📚 GCSE Eduqas Geography: Formula & Theorem Quick Reference Handbook | GCSE Eduqas 地理:公式定理速查手册
Master the essential formulas, equations, and key theoretical models required for the GCSE Eduqas Geography specification. This quick reference handbook summarises the calculations you need for population, urbanisation, rivers, hazards, and development, along with the key models that underpin your understanding of geographical patterns and processes.
掌握 GCSE Eduqas 地理考试所需的公式、方程和关键理论模型。本速查手册汇总了人口、城市化、河流、自然灾害和发展等领域的计算方式,以及帮助理解地理格局和过程的重要模型。
1. Natural Increase & Population Change Rate | 自然增长与人口变化率
The natural increase of a population is the difference between the crude birth rate (BR) and the crude death rate (DR), usually expressed per 1000 people per year.
自然增长是指粗出生率(BR)与粗死亡率(DR)之间的差值,通常以每年每千人计算。
Natural Increase Rate (NIR) = BR – DR
If BR = 25 per 1000 and DR = 8 per 1000, then NIR = 17 per 1000, or 1.7%.
如果出生率为千分之二十五,死亡率为千分之八,那么自然增长率为千分之十七,即 1.7%。
The population change rate includes net migration. The basic equation is:
人口变化率还包括净迁移。基本方程为:
Population Change Rate (PCR) = (BR – DR) + Net Migration Rate (NMR)
Net migration rate is the difference between immigration (in-migration) and emigration (out-migration) per 1000 people.
净迁移率是迁入(移民)与迁出(外迁)每千人的差值。
For example, a country with BR = 18, DR = 10, immigration = 5, emigration = 2 per 1000 will have PCR = (18 – 10) + (5 – 2) = 8 + 3 = 11 per 1000, or 1.1% annual growth.
例如,某国出生率千分之十八,死亡率千分之十,迁入千分之五,迁出千分之二,则人口变化率为 (18 – 10) + (5 – 2) = 8 + 3 = 千分之十一,即年增长率 1.1%。
2. Net Migration & Migration Efficiency | 净迁移与迁移效率
Net migration (NM) is the absolute number of immigrants minus the number of emigrants over a given period, while the net migration rate (NMR) expresses this per 1000 of the population.
净迁移(NM)是在一定时期内迁入人数减去迁出人数的绝对值,而净迁移率(NMR)以每千人的比例表示。
NMR = (Immigrants – Emigrants) / Total Population × 1000
Migration efficiency measures how effective migration is in redistributing population between areas. It is calculated as:
迁移效率衡量迁移在区域间人口再分配中的有效性。计算公式为:
Migration Efficiency = (In‑migration – Out‑migration) / (In‑migration + Out‑migration) × 100%
A value closer to +100% indicates highly effective net inflow; a value closer to −100% indicates a highly effective net outflow.
数值越接近 +100%,表明净流入效率越高;越接近 −100%,表明净流出效率越高。
3. Urbanisation Rate & Level of Urbanisation | 城市化率与城市化水平
The level of urbanisation is the percentage of a country’s total population living in urban areas.
城市化水平是指一国总人口中居住在城市地区的百分比。
Urbanisation Level (%) = (Urban Population / Total Population) × 100
The rate of urbanisation refers to how quickly the urban share is growing, often given as an annual percentage point increase.
城市化率是指城市人口比例的增长速度,通常以每年百分点增加表示。
For example, if a country’s urban population grows from 30% to 33% in 10 years, the average annual urbanisation rate is (33 – 30) / 10 = 0.3 percentage points per year.
例如,如果一个国家的城市人口比例在 10 年内从 30% 上升到 33%,则年均城市化率为 (33 – 30) / 10 = 每年 0.3 个百分点。
The urban growth rate measures the annual increase in the absolute urban population and can be calculated using:
城市增长率衡量城市绝对人口的年增长率,可通过以下公式计算:
Urban Growth Rate (%) = [(Urban Pop (year 2) – Urban Pop (year 1)) / Urban Pop (year 1)] × 100
4. Population Density & Distribution | 人口密度与分布
Population density describes the average number of people living per square kilometre. It is a fundamental measure of how crowded an area is.
人口密度描述每平方公里平均居住人数,是衡量区域拥挤程度的基本指标。
Population Density = Total Population / Total Land Area (km²)
Physiological density refines this by considering only arable (agriculturally productive) land:
生理密度进一步细化,仅考虑可耕地(农业生产力高的土地):
Physiological Density = Total Population / Area of Arable Land (km²)
Agricultural density relates the number of farmers to the amount of arable land, giving insight into agricultural efficiency:
农业密度将农民人数与耕地面积联系起来,反映农业效率:
Agricultural Density = Number of Farmers / Area of Arable Land
These measures help explain patterns of population distribution and the pressure people place on the land.
这些指标有助于解释人口分布格局以及人类对土地造成的压力。
5. River Discharge & Runoff Depth | 河流流量与径流深度
Discharge (Q) is the volume of water flowing past a given point in a river per unit time, usually measured in cubic metres per second (cumecs).
流量(Q)是单位时间内流过河流某一点的水量,通常以立方米/秒(cumecs)为单位。
Discharge (Q) = Cross‑sectional Area (A) × Average Velocity (V)
Cross-sectional area is calculated as average width × average depth. If a river is 12 m wide and 1.5 m deep on average, A = 12 × 1.5 = 18 m². If velocity is 2 m/s, Q = 18 × 2 = 36 m³/s.
横截面积计算为平均宽度 × 平均深度。若某河段平均宽 12 米、深 1.5 米,则 A = 12 × 1.5 = 18 m²。若流速为 2 米/秒,则 Q = 18 × 2 = 36 m³/s。
Runoff depth converts the total volume of water discharged from a catchment into an equivalent depth spread over the whole basin area:
径流深度是将流域输出的总水量换算为均匀覆盖全流域的等效水深:
Runoff Depth (mm) = (Total Discharge Volume (m³) / Catchment Area (m²)) × 1000
This helps compare wet and dry years and assess flood risk.
这有助于比较丰水年和枯水年,并评估洪水风险。
6. Drainage Basin Water Balance | 流域水平衡方程
The water balance equation expresses the relationship between precipitation, evapotranspiration, runoff, and changes in storage within a drainage basin over a given time.
水平衡方程表达了在一定时间内流域内降水、蒸发蒸腾、径流和储水量变化之间的关系。
P = Q + E + ΔS
Where: P = precipitation, Q = runoff, E = evapotranspiration, ΔS = change in storage (soil moisture, groundwater, lakes).
其中:P = 降水量,Q = 径流量,E = 蒸发蒸腾量,ΔS = 储水量变化(土壤水分、地下水、湖泊)。
During a dry spell, ΔS is negative because stored water is being used. During a storm, ΔS becomes positive as the basin stores water.
在干旱期,ΔS 为负,因为储存的水被消耗;在暴雨期间,ΔS 为正,因为流域蓄水。
This equation is essential for understanding river regimes and water resource management.
该方程对于理解河流情势和水资源管理至关重要。
7. Natural Hazard Risk Formula | 自然灾害风险公式
Risk from a natural hazard is not determined by the hazard alone; it depends on the vulnerability of the population and their capacity to cope.
自然灾害的风险不仅由灾害本身决定,还取决于人口的脆弱性和他们的应对能力。
Risk = (Hazard × Vulnerability) / Capacity to Cope
Hazard refers to the magnitude and frequency of the physical event (e.g., earthquake magnitude, flood return period).
灾害指物理事件的规模和频率(如地震震级、洪水重现期)。
Vulnerability includes factors such as population density, building quality, and socioeconomic conditions that increase susceptibility to harm.
脆弱性包括人口密度、建筑质量以及增加受伤害可能性的社会经济条件等因素。
Capacity to cope is the ability of a community to prepare for, respond to, and recover from a hazard, influenced by wealth, education, technology, and governance.
应对能力指社区备灾、响应和恢复的能力,受到财富、教育、技术和治理的影响。
Thus, a moderate earthquake in a highly vulnerable area with low coping capacity can produce a disaster far greater than a stronger earthquake in a well‑prepared region.
因此,在脆弱性高且应对能力低的地区,一次中等强度地震所造成的灾难可能远比在准备充分的地区发生的更强地震更为严重。
8. Demographic Transition Model (DTM) | 人口转变模型
The Demographic Transition Model is a theoretical framework that describes how birth rates, death rates, and total population change as a country develops economically.
人口转变模型是一个理论框架,描述随着经济发展,出生率、死亡率和总人口如何变化。
It is divided into five stages, each with characteristic vital rates.
它分为五个阶段,每个阶段具有典型的生命统计特征。
| Stage 阶段 | Birth Rate 出生率 | Death Rate 死亡率 | Natural Increase 自然增长 | Example 示例 |
|---|---|---|---|---|
| 1 | High, fluctuating | High, fluctuating | Very low or zero | Few remote tribes |
| 2 | High | Falling rapidly | Rapid increase | Afghanistan, Niger |
| 3 | Falling | Low | Slowing increase | India, Kenya |
| 4 | Low | Low | Stable or very slow | UK, USA, France |
| 5 | Very low, below replacement | Low, possibly rising | Declining | Japan, Germany |
Understanding the DTM helps explain population pyramids, dependency ratios, and future population projections.
理解人口转变模型有助于解释人口金字塔、抚养比和未来人口预测。
9. Urban Land Use Models: Burgess & Hoyt | 城市土地利用模型:伯吉斯与霍伊特
The Burgess concentric zone model (1925) suggests that a city grows outwards in a series of rings from the Central Business District (CBD).
伯吉斯同心圈模型(1925年)认为城市从中心商务区(CBD)向外以一系列环带形式扩展。
| Zone 区域 | Description 描述 |
|---|---|
| 1. CBD | Commercial core, highest land values |
| 2. Transition zone | Old industry, low‑quality housing |
| 3. Inner suburbs | Terraced housing, working‑class |
| 4. Outer suburbs | Semi‑detached, middle‑class |
| 5. Commuter zone | Villages / towns linked by transport |
The Hoyt sector model (1939) modifies Burgess by suggesting that land uses develop in wedges or sectors radiating from the CBD along transport routes.
霍伊特扇形模型(1939年)修正了伯吉斯,认为土地利用沿交通路线从CBD向外呈楔形或扇形发展。
For example, high‑status residential areas tend to follow major roads, while industry locates near railways or rivers.
例如,高地位住宅区往往沿主要道路分布,而工业则靠近铁路或河流。
Both models are used to explain patterns of social segregation and land use in UK cities, although real cities are more complex.
这两个模型都用于解释英国城市的社会隔离和土地利用格局,尽管现实城市更为复杂。
10. Development Indicators & Engel’s Coefficient | 发展指标与恩格尔系数
Gross Domestic Product (GDP) per capita and Gross National Income (GNI) per capita are common economic indicators, but they do not capture quality of life fully.
人均国内生产总值(GDP)和人均国民总收入(GNI)是常见的经济指标,但并不能完全反映生活质量。
GDP per capita = Total GDP / Total Population
The Human Development Index (HDI) combines three dimensions: health (life expectancy at birth), education (mean and expected years of schooling), and standard of living (GNI per capita). It is expressed as a value between 0 and 1.
人类发展指数(HDI)综合三个维度:健康(出生时预期寿命)、教育(平均受教育年限和预期受教育年限)和生活水平(人均GNI),数值范围在 0 到 1 之间。
Engel’s coefficient is a measure of food security and living standards. It indicates the proportion of total household expenditure spent on food.
恩格尔系数是衡量粮食安全和生活水平的指标,表示食品支出占家庭总支出的比例。
Engel’s Coefficient (%) = (Food Expenditure / Total Expenditure) × 100
A lower Engel coefficient (below 20‑30%) generally indicates a higher standard of living, as families spend a smaller share on basic needs and more on services and luxuries.
恩格尔系数较低(低于20‑30%)通常意味着较高的生活水平,因为家庭在基本需求上的支出比例较小,而在服务和奢侈品上的支出更多。
Countries in sub‑Saharan Africa may have Engel coefficients of 50‑70%, whereas in western Europe it is often below 15%.
撒哈拉以南非洲国家的恩格尔系数可能在50‑70%,而西欧常低于15%。
Other composite indices, such as the Multidimensional Poverty Index (MPI) and Happy Planet Index (HPI), also feature in GCSE case studies.
其他综合指数,如多维贫困指数(MPI)和快乐星球指数(HPI),也在 GCSE 案例研究中出现。
11. Food Security & Crop Yield Calculations | 粮食安全与作物产量计算
Food security exists when all people have physical, social, and economic access to sufficient, safe, and nutritious food at all times.
粮食安全指所有人在任何时候都能从物质、社会和经济上获得充足、安全和有营养的食物。
Crop yield is a fundamental agricultural statistic, often measured in tonnes per hectare.
作物产量是一项基本的农业统计指标,通常以吨/公顷为单位。
Crop Yield (t/ha) = Total Production (tonnes) / Harvested Area (ha)
The Food Balance Sheet approach evaluates a country’s food availability by comparing domestic production plus imports with uses such as exports, feed, and waste.
食物平衡表方法通过比较国内产量加进口与出口、饲料、浪费等用途,评估一国的粮食供应状况。
A simple availability indicator is the self‑sufficiency ratio:
一个简单的供应指标是自给率:
Self‑sufficiency Ratio (%) = (Domestic Production / Domestic Consumption) × 100
A ratio below 100% means the country relies on imports; above 100% indicates a net surplus.
比率低于100%意味着该国依赖进口;高于100%则表示净盈余。
12. Climate Data & Aridity Index | 气候数据与干旱指数
Climate graphs display average monthly temperature (as a line) and total monthly precipitation (as bars). Mean annual temperature is calculated simply as:
气候图以折线显示月平均气温,以柱状显示月降水量。年平均气温的简单计算为:
Mean Annual Temperature = Sum of 12 Monthly Mean Temperatures / 12
Total annual precipitation is the sum of all monthly precipitation totals. These figures are used to construct climate graphs and classify climate types.
年降水量是所有月降水量的总和。这些数据用于构建气候图并进行气候分类。
The aridity index helps determine how dry a region is, often based on the ratio of precipitation to potential evapotranspiration (PET):
干旱指数有助于确定某区域的干燥程度,通常基于降水量与潜在蒸发蒸腾量(PET)的比值:
Aridity Index = Precipitation / PET
Values below 0.2 indicate hyper‑arid conditions, 0.2‑0.5 arid, 0.5‑0.65 semi‑arid, and above 0.65 sub‑humid or humid.
数值低于 0.2 表示极端干旱,0.2‑0.5 为干旱,0.5‑0.65 为半干旱,高于 0.65 为半湿润或湿润。
This index links to the study of desertification and water scarcity in regions such as the Sahel.
该指数与荒漠化以及萨赫勒等地区的水资源短缺研究相联系。
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