📚 SQA Year 9 Geography: Quick Reference Handbook for Formulas and Theorems | SQA 九年级地理：公式定理速查手册
Geography is not just about memorising places – it requires handling data, measurements and simple calculations to interpret patterns and processes. This handbook brings together all the essential formulas and theorems you need for the SQA Year 9 course, from map skills and population to weather and rivers. Use it to revise quickly and boost your confidence in both the fieldwork and written exam.
地理不仅仅是记住地名——它还需要处理数据、测量和简单计算，以解读格局和过程。本手册汇集了 SQA 九年级课程所需的所有基础公式和定理，涵盖地图技能、人口、天气和河流等内容。用它快速复习，增强你在野外考察和笔试中的信心。
1. Map Scale: Three Types of Expression | 地图比例尺：三种表达方式
Every map uses a scale to show the relationship between a distance on the map and the corresponding distance on the ground. Understanding scale is the foundation of all map work.
每张地图都使用比例尺来表示图上距离与相应地面距离之间的关系。理解比例尺是所有地图工作的基础。
A scale can be written as a statement, a ratio or a linear bar. The statement ‘1 cm represents 0.5 km’ is straightforward, while the ratio 1:50 000 means that 1 unit on the map equals 50 000 of the same units on the ground. A linear scale is a drawn ruler that allows direct reading without calculation.
比例尺可以用文字说明、数字比例或线段比例表示。文字说明“1 厘米代表 0.5 公里”很直接，而比例 1:50 000 表示图上 1 个单位相当于地面 50 000 个相同单位。线段比例尺是一条绘制的尺子，无需计算即可直接读取。
Key formula for converting ratio to statement: To change cm to km, divide by 100 000. So 1:50 000 means 1 cm = 50 000 cm = 0.5 km.
将比例转换为文字说明的关键公式： 将厘米转换为公里，除以 100 000。因此 1:50 000 表示 1 厘米 = 50 000 厘米 = 0.5 公里。
Always check the unit you need. In an exam, you may be asked to calculate real distance: Real distance (km) = Map distance (cm) × scale denominator ÷ 100 000.
始终检查你需要的单位。考试中可能会要求计算实地距离：实地距离（公里）= 图上距离（厘米）× 比例分母 ÷ 100 000。
2. Latitude, Longitude and Distance | 经纬度与距离
Latitude and longitude form a global grid system, allowing every location to be identified precisely. They measure angles from the Earth’s centre, not linear distance – but you can approximate distance using simple rules.
纬度和经度构成全球网格系统，使每一点都能被精确定位。它们测量的是地心夹角，而非直线距离，但你可以用简单规则估算距离。
One degree of latitude equals about 111 km everywhere on Earth. Thus, the distance between two points on the same meridian is: Distance (km) = difference in latitude (°) × 111.
地球上任何地方纬度 1° 约等于 111 公里。因此，同一经线上两点的距离为：距离（公里）= 纬度差（°）× 111。
For longitude, 1° equals 111 km only at the Equator. As you move towards the poles, the distance covered by 1° of longitude decreases. At 60° N or S, it is roughly 55.5 km. The formula is: Distance (km) = difference in longitude (°) × 111 × cos(latitude).
对于经度，只有在赤道上 1° 等于 111 公里。随着向两极移动，每度经度所覆盖的距离逐渐减小。在北纬或南纬 60°，大约是 55.5 公里。公式为：距离（公里）= 经度差（°）× 111 × cos(纬度)。
Use the cosine rule only when you need precision; for simpler tasks, use 111 km per degree of latitude and estimate longitude distances with a globe or atlas.
仅在需要精确时使用余弦规则；对于简单的任务，使用每纬度 111 公里，并借助地球仪或地图集估算经度距离。
3. Contour Lines and Gradient | 等高线与坡度
Contour lines connect points of equal height above sea level. The spacing of contours tells you how steep the land is. Calculating gradient turns visual interpretation into a mathematical value.
等高线连接海平面以上高度相同的点。等高线的间距说明地形的陡缓。计算坡度将视觉解读转化为数学数值。
Gradient formula: Gradient = Vertical difference (rise) ÷ Horizontal distance (run). Both must be in the same units. A gradient of 1:10 means that for every 10 metres horizontally you move, you go up 1 metre.
坡度公式： 坡度 = 垂直高差（升高）÷ 水平距离（水平长度）。两者必须使用相同单位。坡度 1:10 表示水平移动 10 米，垂直上升 1 米。
To find rise, subtract the lower contour height from the higher one. For run, measure the distance between those two contours on the map using the scale. Always express the final ratio with ‘1’ on the left side, e.g. 1:8 rather than 5:40.
要得出升高值，用较高的等高线高度减去较低的高度。水平长度则是在地图上使用比例尺测量这两条等高线之间的距离。最终比值始终将左边写成“1”，例如 1:8 而非 5:40。
Closely spaced contours indicate a steep slope (large gradient), while widely spaced contours show a gentle slope. If contours form a V shape pointing uphill, it indicates a valley; pointing downhill, a spur.
等高线密集表示陡坡（坡度大），等高线稀疏表示缓坡。如果等高线形成指向高处的 V 形，表示山谷；指向低处则表示山嘴。
4. Population Density | 人口密度
Population density describes how crowded an area is. It is one of the most common calculations in human geography, linking population to the land they occupy.
人口密度描述一个地区的拥挤程度。这是人文地理中最常见的计算之一，将人口与其占据的土地联系起来。
Formula: Population density = Total population ÷ Land area (km²). The result is expressed as people per km². For example, 500 000 people living in 250 km² results in a density of 2000 people/km².
公式： 人口密度 = 总人口 ÷ 土地面积（平方公里）。结果以每平方公里人数表示。例如，500 000 人居住在 250 平方公里土地上，密度为 2000人/平方公里。
Always check the units of area. If area is given in m², convert to km² by dividing by 1 000 000. High-density areas like city centres can exceed 10 000 people/km²; rural areas often fall below 10.
始终检查面积单位。如果面积以平方米给出，除以 1 000 000 转化为平方公里。市中心等高密度区域可超过 10 000人/平方公里；农村地区通常低于 10。
Population density does not tell you about the distribution pattern – a map or dot distribution diagram is needed for that.
人口密度不能说明分布格局，这需要地图或点分布图来展示。
5. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率和自然增长率
Demographic calculations help us compare population change between countries. The rates are usually expressed per 1000 people per year, which standardises comparisons regardless of total population size.
人口统计计算有助于比较国家之间的人口变化。比率通常以每年每千人表示，这样无论人口总数大小，都能标准化比较。
Crude Birth Rate (CBR) = (Number of live births in a year ÷ Total population) × 1000. Crude Death Rate (CDR) = (Number of deaths in a year ÷ Total population) × 1000.
粗出生率 (CBR) = (一年内活产数 ÷ 总人口) × 1000。粗死亡率 (CDR) = (一年内死亡数 ÷ 总人口) × 1000。
Natural increase rate (NIR) = CBR − CDR, expressed per 1000. To convert to a percentage, divide by 10. For instance, if CBR = 20 and CDR = 8, NIR = 12 per 1000, or 1.2%.
自然增长率 (NIR) = CBR − CDR，以每千人表示。转化为百分比，除以 10。例如，若 CBR = 20，CDR = 8，则 NIR = 12‰，即 1.2%。
When NIR is positive, the population grows naturally. If it is negative, the population shrinks unless offset by net migration. These figures do not include migration effects, so total population change = natural increase + net migration.
当 NIR 为正时，人口自然增长。如果为负，人口将减少，除非净移民抵消。这些数字不包括迁移影响，因此总人口变化 = 自然增长 + 净迁移。
6. Urbanisation Rate | 城市化率
Urbanisation is the increase in the proportion of people living in towns and cities. The rate of urbanisation is an indicator of economic and social change.
城市化是指居住在城镇和城市的人口比例的增加。城市化率是经济和社会变化的一个指标。
Percentage urban = (Urban population ÷ Total population) × 100. The rate of urbanisation = change in percentage urban over a given time period, often expressed as percentage points per year.
城镇人口百分比 = (城镇人口 ÷ 总人口) × 100。城市化率 = 在一定时期内城镇人口百分比的变化，通常以每年百分点表示。
For example, if the urban percentage rose from 30% to 45% over 15 years, the average annual urbanisation rate = (45 − 30) ÷ 15 = 1 percentage point per year.
例如，如果城镇人口百分比在 15 年内从 30% 上升到 45%，平均年城市化率 = (45 − 30) ÷ 15 = 每年 1 个百分点。
Be careful not to confuse urbanisation rate with urban growth rate (which measures increase in urban population, not the share).
注意不要将城市化率与城市人口增长率（衡量城镇人口数量的增长，而非比例）混淆。
7. Temperature and Rainfall Statistics | 温度与降雨量统计
Climate data is often presented as averages. You need to calculate mean, range and total. These simple statistics allow you to construct climate graphs and compare climates.
气候数据通常以平均值呈现。你需要计算平均数、差值和总量。这些简单统计让你能够绘制气候图并比较气候。
Mean daily temperature = (Max temp + Min temp) ÷ 2. Diurnal range = Max temp − Min temp. Mean monthly temperature = sum of mean daily temperatures in the month ÷ number of days.
日平均气温 = (最高气温 + 最低气温) ÷ 2。日较差 = 最高气温 − 最低气温。月平均气温 = 该月每日平均气温之和 ÷ 天数。
Annual temperature range = temperature of warmest month − temperature of coldest month. Total annual rainfall = sum of all 12 monthly rainfall totals. Calculate both to classify climate types.
年温差 = 最暖月气温 − 最冷月气温。年总降水量 = 12 个月降水量之和。计算这两者以对气候类型进行分类。
When drawing climate graphs, plot temperature as a line and rainfall as bars. Use mean values for the line and totals for the bars.
绘制气候图时，用折线表示温度，用柱状图表示降雨量。折线使用平均值，柱状图使用总量。
8. River Velocity and Discharge | 河流流速与流量
River fieldwork often involves measuring how fast water is moving and how much water flows past a point. These measurements help explain erosion, transportation and flooding.
河流野外考察常涉及测量水流速度和水流通过某点的水量。这些测量有助于解释侵蚀、搬运和洪水。
Velocity (speed) = distance travelled (m) ÷ time taken (s). Use a float and stopwatch over a known distance. Take several readings and calculate the mean.
流速（速度） = 行经距离（米）÷ 所用时间（秒）。在已知距离内使用浮标和秒表测量。取多次读数并计算平均值。
Cross-sectional area (A) = average width (m) × average depth (m). Measure depth at regular intervals across the channel and average them.
横截面积 (A) = 平均宽度（米）× 平均深度（米）。在河道上等间隔测量水深并求平均值。
Discharge (Q) = A × velocity (m³/s). This is the volume of water passing a point per second. Discharge increases downstream as tributaries join the main river.
流量 (Q) = A × 流速（立方米/秒）。这是每秒通过某点的水量。随着支流汇入干流，流量向下游增加。
9. Time Zones and Longitude | 时区与经度
The Earth rotates 360° in 24 hours, so every 15° of longitude equals a one-hour time difference. This is the basis of the global time zone system.
地球 24 小时自转 360°，因此每 15° 经度对应 1 小时的时差。这是全球时区系统的基础。
Time difference (hours) = difference in longitude (°) ÷ 15. If you move eastwards, add time; if you move westwards, subtract time. Always start from a known reference, typically Greenwich Mean Time (GMT) at the Prime Meridian.
时差（小时） = 经度差（°）÷ 15。如果向东移动，时间增加；向西移动，时间减少。始终从已知参考点开始，通常是本初子午线上的格林尼治标准时间 (GMT)。
For example, if GMT is 12:00 noon, a place at 75°E will be 75 ÷ 15 = 5 hours ahead, so the local time is 17:00. Practical time zones may deviate from this simple geometry due to political boundaries.
例如，如果 GMT 是中午 12:00，位于东经 75° 的地方经度差为 75 ÷ 15 = 5 小时，因此当地时间为 17:00。实际的时区可能因政治边界而偏离这个简单的几何划分。
10. Grid References and Area Calculation | 网格参考与面积计算
Ordnance Survey maps use a grid system to locate features accurately. Six-figure grid references pinpoint a location within 100 metres on the ground. They do not involve formulas, but area calculations on grids require scale use.
英国地形测量局地图使用网格系统精确定位地物。六位网格参考可将地面位置定位在 100 米范围内。它们不涉及公式，但网格上的面积计算需要使用比例尺。
To calculate the area of a feature (e.g., a woodland) on a map: measure the length and width in cm using the grid, convert to real ground distance using the scale, then multiply. For irregular shapes, overlay a grid of squares and count the full and partial squares – each square represents a known area (e.g., 1 cm² = 0.25 km² at 1:50 000).
要计算地图上某个地物（例如一片林地）的面积：用网格量出厘米长度和宽度，利用比例尺转换为实地距离，然后相乘。对于不规则形状，叠加方格网格并计算完整和部分格子——每个格子代表已知面积（例如 1:50 000 图上 1 cm² = 0.25 km²）。
Use the formula area on ground (km²) = area on map (cm²) × (scale denominator ÷ 100 000)². Practice with squared paper overlays for precise fieldwork.
使用公式 地面面积（平方公里）= 图上面积（平方厘米）× (比例分母 ÷ 100 000)²。在精确野外作业中，使用方格纸覆盖练习。
11. Environmental Footprints and Sustainability Ratios | 环境足迹与可持续性比率
The ecological footprint measures how much productive land and water a population requires to produce the resources it consumes and to absorb its waste. It is usually expressed in global hectares (gha) per person.
生态足迹衡量人口生产其消费的资源以及吸收其废物所需的生产性土地和水域面积。通常以人均全球公顷 (gha) 表示。
Total footprint (gha) = per capita footprint × total population. A country is in biocapacity deficit if its total footprint exceeds its available biocapacity. The ratio footprint : biocapacity indicates sustainability – a ratio > 1 signals overshoot.
总足迹（全球公顷）= 人均足迹 × 总人口。如果一国的总足迹超过其可用生物承载力，则处于生物承载力赤字。足迹：生物承载力比率指示可持续性——比率 > 1 表示超载。
For local studies, you might calculate a carrying capacity ratio for a tourist site: Number of visitors per day ÷ maximum sustainable visitors. This helps manage pressure on the environment.
在本地研究中，你可能需要计算旅游景点的承载能力比率：每日游客数 ÷ 最大可持续游客数。这有助于管理环境压力。
12. Development Indicators: Rates and Ratios | 发展指标：比率与比值
Development is measured using multiple numeric indicators. Understanding how they are derived allows you to compare countries and regions effectively.
发展使用多种数字指标来衡量。了解它们的推导方式，可以有效地比较国家和地区。
Literacy rate = (number of literate adults ÷ total adult population) × 100. Infant mortality rate = (deaths of infants under 1 year ÷ live births in a year) × 1000. Life expectancy is an average, not a calculation you perform, but you may be given data to compute dependency ratios.
识字率 = (识字成人人数 ÷ 成人总人口) × 100。婴儿死亡率 = (1 岁以下婴儿死亡数 ÷ 一年内的活产数) × 1000。预期寿命是一个平均值，不是你计算出来的，但你可能会获得数据来计算抚养比。
Dependency ratio = [(population aged 0–14 + population aged 65+) ÷ working-age population (15–64)] × 100. A high ratio indicates a large non-working group relying on the workers.
抚养比 = [(0–14 岁人口 + 65 岁以上人口) ÷ 劳动年龄人口 (15–64 岁)] × 100。高比率表明有大量非劳动人口依赖劳动者。
These calculations appear in map analysis, population pyramids and development case studies. Always check whether the data you use is per 100, per 1000 or a percentage.
这些计算会出现在地图分析、人口金字塔和发展案例研究中。始终检查你所使用的数据是按百、按千还是百分比计算。
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