📚 Year 10 Edexcel Geography Formula & Theorem Quick Reference Handbook | Edexcel Year 10 地理公式定理速查手册
This quick reference handbook is designed for Year 10 Edexcel Geography students to rapidly review essential formulas, equations and calculation principles across both physical and human topics. Use it to reinforce fieldwork analysis, master population indicators and boost exam confidence with step-by-step examples.
本速查手册专为 Edexcel 地理 Year 10 学生编写，旨在快速回顾自然与人文地理中必会的公式、方程与计算原理。通过分步示例，帮助你强化田野调查分析、掌握人口指标，并提升备考信心。
1. River Gradient and Discharge | 河流梯度与流量
River gradient expresses the steepness of a channel and is essential for understanding flow energy and erosion potential. It is the ratio of vertical drop to horizontal distance. Discharge gives the volume of water passing a point per second and helps assess flood risk.
河流梯度表示河道的陡峭程度，是理解水流能量与侵蚀潜力的关键。它是垂直落差与水平距离的比值。流量给出每秒通过某一点的水量，用于评估洪水风险。
To calculate gradient:
Gradient = ΔH ÷ L
梯度计算公式：
梯度 = 高差 ÷ 水平距离
Where ΔH is the vertical drop between two points (in metres) and L is the horizontal distance along the river (in metres). Always use the same units. For example, a vertical drop of 5 m over a distance of 200 m gives a gradient of 5 ÷ 200 = 0.025.
其中 ΔH 为两点间的垂直落差（单位：米），L 为沿河道的水平距离（单位：米）。请始终使用相同单位。例如，在200米距离内下降5米，梯度为 5 ÷ 200 = 0.025。
Discharge (Q) is calculated by multiplying cross‑sectional area (A) by average velocity (v):
Q = A × v
流量 (Q) 通过横截面积 (A) 与平均流速 (v) 的乘积求得：
Q = A × v
Cross‑sectional area is measured in m² and is often estimated by multiplying the average depth by the channel width, or by dividing the channel into vertical sections and summing depth × width for each. Velocity is in m/s, so Q is in cumecs (m³/s).
横截面积以平方米为单位，通常用平均水深乘以河宽估算，或将河道分成若干垂直段后分别计算水深×宽度再求和。流速单位为米/秒，因此 Q 的单位为立方米/秒 (cumecs)。
2. Population Dynamics Formulas | 人口动态公式
Population indicators allow geographers to analyse growth, density and structure. The natural increase rate reflects births and deaths, while net migration adds the effect of movement. These formulas are fundamental in the ‘Changing Cities’ and ‘Global Development’ topics.
人口指标帮助地理学者分析增长、密度与结构。自然增长率反映出生与死亡的差额，净迁移则加入人口移动的影响。这些公式是“变化中的城市”和“全球发展”专题的基础。
Crude Birth Rate (CBR) and Crude Death Rate (CDR) are given per 1000 people per year. The natural increase rate (%) is:
Natural Increase Rate (%) = (CBR – CDR) ÷ 10
粗出生率 (CBR) 与粗死亡率 (CDR) 以每年每千人为单位。自然增长率 (%) 为：
自然增长率 (%) = (CBR – CDR) ÷ 10
Population growth rate including migration is:
Growth Rate (%) = ( (Births – Deaths) + (Immigration – Emigration) ) ÷ Total Population × 100
包含迁移的人口增长率：
增长率 (%) = ( (出生数 – 死亡数) + (迁入数 – 迁出数) ) ÷ 总人口 × 100
Population density shows how crowded an area is:
Population Density = Total Population ÷ Area (km²)
人口密度反映一个地区的拥挤程度：
人口密度 = 总人口 ÷ 面积（平方公里）
For example, a city with 800,000 people and an area of 400 km² has a density of 2000 people per km². Remember to convert hectares to km² when needed (1 km² = 100 ha).
例如，一座城市有80万人口，面积400平方公里，则人口密度为每平方公里2000人。必要时记得将公顷转换为平方公里（1 km² = 100 公顷）。
3. Urbanisation and Development Indicators | 城市化与发展指标
Urbanisation rate measures the proportion of a population living in urban areas. It is a key measure in the study of megacities and urban growth. Development indicators like GDP per capita help compare economic output.
城市化率衡量居住在城镇地区的人口比例，是研究超大城市与城市发展的关键指标。人均 GDP 等发展指标有助于比较经济产出。
Urbanisation rate is calculated as:
Urbanisation Rate (%) = (Urban Population ÷ Total Population) × 100
城市化率计算公式：
城市化率 (%) = (城镇人口 ÷ 总人口) × 100
Gross Domestic Product (GDP) per capita is a simple income indicator:
GDP per Capita = Total GDP ÷ Total Population
人均国内生产总值 (GDP) 是简单的收入指标：
人均 GDP = 总 GDP ÷ 总人口
The Human Development Index (HDI) combines life expectancy, education and income. Although the exact formula uses geometric mean of three normalized indices, at Year 10 you are only expected to interpret HDI values (0–1) and understand that a higher score represents higher development.
人类发展指数 (HDI) 综合了预期寿命、教育程度与收入。虽然精确公式是三个标准化指数的几何平均值，但在 Year 10 阶段你只需解读 HDI 数值（0–1）并理解数值越高代表发展水平越高。
Dependency ratio, often used in population structure analysis, is:
Dependency Ratio = ( (Population 0–14 + Population 65+) ÷ Working‑age Population 15–64 ) × 100
抚养比常用于人口结构分析：
抚养比 = ( (0–14岁人口 + 65岁以上人口) ÷ 15–64岁劳动人口 ) × 100
4. Map Skills and Scale Conversions | 地图技能与比例尺转换
Accurate map reading is vital for both fieldwork and the skills paper. The map scale relates distance on a map to actual ground distance. You must be able to convert between statement scale, linear scale and representative fraction.
准确读图对田野调查和技能卷都至关重要。比例尺将地图上的距离与实际地面距离相关联。你必须能够在文字式、线段式和数字式比例尺之间进行转换。
The representative fraction (RF) scale is written as:
Scale 1 : X
数字比例尺记作：
比例尺 1 : X
This means 1 cm on the map equals X cm on the ground. To find real distance:
Actual Distance = Map Distance × Scale Factor
这意味着地图上 1 厘米等于地面上 X 厘米。实际距离计算公式为：
实际距离 = 图上距离 × 比例尺分母
Always convert to sensible units. For example, on a 1:25,000 map, 4 cm represents 4 × 25,000 = 100,000 cm = 1000 m = 1 km. To measure area, square the linear scale: 1 cm² on a 1:50,000 map represents (50,000 cm)² = 2,500,000,000 cm² = 0.25 km² on the ground.
务必转换为合理的单位。例如，在 1:25 000 地图上，4 厘米代表 4 × 25 000 = 100 000 厘米 = 1000 米 = 1 公里。测量面积时，将线性比例尺平方：1:50 000 地图上 1 cm² 代表 (50 000 cm)² = 2 500 000 000 cm² = 0.25 km²。
Gradient can also be calculated from maps by using contour lines:
Gradient = Vertical Interval (contour difference) ÷ Horizontal Equivalent (distance on ground)
利用等高线也可计算坡度：
坡度 = 等高距（垂直高差）÷ 水平距离（地面距离）
Always express the fraction in its simplest form, e.g. 1 in 10 means a rise or fall of 1 m for every 10 m horizontally.
比值应化为最简形式，例如 1:10 表示每 10 米水平距离上升或下降 1 米。
5. Central Tendency and Dispersion | 集中趋势与离散程度
When processing data collected during fieldwork, you need to describe the typical value (mean, median, mode) and the spread (range, interquartile range). These statistics are essential for analysing river depths, pebble sizes or questionnaire results.
在处理野外考察收集的数据时，你需要描述典型值（平均数、中位数、众数）和离散程度（极差、四分位距）。这些统计量对于分析河流深度、卵石大小或调查问卷结果至关重要。
The mean is calculated as:
Mean (x̄) = Σx ÷ n
平均数计算公式：
平均数 (x̄) = 总和 Σx ÷ 数据个数 n
The median is the middle value when data are ordered. For an even number of values, take the mean of the two centre numbers. The mode is the most frequently occurring value.
中位数是数据按顺序排列后的中间值；若数据个数为偶数，则取中间两个数值的平均值。众数是出现频率最高的数值。
The range gives a simple measure of spread:
Range = Maximum Value – Minimum Value
极差是一种简单的离散度量：
极差 = 最大值 – 最小值
The interquartile range (IQR) is less affected by outliers:
IQR = Upper Quartile (Q3) – Lower Quartile (Q1)
四分位距 (IQR) 受极值影响较小：
IQR = 上四分位数 (Q3) – 下四分位数 (Q1)
For example, if Q1 = 12 cm and Q3 = 34 cm, the IQR is 22 cm. Always state the units.
例如，若 Q1 = 12 cm, Q3 = 34 cm，则 IQR 为 22 cm。务必标注单位。
6. Fieldwork Measurement Formulas | 田野调查测量
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