📚 Year 11 WJEC Geography: Quick Reference Handbook of Formulas & Theorems | Year 11 WJEC 地理：公式定理速查手册
This quick reference handbook brings together all the essential formulas, models and theoretical frameworks required for the Year 11 WJEC Geography specification. Whether you are calculating population change, interpreting urban land use patterns or analysing river discharge, having a clear and organised summary of the key equations and theorems will boost your confidence in the exam.
这本速查手册汇集了 Year 11 WJEC 地理课程中所有必需的公式、模型和理论框架。无论你是在计算人口变化、解读城市土地利用模式还是分析河流流量，拥有一份条理清晰的关键方程与定理总结都能提升你在考试中的信心。
1. Demographic Formulas | 人口统计公式
Natural increase is the difference between the birth rate and the death rate in a given area. It does not account for migration.
自然增长率是指某一地区出生率与死亡率之间的差值，它不包含迁移因素。
Natural Increase = Birth rate − Death rate
自然增长率 = 出生率 − 死亡率
To understand overall population change, we add net migration (immigration minus emigration) to the natural increase figure.
要理解整体的人口变动，需要将净迁移（迁入减去迁出）加到自然增长数据上。
Population Change = (Births − Deaths) + (Immigration − Emigration)
人口变化 =（出生人数 − 死亡人数）+（迁入人数 − 迁出人数）
Population density describes how crowded a place is. It is found by dividing the total population by the land area.
人口密度描述一个地方的拥挤程度，用总人口除以土地面积即可求得。
Population Density = Total Population / Area (km²)
人口密度 = 总人口 / 面积（km²）
2. The Demographic Transition Model (DTM) | 人口转变模型
The DTM describes how birth and death rates change as a country develops. It is divided into five stages, each with distinct demographic characteristics.
人口转变模型（DTM）描述随着国家发展，出生率和死亡率如何变化。它分为五个阶段，每个阶段都有鲜明的人口特征。
| Stage | Key Features (EN) | 关键特征 (中文) |
|---|---|---|
| 1 | High fluctuating birth and death rates; slow population growth | 高出生率和高死亡率波动；人口增长缓慢 |
| 2 | Death rate falls rapidly; birth rate remains high; rapid population increase | 死亡率迅速下降；出生率保持高位；人口快速增长 |
| 3 | Birth rate begins to decline; population growth starts to slow | 出生率开始下降；人口增速放缓 |
| 4 | Both birth and death rates are low; population becomes stable | 出生率和死亡率均处于低位；人口趋于稳定 |
| 5 | Very low birth rate falls below death rate; natural decrease possible | 极低出生率降至死亡率以下；可能出现自然减少 |
3. Urban Land Use Models | 城市土地利用模型
Geographers use theoretical models to explain the pattern of land use within cities. The three classic models you need to know for WJEC are Burgess's concentric zone model, Hoyt's sector model and the Harris–Ullman multiple nuclei model.
地理学家用理论模型来解释城市内部土地利用的格局。WJEC 要求你掌握三种经典模型：伯吉斯的同心圆模型、霍伊特的扇形模型以及哈里斯—乌尔曼的多核心模型。
| Model | English description | 中文描述 |
|---|---|---|
| Burgess Concentric Zone | City grows outward from the CBD in a series of rings; inner zones house industry and low-income groups, outer rings are for wealthier commuters. | 城市从中心商务区向外呈同心圆状扩张；内环为工业区和低收入群体，外环为较富裕的通勤者。 |
| Hoyt Sector Model | Land use develops in wedge-shaped sectors radiating from the CBD along transport routes; industry follows railways, high-class housing occupies desirable corridors. | 土地利用沿交通线从 CBD 向外呈扇形扩展；工业沿铁路分布，高收入住宅占据优势廊道。 |
| Harris–Ullman Multiple Nuclei | Cities have several growth points (nuclei) around which different land uses cluster, e.g. industrial estates, retail parks and university campuses may each form separate centres. | 城市有多个增长点（核心），不同的土地利用围绕它们聚集，如工业园区、零售园区和大学校区分别形成独立中心。 |
4. Central Place Theory | 中心地理论
Christaller's Central Place Theory explains the size, number and distribution of settlements. Settlements act as central places providing goods and services to their surrounding market areas.
克里斯塔勒的中心地理论解释了聚落的大小、数量和分布。聚落充当中心地向其周围的腹地市场提供商品和服务。
The threshold population is the minimum number of people needed to support a service. The range is the maximum distance consumers are willing to travel to obtain that service.
门槛人口是维持某项服务所需的最低人口数量。服务范围则是消费者愿意为获取该服务而旅行的最大距离。
In practice, low-order goods (e.g. bread) have a low threshold and a short range, so they are found in many small settlements. High-order goods (e.g. furniture) require a larger threshold and a longer range, so they are only found in larger towns and cities.
在实践中，低等级商品（如面包）门槛低、范围短，因此广泛分布在众多小型居民点中。高等级商品（如家具）需要更高的门槛和更远的范围，因此只出现在较大的市镇和城市中。
Market area viability → Population threshold ≥ required customer base
市场区域可行性 → 人口门槛 ≥ 所需客户基数
5. Development Indicators & HDI Formula | 发展指标与人类发展指数公式
Development is measured using both single indicators (e.g. GNI per capita, literacy rate) and composite indices. The Human Development Index (HDI) combines health, education and income into a single figure between 0 and 1.
发展指标既有单一指标（如人均国民总收入、识字率），也有综合指数。人类发展指数（HDI）将健康、教育和收入综合为一个介于 0 到 1 之间的数值。
HDI is calculated by averaging the three normalised indices: Life Expectancy Index (LEI), Education Index (EI) and Income Index (II).
HDI 通过将预期寿命指数（LEI）、教育指数（EI）和收入指数（II）这三个标准化指数取平均值来计算。
HDI = (LEI + EI + II) / 3
HDI =（预期寿命指数 + 教育指数 + 收入指数）/ 3
Other useful indicators include the Gini coefficient, which measures income inequality, and the Gender Inequality Index (GII). In an exam, you may be asked to select and justify indicators for a specific country or development question.
其他常用指标包括衡量收入不平等的基尼系数，以及性别不平等指数（GII）。考试中可能要求你针对特定国家或发展问题选择并论证合适指标。
6. Rostow's Modernisation Theory | 罗斯托现代化理论
Rostow proposed that all countries pass through five linear stages of economic growth. This theorem is often used to explain differences in development and to justify aid or investment strategies.
罗斯托提出，所有国家都会经历五个线性的经济增长阶段。这一理论常被用来解释发展差异并为援助或投资策略提供依据。
| Stage | Key Characteristics (EN) | 关键特征 (中文) |
|---|---|---|
| 1. Traditional society | Subsistence agriculture; limited technology; rigid social structures | 自给农业；技术有限；僵化的社会结构 |
| 2. Pre-conditions for take-off | Investment in infrastructure; emergence of entrepreneurs; primary sector growth | 基础设施投资；企业家涌现；第一产业增长 |
| 3. Take-off | Rapid industrialisation; rising investment; self-sustaining growth begins | 快速工业化；投资上升；自我维持的增长启动 |
| 4. Drive to maturity | Economy diversifies; technology spreads; secondary sector dominates | 经济多元化；技术传播；第二产业主导 |
| 5. High mass consumption | Service sector expands; consumer goods widely available; high standard of living | 服务业扩展；消费品广泛普及；高生活水平 |
7. River Discharge & Bradshaw Model | 河流流量与布拉德肖模型
River discharge is the volume of water flowing through a channel cross-section per second. It is an essential measurement for understanding flood risk.
河流流量是指每秒钟通过河道横截面的水体体积，它是理解洪涝风险的关键指标。
Discharge (Q) = Cross-sectional area (A) × Average velocity (V)
流量（Q）= 横截面积（A）× 平均流速（V）
The Bradshaw Model summarises how a river's characteristics change from source to mouth. It is not a mathematical formula, but a conceptual theorem often tested in WJEC fieldwork questions.
布拉德肖模型总结了河流特征从源头到河口的变化规律。它并非数学公式，而是一个概念性定理，常出现在 WJEC 的野外作业试题中。
| Variable | Upstream trend | 上游趋势 |
|---|---|---|
| Discharge | Low → increases downstream | 小 → 向下游增大 |
| Velocity | Low → increases downstream | 低 → 向下游增加 |
| Channel width & depth | Narrow, shallow → wider, deeper | 窄而浅 → 宽而深 |
| Load particle size | Large, angular → smaller, rounded | 大而角状 → 小而浑圆 |
| Gradient | Steep → gentle downstream | 陡 → 向下游变缓 |
8. Coastal Sediment Budget | 海岸沉积物收支
A coastal sediment budget compares the inputs and outputs of sediment along a stretch of coastline. When inputs exceed outputs, the beach builds up (positive budget); when outputs exceed inputs, erosion dominates (negative budget).
海岸沉积物收支比较一段海岸线上沉积物的输入与输出。当输入大于输出时，海滩堆积（正收支）；当输出大于输入时，侵蚀占主导（负收支）。
liff erosion + Longshore drift in) − (Longshore drift out + Offshore transport + Extraction)
沉积物收支 =（河流泥沙 + 悬崖侵蚀 + 沿岸流输入）−（沿岸流输出 + 离岸搬运 + 人为采砂）
Understanding this balance helps coastal managers decide where to place groynes, whether to replenish beaches or whether retreat is the most sustainable option.
理解这一平衡有助于海岸管理者决定在哪里设置丁坝、是否需要人工补沙，或者后退是否是最可持续的选择。
9. Gradient Calculation | 坡度计算
Gradient is a measure of slope steepness, frequently encountered in river and fieldwork studies. It can be expressed as a ratio, a fraction or a percentage.
坡度是对倾斜程度的量度，在河流及野外考察中十分常见。它可以用比例、分数或百分比表示。
Gradient = Vertical drop / Horizontal distance
坡度 = 垂直落差 / 水平距离
ance of 120 metres, the gradient is 3/120 = 0.025 or 1:40. In percentage terms this is 2.5%.
例如，若一条溪流在 120 米水平距离内下降了 3 米，则坡度为 3/120 = 0.025，即 1:40，用百分比表示为 2.5%。
Always double-check the units in an exam; vertical and horizontal distances must be in the same unit before you perform the calculation.
考试时务必检查单位；进行计算前，垂直距离和水平距离需使用相同单位。
10. IPAT Equation & Carrying Capacity | IPAT 方程与承载力
The IPAT equation is a theorem used to estimate the environmental impact (I) of human activities. It links impact to three drivers: population, affluence and technology.
IPAT 方程是一个用于估算人类活动环境影响（I）的定理，它将影响与三个驱动因素联系起来：人口、富裕程度和技术。
I = P × A × T
环境影响 = 人口 × 人均消费 × 技术因子
echnology (environmental impact per unit of consumption). This theorem helps explain why two populations of the same size can have dramatically different ecological footprints.
其中 P = 人口规模，A = 富裕程度（人均消费），T = 技术（单位消费的环境影响）。该定理有助于解释为何两个同等规模的人口可能具有截然不同的生态足迹。
Carrying capacity is the maximum number of organisms an environment can support indefinitely without degradation. When a population's ecological footprint exceeds its area's biocapacity, an ecological deficit occurs.
承载力是指环境在不受退化的情况下能够持续支持的最大生物数量。当一个地区的生态足迹超过其生物承载力时，便出现生态赤字。
Published by TutorHao | Geography Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图