📚 AQA GCSE Geography Formula & Theorem Quick-Reference Handbook | AQA GCSE 地理公式定理速查手册
This handy reference guide gathers all the key formulas, calculations, and numerical skills you need to master for the AQA GCSE Geography exam. From measuring river discharge to interpreting population data and map gradients, each formula is presented clearly with worked explanations to help you revise efficiently.
这本速查手册汇集了你在 AQA GCSE 地理考试中需要掌握的所有关键公式、计算和数值技能。从测量河流流量到分析人口数据和地图梯度，每个公式都清晰地列出并配有解释，帮助你高效复习。
1. River Discharge & Hydraulic Geometry | 河流流量与水力学几何
River discharge (Q) is the volume of water flowing past a point in a river channel per unit of time. It is a fundamental measure linking channel dimensions to flow velocity and is expressed in cubic metres per second (m³/s).
河流流量（Q）是单位时间内流过河道某一点的水量。它是连接河道尺寸与流速的基本度量，单位为立方米每秒（m³/s）。
Discharge (Q) = Cross-sectional Area (A) × Mean Velocity (V)
| Symbol | English Meaning | 中文含义 |
|---|---|---|
| Q | Discharge (cubic metres per second, m³/s) | 流量（立方米每秒） |
| A | Cross-sectional area of the channel (square metres, m²) | 河道横截面积（平方米） |
| V | Mean water velocity (metres per second, m/s) | 平均水流速度（米/秒） |
In fieldwork, A is calculated by measuring the channel width and water depth at regular intervals across a transect, then summing the sections' areas. V is often estimated using a flowmeter or by timing a floating object over a known distance and multiplying surface velocity by a correction factor (usually 0.8 or 0.85) to approximate mean velocity.
实地考察中，横截面积 A 通过在一条横断面上等距测量河宽和水深，然后汇总各分块面积来计算。流速 V 通常用流速仪测量，或通过计时浮标漂过已知距离得到表面流速，再乘以校正系数（通常为 0.8 或 0.85）来估算平均流速。
2. Flow Velocity & Gradient | 流速与河道梯度
Velocity and gradient are closely related in river studies. Surface velocity can be measured simply, while gradient quantifies the steepness of the river bed or valley sides along a given reach.
在河流研究中，流速与梯度密切相关。表面流速可以简单测量，而梯度则量化了河床或河谷侧壁在某一河段的陡峭程度。
Surface Velocity (Vsurf) = Distance (d) ÷ Time (t)
Channel Gradient = Vertical fall (Δh) ÷ Horizontal distance (D)
Gradient as a percentage = (Δh ÷ D) × 100
| Term | English Meaning | 中文含义 |
|---|---|---|
| d | Distance travelled by float (m) | 浮标移动距离（米） |
| t | Time taken (seconds) | 所用时间（秒） |
| Δh | Change in height (vertical interval in metres) | 高差（垂直间距，米） |
| D | Horizontal ground distance (m) | 水平地面距离（米） |
Gradient can also be expressed as a ratio, for example '1 in 15', meaning the river falls 1 metre for every 15 metres of horizontal distance. This is calculated as 1 : (D / Δh).
梯度还可以用比例表示，例如 "1 in 15"，意味着每水平延伸 15 米，河流下降 1 米。其计算公式为 1 : (D / Δh)。
3. Population Density & Distribution | 人口密度与分布
Population density is a simple but powerful measure that shows how crowded a place is. It is expressed as the average number of people per unit area, usually per square kilometre (km²).
人口密度是一个简单但有力的指标，显示一个地方的拥挤程度。通常表示为每单位面积（一般为平方公里）上的平均人数。
Population Density = Total population ÷ Total land area (km²)
For example, if a country has 10 million people and a land area of 250,000 km², the density is 40 people per km². Note that the formula uses land area, not total area including water bodies. AQA questions often require interpretation of density figures alongside choropleth maps showing population distribution patterns such as clustered, linear or dispersed.
例如，如果一个国家有 1 千万人口，土地面积为 25 万平方公里，则人口密度为每平方公里 40 人。注意公式中使用的是土地面积，不包括水域面积。AQA 考题通常要求结合等值区域图（choropleth map）解释密度数字与人口分布格局，如聚集型、线型或分散型分布。
4. Birth Rate, Death Rate & Natural Increase | 出生率、死亡率与自然增长率
Demographic calculations form a core part of the Population topic. Crude rates are used to compare population dynamics between countries, while natural increase indicates how fast a population is growing ignoring migration.
人口统计计算构成人口章节的核心内容。粗率用于比较国家间的人口动态，而自然增长率则反映不考虑迁移情况下的人口增长速度。
Crude Birth Rate (CBR) per 1000 = (Number of live births ÷ Total population) × 1000
Crude Death Rate (CDR) per 1000 = (Number of deaths ÷ Total population) × 1000
Natural Increase (%) = ((Number of births - Number of deaths) ÷ Total population) × 100
To convert a natural increase rate from per 1000 to a percentage, simply divide the difference (CBR - CDR) by 10. For instance, a CBR of 25 and CDR of 8 gives a natural increase of 17 per 1000, which equals 1.7%.
要将自然增长率从千分比转换为百分比，只需将（CBR - CDR）的差值除以 10 即可。例如，出生率 25‰，死亡率 8‰，则自然增长率为 17‰，等同于 1.7%。
5. Dependency Ratio | 抚养比
The dependency ratio measures the economic burden on the productive population. It compares those typically not in the labour force (young and old) to those of working age.
抚养比衡量生产性人口的经济负担。它比较了通常不在劳动力队伍中的人口（幼年与老年）与劳动适龄人口的数量。
tio = [(Population aged 0-14 + Population aged 65 and over) ÷ Population aged 15-64] × 100
A ratio of 60 means that for every 100 people of working age, there are 60 dependants. A high dependency ratio can put pressure on public services, healthcare and pensions, whereas a very low ratio might indicate an ageing population with fewer young people entering the workforce.
抚养比为 60 意味着每 100 个劳动适龄人口需要抚养 60 个人口。高抚养比可能会给公共服务、医疗保健和养老金带来压力，而过低的抚养比则可能表明人口老龄化严重，进入劳动力市场的年轻人减少。
6. Urbanisation Rate & Percentage Change | 城市化率与百分比变化
Urbanisation is the increasing percentage of the population living in towns and cities. It can be measured as a level (urban population percentage) and as a rate of change over time. The percentage change formula is also used widely for population growth, economic growth and other data trends.
城市化是指居住于城镇和城市的人口比例不断上升。它可以用城市化水平（城镇人口百分比）和随时间的变化速率来衡量。百分比变化公式也广泛用于人口增长、经济增长和其他数据趋势的分析。
Urban population % = (Urban population ÷ Total population) × 100
Percentage change (%) = [(New value - Original value) ÷ Original value] × 100
To calculate the average annual urbanisation rate between two census years, apply the percentage change formula to the urban populations and then divide by the number of years. A positive percentage change indicates growth, while a negative value indicates decline.
要计算两次人口普查年份之间的年均城市化速率，先将百分比变化公式应用到城镇人口数量上，再除以年数即可。正的百分比变化表示增长，负值则表示下降。
7. Map Scale, Distance & Area | 地图比例尺、距离与面积
Ordnance Survey (OS) map skills are essential in AQA Geography. You must be able to convert map measurements into real-world distances and areas using the scale given.
英国测绘局（OS）地图技能在 AQA 地理中是必考内容。你必须能够利用所给的比例尺，将地图上的测量值转换为实际距离和面积。
Real distance (km) = Map distance (cm) × (Scale denominator ÷ 100,000)
Area on ground (m² or km²) = Map area (cm²) × Scale² factor
on the map equals (0.5 km)² = 0.25 km². You can also estimate irregular areas using grid squares and the dot grid method.
对于 1:50,000 的地图，图上 1 厘米代表实地 50,000 厘米，即 0.5 公里。因此，4 厘米的线段等于 4 × 0.5 = 2 公里。在面积方面，图上一平方厘米相当于 (0.5 公里)² = 0.25 平方公里。你还可以利用网格方格和点格网法估算不规则形状的面积。
8. Contour Gradient & Cross-Section | 等高线梯度与剖面
Calculating gradient from contours is a key geographical skill. It describes the steepness of a slope and is often required when drawing or interpreting cross-sections on OS maps.
根据等高线计算梯度是一项关键的地理技能。它描述了斜坡的陡峭程度，在绘制或判读地形图横剖面时经常需要。
radient = Vertical interval (contour difference) ÷ Horizontal equivalent (ground distance)
Gradient as ratio = 1 : (Horizontal distance ÷ Vertical interval)
ance on the map, convert it to real ground distance in the same units (metres), and apply the formula. If the vertical fall is 100 m and the horizontal distance is 2,000 m, the gradient is 100/2000 = 0.05, or 1 in 20.
要计算两点之间的梯度，先记录每点的等高线高度以得到高差，然后在地图上量出直线距离，将其转换为相同单位（米）的实际地面距离，再代入公式。如果垂直落差 100 米，水平距离 2000 米，则梯度为 100/2000 = 0.05，或 1 比 20。
9. Climate Averages & Range | 气候平均值与较差
Climate graphs and data questions require you to calculate averages and ranges. These basic statistics help describe temperature and rainfall patterns.
气候图表和数据题目要求你计算平均值和较差（范围）。这些基本的统计量有助于描述气温和降水变化规律。
Mean monthly temperature = (Sum of daily mean temperatures) ÷ Number of days in month
Total monthly rainfall = Sum of all daily rainfalls (mm)
Annual temperature range = Warmest month mean temperature - Coldest month mean temperature
In an exam, you might be given a table of monthly temperatures and asked to calculate the annual range or the total rainfall for a season. Always use the same units (usually °C for temperature and mm for rainfall) and check whether the question asks for a mean or a total.
在考试中，你可能会看到一张月平均气温表，并被要求计算年较差或某个季节的总降水量。务必使用相同单位（气温一般为 °C，降水量为 mm），并看清题目要求的是平均值还是总量。
10. Development Indicators & HDI | 发展指标与人类发展指数
Development is measured using a range of economic and social indicators. GDP per capita is a key economic measure, while rates such as infant mortality and literacy reflect social wellbeing. The Human Development Index (HDI) combines several dimensions.
发展程度通过一系列经济和社会指标来衡量。人均 GDP 是核心经济指标，而婴儿死亡率和识字率等比率则反映社会福祉。人类发展指数（HDI）综合了多个维度。
GDP per capita = Total GDP (US$) ÷ Total population
nt Infant Mortality Rate (per 1000) = (Deaths of infants under 1 year ÷ Total live births) × 1000
Literacy Rate (%) = (Number of literate persons aged 15+ ÷ Total population aged 15+) × 100
Although you are not required to calculate HDI itself, you should know it is a composite index combining life expectancy, education (mean and expected years of schooling) and GNI per capita. A higher HDI value closer to 1 indicates a higher level of development.
虽然不要求你计算 HDI 本身，但你应知道它是一个综合指数，结合了预期寿命、教育（平均受教育年限和预期受教育年限）以及人均国民总收入。HDI 值越接近 1，表示发展水平越高。
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