Year 10 WJEC Geography: Formula and Theorem Quick Reference Handbook | 公式定理速查手册

📚 Year 10 WJEC Geography: Formula and Theorem Quick Reference Handbook | 公式定理速查手册

This handbook provides a concise summary of essential formulas, calculations and key theoretical models needed for the Year 10 WJEC Geography course. Mastering these quantitative skills will help you interpret data, analyse geographical patterns and answer exam questions accurately.

本手册简明总结了 Year 10 WJEC 地理课程中必不可少的公式、计算方法和关键理论模型。掌握这些定量技能有助于你解读数据、分析地理格局并准确回答考试题目。

1. Map Scale and Distance Conversion | 地图比例尺与距离换算

Map scale expresses the relationship between a distance on a map and the corresponding distance on the ground. You can convert between the two using the scale factor provided on the map, often shown as a ratio like 1:50 000 or a linear bar.

地图比例尺表示图上距离与实地距离之间的关系。你可以利用地图上给出的比例尺因子（常以 1:50 000 的比率或线段比例尺表示）进行相互转换。

Real Distance = Map Distance × Scale Factor

For a 1:25 000 map, 1 cm on the map equals 25 000 cm (or 250 m) on the ground. Always ensure the units are consistent when calculating. A ruler measurement of 4.5 cm on this map would represent 4.5 × 250 = 1 125 m in reality.

在 1:25 000 的地图上，图上 1 cm 相当于实地 25 000 cm（即 250 m）。计算时务必保证单位一致。若在该地图上量得距离为 4.5 cm，则实地距离为 4.5 × 250 = 1 125 m。

---

2. Gradient (Slope) Calculation | 坡度计算

Gradient measures the steepness of a slope. In geography, it is often used when analysing river long profiles, cross sections or road cuttings. It is expressed as a ratio or fraction, comparing vertical rise to horizontal run.

坡度衡量斜坡的陡峭程度。地理学中常用于分析河流纵剖面、横截面或道路切坡。坡度以比率或分数表示，将垂直升高与水平距离进行比较。

Gradient = Vertical Interval (VI) ÷ Horizontal Distance (HD)

If a hillside rises 20 m over a horizontal distance of 200 m, the gradient is 20 ÷ 200 = 1/10 or 1:10. Make sure both measurements are in the same unit. A smaller denominator indicates a steeper slope.

若山坡在水平距离 200 m 内上升了 20 m，则坡度为 20 ÷ 200 = 1/10 或 1:10。确保两个测量值单位相同。分母越小，表示坡面越陡。

---

3. Area Measurement Using Grid Squares | 网格方格面积测量

Ordnance Survey maps and many topographic sheets contain a grid system. You can estimate ground area by counting grid squares, either as whole squares or by combining partial squares. Each square covers a known area based on the scale.

英国地形测量局地图和许多地形图纸都包含网格系统。通过数方格（完整方格或部分方格的组合），可以估算实地面积。每个方格根据比例尺代表已知的面积。

Area = Number of Squares × Area Represented by One Square

On a 1:50 000 map, a 1 cm grid square represents 1 km² on the ground. If a lake covers 2.5 squares, its approximate ground area is 2.5 km². Use the ‘tick and dot’ method for partial squares to improve accuracy.

在 1:50 000 的地图上，1 cm 网格方格代表实地 1 km²。若某湖泊覆盖 2.5 个方格，其近似实地面积为 2.5 km²。可使用“打点法”处理不完整方格，以提高精度。

---

4. Population Density | 人口密度

Population density describes how crowded or sparsely populated an area is. It is a fundamental measure in human geography, frequently used to compare regions and to examine the relationship between people and land.

人口密度描述某一地区人口分布的稠密或稀疏程度。这是人文地理学的基本指标，常用于区域对比以及探讨人地关系。

Population Density = Total Population ÷ Area (km²)

If a country has 67 million people and an area of 500 000 km², the density is 67 000 000 ÷ 500 000 = 134 persons per km². Remember that density can be misleading if large uninhabitable areas are included within the total area.

若某国拥有 6700 万人口，面积为 500 000 km²，则人口密度为 67 000 000 ÷ 500 000 = 134 人/平方千米。需要注意，如果总面积中包含大片不适宜居住的区域，人口密度可能会产生误导。

---

5. Crude Birth Rate and Crude Death Rate | 粗出生率与粗死亡率

The Crude Birth Rate (CBR) and Crude Death Rate (CDR) are vital demographic indicators. They express the number of live births or deaths per 1 000 people in a population over one year, allowing cross-country comparison independent of total population size.

粗出生率（CBR）和粗死亡率（CDR）是重要的人口指标。它们表示一年内每 1000 人中发生的活产数或死亡数，便于进行跨国比较，不受人口总量影响。

CBR = (Number of Live Births ÷ Total Population) × 1000
CDR = (Number of Deaths ÷ Total Population) × 1000

For example, a population of 1 000 000 with 12 000 births has a CBR of (12 000 / 1 000 000) × 1000 = 12 ‰. Both rates are usually expressed per mille (‰). High CBR values often correlate with less economically developed regions.

例如，一个 100 万人口的国家有 12 000 名新生儿，则粗出生率为 (12 000 / 1 000 000) × 1000 = 12‰。两项比率通常以千分比（‰）表示。高粗出生率常与经济欠发达地区相关。

---

6. Natural Increase Rate | 自然增长率

Natural increase is the difference between live births and deaths, showing how fast a population grows without considering migration. It is a key component of demographic transition analysis.

自然增长是指活产数与死亡数之间的差额，反映在不考虑迁移情况下人口的增长速度。它是分析人口转型的关键组成部分。

Natural Increase Rate (NIR) = CBR － CDR (per 1 000 per year)

If the CBR is 25‰ and the CDR is 9‰, the natural increase rate is 16‰, or 1.6% per year. A negative natural increase occurs when deaths outnumber births, which can indicate an ageing population.

若粗出生率为 25‰，粗死亡率为 9‰，则自然增长率为 16‰，即每年 1.6%。当死亡数超过出生数时，会出现负自然增长，这可能表明人口正在老龄化。

---

7. Net Migration Rate | 净迁移率

Net migration accounts for the movement of people into (immigration) and out of (emigration) a region. Adding it to natural increase gives total population change. Rates are standardised per 1 000 inhabitants to compare different areas.

净迁移衡量人口迁入（外来移民）和迁出（对外移民）的影响。将净迁移率与自然增长率相加，可得出总人口变化。该比率通常以每 1000 人为单位计算，以便跨区域比较。

Net Migration Rate = (Immigrants － Emigrants) ÷ Total Population × 1000

A city with 500 000 residents receives 10 000 immigrants and loses 4 000 emigrants in a year. Its net migration rate is (10 000 － 4 000) ÷ 500 000 × 1000 = 12‰. Positive net migration frequently drives urban growth.

某城市有 50 万居民，一年内接收 1 万名外来移民，迁出 4 千名居民。其净迁移率为 (10 000 － 4 000) ÷ 500 000 × 1000 = 12‰。正的净迁移率往往推动城市发展。

---

8. Percentage Change for Geographical Data | 地理数据的百分比变化

Percentage change normalises data to reveal relative growth or decline over time, crucial for understanding trends in indicators such as GDP, population or climate variables. It allows meaningful comparison between data sets of different magnitudes.

百分比变化将数据标准化，以揭示一段时间内的相对增长或下降，这对于理解 GDP、人口或气候变量等指标的趋势至关重要。它能让不同量级的数据集进行有意义的比较。

Percentage Change = ((New Value － Original Value) ÷ Original Value) × 100

If a town had 40 000 people in 2010 and 46 000 in 2020, the percentage change is ((46 000 － 40 000) ÷ 40 000) × 100 = 15% increase over ten years. Always identify the original and new values correctly to avoid sign errors.

某城镇 2010 年人口为 4 万，2020 年增至 4.6 万，则百分比变化为 ((46 000 － 40 000) ÷ 40 000) × 100 = 十年内增长 15%。务必正确识别原值和新值，以免正负号出错。

---

9. River Discharge | 河流流量

Discharge is the volume of water flowing through a river channel at a given point per unit of time. It is fundamental for flood risk assessment and understanding river regime. The measurement relies on channel cross-sectional area and flow velocity.

流量是指单位时间内通过河流某一横断面的水体体积。它是洪水风险评估和理解河流情势的基础。流量的测量依赖于河道横截面积与流速。

Discharge (Q) = Cross-Sectional Area (A) × Velocity (V)
Q = A × V (m³/s)

If the wetted cross-section of a stream is 12 m² and the average water velocity is 0.8 m/s, the discharge is 12 × 0.8 = 9.6 m³/s. Velocity can be measured with a flowmeter or by timing a float over a known distance, then adjusted with a correction factor (usually 0.8–0.9 for surface floats).

若某溪流的湿横截面积为 12 m²，平均流速为 0.8 m/s，则流量为 12 × 0.8 = 9.6 m³/s。流速可用流速仪或通过漂浮物计时法测定，然后用校正系数（水面漂浮法通常为 0.8–0.9）进行修正。

---

10. Urbanisation Rate | 城市化率

The urbanisation rate expresses the proportion of a country’s population that lives in urban areas. This indicator is widely used to analyse levels of development and to study migration patterns linked to industrialisation and service sector growth.

城市化率表示一国居住在城市地区的人口比例。这一指标广泛用于分析发展水平，以及研究工业化与服务业增长相关的迁移模式。

Urbanisation Rate = (Urban Population ÷ Total Population) × 100

A country with 80 million urban dwellers out of a total population of 120 million has an urbanisation rate of (80 ÷ 120) × 100 = 66.7%. Rapid increases in this rate can indicate rural-to-urban migration and natural increase in cities.

某国总人口 1.2 亿，其中城市人口 8000 万，则城市化率为 (80 ÷ 120) × 100 = 66.7%。城市化率的快速上升可能表明乡村向城市迁移以及城市内部自然增长较强。

---

11. The Bradshaw Model (River Characteristics) | 布拉德肖模型（河流特征）

The Bradshaw model is a theoretical framework that describes how a river’s characteristics change from source to mouth. While not a formula, it is an essential ‘theorem’ for understanding downstream variation and is frequently examined in WJEC geography.

布拉德肖模型是一个理论框架，描述河流特征从源头至河口的变化规律。虽然它不是一个公式，但却是理解下游变化的核心“定理”，在 WJEC 地理考试中频繁出现。

Characteristic / 特征	Change Downstream / 下游变化
Discharge (流量)	Increases / 增大
Channel depth (河道深度)	Increases / 增大
Channel width (河道宽度)	Increases / 增大
Average velocity (平均流速)	Increases / 增大
Load quantity (输沙量)	Increases / 增大
Load particle size (泥沙粒径)	Decreases (more rounded and sorted) / 减小（磨圆度更好、分选性更高）
Gradient (坡度)	Decreases / 减小
Bed roughness (河床粗糙度)	Decreases / 减小

Students should use the Bradshaw model as a basis for fieldwork hypotheses, expecting to find, for example, that velocity and discharge increase downstream while bed material becomes finer. However, local geology and human interference can cause anomalies, so the model is a generalisation.

学生应以布拉德肖模型作为实地考察假设的基础，例如预期流速与流量向下游增大而河床物质变细。然而，局部地质条件和人为干预可能导致异常，因此该模型是一种概化规律。

Published by TutorHao | Geography Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）