📚 Year 7 AQA Geography: Quick Reference Handbook of Formulas and Theorems | Year 7 AQA 地理：公式定理速查手册
This handbook provides a quick reference to essential formulas, calculations and key geographical theorems covered in the Year 7 AQA Geography syllabus. Mastering these tools will help you analyse maps, interpret data and understand human and physical geography patterns.
本手册是 Year 7 AQA 地理课程中核心公式、计算及关键地理定理的速查指南。掌握这些工具将帮助您分析地图、解读数据并理解人文与自然地理格局。
1. Map Scales and Distance Calculation | 地图比例尺与距离计算
A map scale shows the relationship between a distance on the map and the corresponding distance on the ground. Understanding scale is the first step to measuring real-world distances from a map.
地图比例尺表示图上距离与实地对应距离之间的关系。理解比例尺是从地图上测量实地距离的第一步。
Actual Distance (km) = Map Distance (cm) × Scale Denominator ÷ 100,000
实地距离 (km) = 图上距离 (cm) × 比例尺分母 ÷ 100,000
For a 1:50,000 scale map, 1 cm on the map represents 50,000 cm on the ground. Divide by 100,000 to convert centimetres to kilometres, so 1 cm = 0.5 km.
在 1:50,000 比例尺的地图上，图上 1 cm 代表实地 50,000 cm。除以 100,000 将厘米转换为公里，因此 1 cm = 0.5 km。
Three types of scale are commonly used: statement scale (e.g. ‘1 cm to 1 km’), representative fraction (e.g. 1:100,000) and linear scale (a bar divided into kilometres).
常用的比例尺有三种类型：语句式比例尺（如“1厘米代表1公里”）、分数式比例尺（如 1:100,000）和线段式比例尺（被划分为公里数的横条）。
2. Grid References and Coordinates | 网格参考与坐标
Ordnance Survey maps use grid lines to create a system of four‑figure and six‑figure grid references. These allow you to pinpoint exact locations.
英国地形测量局地图使用网格线建立四位数和六位数网格参考系统，可以精确定位地点。
A four‑figure grid reference locates a 1 km × 1 km square. The rule is ‘along the corridor and up the stairs’: read the easting first (horizontal), then the northing (vertical).
四位数网格参考定位一个 1 km × 1 km 的方格。规则是“先横后纵”：先读东向坐标（横轴），再读北向坐标（纵轴）。
A six‑figure grid reference divides the square into tenths to give a more precise location, e.g. 234 098. Estimate how many tenths across and up the point lies within the square.
六位数网格参考将方格各分为十等份，以给出更精确的位置，例如 234 098。确定点在该方格内横向和纵向所处的十分之几即可。
3. Bearings and Direction | 方位角与方向
Direction can be described using the 16 points of the compass or by a three‑figure bearing measured clockwise from north.
方向可以用 16 个罗盘方位点来描述，也可以用从北顺时针测量的三位数方位角来表示。
Bearing = Angle measured clockwise from true north (000° to 360°)
方位角 = 从真北顺时针测量的角度（000° 至 360°）
A bearing is always written with three digits: north is 000°, east is 090°, south is 180° and west is 270°. Use a protractor to measure the angle on a map.
方位角始终用三位数字书写：北为 000°，东为 090°，南为 180°，西为 270°。使用量角器在地图上测量角度即可。
4. Contour Lines, Height and Slope | 等高线、高度与坡度
Contour lines join points of equal height above sea level. The contour interval is the vertical difference between adjacent contour lines.
等高线是连接海平面以上相同高度各点的线。等高距是相邻等高线之间的垂直高差。
Gradient = (Vertical Difference (m) ÷ Horizontal Distance (m)) × 100%
坡度 = (高差 (m) ÷ 水平距离 (m)) × 100%
To calculate gradient, find the height difference between two points and measure the straight‑line distance between them on the map, converted to metres. A steeper slope has a larger percentage.
计算坡度时，找出两点间的高差，并测量地图上两点间的直线距离，换算成米。坡度越陡，百分比越大。
Contour patterns also show landforms: closely spaced contours indicate a steep slope, while widely spaced contours show a gentle slope. Concentric closed contours represent a hill.
等高线的形态也能显示地貌：密集的等高线表示陡坡，稀疏的等高线表示缓坡。闭合的同心等高线代表山丘。
5. Population Density and Change | 人口密度与变化
Population density describes how crowded an area is. It is one of the most useful calculations in human geography.
人口密度描述一个地区的拥挤程度，是人文地理中最有用的计算之一。
Population Density = Total Population ÷ Area (km²)
人口密度 = 总人口 ÷ 面积 (km²)
If a city has 1,200,000 people and covers 800 km², the density is 1,500 persons per km². Always include the units persons/km².
如果某个城市有 1,200,000 人，面积 800 km²，则人口密度为 1,500 人/平方公里。始终要带上单位 人/km²。
Population change over time can be expressed as an absolute increase (final population – initial population) or as a percentage change.
人口随时间的变化可以用绝对增长（末期人口 − 初期人口）或百分比变化来表示。
Percentage Population Change = [(Final − Initial) ÷ Initial] × 100%
人口变化百分比 = [(末期人口 − 初期人口) ÷ 初期人口] × 100%
6. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率与自然增长
Demographers use the crude birth rate (CBR) and crude death rate (CDR) to measure the number of births and deaths per 1000 people in a population each year.
人口学家使用粗出生率 (CBR) 和粗死亡率 (CDR) 来衡量每年每千人中出生和死亡的人数。
CBR = (Number of live births ÷ Total population) × 1000
粗出生率 = (活产婴儿数 ÷ 总人口) × 1000
CDR = (Number of deaths ÷ Total population) × 1000
粗死亡率 = (死亡人数 ÷ 总人口) × 1000
The rate of natural increase (RNI) is the difference between CBR and CDR, often expressed as a percentage when divided by 10. It excludes migration.
自然增长率 (RNI) 是粗出生率与粗死亡率之差，通常除以 10 转换成百分比。它不包括迁移的影响。
Natural Increase (per 1000) = CBR − CDR
自然增长（每千人）= 粗出生率 − 粗死亡率
Natural Increase (%) = (CBR − CDR) ÷ 10
自然增长率 (%) = (粗出生率 − 粗死亡率) ÷ 10
7. Climate Data: Mean, Range and Totals | 气候数据：平均值、较差与总量
Climate graphs display average monthly temperature and total monthly precipitation. The mean annual temperature and temperature range are key summary statistics.
气候图展示月平均气温和月总降水量。年平均气温和气温较差是关键的概括性统计量。
Mean Annual Temperature = Sum of 12 monthly temperatures ÷ 12
年平均气温 = 12 个月的月均温总和 ÷ 12
Annual Temperature Range = Hottest month temperature − Coldest month temperature
年气温较差 = 最热月气温 − 最冷月气温
Total annual precipitation is simply the sum of all 12 monthly precipitation values. Daily mean temperature can be found by averaging the maximum and minimum for that day.
年总降水量就是 12 个月的降水量之和。日平均气温可以通过当日最高气温和最低气温的平均值求得。
These calculations help classify climates and compare the weather of different places, such as equatorial, desert or temperate regions.
这些计算有助于气候分类并比较不同地区的天气，例如赤道气候、沙漠气候或温带气候区。
8. River Measurements: Width, Depth, Velocity and Discharge | 河流测量：宽度、深度、流速与流量
Fieldwork on rivers often involves measuring channel dimensions and flow speed. Velocity is found by timing a float over a known distance.
河流实地考察通常涉及测量河道尺寸和流速。流速可通过记录漂浮物经过已知距离的时间来求得。
Velocity = Distance (m) ÷ Time (s)
流速 = 距离 (m) ÷ 时间 (s)
Discharge is the volume of water passing a point per second. It is a fundamental measure of a river’s flow.
流量是每秒通过某一点的河水体积，是衡量河流水流的基本指标。
Discharge (m³/s) = Cross‑sectional area (m²) × Average velocity (m/s)
流量 (m³/s) = 横截面积 (m²) × 平均流速 (m/s)
Cross‑sectional area can be estimated from the average width multiplied by the average depth of the channel. Take multiple depth readings across the width for accuracy.
横截面积可用河道的平均宽度乘以平均深度来估算。为提高准确性，应在整个宽度上多次测量深度。
9. Fieldwork Sampling and Percentages | 实地考察的抽样与百分比
When collecting primary data, geographers often use sampling methods: random, systematic (e.g. every 10th person) or stratified (by group).
收集一手数据时，地理学者常使用抽样方法：随机抽样、系统抽样（如每 10 人抽 1 人）或分层抽样（按组别）。
The percentage share or proportion is widely used to present results from questionnaires, land‑use surveys or traffic counts.
百分比或比率广泛用于展示问卷调查、土地利用调查或交通流量统计的结果。
Percentage (%) = (Part ÷ Whole) × 100
百分比 (%) = (部分 ÷ 整体) × 100
For example, if 24 out of 80 pedestrians counted were wearing coats, the percentage is (24 ÷ 80) × 100 = 30%. Always round to one decimal place if needed.
例如，如果统计的 80 名行人中有 24 人穿着外套，百分比为 (24 ÷ 80) × 100 = 30%。必要时四舍五入到一位小数。
Simple measures like the mean (average) can summarise pebble sizes or river depths collected during fieldwork.
简单的计量如平均数（均值）可以概括实地考察中收集的卵石大小或河流深度。
Mean = Sum of values ÷ Number of values
平均数 = 数值总和 ÷ 数值个数
10. Key Geographical Theorems and Concepts | 关键地理定理与概念
Several basic theorems and concepts explain physical and human patterns. The environmental lapse rate describes how air temperature changes with altitude.
一些基本定理和概念可以解释自然和人文格局。气温递减率描述了气温如何随海拔高度变化。
Environmental Lapse Rate: Temperature drops about 6.5 °C for every 1000 m rise in altitude
环境气温递减率：海拔每升高 1000 m，气温约下降 6.5 °C
In introductory geography we often use a simplified value of 6 °C per 1000 m for quick estimates. This helps explain why mountain tops are colder than lowlands.
在基础地理中，我们常使用每 1000 m 下降 6 °C 的简化值进行快速估算，这有助于解释为什么山顶比低地更冷。
The latitude‑temperature relationship states that places nearer the equator are generally warmer because they receive more concentrated solar radiation. This is a key control on global climate zones.
纬度–气温关系指出，靠近赤道的地区通常更温暖，因为它们接收到的太阳辐射更加集中。这是全球气候带形成的关键控制因素。
In human geography, the core‑periphery concept describes how economic activity and wealth are often concentrated in core regions, with less developed peripheries. Push‑pull factors explain migration movements.
在人文地理中，核心–边缘概念描述了经济活动与财富往往集中在核心区域，而边缘区域发展较差。推拉因素则解释了迁移运动。
When analysing population pyramids, the shape indicates the stage of the Demographic Transition Model (DTM), which links birth and death rates to levels of development.
分析人口金字塔时，其形状表明人口转变模型 (DTM) 所处的阶段，该模型将出生率和死亡率与发展水平联系起来。
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