📚 Year 11 CCEA Geography: Formulas & Theorems Quick Reference Handbook | Year 11 CCEA 地理：公式定理速查手册
This quick-reference handbook gathers the essential formulas, theorems and quantitative relationships you need for CCEA GCSE Geography. From population dynamics and river discharge to map skills and energy efficiency, every entry is presented with a clear statement of the formula followed by a worked example or a key application. Use it for revision, homework and exam preparation.
本速查手册汇集了 CCEA GCSE 地理课程所必需的核心公式、定理与定量关系。从人口动态、河流流量到地图技能和能源效率，每条公式都配有清晰的陈述和典型的应用示例，适合复习、作业和备考使用。
1. Population Change Formulas | 人口变化公式
Crude Birth Rate (CBR) = (Number of live births ÷ Total population) × 1000
粗出生率 =（活产婴儿数 ÷ 总人口）× 1000
Crude Death Rate (CDR) = (Number of deaths ÷ Total population) × 1000
粗死亡率 =（死亡人数 ÷ 总人口）× 1000
Natural Increase Rate (%) = [(CBR – CDR) ÷ 10] or (Births – Deaths) ÷ Total population × 100
自然增长率（%）= [（粗出生率 – 粗死亡率）÷ 10] 或 （出生人数 – 死亡人数）÷ 总人口 × 100
Net Migration = Immigrants – Emigrants
净迁移 = 迁入人数 – 迁出人数
Total Population Growth Rate (%) = Natural Increase Rate + Net Migration Rate
总人口增长率（%）= 自然增长率 + 净迁移率
Key application: These rates are expressed per 1000 people per year, allowing comparison between countries of different sizes. Demographers use them to construct population pyramids and to predict future resource needs.
应用要点：上述比率均以每年每千人表示，便于在不同规模的国家间进行比较。人口学家利用它们绘制人口金字塔并预测未来的资源需求。
2. Urbanisation Level | 城市化水平
Level of Urbanisation (%) = (Urban population ÷ Total population) × 100
城市化水平（%）=（城市人口 ÷ 总人口）× 100
Rate of Urban Growth (%) = [(Urban population at end – Urban population at start) ÷ Urban population at start] × 100, calculated over a given period.
城市人口增长率（%）= [（期末城市人口 – 期初城市人口）÷ 期初城市人口] × 100，按指定时间段计算。
Doubling Time of Urban Population (years) ≈ 70 ÷ annual urban growth rate (%)
城市人口翻倍时间（年）≈ 70 ÷ 年均城市人口增长率（%）
This measure helps explain the pace of rural-to-urban migration and the expansion of megacities. In CCEA case studies such as Mumbai or Lagos, doubling time can highlight the pressure on housing and services.
城市化速度指标有助于解释乡城迁移的节奏以及超大城市的扩张。在孟买或拉各斯等 CCEA 案例中，翻倍时间可以凸显住房和公共服务的压力。
3. Dependency Ratio | 抚养比
Dependency Ratio = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100
抚养比 = [（0–14 岁人口 + 65 岁以上人口）÷ 15–64 岁人口] × 100
The result is the number of dependants per 100 people of working age. A high ratio indicates greater pressure on the economically active to support the young and the elderly.
结果表示每 100 名劳动年龄人口所负担的非劳动年龄人口数。比值越高，劳动人口赡养幼年与老年人口的压力就越大。
Youth Dependency Ratio = (Population aged 0–14 ÷ Population aged 15–64) × 100
少年儿童抚养比 =（0–14 岁人口 ÷ 15–64 岁人口）× 100
Elderly Dependency Ratio = (Population aged 65+ ÷ Population aged 15–64) × 100
老年抚养比 =（65 岁以上人口 ÷ 15–64 岁人口）× 100
These ratios are fundamental to the Demographic Transition Model and to government planning for schools, healthcare and pensions.
这些比率是人口过渡模型以及政府规划学校、医疗和养老金的基础。
4. Stream Flow Measurements | 河流流量测量
Cross‑sectional Area of a Stream (A) ≈ Stream width (w) × Mean depth (d)
河流横截面积（A）≈ 河宽（w）× 平均水深（d）
Wetted Perimeter (P) is the total length of the channel bed and banks in contact with the water; it is measured directly in fieldwork.
湿周（P）指水流接触的河床与岸壁总长度，通常在野外实测获得。
Hydraulic Radius (R) = A ÷ P
水力半径（R）= A ÷ P
A larger hydraulic radius means less friction and therefore higher velocity for a given gradient. Understanding R helps explain why deeper, narrower channels are more efficient than shallow, wide ones.
水力半径越大，意味着同等坡度下摩擦力越小、流速越高。理解 R 有助于解释为何深窄河道比浅宽河道的输水效率更高。
5. River Velocity and Discharge | 河流流速与流量
Velocity (v) = Distance ÷ Time
流速（v）= 距离 ÷ 时间
In fieldwork, this is often measured by timing a float or using a flow meter. Typical units: metres per second (m/s).
野外常通过浮标计时或流速仪测定，常用单位为米/秒（m/s）。
Discharge (Q) = Cross‑sectional Area (A) × Velocity (v)
流量（Q）= 横截面积（A）× 流速（v）
Discharge is expressed as cubic metres per second (m³/s). When discharge exceeds bankfull, flooding occurs. An increase in Q downstream is normal as tributaries join and drainage area enlarges.
流量以立方米/秒（m³/s）表示。当流量超过满岸流量时便会泛滥。随着支流汇入和流域面积增大，下游流量通常会增加。
Manning’s Equation (simplified concept): v ∝ R²/³ × S¹/², where R is hydraulic radius and S is channel slope. This shows that both channel shape and steepness control velocity.
曼宁公式（简化概念）：v ∝ R²/³ × S¹/²，其中 R 为水力半径，S 为河道坡度，表明断面形状和坡度共同控制流速。
6. Map Skills: Scale and Gradient | 地图技能：比例尺与坡度
True Distance on Ground = Map distance × Denominator of the Representative Fraction (RF)
地面实际距离 = 图上距离 × 比例尺分母
For a 1:50 000 map, 1 cm on the map represents 50 000 cm (500 m) on the ground. Always give the answer in kilometres or metres as required.
对于 1:50 000 地图，图上 1 cm 代表实地 50 000 cm（500 m）。答题时请按要求换算为千米或米。
Gradient = Vertical Rise ÷ Horizontal Distance
坡度 = 垂直高差 ÷ 水平距离
Gradient is expressed as a ratio, e.g. 1:25, or as a percentage. On OS maps, gradient is calculated between two contour lines: difference in height (m) ÷ horizontal distance (m).
坡度以比例如 1:25 或百分比表示。在 OS 地图上，利用两条等高线之间的高差（m）除以水平距离（m）来求得。
Area Measurement: For regular shapes, area = length × width. For irregular shapes, use grid squares where one square on a 1:50 000 map = 1 km².
面积测量：规则图形用长×宽；不规则图形可使用网格法，1:50 000 地图上一个网格代表 1 km²。
7. Climate and Weather Statistics | 气候与天气统计
Mean Annual Temperature = Sum of 12 monthly mean temperatures ÷ 12
年平均气温 = 12 个月月均温之和 ÷ 12
Annual Temperature Range = Warmest monthly mean – Coldest monthly mean
年温差 = 最暖月均温 – 最冷月均温
Total Annual Precipitation = Sum of 12 monthly precipitation totals
年降水总量 = 12 个月月降水量之和
Precipitation Effectiveness: Use the Köppen or simple aridity index: A = P ÷ (T + 10) where P is annual precipitation (mm) and T is mean annual temperature (°C). Typically used when assessing climate types.
降水有效性：可使用柯本气候分类或简易干燥指数：A = P ÷ (T + 10)，其中 P 为年降水量（mm），T 为年均温（°C），常用于判定气候类型。
These calculations underpin climate graph construction and the comparison of stations for CCEA studies of contrasting environments.
这些计算是绘制气候图表和比较不同站点的基础，服务于 CCEA 中对比环境的学习。
8. Energy Efficiency and Carbon Footprint | 能源效率与碳足迹
Energy Efficiency (%) = (Useful energy output ÷ Total energy input) × 100
能源效率（%）=（有用能产出 ÷ 能源总投入）× 100
A typical thermal power station may have an efficiency of 30–40%. Renewable technologies also have efficiency ratings that influence their suitability in different locations.
典型火力发电站效率约为 30–40%。可再生能源技术同样具有效率等级，这会影响其在各地的适用性。
Carbon Footprint (kg CO₂ equivalent) ≈ Activity data × Emission Factor
碳足迹（kg CO₂ 当量）≈ 活动数据 × 排放因子
For example, the carbon footprint of a car journey = litres of fuel consumed × CO₂ emission factor per litre of fuel.
例如，汽车出行的碳足迹 = 耗油升数 × 每升燃油的 CO₂ 排放系数。
Energy Intensity = Energy consumed ÷ GDP. Lower energy intensity indicates an economy that uses energy more efficiently.
能源强度 = 能源消费量 ÷ GDP。能源强度越低，表明经济体使用能源的效率越高。
9. Ecosystems: Productivity and Biomass | 生态系统：生产力与生物量
Primary Productivity (g/m²/year) = Biomass produced by photosynthesis over a unit area per year.
初级生产力（g/m²/年）= 每年单位面积光合作用产生的生物量。
Net Primary Productivity (NPP) = GPP – Respiration losses. NPP is the energy available to consumers.
净初级生产力（NPP）= 总初级生产力（GPP）– 呼吸消耗。NPP 是可供消费者利用的能量。
Biomass at a trophic level can be estimated using: Biomass (g/m²) = Number of organisms × Average individual biomass. Understanding biomass pyramids helps assess ecosystem health.
某一营养级的生物量可估算为：生物量（g/m²）= 个体数量 × 平均个体生物量。理解生物量金字塔有助于评估生态系统健康状况。
Transfer Efficiency between trophic levels usually averages 10%. This formula helps explain why food chains are rarely longer than four or five links.
营养级之间的传递效率平均约 10%，这有助于解释为何食物链很少超过四五个环节。
10. Coastal Processes: Sediment Budget | 海岸过程：沉积物收支
Sediment Budget = Sediment Input – Sediment Output
沉积物收支 = 沉积物输入 – 沉积物输出
Inputs include rivers, cliff erosion and longshore drift from up‑drift. Outputs include deposition down‑drift, removal by waves and currents, and human extraction.
输入项包括河流来沙、崖壁侵蚀和来自上漂向的沿岸输沙；输出项包括下漂向沉积、波浪与潮流搬运以及人为取沙。
When the budget is positive, the coastline progrades (grows seaward); when negative, it erodes. CCEA case studies such as the Holderness Coast require candidates to calculate net drift rates and link them to management strategies.
当沉积物收支为正时，海岸向海淤进；为负时则发生侵蚀。在霍尔德内斯海岸等 CCEA 案例中，考生需计算净输沙率并将其与管理策略相联系。
Longshore Drift Rate (m³/year) = Volume of sediment moved past a point ÷ Time period
沿岸输沙率（m³/年）= 通过某点的沉积物体积 ÷ 时间段
11. Water Balance and Hydrological Budget | 水平衡与水文收支
P = Q + E + (ΔS)
降水量（P）= 径流量（Q）+ 蒸发量（E）+ 蓄水变化（ΔS）
In a drainage basin over a year, the water balance equation is crucial for understanding river regimes. A soil‑moisture surplus occurs when P > potential evapotranspiration (PE); a deficit occurs when P < PE.
在流域一年的水平衡中，该方程对于理解河流流量情势至关重要。当降水大于可能蒸散发时为土壤水分盈余，反之为亏缺。
This formula is central to CCEA topics on water resource management, flooding risk and irrigation planning.
该公式是 CCEA 水资源管理、洪水风险和灌溉规划专题的核心。
12. Development Indicators: Composite Indices | 发展指标：综合指数
HDI (Human Development Index) is a composite of life expectancy, education (mean and expected years of schooling) and GNI per capita. While an exact HDI formula uses geometric mean, students should recall the three components and their influence on ranking.
人类发展指数（HDI）是预期寿命、教育（平均与预期受教育年限）和人均国民总收入的综合指标。虽然精确 HDI 使用几何平均数计算，学生应掌握三个维度的构成及其对排序的影响。
Gender Inequality Index (GII) and Multidimensional Poverty Index (MPI) are also used in CCEA to compare levels of development. These indices combine multiple weighted indicators.
性别不平等指数（GII）和多维贫困指数（MPI）也用于 CCEA 比较发展水平。这些指数综合了多项加权指标。
Knowledge of these formulas helps evaluate the effectiveness of aid, trade and development projects.
掌握这些指标有助于评估援助、贸易和发展项目的成效。
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