📚 Year 7 CIE Geography: Quick Reference Handbook of Formulas and Theorems | Year 7 CIE 地理：公式定理速查手册
This handbook provides a concise summary of the essential formulas, key principles and mapwork techniques you need for the Year 7 CIE Geography course. Whether you are measuring distance on a 1:25,000 Ordnance Survey map, calculating population density or interpreting climate graphs, the quick-reference format will help you revise efficiently.
本手册为 Year 7 CIE 地理课程中必备的公式、关键原理和地图技能提供了简明总结。无论你是在 1:25,000 地形图上测量距离、计算人口密度，还是解读气候图表，这份速查手册都能帮助你高效复习。
1. Map Scale and Conversions | 地图比例尺与换算
A map scale expresses the relationship between a distance on the map and the corresponding distance on the ground. It can be shown as a statement (e.g. ‘1 cm to 1 km’), a linear scale (a ruler-like bar) or a representative fraction (RF) such as 1:50,000.
地图比例尺表示图上距离与对应实地距离的关系。它可以用文字说明（如“图上1厘米代表实地1千米”）、线性比例尺（标尺状图形）或数字比例尺（如1:50,000）表示。
The core formula for all scale conversions is:
所有比例尺换算的核心公式为：
Map Distance (cm) / Actual Distance (cm) = 1 / Scale Denominator
To find actual distance, measure the map distance in centimetres and multiply by the denominator. For a 1:25,000 map, 4 cm on the map equals 4 × 25,000 = 100,000 cm, which is 1000 m or 1 km. Always convert your answer to the most sensible unit.
要计算实地距离，先量出图上厘米距离，再乘以比例尺分母。例如在 1:25,000 地图上，图上 4 cm 代表 4 × 25,000 = 100,000 cm，即 1000 米或 1 千米。答题时始终将结果转换为最合理的单位。
Remember that 100 cm = 1 m, 100,000 cm = 1 km, and 1 km = 1000 m. Using these conversion factors prevents errors when changing between units.
请记住：100 cm = 1 m，100,000 cm = 1 km，1 km = 1000 m。使用这些换算因子可避免单位转换时出错。
2. Measuring Straight-Line Distance on a Map | 地图上的直线距离测量
Straight-line distance (‘as the crow flies’) is measured by placing the edge of a piece of paper between two points, marking the positions, and then aligning the paper against the linear scale. You can also use a ruler to measure the centimetre distance and apply the scale formula.
直线距离（“飞鸟距离”）的测量方法是将一张纸的边缘放在两点之间，标记位置，再将纸对准线性比例尺读数。你也可以用直尺量出厘米距离，然后套用比例尺公式进行换算。
If you are given the RF, use the calculation:
如果题目给出数字比例尺，请使用下列计算：
Actual distance (m) = measured length (cm) × Scale Denominator ÷ 100
For example, a 4.3 cm measurement on a 1:10,000 map gives: 4.3 × 10,000 ÷ 100 = 430 m. Always double-check whether the answer should be in metres or kilometres.
例如，在 1:10,000 地图上量得 4.3 cm，实地距离 = 4.3 × 10,000 ÷ 100 = 430 m。务必检查答案应以米还是千米为单位。
For curved distances, a piece of string or the ‘tick’ method along a road is used. Measure the string’s length, then apply the scale calculation in exactly the same way.
对于弯曲距离，则沿道路使用细线或“分段截取”法，然后测量线的长度，再按同样方式套用比例尺计算即可。
3. Calculating Area from Grid Squares | 利用网格方格计算面积
On many CIE map extracts, grid squares measure 1 km × 1 km, giving an area of 1 km² per square. To find the area of an irregular feature, count the number of complete squares and then add half the number of incomplete (partial) squares that are mostly covered by the feature.
在许多 CIE 地图摘录中，网格方格为 1 km × 1 km，每个方格面积为 1 km²。要计算不规则地物的面积，先数出完整方格数，再加上大部分被地物覆盖的不完整（部分）方格数量的一半。
The straightforward formula is:
其直接公式为：
Area (km²) ≈ (Number of full squares) + (½ × Number of partial squares)
For example, a forest covers 12 full squares and 8 partial squares. Estimated area = 12 + (½ × 8) = 12 + 4 = 16 km². Be careful when the map scale is not 1 km grids – in that case you must first work out the real area of one square using the scale.
例如一片森林覆盖 12 个完整方格和 8 个部分方格。估算面积 = 12 + (½ × 8) = 12 + 4 = 16 km²。当地图比例尺不是每格 1 km 时务必注意——这种情况下必须先利用比例尺算出一个方格代表的实地面积。
4. Gradient and Slope Steepness | 坡度与陡峭程度
Gradient measures how steep a slope is. It compares the vertical rise (change in height) to the horizontal distance between two points. On a contour map, the rise is the difference in contour values, while the horizontal distance is measured along the ground using the scale.
坡度用来衡量斜坡的陡峭程度，比较两点间的垂直升高与水平距离。在等高线地图中，升高值为两点等高线读数之差，水平距离则借助比例尺沿地面量得。
The gradient formula, often expressed as a ratio or percentage, is:
坡度公式通常表现为比值或百分比，写作：
Gradient = Vertical Rise (m) ÷ Horizontal Distance (m)
To write it as a ratio (1:R), divide both numbers by the rise so that the rise becomes 1. If the rise is 25 m and the horizontal distance is 500 m, gradient = 25/500 = 1/20 = 1:20. As a percentage: (25 ÷ 500) × 100 = 5%.
若要以 1:R 比值表示，将两数同时除以升高值，使升高值变为 1。若升高 25 m，水平距离 500 m，坡度 = 25/500 = 1/20 = 1:20。百分数则为 (25 ÷ 500) × 100 = 5%。
A 1:5 slope is much steeper than a 1:50 slope. For CIE exams, always ensure both measurements are in the same unit (usually metres) before dividing.
1:5 的坡度远陡于 1:50 的坡度。在 CIE 考试中，务必确保两项测量值单位一致（通常为米）后再进行除法运算。
5. Compass Points and Bearings | 罗盘方位点与方位角
Direction on a map is described using compass points or bearings. The 8-point compass includes north (N), northeast (NE), east (E), southeast (SE), south (S), southwest (SW), west (W) and northwest (NW). Bearings are measured in degrees clockwise from north, ranging from 0° to 360°.
地图上的方向用罗盘方位点或方位角表示。8 个基本方位点包括北 (N)、东北 (NE)、东 (E)、东南 (SE)、南 (S)、西南 (SW)、西 (W) 和西北 (NW)。方位角是从正北顺时针测得的度数，范围从 0° 到 360°。
To measure a grid bearing, draw a line between the two points, place a protractor with the 0° line pointing to grid north (the vertical blue lines on the map), and read the angle clockwise. A bearing of 045° means northeast, 180° means south, and 315° means northwest.
测量网格方位角时，先连接两点，将量角器的 0° 线对准网格北（地图上垂直的蓝线），然后顺时针读出角度。045° 为东北，180° 为正南，315° 为西北。
No complex formula is needed, but remember this relationship: from a bearing you can find the opposite (back) bearing by adding or subtracting 180°. If the bearing is less than 180°, add 180°; if more than 180°, subtract 180°.
无需复杂公式，但请记住这一关系：由方位角求反向方位角可通过加减 180° 实现。原方位角小于 180° 时加 180°，大于 180° 则减 180°。
6. Contour Lines and Vertical Exaggeration | 等高线与垂直夸大
Contour lines join points of equal height. Closely spaced contours indicate a steep slope; widely spaced contours show a gentle slope. When drawing a cross-section, you plot the heights on graph paper to see the shape of the land.
等高线连接高度相等的各点。等高线密集表示陡坡，疏落表示缓坡。绘制剖面图时，将各点高度点到坐标纸上便能看出地形起伏。
Because the vertical scale of a cross-section is usually larger than the horizontal scale, slopes appear steeper. Vertical exaggeration (VE) quantifies this distortion:
由于剖面图的垂直比例尺通常大于水平比例尺，坡面会显得更陡。垂直夸大 (VE) 用于量化这种变形：
Vertical Exaggeration (VE) = Vertical Scale ÷ Horizontal Scale
Both scales must be expressed as representative fractions or the same unit ratio. If the horizontal scale is 1:50,000 (i.e., 1 cm = 0.5 km) and the vertical scale is 1 cm = 100 m (1:10,000), then VE = (1/10,000) ÷ (1/50,000) = 5. This means the vertical dimension is 5 times larger than the horizontal, making slopes look five times steeper than they really are.
两种比例尺均须用数字比例尺或相同的单位比值表示。若水平比例尺为 1:50,000（即 1 cm 代表 0.5 km），垂直比例尺为 1 cm 代表 100 m（1:10,000），则 VE = (1/10,000) ÷ (1/50,000) = 5。这意味着垂直方向放大了 5 倍，斜坡看起来比实际陡峭 5 倍。
7. Population Density | 人口密度
Population density describes how crowded an area is, linking total population to land area. It helps geographers compare the concentration of people in different regions or countries.
人口密度描述一个地区的拥挤程度，反映总人口与土地面积的关系，帮助地理学家比较不同区域或国家的人口集中度。
The simple, powerful formula is:
其简洁而实用的公式为：
Population Density = Total Population ÷ Total Land Area (km²)
For instance, if a city has 250,000 inhabitants in an area of 50 km², its density = 250,000 ÷ 50 = 5000 people per km². A rural area with 200 people per km² is much less densely populated. Always express density as persons per square kilometre (p/km²).
例如，一座城市有 25 万人口，面积 50 km²，密度 = 250,000 ÷ 50 = 5000 人/km²。而一个密度为 200 人/km² 的乡村地区则远没有那么稠密。密度始终以每平方千米人数表示 (人/km²)。
When comparing areas, remember that very large regions (like the whole of Australia) can have a low average density even though most people live in a few cities. Always look for the pattern, not just the number.
进行比较时要注意，像整个澳大利亚这样的大区域平均密度可能很低，但多数人口却集中在少数城市。务必关注分布格局，而不只是看数字。
8. Climate Graph Summary Statistics | 气候图表汇总统计
Climate graphs (climographs) display monthly temperature and precipitation data on the same chart. From a climate table you can calculate average annual temperature, annual temperature range and total annual rainfall.
气候图表（气候图）将月气温和降水量数据绘制在同一张图上。根据气候数据表，你可以计算年平均气温、气温年较差和年总降水量。
The three most useful climate formulas are:
三个最常用的气候统计公式为：
Mean Annual Temperature = Sum of 12 monthly mean temperatures ÷ 12
Annual Temperature Range = Highest monthly mean − Lowest monthly mean
Total Annual Precipitation = Sum of 12 monthly precipitation totals
For example, if the January mean is -4°C and the July mean is 18°C, the range is 22°C. A small range suggests a maritime climate; a large range often indicates a continental location. Total rainfall is usually given in millimetres (mm).
例如 1 月均温 -4°C，7 月均温 18°C，则年较差为 22°C。较小的较差通常指示海洋性气候，较大的较差则往往反映大陆性位置。总降水量一般以毫米 (mm) 为单位。
When plotting the graph, remember that temperature is shown as a smooth line (left axis, °C) and rainfall as bars (right axis, mm). Always label axes clearly and use a consistent scale.
绘制气候图时记住，气温用平滑曲线表示（左轴，°C），降水量用柱状表示（右轴，mm）。坐标轴要标注清楚，并使用统一的分度值。
9. River Velocity and Discharge (Basics) | 河流流速与流量（基础）
Even at Year 7 level, CIE introduces simple methods to measure how fast a river flows and how much water it carries. Velocity is the speed of the water, and discharge is the volume of water passing a point each second.
即使在 Year 7 阶段，CIE 也会引入测量河流流速和流量的简单方法。流速是水流速度，流量是每秒钟通过某断面的水量。
The fundamental formulas in their most basic form are:
其最基本形式的公式为：
Velocity = Distance travelled by a float ÷ Time taken
Discharge = Cross-sectional area × Velocity
If a cork travels 10 metres in 20 seconds, velocity = 10 m ÷ 20 s = 0.5 m/s. Cross-sectional area is estimated by multiplying average width by average depth at a site. So if the channel is 4 m wide and averages 0.5 m deep, the cross-section area is about 2 m², making discharge ≈ 2 m² × 0.5 m/s = 1 m³/s.
若一片软木塞 20 秒钟流经 10 米，流速 = 10 m ÷ 20 s = 0.5 m/s。横截面积通过测站平均宽度乘以平均水深估算。若河道宽 4 米，平均水深 0.5 米，则截面积约 2 m²，流量 ≈ 2 m² × 0.5 m/s = 1 m³/s。
You will not be tested on full discharge calculations in Year 7, but understanding the relationship is key. Higher velocity and larger cross-section both increase discharge, which is why rivers are stronger near their mouths.
Year 7 考试不要求进行完整的流量计算，但理解其关系至关重要。较高的流速和较大的横截面积都会增大流量，这正是河流在河口附近能量更强的原因。
10. Central Place Theory and Settlement Hierarchy | 中心地理论与定居点等级
Central Place Theory, developed by Walter Christaller, explains how settlements of different sizes are spaced and how they provide services to surrounding areas. It is a key theorem for understanding shopping patterns, service provision and urban hierarchy.
克里斯泰勒的中心地理论解释了不同规模的定居点如何分布，以及它们如何为周边区域提供服务。这是理解购物模式、服务供给和城镇等级体系的关键定理。
The theory’s ‘rule’ can be summarised using two main concepts: the settlement hierarchy and the sphere of influence. The hierarchy is often remembered as: hamlet, village, town, city. The sphere of influence (or market area) is the distance people are willing to travel for a service.
该理论的“法则”可用两个主要概念概括：定居点等级和影响范围。等级通常可记为：小村、村庄、镇、城市。影响范围（市场区）指人们愿意为某项服务出行的距离。
The classic interconnected patterns (K-values) describe settlement arrangement:
经典的互相关联模式 (K 值) 描述了定居点的排列方式：
K=3 (marketing principle): each central place serves three lower-order places
K=4 (transport principle): settlements align along transport routes
K=7 (administrative principle): larger centres surround smaller ones in a nested hexagon
In CIE Year 7 Geography, you are expected to recognise that higher-order settlements (e.g. cities) offer a wider range of goods and services and have larger spheres of influence, while lower-order places (villages) provide basic services. The theory helps you explain why people travel longer distances to access a hospital than a convenience store.
CIE Year 7 地理要求你认识到，高等级定居点（如城市）提供更广泛的商品和服务，并拥有更大的影响范围；低等级定居点（村庄）只提供基本服务。这一理论能帮助你解释为什么人们去医院要走更远，而去便利店路程则短得多。
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