📚 Year 9 Cambridge Geography: Formula & Theorem Quick Reference Handbook | Year 9 剑桥地理：公式定理速查手册
This quick reference handbook brings together the essential formulas, equations and key numerical relationships that you will encounter in the Year 9 Cambridge Geography curriculum. Whether you are analysing population data, measuring river characteristics or interpreting climate statistics, these tools will help you build confidence in calculations and fieldwork. Each entry includes a clear formula explanation, units and a worked example where appropriate, all aligned with the Cambridge Lower Secondary and IGCSE foundation skills.
本速查手册整理了 Year 9 剑桥地理课程中必备的公式、方程与关键数量关系。无论你是在分析人口数据、测量河流特征还是解读气候统计，这些工具都能帮助你在计算与田野调查中建立信心。每个条目都配有清晰的公式解释、单位，并适当提供计算示例，内容与剑桥初中及 IGCSE 基础技能要求紧密衔接。
1. Population Density | 人口密度
Population density measures how crowded an area is. It is defined as the number of people living per unit of land area, normally expressed as people per square kilometre (people/km²). The formula is:
人口密度衡量一个地区的拥挤程度，定义为单位土地面积上居住的人口数量，通常用人/平方千米（人/km²）表示。公式如下：
D = P ÷ A
where D is density, P is total population, and A is land area in km². Geographers use this ratio to compare settlement patterns: Singapore has a very high density (over 8000 people/km²), while Australia’s density is very low (around 3 people/km²).
其中 D 为密度，P 为总人口，A 为土地面积（km²）。地理学家利用该比值比较聚落格局：新加坡人口密度极高（超过 8000 人/km²），而澳大利亚密度很低（约 3 人/km²）。
nd covers an area of 800 km². Its population density is 1,200,000 ÷ 800 = 1500 people/km².
示例：某城市人口为 1 200 000，面积为 800 km²，则人口密度为 1 200 000 ÷ 800 = 1500 人/km²。
2. Crude Birth and Death Rates | 粗出生率与粗死亡率
The crude birth rate (CBR) is the number of live births in a year per 1000 people in the total population. The crude death rate (CDR) is the number of deaths per 1000 people per year.
粗出生率（CBR）是一年内每 1000 人中活产婴儿的数量。粗死亡率（CDR）是一年内每 1000 人中的死亡人数。
CBR = (B ÷ P) × 1000 | CDR = (D ÷ P) × 1000
B is the total number of live births, D is the total number of deaths, and P is the mid-year total population. These rates are expressed per 1000 (‰). High CBR values (above 30‰) are typical in many low-income countries, whereas high-income countries often have CBR below 12‰.
B 为活产总数，D 为死亡总数，P 为年中总人口。这些比率以千分数（‰）表示。高出生率（高于 30‰）常见于许多低收入国家，而高收入国家的出生率常低于 12‰。
year, and its mid-year population was 12,000,000. CBR = (240,000 ÷ 12,000,000) × 1000 = 20‰.
示例：X 国一年内记录活产婴儿 240 000 名，年中人口为 12 000 000。CBR = (240 000 ÷ 12 000 000) × 1000 = 20‰。
3. Natural Increase Rate | 自然增长率
Natural increase shows how fast a population grows from births and deaths alone, ignoring migration. It can be expressed as a percentage (%) or per thousand (‰).
自然增长率反映仅由出生与死亡造成的人口变化速度，不考虑迁移。可用百分比（%）或千分比（‰）表示。
NIR (%) = (CBR – CDR) ÷ 10
Since CBR and CDR are per 1000, subtracting them gives the net change per 1000. Dividing by 10 converts this into a percentage. A positive NIR means the population is growing naturally; a negative NIR indicates natural decrease.
由于 CBR 和 CDR 以千分率表示，相减即得每千人的净变化；再除以 10 就转换为百分比。自然增长率为正，表示人口自然增长；为负则表示自然减少。
Example: CBR = 24‰, CDR = 8‰. Natural increase per 1000 = 16‰. NIR (%) = 16 ÷ 10 = 1.6%.
示例：CBR = 24‰，CDR = 8‰，每千人自然增加 16‰。NIR (%) = 16 ÷ 10 = 1.6%。
4. Total Population Growth Rate | 总人口增长率
The total growth rate adds the effect of net migration (immigration minus emigration) to natural change. It is commonly expressed as a percentage.
总增长率在自然变动的基础上加入了净迁移（迁入减迁出）的影响，通常以百分比表示。
Growth Rate (%) = [(B – D) + (I – E)] ÷ P × 100
Here, I is the number of immigrants, E is emigrants, and P is the mid-year population. This formula gives the overall annual percentage change, which includes both natural increase and migration.
式中，I 为迁入人数，E 为迁出人数，P 为年中人口。该公式计算的是包含自然增长与迁移的年度总体百分比变化。
, 60,000 immigrants and 40,000 emigrants. Mid-year population is 10,000,000. Growth Rate (%) = [(500,000 - 250,000) + (60,000 - 40,000)] ÷ 10,000,000 × 100 = 2.7%.
示例：某国出生 500 000 人，死亡 250 000 人，迁入 60 000 人，迁出 40 000 人，年中人口为 10 000 000。增长率 = [(500 000 - 250 000) + (60 000 - 40 000)] ÷ 10 000 000 × 100 = 2.7%。
5. River Discharge (Stream Flow) | 河流流量
River discharge is the volume of water flowing through a cross-section of a river channel per unit time, usually measured in cubic metres per second (m³/s). It is fundamental for understanding flood risk and water supply.
河流流量是指单位时间内通过河道某一横截面的水体体积，通常以立方米每秒（m³/s）计量，是理解洪水风险与水资源供给的基础。
Q = A × v
Q is discharge (m³/s), A is cross-sectional area of the channel (m²), and v is mean flow velocity (m/s). To obtain A, geographers multiply average width by average depth at that section.
Q 为流量（m³/s），A 为河道横截面积（m²），v 为平均流速（m/s）。获取 A 时，地理工作者将该断面平均宽度乘以平均水深。
ures 15 m² in area, and the average velocity is 0.8 m/s. Discharge Q = 15 × 0.8 = 12 m³/s.
示例：某河道横截面积为 15 m²，平均流速为 0.8 m/s。流量 Q = 15 × 0.8 = 12 m³/s。
6. River Gradient (Slope) | 河道坡度
Gradient describes how steep a river channel is. It is calculated as the vertical fall between two points divided by the horizontal distance along the channel.
坡度描述河道陡峭程度，以两点间的垂直落差除以沿河道的水平距离来计算。
Gradient = Vertical fall ÷ Horizontal distance
This ratio is often expressed in the form 1 in X (e.g. 1:50) or in metres per kilometre (m/km). A high gradient means a steep slope, typical of upland rivers; a low gradient characterises gently flowing lowland reaches.
该比值常以 1:X 的形式（如 1:50）或米/千米（m/km）表示。坡度大意味着地势陡峭，常见于上游山地河段；坡度小则代表平缓的低地河段。
river drops 120 metres over a channel distance of 6 km. Gradient = 120 m ÷ 6 km = 20 m/km.
示例：某河流在 6 千米的河段中下降 120 米。坡度 = 120 m ÷ 6 km = 20 m/km。
7. Drainage Density | 河网密度
Drainage density is the total length of all stream channels in a drainage basin divided by the basin area. It indicates how well a landscape is drained and how quickly water can reach the main river.
河网密度是指流域内所有河道总长度除以流域面积，反映地表排水效率以及水流汇集到主河道的速度。
Dd = L ÷ A
Dd is drainage density (km/km² or km⁻¹), L is total length of streams (km), and A is drainage basin area (km²). High drainage densities are often found in areas with impermeable rocks and steep slopes; low values occur on permeable surfaces like sand or limestone.
Dd 为河网密度（km/km² 或 km⁻¹），L 为河道总长度（km），A 为流域面积（km²）。高河网密度通常出现在不透水岩层和陡坡区域；在砂或石灰岩等透水地表，密度值较低。
ers 50 km² and contains streams with a total length of 120 km. Dd = 120 ÷ 50 = 2.4 km/km².
示例：某流域面积 50 km²，河道总长 120 km，则河网密度 = 120 ÷ 50 = 2.4 km/km²。
8. Annual Precipitation and Mean Monthly Rainfall | 年降水量与月均雨量
Annual precipitation is the total amount of water (in millimetres) that falls as rain, snow, hail, etc., over a year. It is simply the sum of the 12 monthly totals.
年降水量是一年内所有降水（雨、雪、冰雹等）的总量，以毫米为单位，就是把 12 个月的降水量相加。
Annual total = Sum of 12 monthly totals
Mean monthly rainfall helps compare seasonal patterns and is calculated by dividing the annual total by 12. For a more detailed climate analysis, geographers also compute mean for each calendar month over many years (e.g. average July rainfall).
月均雨量有助于比较季节性规律，由年总量除以 12 得到。在更精细的气候分析中，地理学家还会计算多年各月平均值（如七月平均雨量）。
nfall = 960 ÷ 12 = 80 mm. If December recorded 120 mm, that month was wetter than average.
示例：某测站各月降雨量总和为 960 mm，月均雨量 = 960 ÷ 12 = 80 mm。若十二月降雨 120 mm，则该月比平均更湿润。
9. Temperature Range and Mean Temperature | 温度较差与平均温度
The annual temperature range is the difference between the highest and lowest mean monthly temperatures of the year. It gives a quick indication of climate continentality.
年温差或气温年较差是指一年中最热月平均温度与最冷月平均温度之差，能快速反映气候的大陆性程度。
Temperature range = Tmax – Tmin
Mean annual temperature is obtained by adding all 12 monthly mean temperatures and dividing by 12. For fieldwork, you might also calculate the diurnal range (maximum minus minimum within one day).
年平均温度是将 12 个月的月平均温度相加再除以 12。在野外调查中，你还可能计算日较差（一天内最高温与最低温之差）。
: A city’s warmest month averages 28 °C and coolest month averages 7 °C. Annual range = 28 – 7 = 21 °C. Mean annual temperature = sum of 12 monthly means ÷ 12.
示例：某城市最热月均温 28 °C，最冷月均温 7 °C，则年较差 = 28 – 7 = 21 °C。年平均温度 = 12 个月的月均温之和 ÷ 12。
10. Dependency Ratio | 抚养比
The dependency ratio is an age-population measure that compares the economically dependent groups (young and old) with the working-age population. It is widely used to assess the pressure on the productive population.
抚养比是一项年龄人口指标，将需抚养群体（少儿与老人）与劳动年龄人口进行比较，广泛用于评估生产性人口所承受的压力。
Dependency Ratio = [(Pop(0–14) + Pop(65+)) ÷ Pop(15–64)] × 100
The result is a number of dependents per 100 people of working age. A high dependency ratio, often above 60, suggests a large burden on health, education and social services. Many low-income countries have high youth dependency, while ageing populations in high-income countries raise old-age dependency.
结果表示每 100 名劳动年龄人口所对应的抚养人数。抚养比过高（通常高于 60）会给医疗、教育和社会服务带来较大负担。许多低收入国家少儿抚养比高，而高收入国家因人口老龄化推高了老年抚养比。
Example: A population has 18,000 aged 0–14, 12,000 aged 65+, and 45,000 aged 15– ] × 100 ≈ 66.7. This means there are about 67 dependents for every 100 working-age people.
示例：某地区 0–14 岁人口 18 000 人，65 岁及以上 12 000 人，15–64 岁人口 45 000 人。抚养比 = [(18 000 + 12 000) ÷ 45 000] × 100 ≈ 66.7，即每 100 名劳动年龄人口需抚养约 67 人。
11. Percentage Change | 百分比变化
Percentage change is one of the most versatile tools in geography, used to compare how much a value has increased or decreased over time. It is essential for interpreting population growth, urban expansion, economic indicators and fieldwork data.
百分比变化是地理学中最通用的工具之一，用于比较某个数值随时间增加或减少的幅度。解读人口增长、城市扩张、经济指标及田野调查数据时都离不开它。
Percentage Change = [(New value – Old value) ÷ Old value] × 100
A positive result indicates growth; a negative result indicates decline. This formula is widely applied to calculate rate of urbanisation, change in forest cover, or trend in river discharge.
正数表示增长，负数表示下降。该公式广泛应用于计算城市化速率、森林覆盖率变化或河流流量趋势等。
ty’s population grew from 250,000 to 325,000 over ten years. Percentage change = [(325,000 – 250,000) ÷ 250,000] × 100 = 30% increase.
示例：某城市人口十年间从 250 000 增至 325 000。百分比变化 = [(325 000 – 250 000) ÷ 250 000] × 100 = 30% 的增长。
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