📚 Year 8 CAIE Geography: Formula & Theorem Quick Reference Guide | Year 8 CAIE 地理：公式定理速查手册
This is your go-to pocket guide for all the key formulas, calculations and geographical theorems you need to master in Year 8 CAIE Geography. Whether you are analysing population data, interpreting topographic maps or working with climate statistics, the quick reference below will help you answer questions with confidence and accuracy.
这是您在 Year 8 CAIE 地理课程中必须掌握的全部核心公式、计算方法与地理定理的速查手册。无论您是在分析人口数据、解读地形图，还是处理气候统计资料，以下快速参考都将帮助您自信、准确地作答。
1. Population Density | 人口密度
Population density measures how crowded an area is. It is calculated by dividing the total population by the total land area. A high population density suggests that many people live in each square kilometre, while a low density indicates sparse settlement.
人口密度衡量一个地区的拥挤程度。其计算方法为总人口除以土地总面积。高人口密度意味着每平方公里居住着许多人，而低密度则表明定居点稀疏。
Population Density = Total Population ÷ Total Land Area
Units: persons per km². Always make sure your area is in square kilometres. For example, if a country has 10 million people and an area of 2 million km², its population density is 5 persons per km².
单位：人/平方公里(人/km²)。务必确保面积以平方公里为单位。例如，如果一个国家有1000万人口，面积为200万平方公里，则其人口密度为5人/平方公里。
2. Birth Rate and Death Rate | 出生率与死亡率
The crude birth rate (CBR) is the number of live births per 1000 people in a population per year. The crude death rate (CDR) is the number of deaths per 1000 people per year. Both are essential for understanding population change.
粗出生率(CBR)指一年内每1000人中的活产婴儿数量。粗死亡率(CDR)指一年内每1000人中的死亡人数。两者是理解人口变化的关键指标。
Birth Rate (CBR) = (Number of Live Births ÷ Total Population) × 1000
Death Rate (CDR) = (Number of Deaths ÷ Total Population) × 1000
0 records 4,000 births in a year, the birth rate is (4000 ÷ 200,000) × 1000 = 20 per 1000.
这两个比率均以每年每1000人为单位表示。例如，若一座20万人口的城市一年内记录到4000名新生儿，则其出生率为(4000 ÷ 200000)×1000 = 20‰(千分之二十)。
3. Natural Increase and Population Growth Rate | 自然增长率与人口增长率
Natural increase is the difference between the birth rate and the death rate. It shows how fast a population is growing without considering migration. The overall population growth rate also includes net migration.
自然增长率指出生率与死亡率之间的差值，它显示在排除迁移影响下人口的自然增速。总人口增长率则还需计入净迁移量。
Natural Increase = Birth Rate − Death Rate
Population Growth Rate (%) = [(Births − Deaths + Net Migration) ÷ Total Population] × 100
A positive natural increase means the population is rising; a negative value signals decline. Net migration is the number of immigrants minus emigrants. The growth rate is often expressed as a percentage.
自然增长率为正表示人口在增加，为负则表示人口衰减。净迁移量由迁入人数减去迁出人数得出。人口增长率通常以百分数表示。
4. Dependency Ratio | 依赖比例
The dependency ratio compares the economically dependent part of the population (young and elderly) with the working-age population. It highlights the pressure on the productive group to support dependents.
依赖比例将经济上需要抚养的人口（儿童和老年人）与劳动适龄人口进行比较，反映出劳动群体在供养受养人口方面所承受的压力。
Dependency Ratio = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100
For example, if a country has 30 million people aged 0–14 and 65+, and 50 million aged 15– 30 ÷ 50) × 100 = 60. This means for every 100 working-age people, there are 60 dependents.
例如，若某国0–14岁以及65岁以上人口共3000万，15–64岁劳动人口为5000万，则依赖比例为(30÷50)×100 = 60。即每100名劳动适龄人口需抚养60名受养人口。
5. Infant Mortality Rate (IMR) | 婴儿死亡率
Infant mortality rate measures the number of deaths of infants under one year of age per 1000 live births in a given year. It is a powerful indicator of healthcare quality and living standards.
婴儿死亡率指一年内每1000名活产婴儿中未满周岁便死亡的婴儿数量，它是衡量医疗保健质量与生活水准的重要指标。
Infant Mortality Rate = (Number of Deaths of Infants < 1 Year ÷ Total Live Births) × 1000
A low IMR usually means better access to clean water, nutrition and medical care. Many developed countries have IMRs below 5 per 1000, while less developed regions may exceed 50 per 1000.
婴儿死亡率较低通常意味着更易获得清洁用水、营养供给与医疗服务。许多发达国家的婴儿死亡率低于5‰，而欠发达地区可能高于50‰。
6. Map Scale Conversion | 地图比例尺转换
Understanding scale is crucial for measuring real-world distances on a map. Scale can be given as a statement, a representative fraction, or a linear bar. You must be able to convert between map distance and ground distance.
理解比例尺对于在地图上量测实际距离至关重要。比例尺可用文字说明、分数式或直线比例尺表示。你需要能够在图上距离与地面距离之间进行转换。
Actual Ground Distance = Map Distance × Scale Denominator
200,000 cm. Converting to kilometres (÷100,000) gives 2 km. Always pay attention to units.
若地图比例尺为1:50000，图上两点相距4厘米，则实际距离为4厘米×50000 = 200000厘米。换算为千米(除以100000)后为2千米。务必注意单位换算。
| Scale Type | Example |
| Statement | 1 cm represents 1 km |
| Representative Fraction | 1:100,000 |
| Linear/Bar Scale | A drawn line divided into kilometres |
比例尺主要有文字比例尺、分数比例尺和直线比例尺三种。直线比例尺即使地图缩放仍可使用。
7. Gradient (Slope) Calculation on Maps | 地图上的坡度计算
Gradient expresses the steepness of a slope. On a topographic map, it is found by dividing the vertical interval (change in height) by the horizontal equivalent (distance on the ground). The answer is often given as a ratio or percentage.
坡度用来表示坡面的陡峭程度。在地形图上，通过垂直高差除以水平距离求得，结果常用比值或百分数表示。
Gradient = Vertical Interval (VI) ÷ Horizontal Equivalent (HE)
e of 5000 metres, the gradient is 100 ÷ 5000 = 0.02. This can be written as 1:50 or as a 2% slope. Gradient helps hikers, engineers and town planners assess terrain.
若地面在5000米的水平距离上上升了100米，则坡度为100÷5000 = 0.02，即可表示为1:50的比值或2%的坡度。坡度有助于徒步者、工程师和城镇规划者评估地形。
8. Temperature Range and Mean Calculation | 温度范围与平均温度计算
Temperature range shows the difference between the highest and lowest temperatures recorded over a day, month or year. The mean (average) temperature sums all readings and divides by the number of readings.
温度范围指一段时间内所记录的最高温与最低温之间的差值，可计算日温差、月温差或年温差。平均温度则是所有温度读数的总和除以读数次数。
Temperature Range = Tₘₐₓ − Tₘᵢₙ
Mean Daily Temperature = Sum of Hourly Temperatures ÷ 24
For climate studies, we also calculate mean annual temperature range by subtracting the coldest month's average from the warmest month's average. A large annual range often indicates a continental interior location.
在气候研究中，我们还会用最热月平均温度减去最冷月平均温度来计算年温差。年温差较大通常表明该地位于大陆内部。
9. Measuring Distance and Area on Topographic Maps | 在地形图上测量距离与面积
Measuring straight-line distances on a topographic map is done with a ruler and the scale. For curved paths, use a piece of string or the edge of a paper, then measure against the scale. Area can be estimated by counting grid squares.
在地形图上测量直线距离时，使用直尺和比例尺即可。测量弯曲路径时，可用细线或纸边沿路径描绘，再与比例尺对照。测量面积则可通过数方格法估算。
Area on the ground = Map Area × (Scale Denominator)²
5,000 cm)² = 62,500 m². Count full squares and estimate partial ones for irregular shapes.
在1:25000地图上，若一个方格为1厘米×1厘米，其实地面积为(1厘米×25000)² = (25000厘米)² = 62500平方米。对于不规则形状，可数出完整方格并估算部分方格。
10. Rate of Urbanisation | 城市化率
The rate of urbanisation measures how quickly the proportion of people living in towns and cities is increasing. It is distinct from urban population growth; it captures the shift from rural to urban areas.
城市化率衡量的是城镇人口占总人口比例的增长速度。它不同于城市人口增长，而是体现人口从乡村向城镇转移的幅度。
Urbanisation Rate = (Urban Population ÷ Total Population) × 100
To find the annual increase in the level of urbanisation, subtract the urban percentage in one year from the percentage in a later year. High rates are typical in newly industrialising countries where rural-to-urban migration is strong.
要计算城市化水平的年增长率，可用后一年的城市人口百分比减去前一年的百分比。在新兴工业化国家，城乡迁移势头强劲，城市化率往往较高。
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