Year 11 AQA Geography: Formula & Theorem Quick Reference Handbook | Year 11 AQA 地理：公式定理速查手册

📚 Year 11 AQA Geography: Formula & Theorem Quick Reference Handbook | Year 11 AQA 地理：公式定理速查手册

This quick reference handbook brings together all the essential formulas, calculations and quantitative methods you need to master for the AQA GCSE Geography course. Whether you are analysing river processes, measuring population change, working with map scales or handling fieldwork data, these formulas provide the toolkit for exam success. Each section presents the formula with a clear explanation in English and Chinese, followed by worked applications where helpful.

本速查手册汇集了AQA GCSE地理课程必须掌握的所有重要公式、计算方法和定量分析技能。无论是分析河流过程、衡量人口变化、处理地图比例尺还是整理实地考察数据，这些公式都是备考的关键工具箱。每一小节都提供了公式并配以清晰的中英文对照解释，在适当的地方还附上应用示例。

1. River Discharge | 河流流量

River discharge is the volume of water flowing through a cross‑section of a channel every second. It is one of the most important measures in fluvial geomorphology because it directly influences erosion, transportation and deposition. The fundamental relationship is:

河流流量是每秒流经河道某一横断面的水量。它是河流地貌学中最重要的量度之一，因为它直接影响侵蚀、搬运和沉积作用。其基本关系式为：

Q = A × V

where Q is discharge in cubic metres per second (m³/s), A is the cross‑sectional area of the channel in square metres (m²), and V is the mean velocity of the water in metres per second (m/s).

其中 Q 为流量（立方米/秒），A 为河道横截面积（平方米），V 为水流平均流速（米/秒）。

In a fieldwork context, cross‑sectional area is often approximated by multiplying the average width of the river (w) by the average depth (d). The formula for a simple rectangular cross‑section becomes:

在实地考察中，横截面积通常用河流平均宽度 (w) 乘以平均深度 (d) 来近似计算。对于简单的矩形断面，公式变为：

A = w × d

Velocity can be measured directly with a flowmeter. If a flowmeter is unavailable, the float method is often used: a floating object is timed over a known distance. Average velocity is then found using:

流速可用流速仪直接测量。如果没有流速仪，常采用浮标法：记录浮子流经已知距离所需的时间，然后用以下公式计算平均流速：

V = distance ÷ time

Combining these, students can calculate discharge in the field and analyse how it changes downstream, with tributary inputs or under different weather conditions. Remember to convert all units to metres and seconds.

结合以上公式，学生就可以在野外计算出流量，并分析流量如何随下游流向、支流汇入或不同天气条件而变化。注意将所有单位转换为米和秒。

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2. Hydraulic Radius and Channel Efficiency | 水力半径与河道效率

The hydraulic radius (R) describes the efficiency of a river channel: a larger hydraulic radius means less water is in contact with the bed and banks, reducing friction and allowing faster flow. It is defined as the ratio of the cross‑sectional area (A) to the wetted perimeter (P).

水力半径 (R) 描述河道的输水效率：水力半径越大，表示与河床和河岸接触的水体比例越小，摩擦力降低，流速更快。它定义为横截面积 (A) 与湿周 (P) 之比。

R = A ÷ P

Here, the wetted perimeter (P) is the total length of the channel bed and banks that are in contact with the water, measured in metres. For a rectangular channel P is calculated as width + (2 × depth).

其中，湿周 (P) 是水体接触到的河床和河岸的总长度，单位为米。对于矩形河道，P 的计算公式为 宽度 + (2 × 深度)。

A high hydraulic radius indicates a more efficient channel, which is typical of large, deep rivers in their lower course. Conversely, shallow, wide channels in the upper course tend to have a low R value, meaning greater friction and slower flow.

较高的水力半径意味着更高效的河道，这通常出现在下游宽深的大型河流中。相反，上游浅而宽的河道往往水力半径较小，摩擦力较大，流速较慢。

Understanding hydraulic radius helps explain why discharge alone does not determine flow velocity; channel shape is equally important in managing flood risk and river restoration.

理解水力半径有助于说明为什么流量本身并不决定流速；河道形态对洪水管理和河流修复同样重要。

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3. Gradient of a River or Slope | 河流或坡度梯度

Gradient refers to the steepness of a slope or river channel. It is commonly expressed as the ratio between the vertical interval (VI) – the change in height – and the horizontal equivalent (HE) – the ground distance over which that change occurs.

梯度指斜坡或河道的陡峭程度，通常表示为垂直落差 (VI) 与水平等效距离 (HE) 的比率。

Gradient = VI ÷ HE

In many exercises, gradient is written as a ratio in the form 1 : X, where X = HE ÷ VI. For example, if a river falls 10 metres over a distance of 500 metres, the gradient is 10 / 500 = 0.02, which gives a ratio of 1 : 50.

在许多练习中，梯度写为 1 : X 的比值形式，其中 X = HE ÷ VI。例如，如果一条河在 500 米的水平距离内下降了 10 米，梯度为 10 / 500 = 0.02，即比值 1 : 50。

On an Ordnance Survey map, VI is read from contour lines and HE is measured along the slope using the map scale. The same formula applies to road gradients, hillslopes and long profiles of rivers.

在 Ordnance Survey 地图上，VI 可从等高线读取，HE 则用地图比例尺沿斜坡量测。同样的公式适用于道路坡度、山坡和河流纵剖面。

A steeper gradient (smaller X value) gives a stream more energy for vertical erosion, while a gentle gradient is associated with lateral erosion and deposition. This concept links directly to the Bradshaw model of downstream changes.

较陡的梯度（X 值较小）使水流具有更多下蚀能量，而平缓的梯度则与侧蚀和沉积有关。这一概念直接与布拉德肖河流下游变化模型相关联。

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4. Population Change Indicators | 人口变化指标

Demographic calculations are central to human geography. Four vital rates allow us to quantify population dynamics: Crude Birth Rate (CBR), Crude Death Rate (CDR), Natural Increase Rate and Net Migration Rate. The following formulas are per 1000 people per year.

人口统计计算是人文地理的核心。以下四个重要比率可用于量化人口动态：粗出生率 (CBR)、粗死亡率 (CDR)、自然增长率和净迁移率。以下公式均为每千人每年。

CBR = (Number of live births ÷ Total population) × 1000

CDR = (Number of deaths ÷ Total population) × 1000

Natural Increase Rate = CBR − CDR

Net Migration Rate = ((Immigrants − Emigrants) ÷ Total population) × 1000

To obtain the overall population growth rate including migration, use:

要得到包含迁移的总体人口增长率，可使用：

Growth Rate (%) = ((Natural Increase + Net Migration) ÷ Total population) × 100

These indicators allow geographers to compare population change between countries at different stages of the Demographic Transition Model. For example, a CBR of 20 and a CDR of 8 give a natural increase of 12 per 1000, typical of a Stage 2 or early Stage 3 country.

这些指标使地理学家能够比较处于人口转变模型不同阶段的国家。例如，CBR 为 20、CDR 为 8，则自然增长率为千分之十二，这在第 2 阶段或第 3 阶段早期的国家中较为典型。

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5. Population Density | 人口密度

Population density describes how closely people live within a given area. The basic formula is:

人口密度描述给定区域内人们居住的紧密程度。基本公式为：

Population Density = Total population ÷ Land area (km²)

This measure is typically expressed as people per square kilometre (people/km²). It masks internal variations, so geographers also use physiological density (people per unit of arable land) or agricultural density, but total density is the most common statistic in GCSE questions.

该量度通常以每平方公里人数 (人/km²) 表示。由于它掩盖了内部差异，地理学家也会使用生理密度（单位可耕地面积的人口数）或农业密度，但在 GCSE 考题中最常见的是总人口密度。

When analysing population distribution maps, remember that high population density does not necessarily mean overpopulation; it depends on the carrying capacity of the land. A calculation exercise might ask: ‘If a country has 5 million people and an area of 200,000 km², calculate its average population density.’

在分析人口分布图时，记住高人口密度并不一定意味着人口过剩；这取决于土地的承载能力。计算题可能是：”如果一个国家有 500 万人口，面积为 20 万平方公里，请计算其平均人口密度。”

Answer: 5,000,000 ÷ 200,000 = 25 people/km². This figure can then be linked to factors such as relief, climate and economic opportunities.

解答：5,000,000 ÷ 200,000 = 25 人/km²。该数值随后可以与地形、气候和经济机会等因素联系起来。

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6. Urbanisation Rate | 城市化率

Urbanisation refers to the increasing proportion of a country’s population living in urban areas. The level of urbanisation is a simple percentage:

城市化指的是一个国家居住在城市地区的人口比例不断增加。城市化水平是一个简单的百分比：

Level of Urbanisation (%) = (Urban population ÷ Total population) × 100

The rate of urbanisation shows how quickly this proportion is changing over time. It can be calculated as the difference in the percentage urban between two time periods divided by the number of years, or simply presented as an annual change in percentage points.

城市化速率则显示这一比例随时间变化的速度。可计算为两个时期城镇人口百分比的差值除以年数，或直接表示为每年百分点的变化。

For instance, a country whose urban population rises from 30% to 45% over 15 years has an average urbanisation rate of (45 – 30) / 15 = 1 percentage point per year. This metric helps explain the rapid growth of megacities in emerging economies.

例如，一个国家的城镇人口在 15 年内从 30% 上升到 45%，其平均城市化速率为 (45 – 30) / 15 = 每年 1 个百分点。这一度量有助于解释新兴经济体中超大城市的快速增长。

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7. Economic Development Indicators | 经济发展指标

Development is measured using a range of economic indicators that can be calculated from raw data. The most fundamental is Gross Domestic Product (GDP) per capita:

衡量发展水平会用到一系列可从原始数据计算的经济指标。最基本的是人均国内生产总值 (GDP)：

GDP per capita = Total GDP ÷ Total population

Other widely used ratios include the literacy rate and the percentage of the workforce employed in agriculture.

其他广泛使用的比率包括识字率和农业劳动力占比。

Literacy Rate (%) = (Number of literate adults ÷ Total adult population) × 100

Agricultural Employment (%) = (Workers in agriculture ÷ Total workforce) × 100

AQA GCSE also requires understanding of composite indices such as the Human Development Index (HDI). While the exact HDI formula is complex, students should know it combines life expectancy, mean years of schooling and Gross National Income per capita into a score between 0 and 1.

AQA GCSE 还要求理解人类发展指数 (HDI) 等综合指标。尽管 HDI 的精确公式很复杂，但学生应知道它通过将预期寿命、平均受教育年限和人均国民总收入综合成一个 0 到 1 之间的分数来度量发展水平。

Being able to calculate and compare these simple ratios helps explain disparities between countries, such as the gap between sub‑Saharan Africa and Western Europe.

能够计算和比较这些简单比率有助于解释国家间的差距，例如撒哈拉以南非洲与西欧之间的发展鸿沟。

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8. Map Scales and Distance | 地图比例尺与距离

Map skills are assessed across all AQA Geography papers. Understanding scale is fundamental to measuring real‑world distances. A map scale can be given as a ratio scale (e.g. 1:50,000), a linear scale or a statement (e.g. ‘2 cm to 1 km’).

地图技能贯穿于 AQA 地理的各个试卷。理解比例尺是量算实地距离的基础。地图比例尺可以表示为比例式 (如 1:50,000)、直线比例尺或文字式 (如”图上的 2 厘米代表实地 1 千米”)。

The key formula used with a ratio scale is:

使用比例式时的关键公式为：

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