regional development pressures and social policy demands.
人口密度展示了人口的空间集中程度，而抚养比则量化了劳动年龄人口所承受的经济负担。两者结合有助于解释区域发展压力和社会政策需求。
Population Density = Total Population / Land Area (km2)
Dependency Ratio = ((Young (0–14) + Old (65+)) / Working-age (15–64)) × 100
The dependency ratio is expressed as a percentage; a higher value indicates greater pressure on health, education and pension systems. SQA questions often ask you to compare dependency ratios between countries at different stages of the demographic transition model.
抚养比以百分比表示；数值越高，意味着医疗、教育和养老金体系的压力越大。SQA试题常要求你对比处于人口转型模型不同阶段的国家的抚养比。
6. Rank-Size Rule & Primate City Index | 等级规模法则与城市首位度指数
Urban hierarchies can be tested using the rank-size rule and the primate city index. Both concepts appear in the Urban Change and Development section and help explain settlement patterns and regional imbalance.
城镇等级体系可以通过等级规模法则和城市首位度指数来检验。这两个概念都出现在城市变迁与发展单元中，有助于解释聚落格局与区域不均衡。
Rank-Size Rule: Pn = P1 / n
Two-City Index = P1 / P2
Four-City Index = P1 / (P2 + P3 + P4)
where P1 is the population of the largest city, Pn is the population of the city ranked n, and P2, P3, P4 are the next largest cities. A primate city distribution exists when the largest city is disproportionately larger than the rest, often indicated by a two-city index well above 2 or a small four-city index close to 1.
其中 P1 为最大城市的人口，Pn 为第 n 位城市的人口，P2、P3、P4 为第二、三、四大城市的人口。当最大城市不成比例地大于其他城市时，即存在首位分布，通常表现为二城市指数远大于 2，或四城市指数接近 1。
7. Location Quotient | 区位商
The location quotient (LQ) measures the concentration of a specific economic activity in a local area compared with a larger reference region. It is a standard technique in economic geography and regional planning for identifying specialised clusters.
区位商（LQ）用于衡量某一地区中特定经济活动的集中程度，并与更大的参考区域进行比较。它是经济地理和区域规划中识别专业化产业集群的标准方法。
LQ = (ei / et) ÷ (Ei / Et)
ei = local employment in sector i, et = total local employment, Ei = national employment in sector i, Et = total national employment. An LQ > 1 suggests the local area is more specialised in that sector than the national average; LQ < 1 indicates below-average specialisation.
ei 为当地 i 行业的就业人数，et 为当地总就业人数，Ei 为全国 i 行业就业人数，Et 为全国总就业人数。LQ > 1 表明当地在该行业比全国平均水平更为专业化；LQ < 1 则表明专业化程度低于平均。
8. Spearman’s Rank Correlation Coefficient | 斯皮尔曼秩相关系数
Spearman’s rank is a non-parametric statistical test used to measure the strength and direction of association between two ranked variables. It is a core skill in the SQA Geographical Skills component and appears in human and physical geography investigations alike.
斯皮尔曼秩相关是一种非参数统计检验，用于衡量两个排序变量之间关联的强度和方向。它是SQA地理技能部分的核心内容，常见于人文与自然地理调查中。
rs = 1 − [6Σ d2 / (n(n2 − 1))]
rs = Spearman’s rank correlation coefficient, d = difference between the ranks of each pair of observations, n = number of paired observations. The value of rs ranges from −1 (perfect negative correlation) to +1 (perfect positive correlation). A test of significance using a critical value table is required to determine whether the result is statistically meaningful.
rs 为斯皮尔曼秩相关系数，d 为每对观测值排名的差值，n 为配对观测值的数量。rs 的取值范围为 −1（完全负相关）到 +1（完全正相关）。需要使用临界值表进行显著性检验，以判断结果在统计上是否显著。
9. Chi-Squared Test | 卡方检验
The chi-squared test evaluates whether there is a significant association between two categorical variables, or whether an observed distribution differs from an expected one. It is regularly used in geography to analyse questionnaire data, land-use patterns and neighbourhood characteristics.
卡方检验用于评估两个分类变量之间是否存在显著关联，或观测频数分布是否与期望频数分布存在显著差异。在地理中常用于分析问卷调查数据、土地利用格局和街区特征。
χ2 = Σ [(O − E)2 / E]
O = observed frequency, E = expected frequency. Degrees of freedom are calculated as (number of rows − 1) × (number of columns − 1). The calculated χ2 value is compared with a critical value from the chi-squared distribution table at the chosen significance level (often 0.05).
O 为观测频数，E 为期望频数。自由度的计算公式为（行数 − 1）×（列数 − 1）。将计算得出的 χ2 值与所选显著性水平（通常为 0.05）下卡方分布表中的临界值进行比较，即可得出统计推断。
10. Nearest Neighbour Index | 最近邻指数
The nearest neighbour index (Rn) analyses point distribution patterns by comparing the observed mean distance between nearest neighbours with the expected mean distance for a random pattern. It helps geographers describe settlement dispersion, vegetation clustering or the spread of disease incidents.
最近邻指数（Rn）通过比较观测的最近邻平均距离与随机模式下的期望平均距离，来分析点状分布格局。它可帮助地理学者描述聚落离散度、植被群集或疾病事件的散布特征。
Rn = 2 D̄ √(n / A)
D̄ = mean observed nearest-neighbour distance, n = number of points, A = total study area. Rn = 1 indicates a random pattern, Rn close to 0 indicates clustering, and RnPublished by TutorHao | Year 12 Geography Revision Series | aleveler.com
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