📚 Year 8 Cambridge Geography: Key Formulas & Theorems Quick Reference Handbook | Year 8 剑桥地理：公式定理速查手册
This quick reference handbook brings together the essential formulas, theorems and key concepts covered in Year 8 Cambridge Geography. It is designed to support your revision, improve your map-work accuracy, and help you interpret population data, climate statistics and physical processes with confidence.
本速查手册汇集了 Year 8 剑桥地理课程中的所有核心公式、定理和重要概念。它旨在辅助你的复习，提高地图作业的准确性，并帮助你自信地解读人口数据、气候统计和自然地理过程。
1. Map Scales: Converting Distances | 地图比例尺：距离换算
Map scales express the relationship between a distance measured on the map and the corresponding real-world distance. Scales can appear as a statement (e.g. 1 cm to 1 km), a representative fraction (1:100 000) or a linear bar scale.
地图比例尺表示图上测量的距离与对应的实际地面距离之间的关系。比例尺可以表现为文字式（如 1 厘米代表 1 千米）、数字式（1:100 000）或线段式比例尺。
To convert a map measurement into the actual distance on the ground, you multiply the map distance by the scale denominator.
要将图上测量值转换为地面实际距离，你需要用图上的距离乘以比例尺分母。
Real distance = Map distance × Scale denominator
实际距离 = 图上距离 × 比例尺分母
th is 6 cm, the ground distance is 6 × 25 000 = 150 000 cm, which equals 1500 m or 1.5 km.
例如，如果地图的比例尺是 1:25 000，测量的图上长度为 6 厘米，那么地面距离为 6 × 25 000 = 150 000 厘米，即 1500 米或 1.5 千米。
1000 m are usually stated in kilometres. Remember that 100 cm = 1 m and 100 000 cm = 1 km.
始终将答案换算为最合适的单位。大于 1000 米的距离通常用千米表示。请记住 100 厘米 = 1 米，100 000 厘米 = 1 千米。
2. Gradient (Slope) Calculation | 坡度计算
Gradient describes the steepness of a slope and is often used when studying rivers, coastlines or the suitability of land for farming and building. It can be expressed as a ratio (1:10), a percentage or a fraction.
坡度描述斜坡的陡峭程度，常用于研究河流、海岸或土地是否适合农耕与建筑。坡度可以用比率（1:10）、百分比或分数来表示。
The basic formula relates the vertical rise to the horizontal distance travelled. All measurements must be in the same unit.
基本公式将垂直升高与水平距离联系起来。所有测量值必须使用相同的单位。
Gradient = Vertical rise ÷ Horizontal run
坡度 = 垂直升高 ÷ 水平距离
To express gradient as a percentage, multiply the fraction by 100.
若要以百分比表示坡度，则将上述分数乘以 100。
Gradient (%) = (Vertical rise ÷ Horizontal run) × 100
坡度 (%) = (垂直升高 ÷ 水平距离) × 100
otpath rises 30 m over a horizontal length of 150 m. The gradient is 30 ÷ 150 = 0.2, or 20%. This is the same as a 1:5 ratio.
假设一条小径在 150 米的水平距离内升高了 30 米，坡度就是 30 ÷ 150 = 0.2，即 20%，同样可以表示为 1:5 的比率。
3. Population Density | 人口密度
Population density measures how closely together people live within a defined area. It is a fundamental concept in human geography used to compare cities, regions and countries.
人口密度衡量人们在一个特定区域内居住的紧密程度。这是人文地理学中用来比较城市、区域和国家的一个基本概念。
The calculation requires total population and the total land area expressed in square kilometres.
计算需要总人口和以平方千米为单位的总土地面积。
Population density = Total population ÷ Total land area (km²)
人口密度 = 总人口 ÷ 土地总面积 (km²)
00 000 inhabitants spread over 800 km², the density is 2 000 000 ÷ 800 = 2500 persons/km².
结果用每平方千米人数表示。例如，某地区有 200 万居民，分布在 800 km² 的土地上，人口密度为 2 000 000 ÷ 800 = 2500 人/km²。
High density often indicates urban areas, whereas low density suggests rural or desert landscapes. Population distribution describes where people live, not just the average figure.
高密度通常表明城市区域，而低密度则表明农村或沙漠景观。人口分布描述的是人们居住的位置，而不仅仅是平均数值。
4. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率与自然增长率
Crude birth rate (CBR) and crude death rate (CDR) are used to understand population change without considering migration. They are normally expressed per 1000 people per year.
粗出生率 (CBR) 和粗死亡率 (CDR) 用于在不考虑迁移的情况下理解人口变化。它们通常表示为每年每千人的数值。
CBR = (Number of live births in one year ÷ Total population) × 1000
CBR = (一年内活产婴儿数 ÷ 总人口) × 1000
CDR = (Number of deaths in one year ÷ Total population) × 1000
CDR = (一年内死亡人数 ÷ 总人口) × 1000
Natural increase is the difference between birth rate and death rate. A positive figure means the population is growing; a negative figure indicates natural decrease.
自然增长率是出生率与死亡率之间的差值。正值意味着人口正在增长，负值则表示人口自然减少。
Natural increase rate = Birth rate - Death rate
自然增长率 = 出生率 - 死亡率
For example, if a country records a CBR of 25 per 1000 and a CDR of 8 per 1000, its natural increase rate is 17 per 1000, which equals 1.7% when expressed as a percentage.
例如，某国的 CBR 为 25‰，CDR 为 8‰，那么自然增长率为 17‰，换算为百分比即 1.7%。
5. Population Growth Rate Including Migration | 含迁移的人口增长率
The overall population growth rate adds the net migration balance to natural increase. Net migration is immigration (people arriving) minus emigration (people leaving).
整体人口增长率在自然增长的基础上加入了净迁移量。净迁移量等于迁入人口（移入）减去迁出人口（移出）。
Net migration = Immigration - Emigration
净迁移量 = 迁入人数 - 迁出人数
Population growth rate (%) = [(Births - Deaths) + (Immigration - Emigration)] ÷ Total population × 100
人口增长率 (%) = [(出生人数 - 死亡人数) + (迁入人数 - 迁出人数)] ÷ 总人口 × 100
This formula provides a more complete picture of how a settlement or country's population is changing over one year.
这个公式更全面地展示了一个聚落或国家的人口在一年中是如何变化的。
6. Mean Temperature and Temperature Range | 平均气温与气温范围
Climate data often requires calculating averages and identifying extremes. The mean annual temperature is found by adding all twelve mean monthly temperatures and dividing by 12.
气候数据通常需要计算平均值并找出极值。年平均气温是通过将十二个月的月平均气温相加后除以 12 得到的。
Mean annual temperature = Sum of 12 mean monthly temperatures ÷ 12
年平均气温 = 12 个月的月平均气温之和 ÷ 12
Temperature range gives the difference between the highest and the lowest temperature within a given period, usually a month or a year. It describes the climate's variability.
气温范围表示某一给定时间段（通常是一个月或一年）内最高气温与最低气温之间的差值，用以描述气候的变动幅度。
Temperature range = Highest temperature - Lowest temperature
气温范围 = 最高气温 - 最低气温
If a desert region registers a July high of 44 °C and a January low of 2 °C, its annual temperature range is 42 °C.
如果一个沙漠地区七月最高温为 44 °C，一月最低温为 2 °C，那么它的年温差为 42 °C。
7. Precipitation Calculations and Climate Graphs | 降水计算与气候图
Total annual precipitation is obtained by summing the rainfall recorded in each of the twelve months. Climate graphs combine monthly precipitation totals with monthly temperature averages to reveal seasonal patterns.
年降水量是通过将十二个月记录的降水量相加得到的。气候图将月降水总量与月平均气温结合在一起，以揭示季节性规律。
Total annual precipitation = Sum of 12 monthly rainfall totals
