📚 Year 8 CIE Geography: Formula and Theorem Quick Reference Handbook | Year 8 CIE 地理：公式定理速查手册
This handbook compiles essential formulas, definitions, and key concepts for Year 8 CIE Geography. It is designed for quick revision of map skills, population calculations, physical processes, and settlement patterns. Keep this guide handy to master the core quantitative and theoretical tools you will need for your assessments.
本手册汇编了Year 8 CIE地理课程中的核心公式、定义和关键概念，便于快速复习地图技能、人口计算、自然过程与聚落模式。随身携带这份指南，可以帮你熟练掌握评估中所需的量化工具和理论工具。
1. Map Scale and Conversions | 地图比例尺与换算
Map scale expresses the relationship between a distance measured on a map and the true distance on the Earth's surface. Understanding scale allows you to convert map measurements into real-world kilometres or metres, and vice versa.
地图比例尺表示图上测量的距离与地球表面实际距离之间的关系。理解比例尺能够让你将地图测量值转换为真实世界的公里或米，反之亦然。
There are three common ways to show scale on a map: a statement scale (e.g. "1 cm represents 1 km"), a linear scale (a divided line), and a representative fraction or ratio scale (e.g. 1:100,000). You must be able to read and convert between them.
地图上常见三种表示比例尺的方法：文字比例尺（例如“1厘米代表1千米”）、线段比例尺（一条分段的直线）和数字比例尺或分数比例尺（如1:100,000）。你必须能够读懂它们并在不同表示法之间进行换算。
| Type of scale / 比例尺类型 | Example / 示例 |
|---|---|
| Statement / 文字 | 1 cm to 500 m / 1厘米代表500米 |
| Linear / 线段 | A line divided into km segments / 一条分成千米段的线段 |
| Ratio (RF) / 比率 | 1:50,000 |
The basic formula for scale is:
比例尺的基本公式是：
Scale = Map distance ÷ Actual ground distance
For a ratio scale of 1:25,000, 1 cm on the map equals 25,000 cm on the ground (i.e. 0.25 km). To find the real distance in kilometres, divide the map distance in centimetres by 100,000 if the scale factor is already given as a small unit.
对于1:25,000的比例尺，地图上的1厘米等于实地25,000厘米（即0.25千米）。若已知比例尺系数且单位较小，要得到以千米为单位的实际距离，可将图上厘米距离除以100,000。
2. Grid References | 网格坐标
Grid references allow you to pinpoint a location on an Ordnance Survey or topographic map. A four-figure grid reference gives a grid square (e.g. 4523), while a six-figure grid reference identifies a specific point within that square (e.g. 453238).
网格坐标能让你在地形图上精确标定位置。四位数坐标给出一个网格方格（如4523），而六位数坐标则标识该方格内的一个具体点（如453238）。
The golden rule is: "Always go along the Eastings first, then up the Northings." This can be remembered as "along the corridor and up the stairs." Eastings increase eastwards, Northings increase northwards.
黄金法则是：“始终先读东向坐标，再读北向坐标。”可以记为“先沿走廊走，再上楼”。东向坐标向东递增，北向坐标向北递增。
To work out a six-figure reference, divide the space between the numbered grid lines into ten imaginary parts. Estimate how many tenths the point is from the left grid line (Eastings) and from the bottom grid line (Northings). Insert these extra digits into the four‑figure reference.
要确定六位数坐标，将编号网格线之间的空间想象成十等分。估计该点距离左侧网格线（东坐标）和底部网格线（北坐标）各为十分之几，然后将这些额外数字插入四位数坐标中。
3. Measuring Height and Gradient | 高程与坡度测量
Height on a map is shown by spot heights, triangulation pillars, and contour lines. Contours join points of equal height; the vertical interval (contour interval) is the constant height difference between consecutive contours.
地图上的高度通过高程点、三角测量点和等高线来表示。等高线连接高度相等的点；垂直间隔（等高距）是相邻等高线之间恒定的高差。
Gradient describes the steepness of a slope. It is the ratio between the vertical interval (rise) and the horizontal distance (run). The formula for gradient is:
坡度描述斜坡的陡峭程度。它是垂直高差（上升）与水平距离（水平延伸）之比。坡度公式为：
Gradient = Vertical interval ÷ Horizontal distance
often written as 1:10. Always express gradient as a simplified ratio such as 1:5 or 1:20.
如果一条道路在水平距离500米内升高50米，则坡度为50/500 = 1/10，常写作1:10。始终将坡度化简为如1:5或1:20这样的简化比率。
4. Population Density | 人口密度
Population density measures how crowded an area is. It is the average number of people living per square kilometre (or per km²). Densely populated areas contain many people per km², while sparsely populated areas have few people per km².
人口密度衡量一个地区的拥挤程度。它是每平方千米（或每km²）居住的平均人数。人口稠密区每平方千米居住人数多，而人口稀疏区每平方千米居住人数少。
The fundamental formula for population density is:
人口密度的基本公式为：
Population Density = Total population ÷ Area (km²)
For example, if a country has a population of 10 million people and an area of 500,000 km², the density is 20 people per km². Always give units, and use the same unit for area.
例如，某国人口为1000万人，面积为500,000 km²，则密度为20人/km²。始终标明单位，并保持面积单位一致。
5. Birth Rate, Death Rate, and Natural Increase | 出生率、死亡率和自然增长率
Population change is driven by births, deaths, and migration. The crude birth rate (CBR) and crude death rate (CDR) are measured per 1000 people per year. They are calculated as:
人口变化由出生、死亡和迁移驱动。粗出生率（CBR）和粗死亡率（CDR）以每年每千人为单位计量。计算公式为：
Birth Rate = (Total live births ÷ Total population) × 1000
Death Rate = (Total deaths ÷ Total population) × 1000
The natural increase rate (without migration) is found by subtracting the death rate from the birth rate. It can also be expressed as a percentage by dividing by 10.
自然增长率（不含迁移）由出生率减去死亡率得出。也可除以10后以百分比表示。
Natural Increase = Birth Rate − Death Rate
If a town has a birth rate of 14 per 1000 and a death rate of 8 per 1000, the natural increase is 6 per 1000, which equals 0.6%. When the death rate exceeds the birth rate, natural change is negative.
如果某城镇出生率为14‰，死亡率为8‰，则自然增长为6‰，即0.6%。当死亡率高于出生率时，自然变化为负值。
6. Population Pyramids and Dependency Ratio | 人口金字塔与抚养比
A population pyramid is a bar chart showing the age and sex structure of a population. It helps identify the number of young dependents (0‑14), working-age population (15‑64), and elderly dependents (65+).
人口金字塔是显示人口年龄与性别结构的条形图。它有助于识别少儿抚养人口（0‑14岁）、劳动年龄人口（15‑64岁）和老龄抚养人口（65岁及以上）。
The dependency ratio measures the pressure on the working population to support dependents. A high ratio means more dependents for every 100 people of working age. The formula is:
抚养比衡量劳动人口承受的赡养压力。比率高意味着每100名劳动年龄人口需要抚养更多人。计算公式为：
Dependency Ratio = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100
= [(30m + 12m) ÷ 80m] × 100 = 52.5. This means about 53 dependents for every 100 workers.
例如，某国有3000万少儿抚养人口，1200万老年抚养人口，8000万劳动年龄人口，则抚养比 = [(3000万+1200万) ÷ 8000万] × 100 = 52.5。这意味着每100名劳动者需抚养约53人。
7. Settlement Hierarchy and Threshold | 聚落等级与门槛人口
Settlements can be ordered in a hierarchy based on their size, population, and the number and type of services they provide. The settlement hierarchy usually moves from isolated dwelling or hamlet up to village, town, city, and conurbation.
聚落可根据规模、人口以及所提供服务的数量和类型按等级排序。聚落等级通常从孤立的住所或小村庄，向上到村庄、镇、城市和大都市连绵区。
The threshold population is the minimum number of people needed to support a particular service or shop. High-order services (e.g. a department store, a large hospital) require a large threshold population and are found only in higher-order settlements, while low-order services (e.g. a corner shop) have a small threshold and appear in many smaller centres.
门槛人口是维持某一特定服务或商店所需的最低人口数。高阶服务（如百货商店、大型医院）需要较高的门槛人口，只出现在高阶聚落中；而低阶服务（如街角小店）门槛人口低，广泛分布于许多较小中心。
The sphere of influence is the area from which a settlement draws its customers. Larger settlements have a wider sphere of influence.
影响范围是指聚落吸引顾客的区域范围。规模越大的聚落其影响范围越广。
8. Types of Rainfall | 降水类型
Three main types of rainfall are linked to uplift processes. Relief (orographic) rainfall occurs when moist air is forced to rise over highland; it cools, condenses, and produces rain on the windward slopes, leaving a rain shadow on the leeward side.
三种主要降水类型与空气抬升过程有关。地形雨发生当潮湿空气被迫抬升越过山地时；空气冷却、凝结，在迎风坡产生降水，背风坡则形成雨影区。
Convectional rainfall is common in hot regions. The sun heats the ground, warming the air above; this warm air rises rapidly, cumulonimbus clouds form, and heavy showers with thunder may follow.
对流雨常见于炎热地区。太阳加热地面，进而加热上方空气；暖空气迅速上升，形成积雨云，可能产生雷阵雨。
Frontal (cyclonic) rainfall happens where warm and cold air masses meet. The lighter warm air is forced to rise over the denser cold air along a front, leading to widespread and prolonged rainfall.
锋面（气旋）雨在冷暖气团相遇时发生。较轻的暖空气沿锋面被迫爬升到较重的冷空气上方，带来大范围、持续性的降水。
9. River Processes and Erosion | 河流作用与侵蚀
Rivers shape the landscape through erosion, transportation, and deposition. The four main types of river erosion are hydraulic action (the force of water breaking off material), abrasion (rock fragments scraping the bed and banks), attrition (stones knocking together and becoming smaller), and solution (minerals dissolving in the water).
河流通过侵蚀、搬运和沉积作用塑造地貌。四种主要的河流侵蚀类型分别是：水力作用（水流力量冲走物质）、磨蚀（岩石碎块刮蚀河床和河岸）、磨损（石块相互碰撞变小）以及溶蚀（矿物质溶解于水中）。
Transportation processes include traction (large boulders rolled along), saltation (smaller pebbles bounced), suspension (fine silt carried in the flow), and solution (dissolved materials moved invisibly). Deposition happens when a river loses energy and drops its load.
搬运过程包括推搬运（大卵石沿河底滚动）、跃搬运（小砾石弹跳）、悬搬运（细泥砂在水中悬浮输送）和溶运（溶解物质无形移动）。当河流失去能量并卸下其携带物时，便发生沉积。
10. Long Profile and Cross Profile | 河道纵剖面与横剖面
The long profile shows the gradient change from a river's source to its mouth. Typically, the upper course has a steep, irregular profile with vertical erosion dominating. The middle course becomes less steep with more lateral erosion, and the lower course is very gentle with deposition building floodplains.
纵剖面展示河流从源头至河口的坡度变化。通常上游坡度陡峭且不规则，以垂直侵蚀为主；中游坡度趋缓，侧蚀增强；下游坡度十分平缓，以沉积作用为主，形成泛滥平原。
The cross profile is a section across the valley. In the upper course it is V‑shaped with narrow channel; in the middle course valley sides are more open, and in the lower course the valley is wide and flat, often with levees and a meandering channel.
横剖面是横切河谷的截面。上游谷地呈V形，河道狭窄；中游谷坡更加开阔；下游谷地宽阔平坦，常伴有天然堤和蜿蜒的河道。
11. Plate Tectonics and Boundaries | 板块构造与边界类型
Earth's lithosphere is broken into tectonic plates that move on the semi‑molten asthenosphere. Convection currents in the mantle drive this movement. Plate boundaries are areas where plates meet, and they are classified as constructive, destructive, conservative, or collision.
地球岩石圈分裂为若干构造板块，它们在半熔融的软流圈上移动。地幔中的对流驱动了板块运动。板块边界是板块相遇的区域，可划分为建设型、破坏型、转换型或碰撞型边界。
At constructive (divergent) boundaries, plates move apart; magma rises to form new crust, producing mid‑ocean ridges and shield volcanoes. At destructive (convergent) boundaries, an oceanic plate subducts beneath a continental plate, creating deep ocean trenches, fold mountains, and explosive volcanoes. At collision boundaries, two continental plates crumple upward to form high fold mountains such as the Himalayas. At conservative boundaries, plates slide past each other, causing earthquakes along faults like the San Andreas Fault.
在建设型（离散）边界，板块相互分离；岩浆上涌形成新地壳，产生大洋中脊和盾形火山。在破坏型（汇聚）边界，大洋板块俯冲到大陆板块之下，形成深海沟、褶皱山脉和爆发性火山。在碰撞型边界，两个大陆板块挤压隆升，形成如喜马拉雅山这样的高大褶皱山脉。在转换型边界，板块相互水平滑动，沿断层引发地震，如圣安德烈亚斯断层。
12. Weather and Climate Graphs | 天气与气候图表
A climate graph (climograph) combines a line graph of average monthly temperature (°C) with a bar chart of average monthly precipitation (mm). Such graphs help identify seasonal patterns and climate types.
气候图表（气候图）将月均气温（°C）的折线图与月均降水量（mm）的柱状图组合在一起。此类图表有助于识别季节变化规律和气候类型。
To calculate the mean monthly temperature from daily data, you can use:
要从逐日数据计算月平均气温，可用公式：
Mean daily temperature = (Max temperature + Min temperature) ÷ 2
Annual temperature range is the difference between the hottest and coldest month temperatures. Total annual precipitation is the sum of all monthly precipitation figures. Always read the values from the graph carefully, note the units, and interpret the wet and dry seasons.
年温差是最热月与最冷月气温之差。年总降水量为各月降水量之和。读图时务必仔细读取数值、注意单位，并解释干湿季节。
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