📚 Year 9 AQA Geography: Formula & Theorem Quick Reference Handbook | Year 9 AQA地理：公式定理速查手册
Welcome to your essential quick-reference handbook for Year 9 AQA Geography. This guide consolidates the key formulas, calculations, and theoretical models you need to master map skills, population studies, and economic indicators. Understanding these tools will empower you to interpret geographical data accurately and succeed in your assessments.
欢迎使用 Year 9 AQA 地理必备速查手册。本指南汇总了您需要掌握的关键公式、计算方法和理论模型，涵盖地图技能、人口研究和经济指标。理解这些工具将帮助您准确解读地理数据，并在考试中取得成功。
1. Map Scale and Distance Calculation | 地图比例尺与距离计算
The scale of a map shows the relationship between a distance on the map and the corresponding distance on the ground. Every measurement on the page must be multiplied by the scale factor to obtain the real-world distance.
地图比例尺表示地图上的距离与地面上相应距离之间的关系。页面上的每一个测量值必须乘以比例系数，才能得到现实世界中的距离。
There are three common ways to represent scale: as a representative fraction or ratio (1:50,000), as a written statement ('1 cm to 500 m'), or as a linear scale bar printed on the map.
表示比例尺有三种常见方式：以分数或比率形式表达（1:50,000），以文字说明表达（“1厘米代表500米”），或以印刷在地图上的线段比例尺表达。
Real Distance = Map Distance × Scale Denominator
If the scale is 1:50,000, the scale denominator is 50,000. Multiply the map distance in centimetres by this number to get the real distance in centimetres, then convert to metres or kilometres by dividing by 100 or 100,000 respectively.
如果比例尺为1:50,000，比例尺分母为50,000。将地图上的距离（厘米）乘以该数字，得到实际距离（厘米），然后分别除以100或100,000，转换为米或公里。
Divide by 100 to obtain 1,000 m, or by 100,000 to obtain 1 km. Always convert to a sensible unit for real landscapes.
例如，在1:25,000的地图上，一条4厘米的线段代表 4 × 25,000 = 100,000 厘米。除以100得到1,000米，或除以100,000得到1公里。始终转换为适合真实地形的单位。
2. Area Measurement on Maps | 地图上的面积测量
To estimate the area of an irregular feature, such as a forest or a lake, use the grid-square method. Ordnance Survey maps typically have grid squares that represent 1 square kilometre (km²) on the ground.
要估算不规则地物（例如森林或湖泊）的面积，可使用网格法。英国Ordnance Survey地图的网格方格通常代表地面上1平方公里。
Count the number of complete squares covered by the feature. For squares that are only partially covered, count each as half a square (or estimate the fraction). Then apply the simple formula:
计算地物覆盖的完整方格数。对于仅部分覆盖的方格，每个按半个方格（或估算分数）计算。然后应用简单公式：
Area (km²) = Number of full squares + 0.5 × Number of partial squares
resent 0.5 km, so one square = 0.25 km²). Always check the grid spacing in the map legend.
如果地图有不同的网格尺寸，首先使用比例尺计算每个方格的实地面积（例如，在1:25,000地图上，2厘米的网格边可能代表0.5公里，因此一个方格=0.25平方公里）。务必检查图例中的网格间距。
3. Gradient and Slope | 坡度和倾斜度
Gradient describes the steepness of a slope and is expressed as a ratio of vertical rise to horizontal run. It is a vital concept for understanding relief, drainage, and route planning.
坡度描述斜坡的陡峭程度，表示为垂直上升高度与水平距离的比值。这是理解地形、排水和线路规划的重要概念。
Gradient = Vertical difference (height gain) ÷ Horizontal distance
ontal distance of 100 metres gives a gradient of 20/100 = 1/5. This is commonly written as '1 in 5' or '1:5'.
两个测量值必须使用相同的单位。例如，一段路水平距离100米上升了20米，梯度为20/100 = 1/5。通常表示为“1 in 5”或“1:5”。
On a contour map, find the vertical difference between two contour lines and measure the horizontal distance between them along the slope. Convert ground distance to metres, then calculate the ratio. A smaller second number indicates a steeper slope.
在等高线地图上，找出两条等高线之间的垂直差，并沿着坡面测量它们之间的水平距离。将地面距离转换为米，然后计算比值。比值的第二个数字越小，表示坡度越陡。
4. Four-Figure and Six-Figure Grid References | 四位与六位网格坐标
: go along the eastings first (numbers along the bottom or top edge), then go up the northings (numbers along the side).
网格坐标系统用于在Ordnance Survey地图上定位地物。四位坐标确定一个1公里×1公里的方格。规则是：先向右读取东坐标（底部或顶部边缘的数字），再向上读取北坐标（侧面边缘的数字）。
A six-figure grid reference increases precision to 100 metres by imagining each square divided into ten equal parts along both eastings and northings. Add a third digit to each coordinate, representing the number of tenths across and up within the square.
六位坐标将每个方格假想为东西和南北方向各分为十等份，从而将精度提高到100米。在东坐标和北坐标上各添加第三位数字，代表方格内向右和向上的十分之几。
Example: a school located approximately three-tenths east and eight-tenths north inside square 6274 would be recorded as 623748? Wait — careful: easting 62 then 3 tenths gives 623; northing 74 then 8 tenths gives 748. So the six-figure reference is 623748. Always state easting first, northing second, and use six digits total.
示例：一所学校位于方格6274内，大约向东十分之三、向北十分之八，则东坐标62加3成为623，北坐标74加8成为748，因此六位坐标为623748。始终先说东坐标，后说北坐标，共六位数字。
5. Compass Directions and Bearings | 罗盘方向与方位角
Compass bearings are measured clockwise from north in degrees, ranging from 0° to 360°. They are always written as three figures, e.g., 45° is recorded as 045°.
罗盘方位角从正北（0°）开始顺时针测量，范围为0°至360°。始终用三位数表示，例如45°记作045°。
The sixteen cardinal points can be memorised as N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW, NW and NNW. To measure a bearing on a map, draw a line from the origin to the target, align a protractor with grid north, and read the angle.
十六个基本方位点可记为：北、北东北、东北、东东北、东、东东南、东南、南东南、南、南西南、西南、西西南、西、西西北、西北、北西北。在地图上测量方位角时，从起点向目标点画一条线，用量角器对准网格北，然后读取角度。
If you are given a grid bearing, you may need to convert to a magnetic bearing by adding or subtracting the magnetic variation shown on the map legend.
若给出的是网格方位角，可能需要通过加减图例中所示的磁偏角，将其转换为磁方位角。
6. Contour Lines and Cross-Section Profiles | 等高线与剖面图判读
Contour lines are brown lines that join points of equal height above sea level. The difference in height between two consecutive contours is called the contour interval, often 5 or 10 metres on 1:25,000 maps.
等高线是连接海平面上相等高度点的棕色线条。相邻两条等高线之间的高度差称为等高距，在1:25,000地图上通常为5米或10米。
Closely spaced contours indicate a steep slope; widely spaced contours show a gentle slope. Concentric closed contours with increasing heights denote a hill; closed contours with decreasing heights inward suggest a depression.
等高线密集表示坡度陡峭；等高线稀疏表示平缓坡度。同心闭合且高度递增的等高线表示山丘；向内高度递减的闭合等高线则表示洼地。
To draw a cross-section, place a piece of paper along a transect line, mark every point where a contour crosses it, note the height at each mark, then plot these heights on graph paper. Connect the points with a smooth curve to show the land profile.
要绘制剖面图，沿一条横切线放一张纸，标记每条等高线与该线相交的点，记录每个点的高度，然后将这些高度标到方格纸上。用平滑曲线连接这些点，显示地形剖面。
7. Population Density Formula | 人口密度公式
Population density measures how crowded an area is. It is a simple but powerful indicator used to compare regions and understand the pressure on land and resources.
人口密度衡量一个区域的拥挤程度。它是一个简单而有力的指标，用于比较不同区域，并了解土地和资源所承受的压力。
Population Density = Total population ÷ Land area (km²)
0 persons per km². Always express density to one decimal place if needed, and state the units as persons per square kilometre.
例如，如果一个国家有800万人口，土地面积为40,000平方公里，那么密度为8,000,000 ÷ 40,000 = 200人/平方公里。如有需要，密度可保留一位小数，并注明单位为每平方公里人数。
High population densities are typical in cities and fertile plains, while low densities occur in deserts, mountains, or polar regions. Remember that density does not indicate the distribution or the quality of life.
高人口密度通常出现在城市和肥沃平原，而低密度则在沙漠、山区或极地地区。请记住，密度并不能说明人口的分布状况或生活质量。
8. Crude Birth Rate and Crude Death Rate | 粗出生率与粗死亡率
Crude Birth Rate (CBR) and Crude Death Rate (CDR) are fundamental measures of population change. 'Crude' means they are calculated for the whole population without considering age or sex structure.
粗出生率（CBR）和粗死亡率（CDR）是衡量人口变化的基本指标。“粗”意味着它们是针对总人口计算的，不考虑年龄或性别结构。
CBR = (Number of live births in a year ÷ Total mid-year population) × 1000
CDR = (Number of deaths in a year ÷ Total mid-year population) × 1000
000,000) × 1000 = 25 per 1000. A CDR of 10 per 1000 would indicate 10 deaths for every 1000 people.
两个率值都以每年每千人为单位表示。例如，一个国家有2000万人口，出生人数为50万，则CBR = (500,000 ÷ 20,000,000) × 1000 = 25‰。CDR为10‰则表示每1000人中有10人死亡。
High CBRs are often found in less economically developed countries, while low CBRs and CDRs are common in more developed nations. Always check you are using the correct mid-year population estimate.
高出生率常见于欠发达国家，而低出生率和低死亡率在较发达国家常见。始终确保使用的是正确的中期人口估算值。
9. Natural Increase and Population Change | 自然增长与人口变化
Natural increase represents the difference between the number of births and deaths, ignoring migration. It is often expressed as a rate per 1000 population per year.
自然增长是指出生人数与死亡人数之间的差额，不计入迁移。通常以每年每千人的比率表示。
Natural Increase Rate (per 1000) = CBR – CDR
A positive natural increase means the population is growing from births alone; a negative value indicates a natural decrease (more deaths than births). This rate must be combined with net migration to find total population change.
正自然增长率意味着仅靠出生人口就在增长；负值表示自然减少（死亡人数多于出生人数）。此率值必须与净迁移结合，才能算出总人口变化。
Total Population Change = (Births – Deaths) + (Immigration – Emigration)
rds 300 births, 220 deaths, 150 immigrants and 80 emigrants in a year has a change of (300 – 220) + (150 – ) = 80 + 70 = 150 people. The growth is caused by both natural increase and net migration.
例如，一个城镇一年记录出生300人、死亡220人、迁入150人、迁出80人，则人口变化为(300 - 220) + (150 - 80) = 80 + 70 = 150 人。增长由自然增长和净迁移共同造成。
10. Demographic Transition Model (DTM) | 人口转变模型
The Demographic Transition Model (DTM) is a theoretical framework that describes how a country's birth rate and death rate change as it develops. It is divided into five stages.
人口转变模型（DTM）是一个理论框架，描述了一个国家的出生率和死亡率如何随着发展而变化。该模型分为五个阶段。
| Stage | Birth rate | Death rate | Natural increase | Typical example |
|---|---|---|---|---|
| 1 – High stationery | High and fluctuating | High and fluctuating | Very low or zero | Remote tribal groups |
| 2 – Early expanding | High | Falling rapidly | Very high | Least developed countries (e.g. Niger) |
| 3 – Late expanding | Falling |
Published by TutorHao | Year 9 Geography Revision Series | aleveler.com
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