📚 Formula & Theorem Quick Reference for Year 8 OCR Geography | Year 8 OCR 地理：公式定理速查手册
Mastering the essential formulas and theorems in geography gives you the tools to analyse population changes, interpret maps, and understand physical processes. This quick reference guide covers the key calculations you will meet in Year 8 OCR Geography, from population density to river discharge and gradient. Each section presents a clear formula, explains what it tells us, and shows a worked example. A solid grasp of these numerical skills will help you answer exam questions confidently and support your fieldwork investigations.
掌握地理学中的关键公式与定理，能帮助你分析人口变化、判读地图并理解自然过程。这本速查手册涵盖了 Year 8 OCR 地理课程中需要掌握的核心计算，包括人口密度、河流流量与坡度等。每个小节都给出明确的公式，解释其含义，并展示计算实例。扎实掌握这些数字技能，不仅能在考试中从容作答，也能为你的实地考察提供有力支持。
1. Population Density | 人口密度
Population density measures how crowded an area is. It is found by dividing the total population by the total land area. A high density suggests many people live close together, often in cities; a low density points to sparse settlement, perhaps in rural or mountainous regions.
人口密度衡量的是一个地区的拥挤程度。用总人口除以总面积即可得出。密度高意味着许多人聚居在一起，常见于城市；密度低则说明定居点稀疏，常见于农村或山区。
Population Density = Total Population ÷ Total Land Area (km²)
Example: A town has 50,000 people and covers 25 km². Density = 50,000 ÷ 25 = 2,000 people per km².
示例：某镇有 50,000 人，占地 25 km²。密度 = 50,000 ÷ 25 = 2,000 人/公里²。
2. Birth Rate and Death Rate | 出生率与死亡率
Birth rate is the number of live births per 1,000 people per year. Death rate is the number of deaths per 1,000 people per year. They help us understand population change without being misled by the absolute size of a population.
出生率指每年每千人中活产婴儿的数量。死亡率指每年每千人中死亡人数。这两个指标有助于我们理解人口变化，避免被人口绝对规模误导。
Birth Rate = (Total live births ÷ Total population) × 1,000
Death Rate = (Total deaths ÷ Total population) × 1,000
Example: on people records 40,000 births. Birth rate = (40,000 ÷ 2,000,000) × 1,000 = 20 per 1,000.
示例：某国人口 200 万，记录出生 4 万。出生率 = (40,000 ÷ 2,000,000) × 1,000 = 20‰。
3. Natural Increase and Population Growth Rate | 自然增长率与人口增长率
Natural increase is the difference between birth rate and death rate. It shows whether a population is growing from births alone, ignoring migration. Population growth rate adds net migration to give the total annual change as a percentage.
自然增长率是出生率与死亡率之差。它反映出仅凭出生与死亡带来的人口增减，不涉及迁移。人口增长率则加入净迁移量，以百分比表示年度总变化。
Natural Increase = Birth Rate − Death Rate
Population Growth Rate (%) = [(Birth Rate − Death Rate) + Net Migration Rate] ÷ 10
Example: e 25, death rate 8, net migration rate −2 per 1,000. Growth rate = (25 − 8 − 2) ÷ 10 = 1.5%.
示例：出生率 25‰，死亡率 8‰，净迁移率 −2‰。增长率 = (25 − 8 − 2) ÷ 10 = 1.5%。
4. Urbanisation Rate | 城市化率
Urbanisation rate explains how quickly the proportion of people living in towns and cities is changing. It is usually expressed as an annual percentage increase in the urban population share.
城市化率说明城镇人口占比的变化速度，通常以城市人口比例的年均增长百分点来表示。
on ÷ Total Population) × 100) in two different years, then find the average annual change.
To calculate annual rate: (New urban % − Old urban %) ÷ Number of years.
计算年均城市化率：（新的城市人口百分比 − 旧的城市人口百分比）÷ 年数。
Example: Urban % rose from 45% to 55% over 10 years. Annual rate = (55 − 45) ÷ 10 = 1 percentage point per year.
示例：城市人口比例从 45% 上升到 55%，历时 10 年。年均速率 = (55 − 45) ÷ 10 = 每年 1 个百分点。
5. Map Scale and Distance | 地图比例尺与距离
Map scale tells you the relationship between a distance on the map and the real distance on the ground. You can use a linear (line) scale or a representative fraction to calculate straight-line and curved distances.
地图比例尺表示图上距离与实地距离的比值。你可以使用直线比例尺或数字比例尺来计算直线距离和曲线距离。
Real Distance = Map Distance × Scale Factor
Example: :50,000 map, two points are 4 cm apart. Real distance = 4 cm × 50,000 = 200,000 cm = 2 km.
示例：在 1:50,000 地图上，两点相距 4 cm。实地距离 = 4 cm × 50,000 = 200,000 cm = 2 km。
For a curved line, use a piece of string, mark it, then measure against the scale bar.
测量曲线时，可用细绳沿路线放置，标记后再对照比例尺量算。
6. Gradient (Slope) from Contour Lines | 等高线求坡度
Gradient expresses the steepness of a slope. On an Ordnance Survey map, you can work it out using the contour interval and the horizontal distance between two contours.
坡度表示斜坡的陡峭程度。在 Ordnance Survey 地图上，可利用等高距和两条等高线间的水平距离来计算。
Gradient = Vertical Interval (VI) ÷ Horizontal Equivalent (HE)
so the vertical interval is 1. E.g., VI = 50 m, HE = 200 m → gradient = 50 ÷ 200 = 1 in 4.
比例需化简为垂直距离为 1 的形式。如 VI = 50 m，HE = 200 m → 坡度 = 50 ÷ 200 = 1:4。
Example: 000 map. HE = 2 cm × 25,000 = 50,000 cm = 500 m. VI = 50 m. Gradient = 50 / 500 = 1 in 10.
示例：100 m 和 150 m 两条等高线，图上距离 2 cm，比例尺 1:25,000。HE = 2 cm × 25,000 = 500 m，VI = 50 m。坡度 = 50/500 = 1:10。
7. River Discharge | 河流流量
River discharge is the volume of water flowing past a point in the river every second. It depends on the cross-sectional area of the channel and the velocity of the water. Discharge helps explain flood risk and river energy.
河流流量是指每秒钟流过河道某一点的河水体积，取决于过水断面面积和流速。流量有助于解释洪水风险和河流动能。
Discharge (Q) = Cross-sectional Area (A) × Velocity (V)
Calculating area: For a roughly rectangular channel, Area = Width × Average Depth.
计算面积：若河道近似矩形，面积 = 宽度 × 平均水深。
Example: ge depth = 0.5 m, velocity = 0.4 m/s. A = 8 × 0.5 = 4 m², Q = 4 × 0.4 = 1.6 m³/s (cumecs).
示例：宽度 8 m，平均深 0.5 m，流速 0.4 m/s。A = 8 × 0.5 = 4 m²，Q = 4 × 0.4 = 1.6 m³/s。
8. Mean Temperature and Total Precipitation | 平均气温与总降水量
Climate graphs show monthly temperature and rainfall. Mean annual temperature is the average of the 12 monthly averages. Total annual precipitation is the sum of all monthly rainfall totals. These summary statistics let you compare climates easily.
气候图展示各月气温和降水。年平均气温是 12 个月平均气温的平均值；年总降水量则是各月降水量的总和。这些汇总统计能帮你轻松比较不同气候。
Mean Annual Temperature = (Sum of 12 monthly mean temperatures) ÷ 12
Total Annual Precipitation = Sum of 12 monthly rainfall totals
Example: res (°C): 5, 6, 9, 12, 16, 19, 22, 21, 17, 13, 8, 6. Sum = 154. Mean = 154 ÷ 12 ≈ 12.8 °C.
示例：各月均温（°C）：5、6、9、12、16、19、22、21、17、13、8、6。总和 = 154，均值 ≈ 12.8 °C。
infall totals (mm): 50, 45, 40, 55, 60, 65, 70, 75, 70, 80, 75, 60. Sum = 745 mm annually.
降水量（mm）：50、45、40、55、60、65、70、75、70、80、75、60，总和 = 年降水量 745 mm。
9. Percentage Change | 百分比变化
Percentage change is used to describe how much a quantity has grown or shrunk over time. In geography, it is applied to population, employment, forest cover, and many other indicators. It helps compare changes across different-sized places.
百分比变化用于描述数量随时间的增减幅度。地理学中，它被用于人口、就业、森林覆盖率等指标，便于在不同规模的地方之间比较变化。
Percentage Change = [(New Value − Old Value) ÷ Old Value] × 100
A positive result means growth; a negative result means decline.
正数表示增长，负数表示减少。
Example: ge had 1,200 people in 2010 and 1,500 in 2020. Change = (1,500 − 1,200) ÷ 1,200 × 100 = 25% increase.
示例：某村 2010 年有 1,200 人，2020 年 1,500 人。变化 = (1,500 − 1,200) ÷ 1,200 × 100 = 25%，即增长了 25%。
10. Dependency Ratio | 抚养比
The dependency ratio shows the balance between the working-age population and the dependent groups (young and old). It helps governments plan for schools, healthcare, and pensions.
抚养比显示劳动年龄人口与受抚养群体（幼年和老年）之间的比例关系，有助于政府规划教育、医疗和养老金。
Dependency Ratio = [(Population aged 0‑14 + Population aged 65+) ÷ Population aged 15‑64] × 100
Example: A country has 15 million aged 0‑14, 40 million aged 15‑ d 65+. Dependency ratio = (15+10) ÷ 40 × 100 = 62.5 dependants per 100 working-age people.
示例：某国 0‑14 岁 1,500 万，15‑64 岁 4,000 万，65 岁以上 1,000 万。抚养比 = (15+10) ÷ 40 × 100 = 每 100 名劳动人口需抚养 62.5 人。
11. Wind Speed and Beaufort Scale Conversion | 风速与蒲福风级换算
Anemometers measure wind speed, often in km/h or m/s. The Beaufort scale turns this into a descriptive force useful for fieldwork. A simple formula links Beaufort number (B) to wind speed.
风速计测量风速，通常以 km/h 或 m/s 计。蒲福风级把风速转化为描述性等级，适用于野外记录。一个简易公式连接风级 B 与风速。
Wind speed (km/h) ≈ 3 × B¹·⁵ (for B ≤ 8) or use standard table
In practice, use a lookup table: B=0: <1 km/h; B=3: 12‑19 km/h; B=6: 39‑49 km/h, etc.
实际操作中可查表：B=0：<1 km/h；B=3：12‑19 km/h；B=6：39‑49 km/h 等。
Example: If leaves and small twigs are in constant motion (B=3), wind speed is about 12‑19 km/h.
示例：若树叶和小枝持续摇动（B=3），风速约为 12‑19 km/h。
12. Cross‑section Area and Channel Efficiency | 河道断面面积与输水效率
Channel efficiency can be assessed through the hydraulic radius, which compares the cross‑sectional area with the wetted perimeter. A larger hydraulic radius means less friction, so the river flows more efficiently.
河道输水效率可通过水力半径来评估。水力半径是过水断面面积与湿周的比值。半径越大，摩擦力越小，水流越高效。
Hydraulic Radius (R) = Cross‑sectional Area (A) ÷ Wetted Perimeter (P)
The wetted perimeter is the total length of the channel bed and banks in contact with water.
湿周是水流与河床、河岸接触的总长度。
Example: ular channel of the same area would have a smaller P, giving a higher R and smoother flow.
示例：A = 3 m²，P = 5 m → R = 3 ÷ 5 = 0.6 m。若为半圆形河道，同样面积下湿周更小，水力半径更大，水流更顺畅。
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