📚 AQA IGCSE Geography Formula & Theorem Quick-Reference Handbook | AQA IGCSE 地理公式定理速查手册
This quick-reference handbook is designed for AQA IGCSE Geography students, compiling all essential formulas and theorems required for map skills, population dynamics, hydrological processes and geographical investigations. Memorising these will boost your confidence when answering numerical and skills‑based exam questions.
本速查手册面向 AQA IGCSE 地理学生，汇编了地图技能、人口动态、水文过程和地理调查所需的所有重要公式和定理。熟记这些公式有助于自信应对数字和技能类考试题目。
1. Map Scale and Distance Calculations | 地图比例尺与距离计算
A map scale expresses the ratio between a distance on the map and the corresponding distance on the ground. It is often given as a representative fraction (RF), for instance 1:50,000. To calculate the real‑world distance, multiply the map distance by the scale denominator. If the map distance is in centimetres, convert the result into metres or kilometres for practical interpretation.
地图比例尺表示图上距离与对应的实地距离之比。常用数字比例尺（如1:50,000）表示。计算实际距离时，用图上距离乘以比例尺的分母。如果图上距离以厘米为单位，需将结果转换为米或千米以便实际解读。
Real Distance = Map Distance × Scale Denominator
For a 1:25,000 map, 4 cm on the map equals 4 × 25,000 = 100,000 cm, which is 1 km. The reverse formula is also useful: Map Distance = Real Distance ÷ Scale Denominator.
在1:25,000的地图上，4厘米代表4×25,000=100,000厘米，即1千米。反向公式同样实用：图上距离 = 实际距离 ÷ 比例尺分母。
2. Gradient (Slope) Formula | 坡度公式
Gradient measures the steepness of a slope or valley. It is calculated by dividing the vertical rise (difference in height) by the horizontal distance. The result is often expressed as a ratio 1:X, where X = horizontal distance ÷ vertical rise. This skill is essential for analysing cross‑sections on OS maps.
坡度用于衡量斜坡或谷地的陡峭程度，由垂直升高（高差）除以水平距离求得。结果常表示为1:X的比例，其中X = 水平距离 ÷ 垂直升高。该技能对于分析地形测量图（OS地图）的剖面至关重要。
Gradient = Vertical Rise ÷ Horizontal Distance (expressed as 1 : X)
Example: a slope rises 50 m over a horizontal distance of 500 m. Gradient = 50 / 500 = 1/10, so the ratio is 1:10. Steeper slopes have smaller X values.
示例：500米水平距离内升高50米，坡度=50/500=1/10，即1:10。更陡的坡度其X值更小。
3. Population Density | 人口密度
Population density is a fundamental measure describing how crowded a place is. It is expressed as the number of people per square kilometre (km²). This indicator helps geographers study settlement patterns, resource pressure, and variations in human distribution. Always use total population and total land area in the same unit system.
人口密度是描述某地拥挤程度的基本指标，表示每平方千米(km²)的人数。该指标帮助地理学家研究聚落形态、资源压力及人口分布差异。务必确保总人口和土地总面积使用统一的单位制。
Population Density = Total Population ÷ Area (km²)
For example, a town of 25,000 people covering 5 km² has a density of 5,000 persons per km². Densely populated areas often present challenges in housing and transport.
例如，一座有25,000人口、面积5 km²的城镇，其人口密度为每平方千米5,000人。人口密集区通常在住房和交通方面面临挑战。
4. Crude Birth Rate (CBR) and Crude Death Rate (CDR) | 粗出生率（CBR）与粗死亡率（CDR）
Crude Birth Rate is the number of live births per 1,000 population in a year. Crude Death Rate is the number of deaths per 1,000 population in a year. Both are expressed per mille (‰). They are the building blocks for understanding natural population change and for constructing population pyramids.
粗出生率指一年内每千人口中的活产婴儿数；粗死亡率指一年内每千人口中的死亡人数。两者均以千分比(‰)表示。它们是理解自然人口变化和构建人口金字塔的基础。
CBR = (B ÷ P) × 1000 CDR = (D ÷ P) × 1000
Here B = total live births, D = total deaths, P = total mid‑year population. Always use mid‑year estimates for P when available. A high CBR is typical of stage 2 of the Demographic Transition Model, while a low CDR indicates improved healthcare.
这里 B = 活产总数，D = 死亡总数，P = 年中总人口。尽可能使用年中人口估算值。高CBR通常出现在人口转变模型的第二阶段，而低CDR则表明医疗卫生条件改善。
5. Natural Increase Rate (NIR) | 自然增长率（NIR）
The Natural Increase Rate shows the percentage growth or decline of a population excluding migration. Since CBR and CDR are expressed per 1,000, subtracting them gives the net change per 1,000. Dividing by 10 converts this into a percentage. This is a key indicator of population momentum.
自然增长率显示排除迁移因素后的人口增长或下降的百分比。由于CBR和CDR均以千分比表示，相减得到每千人的净变化。再除以10转为百分比。它是衡量人口惯性的关键指标。
Natural Increase Rate (%) = (CBR – CDR) ÷ 10
For example, if CBR = 35 ‰ and CDR = 8 ‰, the NIR = (35 – 8) / 10 = 2.7%. A negative NIR indicates a natural decrease, common in stage 5 countries.
例如，若CBR=35‰，CDR=8‰，则自然增长率=(35−8)/10=2.7%。负的自然增长率表示自然减少，常见于处于第五阶段的国家。
6. Net Migration and Overall Population Change | 净迁移与总人口变化
Total population change combines natural change and net migration. Net migration is the difference between immigration and emigration. A positive net migration adds to the population; a negative net migration reduces it. This formula allows demographers to account for all components of change.
总人口变化结合了自然变动和净迁移。净迁移是迁入和迁出人口之差。正的净迁移使人口增加，负的净迁移使人口减少。该公式使人口学家能够考虑所有变动因素。
Population Change = (Births – Deaths) + (Immigration – Emigration)
Worked example: a city has 2,000 births, 1,200 deaths, 800 immigrants and 300 emigrants. The population change = (2000−1200) + (800−300) = 800 + 500 = 1,300. Thus the population increased by 1,300 over the period.
示例：某城市出生2,000人，死亡1,200人，迁入800人，迁出300人。人口变化=(2000−1200)+(800−300)=800+500=1,300。因此该时期人口增加了1,300。
7. River Discharge (Flow Rate) | 河流流量
River discharge (Q) is the volume of water flowing past a point per unit time, measured in cubic metres per second (m³/s). It is a critical variable for studying river regimes, flood risk, and channel efficiency. Discharge is the product of the cross‑sectional area of the stream and the mean velocity of the water.
河流流量(Q)是单位时间内流过某断面的水体体积，单位为立方米每秒(m³/s)。它是研究河流情势、洪水风险和河道效率的关键变量。流量等于河道横截面积与水流平均流速的乘积。
Q = A × V
Where A = cross‑sectional area (m²) and V = mean velocity (m/s). To calculate A, multiply channel width by average depth. Velocity is often measured with a flowmeter at 0.6 depth. This formula is fundamental in fieldwork and hydrological graphs.
其中A=横截面积(m²)，V=平均流速(m/s)。计算A时，用河道宽度乘以平均水深。流速通常使用流速仪在水深的0.6倍处测量。该公式是野外工作和水文图表分析的基础。
8. Percentage Change | 百分比变化
Percentage change is widely used in geography to compare data over time – from population growth rates to changing erosion rates. It standardises comparisons by showing change relative to the original value. A positive result indicates an increase, while a negative result shows a decrease.
百分比变化在地理中广泛用于比较随时间变化的数据——从人口增长率到侵蚀速率变化。它通过展示相对于原值的变化来实现标准化比较。正值表示增加，负值表示减少。
Percentage Change = ((New Value – Original Value) ÷ Original Value) × 100%
For instance, if a town’s population grew from 15,000 to 16,500, the percentage change = ((16500−15000)/15000)×100 = 10%. Always identify the correct original value to avoid misinterpretation.
例如，若某城镇人口从15,000增至16,500，百分比变化=((16500−15000)/15000)×100=10%。务必使用正确的原值，以免解读错误。
9. Measures of Central Tendency: Mean, Median and Mode | 集中趋势度量：平均数、中位数和众数
Central tendency
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