📚 Year 7 Cambridge Geography: Formula & Theorem Quick Reference Handbook | 七年级剑桥地理：公式定理速查手册
This quick reference handbook gathers all the essential formulas, theorems, and calculation methods you will meet in the Year 7 Cambridge Geography course. Mastering these tools will help you work accurately with maps, population data, weather statistics, and landform profiles. Keep this guide handy whenever you practise map skills, analyse demographic figures, or construct climate graphs.
本速查手册汇集了七年级剑桥地理课程中你将遇到的所有重要公式、定理和计算方法。掌握这些工具能帮助你准确处理地图、人口数据、天气统计和地形剖面。无论你何时练习地图技能、分析人口数据或绘制气候图，都可以随时参考本手册。
1. Map Scale Types and Formula | 地图比例尺类型与公式
Scale expresses the relationship between a distance on a map and the corresponding distance on the ground. There are three ways to show scale: statement scale (e.g. 1 cm represents 1 km), representative fraction or RF (e.g. 1:100 000), and a linear scale (a divided line). No matter which type is used, the core formula remains the same.
比例尺表示地图上的距离与地面上相应距离的关系。显示比例尺的方式有三种：文字式（例如1厘米代表1公里）、分数式或 RF（例如1:100 000）以及线段比例尺（一条等分线段）。无论使用哪种类型，核心公式都是一样的。
Scale = Map Distance ÷ Ground Distance
To use this formula correctly, both distances must be expressed in the same unit. If a map shows a road as 5 cm long and the actual road is 2.5 km, first convert 2.5 km to 250 000 cm. Then scale = 5 cm ÷ 250 000 cm = 1:50 000.
要正确使用这个公式，两个距离必须用相同的单位表示。如果地图上一条路长为5厘米，而实际道路长2.5公里，先将2.5公里转换为250 000厘米。那么比例尺 = 5厘米 ÷ 250 000厘米 = 1:50 000。
2. Measuring Straight-Line Distance | 测量直线距离
Straight-line distance between two points on a map is found by measuring the length of the line joining them and then converting it using the map scale. You can use a ruler to measure in centimetres (cm) or millimetres (mm).
地图上两点之间的直线距离是通过测量连接它们的线段的长度，然后利用地图比例尺换算得到的。你可以用直尺测量厘米或毫米数。
Real Distance = Map Distance × Scale Factor
If the scale is 1:50 000, then 1 cm on the map equals 50 000 cm on the ground, which is 0.5 km. If you measure 7.2 cm on the map, the real straight-line distance is 7.2 × 50 000 cm = 360 000 cm = 3.6 km. Always state the final answer in kilometres or metres as appropriate.
如果比例尺是1:50 000，那么地图上的1厘米等于地面上的50 000厘米，即0.5公里。如果你在地图上量得7.2厘米，实际的直线距离就是7.2 × 50 000厘米 = 360 000厘米 = 3.6公里。最后答案要根据情况用公里或米表示。
3. Calculating Area on a Map | 地图上的面积计算
The area of a feature shown on a map can be estimated by treating the shape as a regular figure or by counting grid squares. For rectangles, use length × width, but remember to convert both sides to ground distances first.
地图上某地物的面积可以通过将其视为规则图形或数方格的方法来估算。对于矩形，使用长×宽，但请记住先要将两者都换算为地面距离。
Ground Area = (Map Length × Scale) × (Map Width × Scale)
For an irregular shape, place a transparent grid over the map. Count the full squares and combine part squares to estimate the total number of map squares. Then multiply by the area each square represents on the ground.
对于不规则形状，可在地图上覆盖一张透明方格纸。数出完整方格，并把部分方格合并起来，估算出总的地图方格数。然后乘以每个方格在地面上代表的面积。
4. Gradient (Slope) Calculation | 坡度（梯度）计算
Gradient measures the steepness of a slope, often used when reading contour lines on a topographic map. It is the ratio of the vertical rise (vertical interval) to the horizontal distance (horizontal equivalent).
坡度用来量度斜坡的陡峭程度，常在阅读地形图的等高线时使用。它是垂直升高量（垂直间隔）与水平距离（水平等值）之比。
Gradient = Vertical Interval (VI) ÷ Horizontal Equivalent (HE)
Both quantities must be in the same unit. If the contour interval between two points is 100 m and the horizontal distance measured on the map (converted to metres) is 500 m, the gradient is 100 ÷ 500 = 1:5. A gradient of 1:5 is very steep; a gentle slope might be 1:20 or less.
这两个量必须使用相同的单位。如果两点间的等高距为100米，而在地图上量得并换算的水平距离为500米，则坡度 = 100 ÷ 500 = 1:5。1:5的坡度非常陡；平缓的坡度可能是1:20或更小。
5. Population Density | 人口密度
Population density describes how crowded an area is. It is the average number of people living on one square unit of land, usually expressed as people per square kilometre (people/km²).
人口密度描述一个地区的拥挤程度。它是单位面积土地上居住的平均人数，通常以每平方公里的人数（人/平方公里）表示。
Population Density = Total Population ÷ Area (km²)
For example, a town of 45 000 people covering an area of 15 km² has a population density of 45 000 ÷ 15 = 3000 people/km². Remember that areas must be in square kilometres to get the standard unit.
例如，一个人口为45 000人、面积为15平方公里的小镇，其人口密度为45 000 ÷ 15 = 3000人/平方公里。请记住，面积必须使用平方公里才能得到标准单位。
6. Natural Increase Rate | 自然增长率
The natural increase rate shows how much the population grows or shrinks from births and deaths alone, without considering migration. It is usually given as a percentage.
自然增长率显示仅由出生和死亡（不考虑迁移）造成的人口增长或减少的程度，通常以百分比表示。
Natural Increase Rate (%) = ((Births − Deaths) ÷ Total Population) × 100
If a country has 500 000 births and 200 000 deaths in a year, and its mid‑year population is 10 000 000, the natural increase is (500 000 − 200 000) = 300 000. Then the rate is (300 000 ÷ 10 000 000) × 100 = 3%. A positive rate means natural growth; a negative rate means natural decrease.
如果一个国家一年内有500 000人出生、200 000人死亡，年中人口为10 000 000人，则自然增长量为500 000 − 200 000 = 300 000人。那么增长率就是(300 000 ÷ 10 000 000) × 100 = 3%。正增长率表示自然增长；负增长率则表示自然减少。
7. Net Migration and Population Growth Rate | 净迁移与人口增长率
When migration is included, overall population change becomes a combination of natural change and net migration (immigrants minus emigrants).
当把迁移考虑在内时，总人口变化就是自然变化与净迁移（迁入者减去迁出者）的组合。
Population Growth Rate (%) = ((Births − Deaths + Net Migration) ÷ Total Population) × 100
Using the previous example: if net migration is +50 000, total change = 300 000 + 50 000 = 350 000. Growth rate = (350 000 ÷ 10 000 000) × 100 = 3.5%. This formula helps geographers understand whether a place is growing because of natural increase, migration, or both.
沿用前面的例子：如果净迁移为+50 000人，总变化量 = 300 000 + 50 000 = 350 000人。增长率 = (350 000 ÷ 10 000 000) × 100 = 3.5%。这个公式能帮助地理学家理解一个地方的增長是源于自然增长、迁移还是两者兼有。
8. Mean Temperature | 平均气温
Mean temperature is used to describe the typical temperature of a day, month or year. The daily mean is often calculated by averaging the maximum and minimum temperatures, but more accurate means use readings taken at several times throughout the day.
平均气温用来说明一日、一月或一年的典型温度。日平均气温通常将最高温度和最低温度取平均值来计算，但更精确的平均值会使用一天中多个时次的读数。
Daily Mean Temp. = (Max. Temp. + Min. Temp.) ÷ 2
For a monthly mean, sum all the daily means and divide by the number of days in that month. For an annual mean, sum the 12 monthly means and divide by 12.
要计算月平均气温，将该月所有日平均气温相加后除以该月的天数。要计算年平均气温，将12个月的月平均气温相加后除以12。
9. Temperature Range | 气温年较差/日较差
Temperature range measures the spread between the highest and lowest temperatures over a given period. This can be daily (diurnal range), monthly, or annual.
气温较差衡量的是在给定时期内最高温度与最低温度之间的差值。可以是日较差、月较差或年较差。
Range = Maximum Temperature − Minimum Temperature
If a station records a January mean of 2°C and a July mean of 22°C, the annual temperature range is 22 − 2 = 20°C. Large ranges often indicate continental climates; small ranges are typical of coastal or equatorial locations.
如果一个测站记录到1月平均气温为2°C，7月平均气温为22°C，那么年较差就是22 − 2 = 20°C。年较差大的地方通常为大陆性气候；年较差小则常见于沿海或赤道地区。
10. Annual Precipitation | 年降水量
Total annual precipitation is the sum of all the rain, snow, hail and sleet that falls over a year. It is normally measured in millimetres (mm).
年降水总量是一年中所有雨、雪、雹和霰的总和，通常以毫米为单位。
Annual Precipitation = Σ Monthly Precipitation (mm)
To find this value, add the precipitation totals for each of the 12 months. If a weather station reports 50 mm in January, 45 mm in February, … and 60 mm in December, the annual total is the sum of those 12 figures. This value is a key part of a climate graph.
要计算这个数值，将每个月的降水量加总。如果一个气象站报告1月降水量为50毫米，2月为45毫米，……，12月为60毫米，年总量就是这12个数字的总和。该数值是气候图的关键部分。
11. Vertical Exaggeration | 垂直夸大率
When drawing a cross‑section from a contour map, we often use a larger vertical scale than the horizontal scale to make relief features visible. Vertical exaggeration tells us how many times the vertical scale has been stretched compared with the horizontal scale.
在根据等高线地图绘制剖面图时，我们常常使用比水平比例尺更大的垂直比例尺，以便清晰地看到地形起伏。垂直夸大率告诉我们垂直比例尺相对于水平比例尺放大了多少倍。
Vertical Exaggeration (VE) = Vertical Scale ÷ Horizontal Scale
First express both scales as representative fractions. If the horizontal scale is 1:50 000, the vertical scale might be 1 cm represents 100 m (i.e. 1:10 000). Then VE = (1/10 000) ÷ (1/50 000) = 5. This means heights and depths appear five times steeper on the cross‑section than in reality. Always interpret the profile with this in mind.
首先将两个比例尺都表示为分数式。如果水平比例尺为1:50 000，垂直比例尺可能为1厘米代表100米（即1:10 000）。那么垂直夸大率 = (1/10 000) ÷ (1/50 000) = 5。这意味着在剖面图上，高度和深度会比实际陡峭五倍。在判读剖面图时务必牢记这一点。
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Cancel reply