📚 Year 8 AQA Geography: Quick Reference Handbook of Formulas and Theorems | 八年级 AQA 地理：公式定理速查手册
In Year 8 AQA Geography, being able to apply key formulas and understand important geographical relationships is essential for success. This quick reference handbook gathers all the must-know calculations, rules, and summary notes for map skills, population, rivers, and weather & climate. Each entry is presented clearly with a concise explanation and the formula written in a highlighted box. Whether you are doing fieldwork, preparing for a test, or simply revising key concepts, this handbook will help you work accurately and efficiently.
在八年级 AQA 地理课程中，能够应用关键公式并理解重要的地理关系是取得成功的基础。本速查手册汇集了地图技能、人口、河流以及天气与气候等板块必须掌握的全部计算、规则和要点总结。每个条目都配有清晰的说明，公式以突出显示的方式呈现。无论你是在进行实地调查、准备测验，还是只是复习核心概念，这本手册都能帮助你准确、高效地工作。
1. Map Scale and Distance Calculations | 地图比例尺与距离计算
On a map, the scale tells you how much the real world has been reduced. The three types of scale are the statement scale (e.g., 1 cm to 1 km), the linear (bar) scale, and the representative fraction (RF) scale (e.g., 1:50 000). To find the actual straight-line distance between two points, you measure the map distance with a ruler and then convert it using the scale.
在地图上，比例尺告诉你现实世界被缩小了多少。比例尺有三种类型：文字比例尺（例如 1 厘米代表 1 千米）、直线比例尺（图示）和数字比例尺（如 1:50 000）。要找出两点之间的实际直线距离，你需要用直尺量出图上距离，然后利用比例尺进行换算。
Formula: Actual Distance = Map Distance × Scale Denominator. If the scale is 1:50,000 and the map distance is 4 cm, actual distance = 4 cm × 50,000 = 200,000 cm = 2 km. Always convert units consistently: 1 km = 100,000 cm.
公式：实际距离 = 图上距离 × 比例尺分母。若比例尺是 1:50,000，图上距离为 4 厘米，则实际距离 = 4 厘米 × 50,000 = 200,000 厘米 = 2 千米。务必统一单位：1 千米 = 100,000 厘米。
Actual Distance = Map Distance × Denominator of RF
For distances that are not straight, you can use a piece of string to follow the curve, then measure the string length against the scale. This gives a reasonably accurate ground distance.
对于非直线距离，你可以用一根细绳沿着曲线摆放，再根据比例尺量出绳子的长度。这样能得出相当准确的地面距离。
2. Measuring Area on Maps | 地图面积测量
To estimate the area of a feature on a map, such as a lake or a woodland, you often overlay a grid of squares. On an Ordnance Survey map, each blue grid square is 1 km². You count the number of full squares the feature covers, and then estimate the area of partial squares to add to the total.
要估算地图上图斑的面积，例如湖泊或林地，通常会在上面覆上一个方格网。在英国地形测量地图上，每一个蓝色网格方块的面积是 1 平方千米。你可以数出图斑占据的完整方格数量，再估算部分方格面积并累加。
If your map uses a grid where each square represents a smaller unit, the area formula becomes: Area = (Number of full squares + 0.5 × number of half-covered squares) × area per square. For irregular shapes, the ‘grid square method’ is the standard approach.
如果地图上每个方格代表更小的面积，面积计算公式为：面积 = （完整方格数 + 0.5 × 半覆盖方格数）× 每个方格代表的面积。对于不规则形状，“方格法”是标准方法。
3. Gradient (Slope) Calculation | 坡度（梯度）计算
Gradient describes how steep a slope is by comparing the vertical rise to the horizontal run. It is commonly expressed as a ratio, such as 1:10, meaning the land rises 1 unit for every 10 units horizontally. The formula is: Gradient = Vertical Height Difference ÷ Horizontal Distance. Both must be in the same units.
坡度通过垂直高差与水平距离的比值来描述斜坡的陡峭程度。它通常用比数表示，例如 1:10，表示每水平移动 10 个单位，高度上升 1 个单位。公式为：坡度 = 垂直高差 ÷ 水平距离。两者单位必须一致。
Gradient = Height Difference (rise) ÷ Distance (run)
When reading a contour map, find the height of two neighbouring contours, subtract the lower from the higher, and measure the map distance between them. Convert the map distance to real-world ground distance before dividing. Simplify the ratio so that the first number is 1, e.g., 50 m / 500 m = 1:10.
阅读等高线地图时，找出两条相邻等高线的高程值，用较高值减去较低值，并测量它们之间的图上距离。在计算除法之前，先将图上距离换算为实地距离。将比值化简，使第一个数字为 1，例如 50 米 / 500 米 = 1:10。
4. Population Density | 人口密度
Population density measures how crowded or sparsely populated a place is. It is expressed as the number of people per square kilometre. The formula is straightforward and used frequently in human geography topics like settlements and urbanisation.
人口密度衡量一个地方的拥挤或稀疏程度，通常表示为每平方千米的人口数量。公式非常简单，在聚落和城市化等人文地理专题中经常使用。
Population Density = Total Population ÷ Total Land Area (km²)
For example, if a city has 2,000,000 people and covers an area of 500 km², its population density is 2,000,000 ÷ 500 = 4,000 people/km². Remember that the total land area should exclude large water bodies. A high density suggests a built-up urban area, while a low density points to a rural area.
例如，若某城市有 2,000,000 人口，面积为 500 平方千米，则人口密度为 2,000,000 ÷ 500 = 4,000 人/平方千米。注意，总面积应扣除大型水体。高密度表明是建成城市区，低密度则指向乡村地区。
5. Birth Rate, Death Rate, and Natural Increase | 出生率、死亡率与自然增长率
Birth rate and death rate are usually given per 1,000 people per year. The crude birth rate is the number of live births per 1,000 of the population; the death rate is similar. They allow comparisons between countries of different sizes. The formula for each is:
出生率和死亡率通常以每年每千人为单位。粗出生率是指每千人中活产婴儿的数量；死亡率类似。它们便于在不同规模的国家之间进行比较。各自的公式如下：
Crude Birth Rate = (Number of live births ÷ Total population) × 1000
Crude Death Rate = (Number of deaths ÷ Total population) × 1000
Natural increase is the difference between the birth rate and the death rate. It is also expressed per 1,000. The rate of natural increase can be positive (more births than deaths) or negative.
自然增长率是出生率与死亡率之差，同样以每千人为单位。自然增长率可以是正数（出生多于死亡）或负数。
Natural Increase = Birth Rate − Death Rate (per 1000)
To find the annual population growth from natural increase, you divide the natural increase per 1000 by 10 to get a percentage. For example, a birth rate of 32 and death rate of 8 gives a natural increase of 24 per 1000, or 2.4% growth.
要通过自然增长率计算年度人口增长百分比，可以将每千人自然增长值除以 10。例如，出生率 32，死亡率 8，则自然增长为每千人 24，即 2.4% 的增长。
6. Percentage Urbanisation and Rural-Urban Change | 城市化百分比与城乡变化
Urbanisation is the increasing proportion of a country’s population living in towns and cities. The level of urbanisation is expressed as a percentage. It is a key indicator of development.
城市化是指一个国家居住在城镇和城市的人口比例不断增加的过程。城市化水平以百分比表示，是衡量发展的关键指标。
Urban Population % = (Urban Population ÷ Total Population) × 100
If a country has a total population of 50 million, with 35 million living in urban areas, the urbanisation rate is (35 ÷ 50) × 100 = 70%. The annual rate of urbanisation can be calculated by the percentage point change over time.
如果一个国家总人口为 5000 万，其中 3500 万居住在城市地区，那么城市化率为 (35 ÷ 50) × 100 = 70%。年度城市化速率可以通过百分比点的逐年变化来计算。
7. River Discharge | 河流流量
River discharge is the volume of water passing a point in the river channel per second. It is measured in cubic metres per second (cumecs). Discharge is a fundamental concept when studying flooding, erosion, and river regimes.
河流流量是指每秒钟通过河道中某一点的体积，以立方米每秒（cumecs）为单位。在研究洪水、侵蚀和河流情势时，流量是一个基本概念。
Discharge (Q) = Cross-Sectional Area (A) × Velocity (V)
Velocity is the speed of the water, measured in metres per second, usually found with a flowmeter. The cross-sectional area is measured at the same spot, as explained in the next section. If area = 8 m² and velocity = 0.5 m/s, then Q = 4 cumecs.
流速是水流速度，以米/秒为单位，通常用流速仪测得。横截面积在同一地点测量，下一节会解释。如果面积 = 8 平方米，流速 = 0.5 米/秒，那么流量 Q = 4 立方米每秒。
8. Cross-Sectional Area of a River Channel | 河道横截面积
To find the cross-sectional area, you measure the width of the river and the water depth at several equally spaced points across the channel. The area can be approximated by dividing the channel into several trapezoids or rectangles and summing their areas.
要计算横截面积，你需要测量河宽以及在河道上等间距多个点的水深。可以将河道划分为若干个梯形或矩形，将其面积相加来近似计算。
For a simple estimate: Average Depth = Sum of all depth measurements ÷ Number of measurements. Then, Cross-sectional Area = Width × Average Depth. A more accurate field method uses the formula: Area = Σ (Width of segment × Average depth of segment).
简单估算：平均水深 = 所有水深测量值之和 ÷ 测量点数量。然后，横截面积 = 河宽 × 平均水深。更精确的实地方法使用公式：面积 = Σ（分段宽度 × 分段平均水深）。
Cross-Sectional Area ≈ River Width × Mean Depth
9. Mean, Median, and Range in Climate Data | 气候数据的平均数、中位数和极差
When analysing climate graphs or weather records, you frequently calculate the mean (average) temperature or rainfall. The mean is found by adding all values and dividing by the number of values. The median is the middle value when data is ordered.
在分析气候图表或天气记录时，你经常需要计算平均气温或降雨量。平均数是将所有数值相加再除以数值个数得到的。中位数是将数据排序后位于中间的值。
Mean = Sum of all data values ÷ Number of data values
The temperature range (diurnal or annual) reveals the variation. The annual temperature range is the difference between the highest and lowest monthly mean temperatures. Similarly, total annual rainfall is the sum of all monthly rainfall totals.
温度极差（日较差或年较差）揭示了变化幅度。年温度极差是最高月均温与最低月均温的差值。类似地，年总降水量是所有月降水量之和。
Range = Maximum Value − Minimum Value
10. Wind Direction and Compass Bearings | 风向与罗盘方位
Wind direction is given by the compass point the wind is blowing from. A north wind blows from the north to the south. To express directions precisely, we use three-figure bearings, measured clockwise from north (000°). East is 090°, south 180°, and west 270°.
风向由风吹来的罗盘方向表示。北风指的是从北向南吹的风。为了精确表示方向，我们使用三位数方位角，从正北（000°）起顺时针测量。东是 090°，南是 180°，西是 270°。
Although bearings are not a strict formula, the conversion between compass points and degrees is a key geographical skill. To find a bearing between two points on a map, draw a line, align a protractor with grid north, and read the angle clockwise.
虽然方位角不是严格的公式，但罗盘方位点与角度之间的转换是一项关键的地理技能。要在地图上找出两点之间的方位角，需要画一条线，将量角器与网格北对齐，然后顺时针读取角度。
11. Percentage Change in Land Use | 土地利用百分比变化
When studying urban sprawl or deforestation, you may need to calculate the percentage change in an area of land use over time. The formula is exactly the same as in other percentage change calculations.
在研究城市扩张或森林砍伐时，你可能需要计算某类土地利用面积随时间变化的百分比变化。这个公式与其他百分比变化的计算方法完全相同。
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100
For instance, if forest cover decreased from 15,000 hectares to 12,000 hectares, the change is (12,000 − 15,000) ÷ 15,000 × 100 = -20%, a 20% decrease. A positive result means an increase.
例如，如果森林覆盖面积从 15,000 公顷减少到 12,000 公顷，变化率为 (12,000 − 15,000) ÷ 15,000 × 100 = -20%，即减少了 20%。正数结果则表示增加。
12. The Four-Figure and Six-Figure Grid References | 四位数和六位数网格坐标
Grid references allow you to locate features precisely on an Ordnance Survey map. The rule ‘along the corridor and up the stairs’ reminds you to read eastings first (left to right) and then northings (upwards). A four-figure reference (e.g., 1532) gives the grid square; a six-figure reference (e.g., 155325) pinpoints a location within that square to a 100-metre accuracy.
网格坐标能让你在地形测量地图上精确定位地物。“先横后纵”的规则提醒你先读东向值（从左到右），再读北向值（向上）。四位数坐标（如 1532）给出所在格网方格；六位数坐标（如 155325）则能将方格内的位置定位到 100 米的精确度。
To get a six-figure reference, take the two-figure easting and northing from the bottom-left corner of the square, then estimate how many tenths the point lies across the square and add that digit. This system is vital for fieldwork and map-reading tests.
要得到六位数坐标，先取方格左下角的东西向和北向两位数字，再估算该点在方格内十分之几的位置，并将该数字加在相应坐标后。这个系统对于野外实地考察和地图判读测试至关重要。
Published by TutorHao | Geography Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导