📚 SQA Geography Formula & Theorem Quick Reference Handbook | SQA 地理公式定理速查手册
This handbook compiles all the essential quantitative formulas and key relationships you need to master for the Year 11 SQA Geography course. Use it as a quick revision tool to ensure accuracy in describe, explain and calculate exam questions.
本手册汇总了Year 11 SQA地理课程中所有必须掌握的定量公式与核心关系，方便你快速复习，确保在描述、解释和计算类考题中准确无误。
1. Population Change Formula | 人口变化公式
The total population change in an area involves natural change (births minus deaths) and net migration (immigrants minus emigrants). The basic equation is:
一个地区的总人口变化由自然变动（出生减死亡）和净迁移（迁入减迁出）两部分组成。基本公式如下：
ΔP = B − D + (I − E)
number of births, D = number of deaths, I = number of immigrants, E = number of emigrants.
其中，ΔP = 人口变化，B = 出生人数，D = 死亡人数，I = 迁入人数，E = 迁出人数。
This formula underpins many demographic calculations and helps explain population growth or decline in specific places.
这一公式是诸多人口统计计算的基础，可以解释某个区域人口的增长或下降。
2. Crude Birth Rate and Death Rate | 粗出生率与粗死亡率
The crude birth rate (CBR) and crude death rate (CDR) are expressed per 1,000 people to allow comparisons between areas of different population sizes.
粗出生率（CBR）和粗死亡率（CDR）以每千人为单位，便于在不同人口规模的地区之间进行比较。
CBR = (B ÷ P) × 1000
CDR = (D ÷ P) × 1000
B = total live births in a year, D = total deaths in a year, P = mid-year population.
B = 年内活产婴儿总数，D = 年内死亡总数，P = 年中人口总数。
Note that these are 'crude' because they do not consider the age structure of the population.
请注意，之所以称为“粗”率，是因为没有考虑人口的年龄结构。
3. Natural Increase Rate | 自然增长率
Natural increase is the difference between the birth rate and the death rate, usually expressed per 1,000 population. It can be positive (natural increase) or negative (natural decrease).
自然增长是出生率与死亡率的差值，通常以每千人为单位表示。该值可以是正数（自然增长）或负数（自然减少）。
NIR = CBR − CDR
The rate can also be converted to a percentage: Natural Increase (%) = NIR ÷ 10.
自然增长率也可以转换为百分数：自然增长(%) = NIR ÷ 10。
When combined with net migration, the NIR contributes to the overall population growth rate.
当与净迁移结合时，自然增长率是人口总体增长率的一部分。
4. Net Migration Rate | 净迁移率
The net migration rate measures the difference between in-migrants and out-migrants for every 1,000 people in a population.
净迁移率衡量每千人中迁入者与迁出者的差额。
NMR = [(I − E) ÷ P] × 1000
I = number of in-migrants, E = number of out-migrants, P = mid-year population.
I = 迁入人数，E = 迁出人数，P = 年中人口总数。
A positive net migration rate indicates more people moving in than out, boosting population growth.
净迁移率为正，表明迁入人数多于迁出人数，推动人口增长。
5. Population Density | 人口密度
Population density describes how crowded an area is. It is calculated as the number of people per unit area (usually per square kilometre).
人口密度描述一个地区的拥挤程度，通常以每平方千米人口数表示。
Population Density = Total Population ÷ Land Area (km²)
Be mindful of the units: ensure area is in km². Comparing densities helps identify high-density urban areas and sparsely populated rural regions.
注意单位：面积须为平方千米。比较人口密度有助于识别高密度城区和人口稀少的农村地区。
6. Dependency Ratio | 抚养比 / 依赖比率
The dependency ratio indicates the proportion of economically dependent people (aged 0–14 and 65+) relative to the working-age population (aged 15–64). It is usually expressed as a percentage.
抚养比表示非劳动年龄人口（0-14岁和65岁以上）相对于劳动年龄人口（15-64岁）的比例，通常以百分数表示。
Dependency Ratio = [(Population 0−14 + Population 65+) ÷ Population 15−64] × 100
A higher ratio means a greater burden on the working population, which has implications for healthcare, pensions and education.
该比值越高，意味着劳动人口承受的扶养负担越重，对医疗、养老和教育产生影响。
7. River Discharge and Hydraulic Geometry | 河流流量与水力几何
River discharge (Q) is the volume of water flowing through a cross-section of a river per unit time, measured in cubic metres per second (m³ s⁻¹).
河流流量（Q）是单位时间内通过河流某一横截面的水量，单位为立方米每秒（m³ s⁻¹）。
Q = A × v
Where A = cross-sectional area (width × mean depth) in m², v = mean velocity in m s⁻¹.
其中 A = 横截面积（宽度 × 平均水深），单位为 m²；v = 平均流速，单位为 m s⁻¹。
To measure discharge in fieldwork, calculate area from channel measurements and average velocity using a flowmeter or float method.
在野外实习中，通过测量河道宽度和平均水深求得截面积，再用流速仪或浮标法测速，便可计算流量。
8. Drainage Density | 排水密度
Drainage density is a measure of the total length of streams per unit area of a drainage basin, typically expressed in kilometres per square kilometre (km km⁻²).
排水密度衡量流域内单位面积上河流的总长度，通常以千米每平方千米（km km⁻²）表示。
Drainage Density = Total stream length (km) ÷ Drainage basin area (km²)
High drainage density indicates a well-drained basin with numerous streams, often found in areas of impermeable rock or high rainfall. Low drainage density suggests permeable surfaces and fewer surface streams.
排水密度高表示流域排水良好、河道众多，常见于不透水岩层或多雨地区。密度低则表明地表渗透性强，地表径流较少。
9. Gradient and Slope Calculations | 坡度与梯度计算
Gradient measures the steepness of a slope or river channel. It is the ratio of the vertical interval (rise) to the horizontal distance (run).
坡度用于衡量山坡或河道的陡峭程度，是垂直高差（上升）与水平距离的比值。
Gradient = Vertical Interval (VI) ÷ Horizontal Equivalent (HE)
The result is often expressed as a ratio, e.g., 1:50, meaning a 1 m rise over 50 m horizontal distance. Use the same units for VI and HE before dividing.
结果常表示为比值，如 1:50 表示水平每前进 50 米，高度上升 1 米。计算前务必使 VI 和 HE 单位一致。
A steeper gradient is indicated by a smaller second number in the ratio (e.g., 1:10 is steeper than 1:100).
比值中的第二个数字越小，坡度越陡（例如 1:10 比 1:100 更陡）。
10. Climate Statistics: Mean, Range and Total | 气候统计：平均值、温差与总量
You need to be comfortable calculating simple climate statistics from weather data, including mean temperature, temperature range and total precipitation.
你需要能够根据天气数据计算简单的气候统计量，包括平均温度、温度较差及总降水量。
Mean Temperature = Sum of temperatures ÷ Number of readings
Diurnal Range = Maximum temp − Minimum temp in one day
Annual Temperature Range = Hottest month mean − Coldest month mean
Total Annual Precipitation = Sum of all monthly precipitation values
These statistics help describe a climate graph and compare the climates of different regions, an essential skill for the Physical Environments unit.
这些统计量有助于描述气候图表并比较不同地区的气候，是自然地理单元的关键技能。
11. Map Scale, Distance and Area Calculation | 地图比例尺、距离与面积计算
Ordnance Survey (OS) map skills are a core part of SQA Geography. You must be able to interpret scale to calculate real-world distances and areas.
地形图（OS 地图）技能是 SQA 地理的核心内容。你必须能够运用比例尺计算实地距离与面积。
Ground Distance = Map Distance × Scale Factor
For example, on a 1:50,000 map, 1 cm on the map represents 50,000 cm (500 m) on the ground. Area measurements: for a square or rectangle, calculate ground length and width, then multiply.
例如，在 1:50 000 地图上，图上 1 厘米代表实地 50 000 厘米（500 米）。面积测量：若为矩形或正方形，先求出实地长度和宽度，再相乘。
To estimate the area of an irregular shape, count whole squares and part squares on a grid overlay and convert using the scale.
估算不规则形状面积时，可数方格网中的整格与部分格，再根据
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