📚 Year 7 CIE Geography: Formulas & Key Concepts Quick Reference Handbook | CIE Year 7 地理公式定理速查手册
This quick reference handbook brings together the essential formulas, definitions and practical rules you will meet in Year 7 CIE Geography. It is designed for speedy revision of map skills, population figures, climate data analysis and the key ‘theorems’ that describe how physical and human landscapes are measured. Mastering these tools will help you read maps accurately, interpret graphs and answer calculation questions with confidence.
本速查手册汇集了 Year 7 CIE 地理课程中的核心公式、定义和实用法则。它专为高效复习地图技能、人口数据、气候资料分析以及描述自然与人文景观测量方式的重点“定理”而编排。掌握这些工具，你将能够准确判读地图、解读图表，并自信地解答计算类题目。
1. Map Scales and Distance Conversion | 地图比例尺与距离换算
Map scale describes the relationship between a distance on the map and the corresponding distance on the ground. It can be expressed as a statement (e.g. ‘1 cm represents 1 km’), a linear scale bar or a representative fraction (RF) such as 1:50 000. The most useful formula for converting map distances into real-world distances is:
地图比例尺描述的是图上距离与实际地面距离之间的关系。它可以采用文字说明（如“1厘米代表1公里”）、线性比例尺或数字比例尺（如1:50 000）来表示。将图上距离转换为实地距离最常用的公式是：
Actual Ground Distance = Map Distance × Scale Denominator
实际地面距离 = 图上距离 × 比例尺分母
For a map with an RF of 1:25 000, a measured length of 6 cm gives: Actual distance = 6 cm × 25 000 = 150 000 cm. Convert to metres by dividing by 100, giving 1 500 m, or 1.5 km. Always express the final answer in sensible units such as metres or kilometres, and show the unit conversion steps clearly.
对于比例尺为1:25 000的地图，量得长度为6厘米，计算如下：实际距离 = 6 cm × 25 000 = 150 000 cm。除以100化为米，得到1 500 m，即1.5 km。最终答案一定要用合理的单位（米或千米）表示，并清晰地展示单位换算过程。
2. Calculating Gradient (Slope) | 计算坡度（倾斜度）
Gradient measures how steep a slope is. In geography it is nearly always expressed as a ratio of vertical rise to horizontal run, simplified so that the horizontal value is 1. The formula uses the vertical interval (VI) – the difference in height between two points – and the horizontal equivalent (HE) – the horizontal ground distance between them.
坡度用来衡量斜坡的陡峭程度。在地理中，它几乎总是表示为垂直升高与水平距离的比值，并简化成水平值为1的形式。公式中使用垂直高差（VI，即两点高度之差）和水平距离（HE，即两点之间的水平实地距离）。
Gradient = VI ÷ HE, then expressed as 1 : (HE ÷ VI)
坡度 = VI ÷ HE，再表示为 1 : (HE ÷ VI)
If a hillside rises 40 m over a horizontal distance of 800 m, VI = 40 m, HE = 800 m. Divide both numbers by 40: 40/40 = 1 and 800/40 = 20, so the gradient is 1 : 20. This means that for every 1 m of vertical rise you travel 20 m horizontally. On Ordnance Survey maps you obtain VI from contour values and measure HE using the scale bar.
如果山坡在800米水平距离内上升了40米，VI = 40 m，HE = 800 m。将两个数值同除以40：40/40 = 1，800/40 = 20，因此坡度为1 : 20。这意味着每上升1米，水平方向上前进20米。在使用地形测量图时，VI可从等高线注记得到，HE则借助比例尺量取。
3. Determining Area Using Grid Squares | 用方格网确定面积
On many topographical maps the grid lines form squares that represent a fixed area on the ground. You can estimate the area of a feature (a lake, a forest, a farm) by counting the number of complete and partial squares it covers. The key formula links the counted squares to the map scale.
在许多地形图上，网格线构成的正方形代表地面固定面积。通过数出地物（湖泊、森林、农田）所占的整格和不完整格数，就能估算其面积。关键公式将数出的方格数与地图比例尺联系起来。
Area = Number of Squares × Area Represented by One Grid Square
面积 = 方格数 × 每个方格代表的实际面积
On a 1:50 000 map, a grid square with sides of 2 cm represents an area of 1 km² (since 2 cm × 50 000 = 100 000 cm = 1 km, and 1 km × 1 km = 1 km²). If a wetland covers 8 full squares and about 4 half squares (treat each half square as 0.5), the total number of squares is 8 + (4 × 0.5) = 10 squares. Estimated area = 10 × 1 km² = 10 km². For irregular shapes, the dot grid method or mathematical approximations can also be used.
在1:50 000地图上，边长为2 cm的方格代表1 km²的面积（因为2 cm × 50 000 = 100 000 cm = 1 km，1 km × 1 km = 1 km²）。如果一片湿地占满8个整格和大约4个半格（每个半格按0.5计），方格总数 = 8 + (4 × 0.5) = 10格。估算面积 = 10 × 1 km² = 10 km²。对于不规则形状，还可采用点格法或数学近似法。
4. Population Density | 人口密度
Population density describes how crowded an area is. It is the average number of people living per unit of land area and is a fundamental indicator in human geography. The formula is straightforward but must be used with both numbers correctly sourced.
人口密度描述的是一个地区的拥挤程度。它是单位土地面积上居住的平均人数，是人文地理学中的一项基本指标。公式虽然简单，但必须确保两个数据来源正确。
Population Density = Total Population ÷ Land Area
人口密度 = 总人口 ÷ 土地面积
The result is usually expressed in persons per square kilometre (persons/km²). If a city has 2 400 000 people and covers 800 km², its population density = 2 400 000 ÷ 800 = 3 000 persons/km². Remember to use the total land area, not total area including large inland water bodies, and check whether the population figure is from the same year as the area measurement.
结果通常表示为每平方公里人数（人/km²）。如果一座城市有240万人，占地800 km²，人口密度 = 2 400 000 ÷ 800 = 3 000人/km²。计算时需使用土地总面积，而非包含大面积内陆水域的总面积，并核对人口数据是否与面积测算年份一致。
5. Natural Population Change: Births, Deaths and RNI | 人口自然变动：出生、死亡与自然增长率
Natural population change ignores migration and focuses on births and deaths. The crude birth rate (CBR) and crude death rate (CDR) are statistics per 1 000 people per year. The rate of natural increase (RNI) shows how fast a population is growing (or declining) without migration.
人口自然变动不考虑迁移，只关注出生与死亡。粗出生率（CBR）和粗死亡率（CDR）是每年每千人的统计值。自然增长率（RNI）显示在不考虑迁移的情况下，人口增长（或减少）的速度。
CBR = (Number of live births ÷ Total population) × 1 000
CDR = (Number of deaths ÷ Total population) × 1 000
RNI = CBR − CDR (per 1 000)
粗出生率 = (活产婴儿数 ÷ 总人口) × 1 000
粗死亡率 = (死亡人数 ÷ 总人口) × 1 000
自然增长率 = CBR − CDR（每千人）
The RNI can also be expressed as a percentage by dividing the per 1 000 figure by 10. For example, if CBR = 24 per 1 000 and CDR = 8 per 1 000, then RNI = 16 per 1 000, which is 1.6% per year. This formula helps geographers compare population dynamics between countries and predict future changes.
自然增长率也可通过将千分数除以10转化为百分比。例如，若CBR = 24‰，CDR = 8‰，则RNI = 16‰，即每年1.6%。这一公式帮助地理学家比较不同国家的人口动态，并预测未来变化。
6. Mean, Median, Mode and Range in Climate Data | 气候数据中的平均数、中位数、众数和范围
When analysing temperature or rainfall records, you often summarise data using four measures of central tendency and spread. The mean is the arithmetic average; the median is the middle value when data are ordered; the mode is the most frequent value; the range shows the spread between the highest and lowest values.
在分析气温或降水记录时，常借助集中趋势和离散程度的四项指标来概括数据。平均数即算术平均值；中位数是数据排序后位于中间的值；众数是出现次数最多的值；范围则展示最大值与最小值之间的跨度。
Mean = Sum of all values ÷ Number of values
Range = Maximum value − Minimum value
平均值 = 所有数据之和 ÷ 数据个数
范围 = 最大值 − 最小值
For a set of monthly rainfall totals: 45, 52, 48, 52, 39, 55 (mm), the mean = (45+52+48+52+39+55) ÷ 6 = 291 ÷ 6 = 48.5 mm. The ordered list is 39, 45, 48, 52, 52, 55; the median is halfway between 48 and 52, i.e. 50 mm; the mode is 52 mm; the range = 55 − 39 = 16 mm. These statistics allow you to describe a climate in numbers, not just words.
对于一组月降水量数据：45, 52, 48, 52, 39, 55 (mm)，平均值 = (45+52+48+52+39+55) ÷ 6 = 291 ÷ 6 = 48.5 mm。排序后：39, 45, 48, 52, 52, 55；中位数是48和52中间的数，即50 mm；众数为52 mm；范围 = 55 − 39 = 16 mm。有了这些统计量，就能用数字而不仅仅是文字描述气候。
7. Compass Bearings and Direction | 罗盘方位角与方向
A bearing is an angle measured clockwise from true north, ranging from 0° to 360°. Bearings provide a precise method of describing direction on maps, much more accurate than using words such as ‘northeast’. A standard compass rose divides the circle into 360 degrees, with north at 0°/360°, east at 90°, south at 180° and west at 270°.
方位角是从正北方向顺时针测量的角度，范围从0°到360°。方位角为在地图上描述方向提供了精确的方法，比使用“东北”这样的词语要准确得多。标准罗经花将圆周分为360度，正北为0°/360°，正东为90°，正南为180°，正西为270°。
Bearing = Angle measured clockwise from North
方位角 = 从正北顺时针方向测得的夹角
To measure a bearing on a paper map, draw a line from the starting point to the target point, place a protractor centred on the starting point with the 0° mark aligned to grid north, and read the angle at the target line. Bearings are always written with three digits (e.g. 045° for northeast, 225° for southwest). Practise with a protractor until you can measure angles quickly and accurately.
要在纸质地图上量取方位角，先从起点向目标点画一条连线，将量角器中心对准起点，0°刻线对准网格北，然后读取目标连线处的角度。方位角总是用三位数字书写（如东北为045°，西南为225°）。使用量角器反复练习，直到能快速准确测角。
8. Contour Lines, Height and Relief | 等高线、高度和地形
Contour lines join places of equal height above sea level and are the chief method of showing relief on topographic maps. A set of ‘theorems’ or reliable rules governs their behaviour: contours never cross (except at a vertical cliff), they form V-shapes pointing upstream when crossing valleys, and their spacing instantly reveals slope steepness.
等高线是连接海拔高度相同点的连线，是地形图上表示地势起伏的主要方法。一组可靠的“定理”支配着它们的特征：等高线永不相交（垂直悬崖除外）；穿越河谷时，等高线向上游方向突出形成V字形；它们的间距直接揭示坡度陡缓。
Steep slope: contours lie close together
Gentle slope: contours are widely spaced
Hilltop: closed contours, increasing height inward
Valley: contours curve upstream
陡坡：等高线密集
缓坡：等高线稀疏
山顶：闭合等高线，数值向内递增
山谷：等高线向上游方向弯曲
When a contour line has small inward-pointing marks (hachures), it indicates a depression or hollow. Counting the number of contours crossed within a given horizontal distance is a quick way to compare slope steepness between two places. Always read the contour interval stated in the map legend, because it sets the vertical step between neighbouring contour lines.
如果等高线上带有向内指向的小短线（示坡线），则表示洼地或凹陷。数一数在给定水平距离内穿过的等高线数量，是比较两地坡度陡缓的快捷方法。一定要阅读图例中标明的等高距，因为它决定了相邻等高线之间的高差值。
9. Latitude, Longitude and Distance | 纬度、经度与距离
Latitude and longitude provide a global grid for locating places. For approximate distance calculations, the length of one degree of latitude is roughly constant at about 111 km. The length of one degree of longitude varies with the cosine of latitude because the meridians converge towards the poles.
纬度和经度构成定位全球地点的网格。用于近似距离计算时，1度纬线长度大致恒定，约为111 km。1度经线长度则随纬度的余弦变化，因为子午线向两极汇聚。
1° of latitude ≈ 111 km
1° of longitude ≈ 111 km × cos(latitude)
纬度1° ≈ 111 km
经度1° ≈ 111 km × cos(纬度)
At the equator (0°), cos(0) = 1, so 1° longitude is about 111 km. At 60°N, cos(60°) = 0.5, making 1° longitude roughly 55.5 km. These relationships help when drawing sketch maps or comparing the distances between cities located on the same parallel. For precise work, use the exact formula with the Earth’s radius (6 371 km).
在赤道（0°），cos(0) = 1，1°经度约为111 km。在北纬60°，cos(60°) = 0.5，1°经度约55.5 km。绘制示意图或比较同纬线上城市间的距离时，这些关系就很有用了。精确计算时，可使用地球半径（6 371 km）的精确公式。
10. Calculating Percentage Change | 计算百分比变化
Geographers frequently use percentage change to describe how a value has grown or shrunk over time – for instance, population increase, change in forest cover or variation in annual rainfall. The formula compares the difference between the new and old values with the original value.
地理学家经常用百分比变化来描述数值随时间增长或减少的幅度，例如人口增长、森林覆盖率变化或年降水量的变动。该公式比较的是新旧值之差相对于原始值的比例。
Percentage Change = [(New Value − Original Value) ÷ Original Value] × 100%
百分比变化 = [(新值 − 原值) ÷ 原值] × 100%
If a town’s population was 12 000 in 2010 and 15 000 in 2020, the change = (15 000 − 12 000) ÷ 12 000 × 100% = (3 000 ÷ 12 000) × 100% = 25%. A negative result would indicate a decrease. Be careful to use the original (earlier) value as the denominator; otherwise the interpretation will be incorrect. This formula appears in population, economic and environmental geography questions.
如果某镇人口在2010年为12 000，2020年为15 000，变化 = (15 000 − 12 000) ÷ 12 000 × 100% = (3 000 ÷ 12 000) × 100% = 25%。负结果则表示下降。注意一定要用原值（较早的值）作为分母，否则得出错误的解读。这个公式广泛出现在人口、经济和环境地理的试题中。
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