📚 Year 11 OCR Geography: Formula & Theorem Quick-Reference Handbook | 公式定理速查手册
Geography at Year 11 involves not only descriptive understanding of the world but also the ability to calculate, analyse and interpret data. This quick‑reference handbook gathers all the essential formulas, indices and key relationships you need for OCR GCSE Geography – from population change and development indicators to river discharge, slope gradients and statistical measures used in fieldwork. Keep it handy when revising Paper 1 (Living in the UK Today), Paper 2 (The World Around Us) and Paper 3 (Geographical Skills).
11 年级地理不仅需要对世界的描述性理解，还需要计算、分析和解读数据的能力。本速查手册汇集了 OCR GCSE 地理所有关键的公式、指数和重要关系——从人口变化、发展指标到河流流量、坡度计算以及野外实地考察中使用的统计指标。在复习 Paper 1（当今英国的生活）、Paper 2（我们周围的世界）和 Paper 3（地理技能）时，请随时查阅。
1. Population Geography | 人口地理
Birth rate is calculated as the number of live births per 1000 people per year. It reflects the fertility level of a population.
出生率是指每年每 1000 人中活产婴儿的数量，反映了一个群体的生育水平。
Birth Rate = (Total live births ÷ Total population) × 1000
Death rate is the number of deaths per 1000 people per year, indicating overall mortality.
死亡率是每年每 1000 人中的死亡人数，反映总死亡水平。
Death Rate = (Total deaths ÷ Total population) × 1000
Natural increase is the difference between birth rate and death rate, usually expressed as a percentage. It shows whether a population is growing without considering migration.
自然增长率是出生率与死亡率的差值，通常以百分比表示。它显示在不考虑迁移的情况下人口是否增长。
Natural Increase (%) = (Birth Rate − Death Rate) ÷ 10
Population density describes how crowded an area is. It is simply the number of people per square kilometre.
人口密度描述一个地区的拥挤程度，即每平方千米的人口数。
Population Density = Total population ÷ Land area (km²)
Dependency ratio measures the pressure on the productive population. It compares the number of dependants (young and old) to the working‑age population.
抚养比衡量的是生产性人口承受的压力，它将受抚养人口（青少年和老人）与劳动年龄人口进行比较。
Dependency Ratio = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100
2. Development Indicators | 发展指标
Gross Domestic Product (GDP) per capita is the total value of goods and services produced in a country divided by the mid‑year population. It gives an average income but does not show inequality.
人均国内生产总值是一个国家生产的商品和服务的总价值除以年中人口，反映平均收入，但无法体现不平等。
GDP per capita = Total GDP ÷ Population
The Human Development Index (HDI) combines life expectancy, education (mean years of schooling and expected years) and GNI per capita. The formula uses a geometric mean of three normalised indices; you are not required to memorise the full calculation but must understand it ranges from 0 to 1.
人类发展指数综合了预期寿命、教育（平均受教育年限和预期受教育年限）以及人均国民总收入。该指数使用三个标准化指数的几何平均数，你不必记住完整计算过程，但要知道其取值范围是 0 到 1。
Infant mortality rate is the number of deaths of infants under one year old per 1000 live births. It is a sensitive indicator of healthcare quality.
婴儿死亡率是每 1000 个活产婴儿中一岁前死亡的数量，是衡量医疗质量的敏感指标。
Infant Mortality Rate = (Deaths under 1 year ÷ Total live births) × 1000
Literacy rate is the percentage of people aged 15 and above who can read and write a simple statement. It helps measure education levels.
识字率是 15 岁及以上人口中能读写简单语句的百分比，用于衡量教育水平。
Literacy Rate = (Number of literate adults ÷ Total adult population) × 100
3. River Studies | 河流研究
River discharge (Q) is the volume of water flowing past a point per second. It is fundamental in flood studies and links cross‑sectional area with velocity.
河流流量 (Q) 是每秒流过某点的水量，是洪水研究的基础，它连接了横截面积与流速。
Discharge (m³/s) = Cross‑sectional area (m²) × Velocity (m/s)
Velocity can be measured by timing a float over a known distance. The surface velocity is then multiplied by a correction factor (commonly 0.85 for rough beds) to estimate mean velocity.
流速可通过浮标经过已知距离的时间来测算，表面流速通常要乘以一个校正系数（粗糙河床常用 0.85）以估算平均流速。
Mean Velocity = Distance (m) ÷ Time (s) × Correction factor
Hydraulic radius is a measure of channel efficiency. It is the cross‑sectional area divided by the wetted perimeter. A higher hydraulic radius means less friction and faster flow.
水力半径是衡量河道效率的指标，它是横截面积除以湿周长。水力半径越大，摩擦力越小，流速越快。
Hydraulic Radius (R) = Cross‑sectional area (A) ÷ Wetted perimeter (P)
Gradient (or slope) of a river can be calculated using the vertical fall and the horizontal distance along the channel. Express as a ratio or percentage.
河流的比降（坡度）可以用垂直落差除以河道水平距离来计算，以比值或百分比表示。
Gradient = Vertical drop (m) ÷ Horizontal distance (m)
4. Coastal Processes | 海岸过程
Wave energy depends on wave height, wind speed and fetch. While there is no single numeric formula required at GCSE, you should understand the relationship: longer fetch and stronger winds produce higher, more energetic waves.
波浪能量取决于波高、风速和风区长度。GCSE 不要求具体的数值公式，但应理解：风区越长、风力越强，产生的波浪越高、能量越大。
Longshore drift is the transport of sediment along the coast. The direction and rate can be estimated by tracking the movement of tracer material over a known time and measuring the distance travelled.
沿岸漂移是沉积物沿海岸线的输运。可通过追踪示踪物在一定时间内的移动距离来估算方向和速率。
Longshore Drift Rate (m/day) = Distance moved (m) ÷ Time (days)
Beach sediment analysis often involves calculating the average size of pebbles (e.g. using the length of the a, b and c axes) or the percentage of different sediment types. Use the mean of axis lengths to represent particle size.
海滩沉积物分析通常涉及计算卵石的平均大小（如使用 a、b、c 轴的长度）或不同沉积物类型的百分比。用轴长的平均值表示颗粒大小。
Mean pebble size = (Axis a + Axis b + Axis c) ÷ 3
5. Weather & Climate | 天气与气候
Mean annual temperature is the average of all monthly mean temperatures over a year. It helps characterise a climate.
年平均气温是一年中各月平均气温的均值，用于表征气候特征。
Mean Annual Temperature = Sum of 12 monthly mean temperatures ÷ 12
Temperature range is the difference between the highest and lowest monthly means. It indicates the degree of continentality or seasonality.
气温年较差是最高月均温与最低月均温的差，反映大陆度或季节性。
Temperature Range = Max monthly mean − Min monthly mean
Total annual precipitation is simply the sum of all monthly precipitation totals. Precipitation includes rain, snow, hail and sleet, all converted to water equivalent (mm).
年降水总量是各月降水量的总和。降水包括雨、雪、冰雹和雨夹雪，全部折算为毫米水当量。
Total Annual Precipitation = Sum of 12 monthly totals
Climate anomalies refer to the departure from a long‑term average (e.g. 1981–2010 baseline). Calculate as: anomaly = observed value − average baseline value.
气候距平是指相对于长期平均值（如 1981–2010 年基准）的偏差。计算方法：距平 = 观测值 − 基准平均值。
Anomaly = Observed value − Long‑term mean
6. Map Skills & Fieldwork | 地图技能与实地考察
Scale conversion on Ordnance Survey maps allows you to translate map distance into real‑world distance. A 1:25 000 scale means 1 cm on the map equals 25 000 cm (0.25 km) in reality.
英国地形测量图的比例尺换算可将地图距离转换为实地距离。1:25 000 的比例尺表示地图上 1 厘米等于实地 25 000 厘米（0.25 千米）。
Real distance (km) = Map distance (cm) × Scale denominator ÷ 100 000
Area of an irregular shape on a map can be estimated using a grid square method. Count full squares and fractions of squares, then multiply by the area each square represents on the ground.
地图上不规则形状的面积可以用网格方格法估算。统计完整方格和部分方格，再乘以每个方格所代表的实地面积。
Area (m²) = Number of squares × Ground area per square (m²)
Slope gradient between two contour lines is the vertical interval divided by horizontal equivalent. It is often expressed as a ratio (e.g. 1:10) or a percentage.
两条等高线之间的坡度是垂直间距除以水平距离，通常以比值（如 1:10）或百分比表示。
Gradient = Vertical interval (m) ÷ Horizontal distance (m)
Slope (%) = (Vertical interval ÷ Horizontal distance) × 100
Angle of slope in degrees can be found using trigonometry: the gradient is the tangent of the angle. For field sketches, you may need to estimate slope angle visually using a clinometer.
坡度角度可通过三角函数求得：坡度是角度的正切值。野外素描时可能需要用倾角仪目估坡度。
Angle (°) = tan⁻¹ (Vertical ÷ Horizontal)
7. Climate Change & Carbon | 气候变化与碳
Carbon footprint is the total amount of greenhouse gases (measured in kg or tonnes of CO₂ equivalent) produced directly and indirectly by an individual, organisation or country. GCSE questions may ask you to multiply emission factors by activity data.
碳足迹是个人、组织或国家直接和间接产生的温室气体总量（以千克或吨 CO₂ 当量计）。GCSE 题目可能要求用排放因子乘以活动数据。
Carbon footprint (kg CO₂e) = Activity data × Emission factor
Per capita carbon emissions are useful for comparing countries of different sizes. Divide the total national emissions by the population.
人均碳排放有助于比较不同大小的国家。用国家排放总量除以人口总数。
Per Capita Emissions = Total CO₂ emissions ÷ Population
Percentage change in emissions or temperature anomaly is often used to show trends over time.
排放量或温度距平的百分比变化常用于显示时间趋势。
% Change = [(New value − Original value) ÷ Original value] × 100
8. Urban Geography | 城市地理
Urban population density in different parts of a city can be calculated using the same formula as general population density. It may be used to compare the inner city with suburbs.
城市不同区域的人口密度可用与一般人口密度相同的公式计算，用于比较内城区与郊区。
Urban Density = Population ÷ Area (hectares or km²)
Rate of urbanisation measures how quickly an area is becoming urban. It can be expressed as the average annual increase in the percentage of population living in urban areas.
城镇化率衡量一个地区城市化的速度，可用城市人口比例的年均增加量表示。
Urbanisation Rate = (% urban in year t2 − % urban in year t1) ÷ Number of years
Land‑use mix can be quantified by counting the number of different services or categories in a transect and expressing as a diversity index or simple percentage.
功能混合度可通过计数样线中不同服务设施或类别的数量来表示，采用多样性指数或简单百分比。
Land‑use Mix (%) = (Number of building types observed ÷ Total buildings surveyed) × 100
9. Environmental Quality Surveys | 环境质量调查
Bipolar scoring assesses environmental quality on a scale, e.g. from −2 (very poor) to +2 (excellent) for criteria such as litter, noise and greenery. Calculating the mean score for a site allows comparisons.
双向评分按等级评估环境质量，例如对垃圾、噪音、绿化等标准从 −2（非常差）到 +2（非常好）打分。计算某个地点的平均分以便比较。
Mean Bipolar Score = Sum of all criterion scores ÷ Number of criteria
An overall environmental quality index can be built by summing the scores or by weighting certain factors. Simple addition is most common at GCSE.
可将各项分数相加或对某些因素加权来构建综合环境质量指数，在 GCSE 中最常用的是简单相加。
EQ Index = Score 1 + Score 2 + Score 3 + … + Score n
If you use a Likert scale (1–5) for a perception survey, you can calculate the percentage of respondents choosing each option and then find the modal category.
如果在感知调查中使用李克特量表（1−5 分），可计算选择每个选项的受访者百分比，并找出众数类别。
Percentage = (Number in category ÷ Total respondents) × 100
10. Statistical Measures for Fieldwork | 实地考察的统计测量
Mean (average) is the sum of values divided by the count. It is the most common measure of central tendency in river depth, pebble size or survey data.
平均数是将数值之和除以个数，是河流深度、卵石大小或调查数据中最常用的集中趋势指标。
Mean = Sum of all values ÷ Number of values
Median is the middle value when data are ordered. It is less affected by outliers. For an even number of values, take the mean of the two middle numbers.
中位数是将数据排序后中间的值，不易受异常值影响。若数据个数为偶数，则取中间两个数的平均值。
Mode is the value that appears most frequently. It can be used with categorical data like land‑use types. There may be more than one mode (bimodal/multimodal).
众数是出现频率最高的值，可用于土地利用类型等分类数据。可能存在多个众数（双峰/多峰）。
Range shows the spread of data: highest value minus lowest value. Interquartile range (IQR) is the difference between the upper quartile (Q3) and lower quartile (Q1); it shows the spread of the middle 50% and is robust against outliers.
极差显示数据的离散程度：最大值减去最小值。四分位距 (IQR) 是上四分位数 (Q3) 与下四分位数 (Q1) 之差，显示中间 50% 数据的分布范围，对异常值稳健。
Range = Max value − Min value
Interquartile Range = Q3 − Q1
Percentage increase or decrease is commonly needed when comparing field data between two sites or time periods.
比较两个地点或时间段的数据时常常需要计算百分比增减。
% Change = [(New − Old) ÷ Old] × 100
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