GCSE WJEC Geography: Formula & Theorem Quick Reference Handbook | GCSE WJEC 地理：公式定理速查手册

📚 GCSE WJEC Geography: Formula & Theorem Quick Reference Handbook | GCSE WJEC 地理：公式定理速查手册

This handbook provides a concise, exam-focused summary of all essential formulae, key models and statistical techniques required for the WJEC GCSE Geography specification. It covers river processes, population studies, map skills and fieldwork calculations. Mastering these tools will help you answer calculation questions accurately and apply geographical concepts with confidence.

本手册紧扣 WJEC GCSE 地理考纲，浓缩了所有必考公式、重要模型与统计方法，涵盖河流过程、人口研究、地图技能和实地调查计算。熟练掌握这些工具，能帮助你精准解答计算题，自信运用地理概念。

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1. River Discharge and Hydraulic Geometry | 河流流量与水力几何

Discharge is the volume of water flowing through a river channel per second. It is calculated using the continuity equation: Q = A × v, where Q is discharge (cubic metres per second, m³/s), A is the cross-sectional area of the channel (m²), and v is the average flow velocity (m/s).

流量是指每秒流过河道某一断面的水体体积，其连续方程为 Q = A × v，Q 为流量（立方米/秒，m³/s），A 为河道横截面积（m²），v 为平均流速（m/s）。

To obtain cross-sectional area, measure the channel width and several depths at equal intervals, then use A = average depth × width or sum of depth segments × segment width. Velocity is often measured with a float and corrected using average velocity = surface velocity × 0.85.

横截面积可通过测量河道宽度和若干等间距点的水深求得，使用 A = 平均水深 × 宽度 或将各段水深 × 段宽后求和。流速常用浮标法测量，再用 平均流速 = 表面流速 × 0.85 校正。

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2. River Gradient and Velocity | 河流梯度与流速

Gradient describes the steepness of a river channel or valley. It is calculated as gradient = vertical drop (m) ÷ horizontal distance (m), often expressed as a ratio such as 1:50 or as a percentage.

梯度描述河道或谷坡的陡峭程度，公式为 梯度 = 垂直落差 (m) ÷ 水平距离 (m)，常以比值（如 1:50）或百分比表示。

Velocity is the speed of water flow, found by velocity = distance (m) ÷ time (s). Use a measured section of river and record the time a float takes to travel between two points. Remember to multiply the surface velocity by 0.85 to estimate average velocity in turbulent flow.

流速是水流的速度，由 流速 = 距离 (m) ÷ 时间 (s) 求得。选取河段，记录浮标流经两点的时间。湍流中应将表面流速乘以 0.85 以估算平均流速。

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3. Bradshaw Model: Changes Along a River’s Course | 布拉德肖模型：河流沿途变化

The Bradshaw Model is a conceptual model showing how channel characteristics change from source to mouth. As a river travels downstream, average velocity, discharge, channel depth and width typically increase, while gradient, bedload size and channel roughness decrease.

布拉德肖模型是一个概念模型，展示河道特征从源头到河口的变化规律。随着河流向下游流动，平均流速、流量、河道深度和宽度通常增加，而梯度、推移质粒径和河床粗糙度则减小。

This model helps geographers compare expected changes with actual fieldwork data. For example, an upper-course site should have steeper gradient, coarser bedload and smaller discharge than a lower-course site.

该模型帮助地理学者对比预期变化与实际野外数据。例如，上游河段应比下游河段具有更陡的坡降、更粗的沉积物和更小的流量。

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4. Drainage Basin Water Balance | 流域水量平衡

The water balance equation expresses the relationship between inputs, outputs and storage in a drainage basin: P = Q + E + ΔS, where P is precipitation, Q is runoff (streamflow), E is evapotranspiration, and ΔS is the change in storage (soil water, groundwater, etc.).

水量平衡方程表达了流域输入、输出与储存量的关系：P = Q + E + ΔS，P 为降水量，Q 为径流量（河川流量），E 为蒸散发量，ΔS 为储水变化量（土壤水、地下水等）。

At times of the year when precipitation exceeds evapotranspiration and runoff, storage increases and there is a water surplus. In drier periods, storage may be depleted, leading to a deficit. This principle underlies river regime analysis.

当降水量超过蒸散发和径流时，储水增加，出现水分盈余；干旱时期储存水被消耗，形成水分亏缺。这一原理是河流情势分析的基础。

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5. Population Change and Structure | 人口变化与结构

Natural population change is calculated as natural increase = birth rate − death rate, with both rates expressed per 1000 people per year. Net migration is immigrants − emigrants. Total population change = natural increase + net migration.

人口自然变化公式为 自然增长 = 出生率 − 死亡率，两率均为每千人每年的数值。净迁移为 迁入人口 − 迁出人口。总人口变化 = 自然增长 + 净迁移。

The dependency ratio measures the pressure on the working population: dependency ratio = [(population 0−14 + 65+) ÷ population 15−64] × 100. The infant mortality rate is (deaths under 1 year ÷ total live births) × 1000.

抚养比衡量劳动人口承受的压力：抚养比 = [(0−14 岁人口 + 65 岁以上人口) ÷ 15−64 岁人口] × 100。婴儿死亡率公式为 (1 岁以下死亡人数 ÷ 活产婴儿总数) × 1000。

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6. Population Density and Urbanisation | 人口密度与城市化

Population density is a measure of average number of people per unit area: density = total population ÷ land area (km²). It indicates how crowded a region is and helps in comparing different settlements.

人口密度衡量单位面积上的平均人口数：密度 = 总人口 ÷ 土地面积 (km²)。它能反映区域的拥挤程度，并可用于比较不同聚落。

Urbanisation level is expressed as % urban = (urban population ÷ total population) × 100. The rate of urbanisation refers to the speed at which this percentage grows over a given period.

城市化水平表示为 城市化率 = (城镇人口 ÷ 总人口) × 100。城市化速度则指该百分比在一定时期内的增长速度。

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7. Development and Economic Indicators | 发展与经济指标

Gross Domestic Product (GDP) per capita is total GDP ÷ population, usually given in US dollars. A related measure is Gross National Income (GNI) per capita. Both indicate average wealth but hide internal inequality.

人均国内生产总值（GDP）为 GDP 总额 ÷ 人口，通常以美元计。相关指标为人均国民总收入（GNI）。两者反映平均财富水平，但掩盖了内部不平等。

The Human Development Index (HDI) combines life expectancy, education and income into a single value between 0 and 1. While not a simple formula, HDI provides a broader welfare measure than income alone.

人类发展指数（HDI）将预期寿命、教育和收入整合为一个 0 到 1 之间的数值。虽无简单公式，HDI 提供了比单一收入更全面的福利衡量标准。

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8. Weather and Climate Calculations | 天气与气候计算

Mean daily temperature = (max temp + min temp) ÷ 2. Monthly mean = sum of daily means ÷ number of days. Annual mean = sum of monthly means ÷ 12. Temperature range = maximum value − minimum value for any given period.

日平均气温 = (最高温 + 最低温) ÷ 2。月平均气温 = 各日平均气温之和 ÷ 天数。年平均气温 = 各月平均气温之和 ÷ 12。气温较差 = 某时段最大值 − 最小值。

Total precipitation is simply the sum of all recorded rainfall over a day, month or year. Annual precipitation patterns can be shown on a climate graph alongside temperature to identify seasonal regimes.

总降水量就是某一日、月或年内所有记录降水量的总和。年降水分布可在气候图上与气温一起展示，用以识别季节性规律。

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9. Map Skills: Scale, Distance, Area and Gradient | 地图技能：比例尺、距离、面积与坡度

Map scale is the ratio of a feature’s size on a map to its size in the real world. For a 1:25 000 map, 1 cm represents 25 000 cm (250 m). Real distance (km) = map distance (cm) × scale denominator ÷ 100 000.

地图比例尺是图上距离与实地距离的比值。在 1:25 000 地图上，1 cm 代表 25 000 cm（250 m）。实地距离 (km) = 图上距离 (cm) × 比例尺分母 ÷ 100 000。

Area can be estimated by counting grid squares. On a 1:25 000 scale map, a 1 cm × 1 cm square equals 0.0625 km². For irregular shapes, count full squares and combine partial squares. Gradient is calculated as vertical interval (m) ÷ horizontal equivalent (m) and may be written as a ratio like 1:8.

面积可通过计算网格方格数量来估算。在 1:25 000 地图上，1 cm × 1 cm 方格代表 0.0625 km²。不规则形状可计算完整方格并合并部分方格。坡度由 高差 (m) ÷ 水平距离 (m) 计算，可书写为 1:8 等形式。

Vertical exaggeration is used when drawing cross-sections: vertical exaggeration = vertical scale ÷ horizontal scale. If the vertical scale is 1:1000 and the horizontal scale is 1:25 000, VE = 25.

绘制剖面图时使用垂直夸大：垂直夸大 = 垂直比例尺 ÷ 水平比例尺。若垂直比例尺为 1:1000，水平比例尺为 1:25 000，则垂直夸大倍数为 25。

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10. Fieldwork Measurements and Statistical Tools | 野外调查测量与统计工具

Sediment size describes long axis length (mm). Angularity can be assessed using the Cailleux roundness index: RI = (2r ÷ L) × 1000, where r is the radius of the sharpest corner and L is the longest axis length. Higher values indicate more rounded pebbles.

沉积物粒径指长轴长度（mm）。棱角度可用卡耶圆度指数评估：圆度指数 = (2r ÷ L) × 1000，r 为最锐角曲率半径，L 为长轴长度。数值越高表示卵石越圆润。

Percentage cover of vegetation or land use along a transect: % cover = (length covered by the category ÷ total transect length) × 100. This technique helps quantify changes in ecosystems or beach profiles.

样线上植被或土地利用的覆盖百分比：覆盖率 = (某类别覆盖长度 ÷ 样线总长) × 100。此法可量化生态系统或海滩剖面的变化。

Common statistical measures include mean = sum of data values ÷ number of values, median (central value when ordered), mode (most frequent), range = max − min, and interquartile range (IQR) = upper quartile − lower quartile. Use IQR to describe spread around the median, reducing the effect of outliers.

常用统计量包括 平均值 = 数据值之和 ÷ 数据个数、中位数（排序后正中值）、众数（出现最频繁的值）、极差 = 最大值 − 最小值，以及四分位距（IQR）= 上四分位数 − 下四分位数。利用 IQR 描述围绕中位数的离散程度，可减少异常值的影响。

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