📚 Year 10 SQA Geography: Formula & Theorem Quick Reference Handbook | SQA十年级地理：公式定理速查手册
This handbook compiles essential formulas and theorems for Year 10 SQA Geography, providing a bilingual quick reference to support revision and exam preparation. It covers map skills, river measurements, population statistics, weather calculations, and key geographical models.
本手册汇编了十年级SQA地理必备公式与定理，提供双语速查参考以辅助复习与备考。内容涵盖地图技能、河流测量、人口统计、天气计算以及重要的地理模型。
1. Map Skills Fundamentals | 地图技能基础
The scale of a map expresses the relationship between a distance on the map and the corresponding distance on the ground. It can be stated as a ratio, fraction, or linear bar.
地图比例尺表示图上距离与对应实际地面距离之间的关系。它可以表示为比率、分数或直线比例尺。
Scale = Map distance ÷ Actual ground distance
比例尺 = 图上距离 ÷ 实际地面距离
When interpreting a 1:50 000 Ordnance Survey map, 1 cm on the map represents 50 000 cm (or 0.5 km) in reality.
阅读1:50 000地形测量地图时，图上1厘米代表实际50 000厘米（即0.5千米）。
To calculate real-world distance, measure the straight‑line map distance in centimetres and multiply by the scale factor, then convert to metres or kilometres.
计算实际距离时，先量出图上直线距离（厘米），乘以比例尺分母，再换算为米或千米。
2. Gradient and Slope Calculations | 梯度与坡度计算
Gradient is a measure of the steepness of a slope. It is the ratio of the vertical interval (rise) to the horizontal equivalent (run).
梯度是量度斜坡陡峭程度的指标，即垂直高差与水平距离的比值。
Gradient = Vertical interval ÷ Horizontal equivalent
梯度 = 垂直高差 ÷ 水平距离
Both measurements must be in the same units. The gradient is often simplified to a ratio such as 1:10 or expressed as a percentage by multiplying the fraction by 100.
两项测量必须使用相同单位。梯度通常简化为1:这样的比率，或将分数乘以100表示为百分比。
20 m rise over a 200 m horizontal distance gives 20/200 = 0.1 or 1:10, equivalent to a 10% slope.
例如：垂直上升20米，水平距离200米，梯度为20/200 = 0.1，即1:，相当于10%的坡度。
3. River Channel Measurements | 河流河道测量
Fieldwork on rivers requires accurate measurement of channel dimensions. The cross‑sectional area (A) is found by multiplying the channel width by the mean water depth.
河流实地考察需要精确测量河道尺寸。横截面积（A）由河道宽度乘以平均水深求得。
A = Width × Mean depth
横截面积 = 宽度 × 平均水深
Mean depth is calculated by taking several depth readings at regular intervals across the channel and finding their average.
平均水深是通过在河道中等间距取若干深度读数并计算平均值得到的。
Velocity (V) is measured by timing a float over a known distance. The formula is:
流速（V）通过测量浮标流经已知距离的时间来确定，公式为：
V = Distance ÷ Time
流速 = 距离 ÷ 时间
Units are typically metres per second (m/s). For accuracy, the float velocity is multiplied by a correction factor (0.85 for a rough bed).
单位通常为米/秒（m/s）。为求准确，需将浮标流速乘以修正系数（粗糙河床取0.85）。
4. Discharge and Hydraulic Radius | 流量与水力半径
Discharge (Q) is the volume of water passing a point in the river per unit time. It is the product of cross‑sectional area and average velocity.
流量（Q）是指单位时间内通过河流某一点的水量，等于横截面积与平均流速的乘积。
Q = A × V
流量 = 横截面积 × 流速
Discharge is measured in cubic metres per second (m³/s or cumecs).
流量的度量单位是立方米/秒（m³/s 或 cumecs）。
Hydraulic radius (R) indicates the efficiency of a channel shape. It is the ratio of cross‑sectional area to wetted perimeter.
水力半径（R）反映河道形状的效率，是横截面积与湿周长的比值。
R = A ÷ Wetted perimeter
水力半径 = 横截面积 ÷ 湿周长
A higher hydraulic radius means less friction and more efficient flow. It typically increases downstream as the channel becomes wider and deeper.
水力半径越高，摩擦力越小，水流效率越高。通常从上游到下游，河道变宽变深，水力半径也随之增大。
5. Population Density and Distribution | 人口密度与分布
Population density measures how crowded an area is. It is a fundamental formula for comparing different regions.
人口密度衡量某一区域的拥挤程度，是比较不同地区的基本公式。
Population density = Total population ÷ Area (km²)
人口密度 = 总人口 ÷ 面积（平方千米）
Use the table below for quick reference of typical density categories and their implications:
使用下表快速参考典型密度类别及其含义：
| Density (people/km²) | Description | 描述 |
|---|---|
| Below 10 | Sparsely populated (e.g. rural Canada) | 人口稀少（如加拿大农村） |
| 10 – 100 | Moderate population density | 中等人口密度 |
| 101 – 500 | High density (e.g. many European countries) | 高密度（如许多欧洲国家） |
| Above 500 | Very high density (e.g. Singapore, urban cores) | 极高密度（如新加坡、城市核心区） |
Remember that physical factors (relief, climate) and human factors (jobs, transport) heavily influence population distribution.
记住，自然因素（地形、气候）和人文因素（就业、交通）对人口分布影响很大。
6. Crude Birth Rate and Death Rate | 粗出生率与粗死亡率
These demographic indicators are expressed per 1000 people per year and allow countries of different sizes to be compared fairly.
这些人口指标以每年每千人为单位表示，便于公正比较不同规模的国家。
Crude Birth Rate (CBR) = (Number of live births ÷ Total population) × 1000
粗出生率（CBR）= （活产婴儿数 ÷ 总人口）× 1000
Crude Death Rate (CDR) = (Number of deaths ÷ Total population) × 1000
粗死亡率（CDR）= （死亡人数 ÷ 总人口）× 1000
High birth rates (above 30 per 1000) are typical in developing nations, while low rates (below 10) appear in developed countries.
高出生率（每千人以上）常见于发展中国家，而低出生率（每千人以下）则出现在发达国家。
Death rates can spike during famines, epidemics, or natural disasters, but generally decrease with improved healthcare.
死亡率在饥荒、疫病或自然灾害时会骤升，但随着医疗保健改善，通常呈下降趋势。
7. Natural Increase and Dependency Ratio | 自然增长率与抚养比
Natural increase (NI) is the difference between the crude birth rate and the crude death rate, indicating whether a population is growing without migration.
自然增长率（NI）是粗出生率与粗死亡率的差值，表示在不考虑迁移的情况下人口是否增长。
Natural increase = CBR - CDR
自然增长率 = 粗出生率 - 粗死亡率
The result is in per 1000. To convert it to a percentage, divide by 10. For example, a natural increase of 12 per 1000 equals 1.2%.
结果以每千人计。若要转换为百分比，除以10即可。例如，自然增长率为每千人12，相当于1.2%。
The dependency ratio measures the pressure on the productive population (aged 15–64) to support the young and elderly.
抚养比衡量劳动适龄人口（15–64岁）抚养少儿和老人的负担程度。
Dependency ratio = ((Population aged 0–14 + 65+) ÷ Population aged 15–64) × 100
抚养比 = （（0–14岁人口 + 65岁以上人口） ÷ 15–64岁人口）× 100
A high dependency ratio (e.g. above 55) suggests a greater economic burden on workers. Many ageing European countries face this challenge.
高抚养比（例如55以上）表明劳动者承担更重的经济负担。许多面临老龄化的欧洲国家正面临此挑战。
8. Weather and Climate Statistics | 天气与气候统计
Weather data analysis requires simple arithmetic to describe temperature and precipitation patterns.
天气数据分析需要简单的计算来描述温度和降水规律。
Daily mean temperature = (Max temp + Min temp) ÷ 2
日平均气温 = （最高气温 + 最低气温） ÷ 2
Diurnal temperature range = Max temp - Min temp
日温差 = 最高气温 - 最低气温
Monthly mean temperature is the average of all daily mean temperatures in that month. Annual mean temperature averages the 12 monthly values.
月平均气温是该月各日平均气温的平均值。年平均气温则是12个月平均气温的平均。
Total annual precipitation = Sum of 12 months' rainfall (or snowfall melted)
年降水总量 = 12个月降雨量（或融雪量）之和
For SQA exams, you may need to calculate seasonal rainfall totals or identify the wettest/driest month from a climate graph.
在SQA考试中，您可能需要计算季节性降雨总量，或根据气候图判断最湿/最干的月份。
9. The Bradshaw Model (River Dynamics) | 布拉德肖模型（河流动力学）
The Bradshaw model is a theoretical framework that predicts how river characteristics change from source to mouth. It is often represented by a series of arrows indicating increase or decrease downstream.
布拉德肖模型是一个预测河流特征从源头到河口如何变化的理论框架，通常用一系列箭头表示下游方向上的增减趋势。
According to the model, the following variables increase downstream: discharge, occupied channel width, mean depth, average velocity, and load quantity.
根据该模型，以下变量向下游递增：流量、河道宽度、平均水深、平均流速和搬运物质总量。
The variables that decrease downstream are: slope gradient, bedload particle size, and channel bed roughness. This is shown in the table below.
向下游递减的变量有：坡度、河床负载粒径和河道粗糙度。如下表所示。
| Characteristics | 特征 | Change downstream | 下游变化 |
|---|---|
| Discharge | Increases ↑ | 增大 ↑ |
| Width, depth, velocity | Increase ↑ | 增大 ↑ |
| Bedload particle size | Decreases ↓ (more attrition) | 减小 ↓（磨蚀增强） |
| Channel bed roughness | Decreases ↓ | 减小 ↓ |
| Gradient | Decreases ↓ | 减小 ↓ |
This model helps explain why V-shaped valleys in the upper course change to wide floodplains near the mouth.
此模型有助于解释上游的V形谷为何在河口附近变为宽广的泛滥平原。
10. Key Theorems in Coastal Processes | 海岸过程关键定理
Coastal environments are shaped by wave action. Two fundamental wave types are constructive and destructive waves, each with distinct characteristics.
海岸环境由波浪作用塑造。两种基本波型为建设性波浪和破坏性波浪，各自具有不同特征。
Constructive waves: low frequency (6–8/min), strong swash, weak backwash → build beaches
建设性波浪：低频（6–8次/分钟），冲流强，回流弱 → 堆积海滩
Destructive waves: high frequency (10–14/min), weak swash, strong backwash → erode beaches
破坏性波浪：高频（10–14次/分钟），冲流弱，回流强 → 侵蚀海滩
Longshore drift is the movement of sediment along a coast by waves approaching at an angle. The direction of prevailing wind determines the sediment transport pathway.
沿岸物质搬运是指波浪以一定角度接近海岸时沉积物沿海岸移动的过程。盛行风向决定了输沙路径。
The theorem of coastal erosion sequence: headlands are attacked by hydraulic action and abrasion, forming caves, arches, stacks, and stumps. This succession is a classic SQA case study.
海岸侵蚀序列定理：海岬受水力作用和磨蚀袭击，依次形成海蚀洞、海蚀拱、海蚀柱和海蚀残礁。这一演替序列是SQA经典案例。
In sand dune succession, psammosere stages can be described by a theorem of pioneer plants (marram grass) stabilising dunes, followed by scrub and climax woodland – an important model for managing coastal ecosystems.
在沙丘演替中，沙生演替系列定理描述了先锋植物（滨草）固定沙丘，继之出现灌木和顶级林地——这是管理海岸生态系统的重要模型。
Published by TutorHao | Geography Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图