📚 Year 11 Eduqas Geography: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This quick reference handbook compiles essential formulas, equations and key theoretical models you need to master for Year 11 Eduqas Geography. From population dynamics and urbanisation rates to fieldwork statistics and river processes, each entry is presented with clear definitions and worked-style examples to support your revision.
这本速查手册汇总了Year 11 Eduqas地理必须掌握的关键公式、方程式和重要理论模型。从人口动态和城市化率到实地考察统计和河流过程，每个条目都以清晰的定义和实例式讲解呈现，助力你的复习备考。
1. Population Density & Vital Rates | 人口密度与人口动态率
Population density measures the spatial concentration of people and is calculated by dividing total population by total land area.
人口密度衡量人口的空间集中程度，通过总人口除以总土地面积计算得出。
Population Density = Total Population ÷ Land Area (km²)
The crude birth rate (CBR) expresses the number of live births per 1000 individuals in a given year.
粗出生率（CBR）表示一年内每千人的活产婴儿数。
Birth Rate = (Number of live births ÷ Total population) × 1000
Similarly, the crude death rate (CDR) captures the number of deaths per 1000 people each year.
类似地，粗死亡率（CDR）反映每年每千人的死亡人数。
Death Rate = (Number of deaths ÷ Total population) × 1000
Natural increase is the difference between the birth rate and the death rate, often expressed per 1000.
自然增长率是出生率与死亡率之差，通常以千分比表示。
Natural Increase = Birth Rate − Death Rate
To understand the economic burden on the working population, the dependency ratio is used.
为了解劳动人口的经济负担，运用抚养比这一指标。
Dependency Ratio = [(Population 0−14 + Population 65+) ÷ Population 15−64] × 100
Population growth rate that includes migration can be expressed as a percentage.
包含迁移的人口增长率可以用百分比表示。
Growth Rate (%) = [(Births − Deaths) + (Immigration − Emigration)] ÷ Total population × 100
2. Percentage Change & Urbanisation | 百分比变化与城市化
Percentage change is a fundamental tool for comparing data over time, whether for population, rainfall or urban area.
百分比变化是比较数据随时间变化的基本工具，无论是用于人口、降雨量还是城市面积。
Percentage Change = [(New value − Original value) ÷ Original value] × 100
The level of urbanisation is simply the share of a country’s population living in urban settlements.
城市化水平仅仅是一个国家居住在城市聚落中的人口比例。
Urban Population (%) = (Urban population ÷ Total population) × 100
The rate of urbanisation, often measured over decades, shows how quickly this proportion is growing.
城市化速度通常以十年为单位衡量，显示这一比例的增长快慢。
Urbanisation Rate (%) = [(Urban % at end − Urban % at start) ÷ Urban % at start] × 100 per time period
3. River Discharge & Stream Flow | 河流流量与流速
Discharge is the volume of water passing a point in the channel per second, a vital measure of a river’s capacity.
流量是每秒通过河道某一点的水量，是衡量河流输送能力的重要指标。
Discharge (Q) = Cross-sectional Area (A) × Average Velocity (v)
The cross-sectional area can be estimated from channel width and mean depth measured during fieldwork.
横截面积可通过实地测量河道宽度和平均深度来估算。
A (m²) = Channel Width (m) × Average Depth (m)
Velocity is often obtained by timing a float over a known distance, giving a straightforward speed calculation.
流速通常通过记录浮标通过已知距离的时间来获得，是一个简单的速度计算。
Velocity (m/s) = Distance (m) ÷ Time (s)
4. Drainage Density & Basin Characteristics | 排水密度与流域特征
Drainage density describes how well a basin is drained by its stream network, influencing flood risk and runoff response.
排水密度描述流域内河网排水的充分程度，影响洪水风险和径流响应。
Drainage Density = Total length of all streams (km) ÷ Drainage basin area (km²)
A high drainage density means water is carried away rapidly, while a low density often relates to permeable rocks.
高排水密度意味着水流被迅速带走，而低密度常与透水岩石有关。
Basin shape and relief can be expressed using the elongation ratio or relief ratio, though Year 11 mainly requires qualitative interpretation.
流域形状和起伏可用伸长比或起伏比表示，不过Year 11阶段主要进行定性解读。
5. Slope Gradient & Beach Profile | 坡度与海滩剖面
Gradient is the steepness of a slope or beach face, essential for measuring valley sides, sand dune angles and coastal profiles.
坡度是坡面或海滩面的陡峭程度，对测量谷壁、沙丘角度和海岸剖面至关重要。
Gradient = Vertical Rise (m) ÷ Horizontal Distance (m)
Gradient is often expressed as a ratio (1:x) or as a percentage by multiplying the decimal result by 100.
坡度常以比（1:x）或百分比表示，即将小数结果乘以100。
On beaches, gradient changes with sediment size and wave energy; steeper beaches often indicate larger shingle.
在海滩上，坡度随沉积物粒径和波浪能量变化；较陡的海滩往往指示较大的鹅卵石。
6. Fieldwork Statistics: Central Tendency | 实地统计：集中趋势
When analysing fieldwork data, measures of central tendency summarise the typical value of a dataset.
在分析实地考察数据时，集中趋势的度量指标概括了数据集的典型值。
The mean is the arithmetic average and is sensitive to extreme values.
平均值是算术平均数，易受极端值影响。
Mean = ∑ x / n
The median is the middle value when data are ordered; it is less affected by outliers.
中位数是排序后位于中间的值，受异常值影响较小。
The mode is the most frequently occurring value, useful for categorical data like sediment shape.
众数是出现频率最高的值，适用于如沉积物形状的分类数据。
Spread can be described by the range and interquartile range (IQR = upper quartile − lower quartile).
数据离散程度可用极差和四分位距（IQR = 上四分位数 − 下四分位数）来描述。
7. Spearman’s Rank Correlation | 斯皮尔曼等级相关系数
Spearman’s rank is a non-parametric test used frequently in geography fieldwork to assess the strength of a relationship between two variables, e.g. distance from CBD and environmental quality.
斯皮尔曼等级相关是地理实地考察中常用的非参数检验，用于评估两个变量之间的关联强度，例如距CBD的距离与环境质量。
rs = 1 − (6 Σ d²) / (n (n² − 1))
Here d is the difference in ranks for each pair, and n is the number of pairs. The result ranges from −1 (perfect negative) to +1 (perfect positive).
其中d是每对数据的等级差，n是对数。结果范围从−1（完全负相关）到+1（完全正相关）。
Always check the significance of your calculated rs against a critical values table at the 0.05 confidence level.
始终将计算出的rs与0.05置信水平的临界值表进行比对以检验显著性。
8. The Bradshaw Model | 布拉德肖模型
The Bradshaw model is a theoretical downstream model predicting how channel characteristics change from source to mouth.
布拉德肖模型是一个理论性的下游变化模型，预测河道特征从源头到河口如何变化。
It states that as you move downstream, discharge, occupied channel width, average depth and average velocity all increase, while load particle size, channel bed roughness and slope gradient decrease.
它指出，向下游行进时，流量、占用河道宽度、平均深度和平均流速都增加，而搬运物粒径、河床粗糙度和河道坡度减小。
This theorem helps students compare real river data against expected trends and evaluate anomalies.
该定理帮助学生将真实河流数据与预期趋势进行比较，并评估异常现象。
9. The Hjulström Curve Theorem | Hjulström曲线定理
The Hjulström curve illustrates the relationship between particle size and the critical velocity required for erosion, transportation and deposition in a river.
Hjulström曲线说明了河流中颗粒大小与侵蚀、搬运和沉积所需临界流速之间的关系。
A key theorem from the curve is that fine cohesive particles like clay require a surprisingly high velocity to be eroded once compacted, but they can stay in suspension at very low velocities.
该曲线的一个关键定理是，像黏土这样的细颗粒粘结性物质一旦压实，需要惊人的高流速才能被侵蚀，但它们能在极低流速下保持悬浮。
Sand-sized particles are eroded most easily; the lowest critical erosion velocity occurs around 0.2 mm grain size.
砂粒大小的颗粒最容易被侵蚀；最低的临界侵蚀速度出现在约0.2毫米的粒径处。
10. The Demographic Transition Model | 人口转变模型
The Demographic Transition Model (DTM) acts as a theorem to explain how birth rates, death rates and total population change as a country develops.
人口转变模型（DTM）作为一个定理，用以解释出生率、死亡率和总人口如何随国家发展而变化。
It links directly to the vital rate formulas: in Stage 1 both rates are high, so natural increase is low; Stage 2 sees death rates fall while birth rates remain high, causing rapid population growth.
它与人口动态率公式直接相关：在第一阶段两率均高，自然增长低；第二阶段死亡率下降而出生率保持高位，导致人口快速增长。
In Stage 3 birth rates decline, slowing growth; Stage 4 sees low, balanced rates; Stage 5 may have death rates exceeding birth rates, leading to natural decrease.
在第三阶段，出生率下降，增长放缓；第四阶段两率低且平衡；第五阶段可能出现死亡率超过出生率，导致自然减少。
11. Hydraulic Radius & Channel Efficiency | 水力半径与河道效率
Channel efficiency, describing how little energy is lost to friction, can be assessed using the hydraulic radius.
河道效率描述摩擦能量损失的程度，可利用水力半径进行评估。
Hydraulic Radius (R) = Cross-sectional Area ÷ Wetted Perimeter
A larger hydraulic radius indicates a more efficient channel with less contact between water and the bed/banks.
较大的水力半径表明河道效率更高，水流与河床及河岸的接触更少。
This concept supports the Bradshaw model’s prediction of increasing efficiency downstream.
这一概念支持布拉德肖模型关于下游效率增加的预测。
12. Soil Moisture Budget Formula | 土壤水分收支公式
The simple water balance equation relates precipitation, evapotranspiration and soil moisture storage, useful in arid and semi‑arid regions.
简单的水量平衡方程将降水、蒸散和土壤水分储存联系起来，在干旱和半干旱地区十分有用。
Surplus/Deficit = Precipitation (P) − Potential Evapotranspiration (PET)
When P exceeds PET there is a soil moisture surplus (recharge); when PET exceeds P a deficit occurs and plants rely on stored soil moisture.
当P大于PET时，出现土壤水分盈余（补充）；当PET大于P时，产生亏缺，植物依赖储存的土壤水分。
This fundamental theorem aids decision‑making in water management and agriculture in the GCSE context.
这一基本定理在GCSE背景下有助于水资源管理和农业的决策。
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