📚 Year 9 OCR Geography: Formula & Theorem Quick Reference Handbook | Year 9 OCR 地理：公式定理速查手册
Mastering geographical skills requires fluency with key formulas and quantitative techniques. This handbook compiles the essential equations, calculations, and rules you will encounter in the Year 9 OCR Geography course, from map work to population and development indicators. Each entry presents the formula in a clear centered layout, followed by a practical explanation and a worked example so you can check your understanding. Keep this guide handy for revision and classroom use.
掌握地理技能需要熟练运用关键公式和定量方法。本手册汇总了你在 Year 9 OCR 地理课程中会遇到的核心方程、计算与规则，涵盖地图技能、人口与发展指标等主题。每个条目均以清晰的居中公式呈现，并配以实用说明和计算示例，方便你随时检查理解程度。复习和课堂学习时随身携带本指南。
1. Map Scale Conversion | 地图比例尺换算
The three forms of map scale – statement, linear, and representative fraction (RF) – allow you to convert map distances into real‑world measurements. The key conversion is: 1 cm on the map represents the given number of centimetres (or metres/kilometres) on the ground. Always check that your units match before multiplying or dividing.
地图比例尺有三种形式——文字比例尺、线段比例尺和数字比例尺（RF），它们能将图上距离转换为实地距离。关键换算为：图上 1 cm 代表实地相应数量的厘米（或米/千米）。在乘除之前，务必确保单位一致。
Real Distance (cm) = Map Distance (cm) × Scale Denominator
实地距离 (cm) = 图上距离 (cm) × 比例尺分母
Example: On a 1:50,000 map, a road measures 4 cm. Real distance = 4 × 50,000 = 200,000 cm = 2 km.
示例： 在 1:50000 地图上，一条路长 4 cm。实地距离 = 4 × 50000 = 200000 cm = 2 km。
2. Gradient (Slope) Calculation | 坡度计算
Gradient expresses the steepness of a slope as a ratio of vertical rise to horizontal distance. OCR often asks you to calculate gradient between two contour lines. The result is typically simplified to a form such as 1:25, meaning the land rises 1 unit for every 25 units horizontally.
坡度表示斜坡的陡峭程度，是垂直升高与水平距离之比。OCR 常要求计算两条等高线之间的坡度。结果通常简化为 1:25 的形式，即每水平移动 25 个单位，高度上升 1 个单位。
Gradient = Vertical Rise (m) ÷ Horizontal Distance (m)
坡度 = 垂直升高 (m) ÷ 水平距离 (m)
Example: A footpath climbs 80 m over a horizontal distance of 2,000 m. Gradient = 80 ÷ 2000 = 1:25.
示例： 一条步道水平距离 2000 m 上升 80 m。坡度 = 80 ÷ 2000 = 1:25。
3. Population Density | 人口密度
Population density describes how crowded an area is. It is one of the most frequently used indicators in human geography and helps compare regions of different sizes. Remember that high density does not always mean overpopulation; it simply shows concentration.
人口密度描述一个地区的拥挤程度。这是人文地理中最常用的指标之一，有助于比较大小不同的区域。请记住，高密度并不总是意味着人口过剩，它仅表示人口集中程度。
Population Density = Total Population ÷ Land Area (km²)
人口密度 = 总人口 ÷ 土地面积 (km²)
Example: on people and an area of 500,000 km². Density = 65,000,000 ÷ 500,000 = 130 people per km².
示例： 某国人口 6500 万，面积 500000 km²。密度 = 65000000 ÷ 500000 = 130 人/km²。
4. Crude Birth Rate (CBR) and Crude Death Rate (CDR) | 粗出生率与粗死亡率
CBR and CDR measure the number of live births or deaths per 1,000 people per year. These crude rates are fundamental for analysing natural population change and constructing population pyramids. OCR exams may ask you to calculate one of these from given data.
粗出生率 (CBR) 和粗死亡率 (CDR) 衡量每年每 1000 人中的活产或死亡人数。这些粗率是分析人口自然变动和绘制人口金字塔的基础。OCR 考试可能要求你根据给定数据计算其中之一。
CBR = (Live Births ÷ Total Population) × 1,000
粗出生率 = (活产人数 ÷ 总人口) × 1000
CDR = (Deaths ÷ Total Population) × 1,000
粗死亡率 = (死亡人数 ÷ 总人口) × 1000
Example: town of 25,000 records 300 births in a year. CBR = (300 ÷ 25,000) × 1,000 = 12 per 1,000.
示例： 某镇人口 25000，一年记录出生 300 人。CBR = (300 ÷ 25000) × 1000 = 12‰。
5. Natural Increase Rate (NIR) | 自然增长率
Natural increase (or decrease) ignores migration and shows whether a population is growing solely from the balance of births and deaths. It is expressed as a percentage (%). A negative NIR indicates natural decrease.
自然增长（或减少）不考虑迁移，仅显示人口是否仅凭出生与死亡的平衡而增长。它以百分比 (%) 表示。负自然增长率表明人口自然减少。
NIR (%) = (CBR − CDR) ÷ 10
自然增长率 (%) = (粗出生率 − 粗死亡率) ÷ 10
Example: CBR = 20 per 1,000, CDR = 8 per 1,000. NIR = (20 − 8) ÷ 10 = 1.2%.
示例： CBR = 20‰，CDR = 8‰。自然增长率 = (20 − 8) ÷ 10 = 1.2%。
6. Doubling Time (Rule of 70) | 人口倍增时间（70 法则）
Doubling time estimates how many years it takes for a population to double in size, assuming a constant rate of natural increase. The 'Rule of 70' divides 70 by the percentage growth rate. This rule is widely used for population projections.
倍增时间估算在自然增长率恒定的情况下，人口数量翻一番所需的年数。“70 法则”用 70 除以百分比增长率。该法则广泛用于人口预测。
Doubling Time (years) = 70 ÷ Growth Rate (%)
倍增时间 (年) = 70 ÷ 增长率 (%)
Example: A country's NIR is 2.1%. Doubling time = 70 ÷ 2.1 ≈ 33.3 years.
示例： 某国自然增长率为 2.1%。倍增时间 = 70 ÷ 2.1 ≈ 33.3 年。
7. Population Growth Rate (Including Migration) | 人口增长率（含迁移）
When migration data are available, the total population growth rate combines natural increase and net migration. This rate gives the overall percentage change in population per year and is crucial for studying urbanisation and international movements.
当有迁移数据时，总人口增长率要结合自然增长和净迁移。该比率给出每年人口变动的总百分比，对于研究城市化和国际人口流动至关重要。
Growth Rate (%) = [(CBR − CDR) ÷ 10] + (Net Migration Rate ÷ 10)
增长率 (%) = [(CBR − CDR) ÷ 10] + (净迁移率 ÷ 10)
Example: NIR = 1.5%, Net migration rate = 5 per 1,000 (0.5%). Total growth = 1.5 + 0.5 = 2.0%.
示例： NIR = 1.5%，净迁移率为 5‰（0.5%）。总增长 = 1.5 + 0.5 = 2.0%。
8. Dependency Ratio | 抚养比
The dependency ratio compares the economically active population (usually 15–64) with the dependent age groups (0–14 and 65+). It is expressed as the number of dependents per 100 working‑age people. This indicator helps plan health, education and pension services.
抚养比将经济活动人口（通常为 15–64 岁）与被抚养年龄组（0–14 岁和 65 岁以上）进行比较。它以每 100 名劳动年龄人口对应的被抚养人口数表示。该指标有助于规划医疗、教育和养老金服务。
Dependency Ratio = [(Population 0–14 + Population 65+) ÷ Population 15–64] × 100
抚养比 = [(0–14 岁人口 + 65 岁以上人口) ÷ 15–64 岁人口] × 100
Example: A country has 20 million aged 0–14, 10 million aged 65+, and 55 million aged 15–64. Dependency ratio = [(20+10) ÷ 55] × 100 ≈ 54.5 dependents per 100 workers.
示例： 某国 0–14 岁 2000 万，65 岁以上 1000 万，15–64 岁 5500 万。抚养比 = [(20+10) ÷ 55] × 100 ≈ 每 100 名劳动者抚养 54.5 人。
9. Urbanisation Rate | 城市化率
Urbanisation rate measures the percentage of a country’s population living in urban areas. It is a key indicator of development and changes over time as people move from rural to urban areas. OCR often links this to case studies of megacities.
城市化率衡量一国居住在城市地区的人口百分比。它是发展水平的重要指标，并随着人口从农村向城市迁移而随时间变化。OCR 常将此指标与超大城市案例研究相结合。
Urbanisation (%) = (Urban Population ÷ Total Population) × 100
城市化率 (%) = (城市人口 ÷ 总人口) × 100
Example: al : Total population 80 million, urban population 48 million. Urbanisation = (48 ÷ 80) × 100 = 60%.
示例： 总人口 8000 万，城市人口 4800 万。城市化率 = (48 ÷ 80) × 100 = 60%。
10. GDP and GDP per Capita | 国内生产总值与人均 GDP
Gross Domestic Product (GDP) is the total value of goods and services produced in a country in a year. GDP per capita divides this by the population to give an average income per person. While useful, remember it does not show wealth distribution.
国内生产总值 (GDP) 是一国一年内生产的商品和服务的总价值。人均 GDP 将其除以人口，得出人均平均收入。此指标虽有用，但要记住它不反映财富分配情况。
GDP per Capita = GDP ÷ Total Population
人均 GDP = GDP ÷ 总人口
Example: GDP = $2 trillion, population = 50 million. GDP per capita = $2,000,000,000,000 ÷ 50,000,000 = $40,000.
示例： GDP = 2 万亿美元，人口 5000 万。人均 GDP = 2000000000000 ÷ 50000000 = 40000 美元。
11. River Discharge | 河流流量
River discharge is the volume of water flowing past a point per second. It helps geographers understand flood risk and channel processes. The formula multiplies cross‑sectional area by velocity. OCR fieldwork may include measuring width, depth, and velocity.
河流流量是每秒流过某一点的水量。它帮助地理学家了解洪水风险和河道过程。公式为横截面积乘以流速。OCR 的野外调查可能包括测量宽度、深度和流速。
Discharge (m³/s) = Cross‑sectional Area (m²) × Velocity (m/s)
流量 (m³/s) = 横截面积 (m²) × 流速 (m/s)
Example: A river cross‑section is 12 m² and the average velocity is 0.8 m/s. Discharge = 12 × 0.8 = 9.6 m³/s.
示例： 某河流横截面积为 12 m²，平均流速 0.8 m/s。流量 = 12 × 0.8 = 9.6 m³/s。
12. Climate Graph Interpretation: Temperature Range and Total Rainfall | 气候图判读：气温较差与总降水量
Climate graphs display monthly temperature and precipitation. Two simple calculations help you compare climates: annual temperature range (difference between the warmest and coldest month) and total annual rainfall (sum of all monthly precipitation). OCR expects you to extract and calculate these from graphs.
气候图显示月均气温和降水量。两个简单的计算可帮助你比较气候：年较差（最热月与最冷月气温之差）和年总降水量（各月降水量之和）。OCR 期望你从图中获取并计算这些数据。
Annual Temperature Range = Tₘₐₓ − Tₘᵢₙ (where T is in °C)
年较差 = T 最热月 − T 最冷月（单位 °C）
Total Annual Rainfall = Σ Monthly Precipitation (mm)
年总降水量 = 各月降水量之和 (mm)
Example: Warmest month = 28°C, coldest month = 4°C. Range = 24°C. Monthly rainfall totals 980 mm.
示例： 最热月 28°C，最冷月 4°C。年较差 = 24°C。各月降水量合计 980 mm。
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