📚 Year 8 WJEC Geography: Formula & Key Concepts Quick Reference Handbook | Year 8 WJEC 地理：公式定理速查手册
Geography is not just about memorising places; it is a subject full of useful formulas and key ideas that help you understand the world. This quick reference handbook brings together the most important calculations, definitions and concepts you will need for Year 8 WJEC Geography. Keep it handy for homework, revision and fieldwork.
地理不仅仅是记住地名，它是一门充满实用公式和关键理念的学科，能帮助你理解世界。这本速查手册汇集了 Year 8 WJEC 地理课程中最重要的计算、定义和概念。随身携带，用于作业、复习和实地考察。
1. Map Scale: Converting Distances | 地图比例尺：距离换算
Map scale tells you how much the real world has been reduced. It is usually given as a ratio, such as 1:25 000. This means 1 cm on the map represents 25 000 cm in reality. To find the actual distance on the ground, measure the map distance in centimetres and multiply by the scale factor, then convert to metres or kilometres. Always remember: 100 cm = 1 m, 1000 m = 1 km.
地图比例尺表示真实世界被缩小的程度。它通常以比例如 1:25 000 表示，意味着地图上的 1 厘米代表实际地面 25 000 厘米。要计算实际地面距离，先量出地图上的厘米数，乘以比例尺因子，再换算成米或千米。请牢记：100 厘米 = 1 米，1000 米 = 1 千米。
Actual distance (cm) = Map distance (cm) × Scale denominator
实际距离（厘米）= 图上距离（厘米）× 比例尺分母
For example, a 5 cm length on a 1:50 000 map represents 5 × 50 000 = 250 000 cm = 2500 m = 2.5 km on the ground. When using a linear scale, simply align your paper strip with the scale bar and read the distance directly.
例如，1:50 000 地图上的 5 厘米长度代表实地 5 × 50 000 = 250 000 厘米 = 2500 米 = 2.5 公里。使用直线比例尺时，只需将纸条与比例尺对齐即可直接读取距离。
2. Grid References: 4-figure and 6-figure | 网格坐标：四位与六位坐标
A 4-figure grid reference locates a whole grid square. Always read along the bottom of the map first (eastings), then up the side (northings). The phrase ‘Along the corridor and up the stairs’ helps you remember. The reference is given without commas, e.g. 4523. For a 6-figure grid reference, imagine the square divided into tenths; estimate how many tenths the point lies across and up. A 6-figure reference gives a much more precise location, e.g. 453237.
四位网格坐标定位整个网格方格。总是先沿着地图底部读（东经值），再沿旁边向上读（北经值）。记住“沿着走廊再上楼”的口诀。坐标不带逗号给出，如 4523。六位网格坐标则需要将方格想象成十等分；估计该点横跨和向上各占十分之几。六位坐标可给出更精确的位置，例如 453237。
- 4-figure: 45 23 → square between eastings 45 and 46, northings 23 and 24.
- 四位坐标：45 23 → 方格位于东经坐标 45 与 46、北经坐标 23 与 24 之间。
- 6-figure: 453 237 → point 5 tenths across inside easting 45, and 7 tenths up inside northing 23.
- 六位坐标：453 237 → 点位在东经坐标 45 内往右 5/10、北经坐标 23 内往上 7/10 处。
3. Gradient of a Slope | 坡度的计算
Gradient measures the steepness of a slope. It is calculated by dividing the vertical rise (change in height) by the horizontal distance (run). The result is often expressed as a ratio, e.g. 1:10, or as a fraction. The vertical interval is found using contour lines on a map; count the number of contour lines crossed and multiply by the contour interval (e.g. 10 m). The horizontal distance is measured along the ground.
坡度衡量斜坡的陡峭程度。计算方法是用垂直高差（上升的高度）除以水平距离（平距）。结果通常表示为比例，如 1:10，或分数。垂直高差通过地图上的等高线求出；数出跨越的等高线条数并乘以等高距（例如 10 米）。水平距离则沿地面量测。
Gradient = Vertical rise (m) ÷ Horizontal distance (m)
坡度 = 垂直高差（米）÷ 水平距离（米）
If a path climbs 40 m over a horizontal distance of 200 m, the gradient is 40 ÷ 200 = 0.2, or 1:5. Remember to use the same units for both rise and run.
如果一条小路在水平距离 200 米内上升 40 米，坡度 = 40 ÷ 200 = 0.2，即 1:5。切记上升和水平距离单位需相同。
4. Population Density | 人口密度
Population density shows how crowded an area is. It is the number of people living per square kilometre (or per km²). This measure helps compare urban and rural areas, or different countries. You need two figures: total population and total land area.
人口密度反映一个地区的拥挤程度，即每平方公里居住的人口数（人/km²）。这一指标有助于比较城市和乡村地区，或不同国家。需要两个数据：总人口和土地总面积。
Population density = Total population ÷ Total land area (km²)
人口密度 = 总人口 ÷ 土地总面积（km²）
For example, a city with 800 000 people and an area of 400 km² has a density of 800 000 ÷ 400 = 2000 people/km². Be careful with units: if the area is given in hectares, remember 1 km² = 100 hectares.
例如，一个城市有 80 万人，面积为 400 km²，则人口密度 = 800 000 ÷ 400 = 2000 人/km²。注意单位：若面积以公顷给出，请记住 1 km² = 100 公顷。
5. Birth Rate, Death Rate and Natural Change | 出生率、死亡率与自然变化
Birth rate is the number of live births per 1000 people per year. Death rate is the number of deaths per 1000 people per year. These rates allow fair comparisons between countries of different population sizes. Natural change is the difference between birth rate and death rate; a positive value means natural increase, a negative value means natural decrease.
出生率是每年每千人中的活产婴儿数。死亡率是每年每千人中的死亡人数。这些比率能在不同人口规模的国家间公平比较。自然变化是出生率与死亡率之差；正数为自然增长，负数为自然减少。
Birth rate = (Total live births ÷ Total population) × 1000
出生率 = （活产婴儿总数 ÷ 总人口）× 1000
Death rate = (Total deaths ÷ Total population) × 1000
死亡率 = （死亡总数 ÷ 总人口）× 1000
Natural change = Birth rate − Death rate
自然变化 = 出生率 − 死亡率
A country with 12 births per 1000 and 8 deaths per 1000 has a natural increase of 4 per 1000, or 0.4% per year. When net migration is added to natural change, you get the total population growth rate.
一个出生率为千分之十二、死亡率为千分之八的国家，其自然增长率为千分之四，即每年 0.4%。将净迁移加入自然增长，即可得到总人口增长率。
6. Population Pyramids and Dependency Ratios | 人口金字塔与抚养比率
A population pyramid shows the age and sex structure of a population. It is divided into males (left) and females (right), with age groups on the vertical axis. The shape tells you about birth rates, death rates and life expectancy. The dependency ratio compares the economically dependent population (young 0–14 and old 65+) to the working-age population (15–64). It is usually expressed as a percentage.
人口金字塔显示人口的年龄和性别结构。左侧为男性，右侧为女性，纵轴为年龄组。形状反映出生率、死亡率和预期寿命。抚养比率是将经济依赖人口（0–14 岁少儿和 65 岁以上老年）与劳动适龄人口（15–64 岁）进行比较，通常以百分比表示。
Dependency ratio = [(Population 0–14 + Population 65+) ÷ Population 15–64] × 100
抚养比率 = [（0–14 岁人口 + 65 岁以上人口）÷ 15–64 岁人口] × 100
A dependency ratio of 60 means there are 60 dependants for every 100 people of working age. High ratios often put pressure on schools and healthcare services.
抚养比率为 60 意味着每 100 名劳动适龄人口需抚养 60 个依赖人口。高比率常给学校和医疗服务带来压力。
7. River Discharge | 河流流量
River discharge is the volume of water passing a point in the river per unit time, usually measured in cubic metres per second (cumecs, m³/s). It is calculated by multiplying the cross-sectional area of the river channel by the average flow velocity. Fieldwork often involves measuring width, depth and velocity at several points across a stream.
河流流量是单位时间内通过河流某一点的水量，通常以每秒立方米（cumecs, m³/s）表示。其计算方法为河道横截面积乘以平均流速。实地考察通常需要测量河道不同位置的宽度、深度和流速。
Discharge (Q) = Cross-sectional area (A) × Mean velocity (V)
流量（Q）= 横截面积（A）× 平均流速（V）
To find the cross-sectional area, multiply the average width by the average depth (for an approximate rectangle). Velocity can be measured with a flowmeter or by timing a float over a known distance. Always repeat measurements and calculate a mean for accuracy.
求横截面积时，可将平均宽度乘以平均深度（近似矩形）。流速可用流速仪或通过计时浮标漂过已知距离来测量。务必重复测量并计算平均值以确保准确。
| Step | Action |
| 1 | Measure channel width (m) at three places, find average. |
| 步骤 1 | 在三个位置测量河道宽度（米），求平均值。 |
| 2 | Measure depth (m) at regular intervals across the section, average them. |
| 步骤 2 | 沿断面按等距测深（米），取平均值。 |
| 3 | Area = average width × average depth. |
| 步骤 3 | 面积 = 平均宽度 × 平均深度。 |
| 4 | Measure surface velocity (m/s) with a float, multiply by 0.85 to estimate mean velocity. |
| 步骤 4 | 用浮标测表流速度（m/s），乘以 0.85 估算平均流速。 |
| 5 | Discharge = Area × Mean velocity. |
| 步骤 5 | 流量 = 面积 × 平均流速。 |
8. Climate Averages: Mean, Range and Total | 气候平均值：均值、较差与总降水量
When analysing climate data, you need to calculate the mean monthly temperature, the temperature range and the total annual rainfall. The mean is the sum of all values divided by the number of values. The range is the difference between the maximum and minimum. These statistics help you construct climate graphs and compare different climate zones.
分析气候数据时，需要计算月平均温度、温度年较差和年总降水量。均值是所有数值之和除以数值的个数。较差是最大值与最小值之差。这些统计量有助于绘制气候图表并比较不同气候带。
Mean temperature = Sum of all monthly temperatures ÷ 12
平均气温 = 各月气温总和 ÷ 12
Temperature range = Hottest month temperature − Coldest month temperature
温度年较差 = 最热月气温 − 最冷月气温
Total annual rainfall = Sum of all monthly rainfall totals
年总降水量 = 各月降水量之和
Always label units: temperature in °C, rainfall in millimetres (mm). A high annual temperature range often indicates a continental climate far from the sea.
务必标注单位：温度以 °C 计，降水量以毫米（mm）计。年较差大通常表明该地属远离海洋的大陆性气候。
9. Fieldwork: Proportional Symbols and Flow Lines | 实地考察：比例符号与流量线
When presenting fieldwork data, proportional symbols are used to show quantities. The area of each symbol (circle, square) is drawn in proportion to the data value. To calculate the radius of a proportional circle, use the square root of the value, so that the area, not just the radius, represents the data. Flow lines show movement; their width is proportional to the quantity moving.
在呈现实地考察数据时，比例符号用来表示数量。每个符号（圆形、方形）的面积与数据值成比例绘制。要计算比例圆的半径，需使用数据值的平方根，使面积而非仅仅半径代表数据。流量线表示移动；其宽度与移动量成比例。
Radius of proportional circle = √(Data value ÷ π)
比例圆半径 = √（数据值 ÷ π）
In practice, choose a scale so that your largest symbol fits on the map, and scale other values accordingly. For example, a traffic survey might use line thickness to represent the number of vehicles per hour. Add a clear key to your map.
实际操作中，选定一个比例尺使最大符号适合地图，然后依此缩放其他数值。例如，交通调查可用线条粗细表示每小时车流量。务必给地图添加清晰的图例。
10. Carbon Footprint: Simplified Calculation | 碳足迹：简化计算
A carbon footprint estimates the total greenhouse gases (mainly CO₂) produced by an individual, event or organisation. In Year 8, you learn to calculate it using everyday activities such as energy use, travel and food choices. Although full calculations are complex, you can use multiplication factors. For instance, each kilometre travelled by car might generate about 0.2 kg of CO₂.
碳足迹估算的是个人、活动或组织产生的温室气体总量（主要是 CO₂）。在 Year 8，你学习使用日常活动如能源使用、出行和食物选择来计算。虽然完整计算较复杂，但可用乘法因子。例如，汽车每行驶一公里约产生 0.2 千克 CO₂。
CO₂ from car travel = Distance travelled (km) × Emission factor (kg CO₂ per km)
汽车出行 CO₂ 排放 = 行驶距离（公里）× 排放因子（千克 CO₂/公里）
Similar factors exist for electricity (per kWh), diet (e.g. beef vs vegetables) and flights. Adding these gives a rough personal footprint. Understanding these formulas helps you think about sustainability and ways to reduce your impact.
类似因子也适用于电力（每度电）、饮食（如牛肉与蔬菜对比）和航空等。将它们累加即得大致的个人碳足迹。理解这些公式有助于思考可持续性以及如何减少自身影响。
11. Water Cycle: Key Stores and Fluxes | 水循环：关键储库与通量
The water cycle is a closed system: water moves between the atmosphere, land and oceans through processes like evaporation, transpiration, condensation, precipitation and run-off. The basic equation for the water balance in a drainage basin is: Precipitation = Evapotranspiration + Run-off + Change in storage. Although simplified, it helps you understand how water moves through the landscape.
水循环是一个封闭系统：水通过蒸发、蒸腾、凝结、降水和径流等过程在大气、陆地和海洋之间移动。流域水平衡的基本公式为：降水量 = 蒸散量 + 径流量 + 蓄水量变化。虽是简化模型，但有助于理解水如何在景观中移动。
P = E + R ± ΔS (where P=precipitation, E=evapotranspiration, R=run-off, ΔS=change in storage)
P = E + R ± ΔS（P=降水量，E=蒸散量，R=径流量，ΔS=蓄水量变化）
Fieldwork often involves measuring infiltration rates, interception by leaves, or stream velocity to observe parts of this cycle. Remember, stores include soil moisture, groundwater, lakes and glaciers, while fluxes are the movements between stores.
实地考察常涉及测量入渗率、树叶截留量或溪流流速，以观察水循环的各个环节。记住，储库包括土壤水分、地下水、湖泊和冰川，通量则是储库之间的移动。
12. Choropleth Maps and Data Classification | 分级统计地图与数据分类
Choropleth maps use different shades or colours to represent data values across areas. To create one, you must classify your data into groups. Common methods include equal intervals, where each class covers the same numerical range, and quantiles, where each class contains an equal number of areas. The formula for equal interval width is: (Maximum value − Minimum value) ÷ Number of classes.
分级统计地图使用不同深浅或颜色表示各区域的数值。要制作此类地图，需将数据分组。常见方法有等间距法（每级数值范围相同）和分位数法（每级包含相同数量的区域）。等间距分组宽度的公式为：（最大值 − 最小值）÷ 组数。
Class interval width = (Maximum value − Minimum value) ÷ Number of classes
组距宽度 = （最大值 − 最小值）÷ 组数
For example, with data ranging from 12% to 68% and 4 classes, the interval is (68−12) ÷ 4 = 14. So classes become 12–25, 26–39, 40–53, 54–68. Always shade from light (low values) to dark (high values) and include a legend.
例如，数据范围从 12% 到 68%，分 4 组，则组距为 (68−12) ÷ 4 = 14，因此分组为 12–25，26–39，40–53，54–68。着色总是由浅（低值）到深（高值），并包含图例。
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