📚 Year 9 CCEA Geography: Formula and Theorem Quick Reference Handbook | CCEA 九年级地理公式定理速查手册
Welcome to your essential quick reference for all the key formulas and theorems you'll encounter in the Year 9 CCEA Geography curriculum. This handbook covers map skills, population, settlement, rivers, and coasts, providing clear formulas and worked examples to support your revision and exam preparation.
欢迎使用这本速查手册，它涵盖了 CCEA 九年级地理课程中所有关键的公式和定理。本手册包括地图技能、人口、聚落、河流和海岸等内容，提供清晰的公式和解题范例，助力你的复习和考试准备。
1. Map Scales: Converting Map Distance to Real Distance | 地图比例尺：图上距离与实际距离的换算
The scale of a map tells you the relationship between a distance on the map and the corresponding distance on the ground. It is expressed as a ratio, a written statement, or a linear scale. Always check the scale before making any measurements.
地图比例尺表示图上距离与相应地面上实际距离之间的关系。比例尺通常以比值、文字说明或直线比例尺的形式表示。在进行任何测量之前，请务必先查看比例尺。
0 and the map distance is 8 cm, the real distance is 8 cm × 50,000 = 400,000 cm, which is 4,000 m or 4 km. Remember to convert units appropriately: 100 cm = 1 m, 1,000 m = 1 km.
将图上距离转换为实际地面距离的公式为：实际距离 = 图上距离 × 比例尺分母。例如，若比例尺为 1:50,000，图上距离为 8 厘米，则实际距离 = 8 厘米 × 50,000 = 400,000 厘米，即 4,000 米或 4 公里。请注意正确换算单位：100 厘米 = 1 米，1,000 米 = 1 公里。
When measuring a curved distance, such as a winding river, use a piece of string to trace the curves, then measure the length of the string against the linear scale or calculate using the map scale. This method allows you to handle irregular lines accurately.
测量弯曲距离时（例如蜿蜒的河流），可用一根细绳沿着曲线描摹，然后将绳子的长度与直线比例尺比对，或利用地图比例尺进行计算。这种方法能帮你准确处理不规则的线状物体。
2. Area Calculation: Grid Squares and Irregular Shapes | 面积计算：网格方格与不规则图形
On Ordnance Survey maps, each grid square typically represents an area of 1 km². By counting the number of full and partial squares within a designated area, you can estimate the ground area. Remember that each grid square is formed by lines spaced 1 km apart, so one square equals 1 km².
在军械测量局地图上，每个网格方格通常代表 1 平方公里的面积。通过数出指定区域内完整和部分方格的数量，可以估算出地面面积。请记住，每个网格方格由间隔 1 公里的格网线构成，因此一个方格等于 1 平方公里。
For irregular shapes, apply the 'dot grid' or 'square counting' method. If more than half of a square is covered, count it as one; if less than half, ignore it. Alternatively, divide the area into simpler geometric shapes like rectangles and triangles, calculate each area, and sum them up. Always express the answer in km².
对于不规则图形，可采用“点格法”或“方格计数法”。若一个方格有一半以上被覆盖，则计为 1 个完整方格；若不足一半，则忽略不计。另一种方法是，将区域划分为矩形和三角形等简单几何图形，分别计算面积，然后相加。最终答案应以平方公里表示。
| Shape / 图形 | Area Formula / 面积公式 |
|---|---|
| Rectangle / 矩形 | Length × Width / 长 × 宽 |
| Triangle / 三角形 | ½ × Base × Height / ½ × 底 × 高 |
| Square / 正方形 | Side × Side / 边长 × 边长 |
3. Gradient: Measuring Slope Steepness | 坡度：测量斜坡陡峭程度
Gradient describes the steepness of a slope, typically expressed as a ratio like 1:10. It is calculated by dividing the vertical interval (difference in height) by the horizontal equivalent (distance on the ground). Both must be in the same units before division.
坡度表示斜坡的陡峭程度，通常用如 1:10 的比率表示。计算方法是垂直高差（高度差）除以水平距离（地面距离）。在相除之前，两者必须换算为相同的单位。
VI is 100 m and HE is 2,000 m, the gradient is 100 m ÷ 2,000 m = 1/20, expressed as 1:20. A steeper slope will have a smaller denominator (e.g., 1:5 is steeper than 1:20).
基本公式为：坡度 = 垂直高差 (VI) ÷ 水平距离 (HE)。将比率化简，使分子为 1。例如，若 VI 为 100 米，HE 为 2,000 米，则坡度 = 100 米 ÷ 2,000 米 = 1/20，表示为 1:20。坡度越陡，分母越小（如 1:5 比 1:20 更陡）。
Gradient = VI ÷ HE
坡度 = 垂直高差 ÷ 水平距离
On contour maps, identify two contour lines, note their heights to find the VI, then measure the horizontal distance between them using the map scale. Ensure you convert the distance to the same unit as the height (usually metres).
在等高线地图上，选择两条等高线，记录其高程以求出垂直高差，然后利用比例尺测量它们之间的水平距离。务必把距离单位转换为与高程相同的单位（通常为米）。
4. Population Density: People per Square Kilometre | 人口密度：每平方公里人口数
Population density measures how crowded an area is. It is one of the most fundamental demographic formulas in geography. The calculation requires total population and the land area in square kilometres.
人口密度衡量一个地区的拥挤程度。这是地理学中最基本的人口统计公式之一。计算时需要总人口和以平方公里为单位的土地面积。
ity of 200,000 ÷ 50 = 4,000 people per km². Always check the area unit; if given in hectares or square metres, convert to km² first (1 km² = 100 ha).
公式：人口密度 = 总人口 ÷ 土地总面积（平方公里）。例如，一个城市有 200,000 人口，面积为 50 平方公里，则人口密度为 200,000 ÷ 50 = 4,000 人/平方公里。务必检查面积单位；若以公顷或平方米给出，需先转换为平方公里（1 平方公里 = 100 公顷）。
Population Density = Total Population ÷ Area
人口密度 = 总人口 ÷ 面积
High population densities (e.g., > 1,000 people/km²) often correspond to urban or fertile lowland regions, while low densities (< 10 people/km²) are typical of deserts, mountains, or polar areas.
高人口密度（如 > 1,000 人/平方公里）通常出现在城市或肥沃的低地地区，而低人口密度（< 10 人/平方公里）则常见于沙漠、山区或极地地区。
5. Population Growth Rate: Birth, Death, and Migration | 人口增长率：出生、死亡与迁移
Population change is driven by natural change (births minus deaths) and net migration (immigrants minus emigrants). The growth rate is often expressed as a percentage. This formula helps geographers understand how fast a population is expanding or shrinking.
人口变动由自然变动（出生减死亡）和净迁移（迁入减迁出）驱动。增长率通常以百分比表示。这个公式帮助地理学家了解人口增长或萎缩的速度。
Basic natural increase is calculated as: Crude Birth Rate (CBR) – ge, divide the result by 10. Full population growth rate includes migration: Growth Rate (%) = [(CBR – CDR)/10] + Net Migration Rate (as a %). Net migration rate is (immigrants – emigrants) / total population × 100.
基本自然增长的计算方法为：粗出生率（每千人中出生人数）减去粗死亡率（每千人中死亡人数）。若要以百分比表示，则将结果除以 10。全面的人口增长率则包含迁移因素：增长率 (%) = [(粗出生率 – 粗死亡率)/10] + 净迁移率 (%)。净迁移率 = (迁入人口 – 迁出人口) / 总人口 × 100。
For example, if CBR = 25/1000, CDR = 12/1000, net migration rate = +0.5%, then growth rate = (25 – 12)/10 + 0.5 = 1.3% + 0.5% = 1.8%.
例如，若粗出生率为 25/1000，粗死亡率为 12/1000，净迁移率为 +0.5%，则增长率 = (25 – 12)/10 + 0.5 = 1.3% + 0.5% = 1.8%。
6. Dependency Ratio: Balancing the Non-Working Age Groups | 抚养比：非劳动年龄人口与劳动年龄人口之比
The dependency ratio compares the economically dependent part of the population (youth aged 0–14 and elderly aged 65+) with the working-age population (15–64). It highlights the pressure on the productive segment of society.
抚养比将经济上依赖他人的群体（0–14 岁青少年和 65 岁及以上老年人口）与劳动年龄人口（15–64 岁）进行比较。它反映了社会生产性群体所承受的压力。
Formula: Dependency Ratio = [(Number of people aged 0–14 + Number of people aged 65+) ÷ Number of people aged 15– elderly, and 1,000,000 working-age, then DR = [(300,000 + 200,000) / 1,000,000] × 100 = 50%.
公式：抚养比 = [(0–14 岁人口数 + 65 岁及以上人口数) ÷ 15–64 岁人口数] × 100。结果以百分比表示；比率越高，意味着每 100 名劳动者需要抚养的人数越多。例如，若某国有 30 万青少年、20 万老年人和 100 万劳动年龄人口，则抚养比 = [(300,000 + 200,000) / 1,000,000] × 100 = 50%。
Youth dependency and old-age dependency can also be calculated separately to understand the structure of demand on services like schools and healthcare.
少儿抚养比和老年抚养比也可分别计算，以了解教育和医疗等服务的需求结构。
7. Settlement Hierarchy: Threshold Population and Sphere of Influence | 聚落等级体系：门槛人口与影响范围
Settlements are arranged in a hierarchy based on size and the services they provide. The concept of threshold population refers to the minimum number of people needed to support a service. If the population falls below the threshold, the service may close.
聚落根据其规模和提供的服务形成等级体系。门槛人口这一概念指的是维持某项服务所需的最低人口数量。如果人口低于门槛，该服务就可能关闭。
Sphere of influence is the area from which a settlement draws its customers or users. It is influenced by the range of a good or service — the maximum distance people are willing to travel to obtain it. High-order goods (e.g., furniture, jewellery) have a large range and high threshold, while low-order goods (e.g., bread, newspapers) have a small range and low threshold.
影响范围是指聚落吸引顾客或用户的区域。它受商品或服务的服务范围影响——即人们愿意为获得该服务而赶路的极限距离。高级商品（如家具、珠宝）服务范围大、门槛高，而低级商品（如面包、报纸）服务范围小、门槛低。
No single formula gives the sphere of influence directly, but it can be estimated by drawing circles or polygons around central places and measuring the distance travelled by consumers. Geographers use models like Christaller's Central Place Theory to understand this hierarchy.
虽然没有直接给出影响范围的单一公式，但可以通过围绕中心地画圆或多边形，并测量消费者移动的距离来估算。地理学家利用克里斯塔勒的中心地理论等模型来理解这种等级关系。
8. River Discharge: Calculating the Flow of Water | 河流流量：计算水流
River discharge is the volume of water flowing through a river channel cross-section per second, measured in cubic metres per second (m³/s). It is a crucial concept in understanding river dynamics and flooding.
河流流量是指每秒通过河道横截面的水体积，单位为立方米每秒 (m³/s)。这是理解河流动力学和洪水灾害的关键概念。
by multiplying average depth by width of the channel (A = width × mean depth). Velocity can be measured using a flowmeter or by timing a floating object over a known distance.
流量的计算公式为：流量 (Q) = 横截面积 (A) × 平均流速 (V)。横截面积通过平均水深乘以河宽求得（面积 = 宽度 × 平均深度）。流速可使用流速仪测量，或通过计时漂浮物通过已知距离来测算。
Q = A × V
流量 = 横截面积 × 平均流速
and Q = 20 × 0.5 = 10 m³/s. Discharge increases downstream as tributaries add more water.
对于一个典型的河段，若宽度为 10 米，平均水深为 2 米，流速为 0.5 米/秒，则横截面积 = 10 × 2 = 20 平方米，流量 = 20 × 0.5 = 10 立方米/秒。随着支流汇入，下游的流量会增大。
9. Drainage Basin Terminology and the Hydrological Cycle | 流域术语与水文循环
A drainage basin is an area of land drained by a river and its tributaries. The boundary of a drainage basin is called the watershed. While not a formula, knowing these terms is essential for understanding river systems and calculating water budgets.
流域是指由一条河流及其支流排水的陆地区域。流域的边界称为分水岭。尽管这些不是公式，但了解这些术语对于理解河流系统和计算水量平衡至关重要。
vapotranspiration (E) + Runoff (Q) + Change in Storage (ΔS). Runoff includes both surface runoff and groundwater flow. This equation shows how water moves through a drainage basin.
简单的水量平衡方程可表示为：降水量 (P) = 蒸发蒸腾量 (E) + 径流量 (Q) + 蓄水量变化 (ΔS)。径流包括地表径流和地下水流。该方程显示了水在流域中的运动方式。
P = E + Q + ΔS
降水量 = 蒸发蒸腾量 + 径流量 + 蓄水量变化
= E + Q. This means roughly that precipitation is either evaporated or turned into runoff.
在许多情况下，长期来看蓄水量变化可假定为零，方程简化为 P = E + Q。这大致意味着降水要么蒸发，要么转化为径流。
10. Coastline Erosion and Deposition: Longshore Drift and Sediment Budget | 海岸侵蚀与沉积：沿岸漂沙与泥沙收支
Longshore drift is the movement of sediment along the coast by waves approaching at an angle. It follows a zigzag pattern: swash carries material up the beach at an angle, and backwash returns straight down the slope due to gravity.
沿岸漂沙是指波浪以一定角度接近海岸时，沉积物沿海岸的移动。它呈之字形运动：冲流以一定角度将物质带上沙滩，回流则因重力作用沿斜坡直线返回。
No direct mathematical formula is used for longshore drift in Year 9, but the concept of sediment budget is important. A sediment budget compares inputs of sand (from rivers, cliff erosion) with outputs (removal by waves, currents). If inputs exceed outputs, the beach builds up (accretion); if outputs exceed inputs, the beach erodes.
九年级阶段没有直接用于沿岸漂沙的数学公式，但泥沙收支概念很重要。泥沙收支对比了沙的输入（来自河流、悬崖侵蚀）和输出（被海浪、海流带走）。若输入大于输出，海滩就会堆积（加积）；若输出大于输入，海滩就会受到侵蚀。
aps or photos, providing a simple formula: Erosion Rate = Total Retreat ÷ Number of Years.
海岸侵蚀速率可用年均后退距离表示（如 1 米/年）。通常通过对比历史地图或照片来测算，简单公式为：侵蚀速率 = 总后退距离 ÷ 年数。
11. Weather and Climate: Mean, Range, and Total Rainfall | 天气与气候：平均值、变幅与总降雨量
Understanding climatic data requires basic statistical formulas. These help you describe temperature and rainfall patterns from weather station data.
理解气候数据需要掌握基本的统计公式。这些公式帮助根据气象站数据描述气温和降水模式。
Daily or monthly mean temperature: Sum of all temperature readings ÷ Number of readings. Diurnal temperature range: maximum daily temperature – minimum daily temperature. Annual temperature range: highest monthly mean temperature – lowest monthly mean temperature. Total annual rainfall: sum of 12 monthly rainfall totals.
日或月平均气温：所有温度读数之和 ÷ 读数数量。日较差：当日最高气温 – 当日最低气温。年较差：最热月平均气温 – 最冷月平均气温。年降水总量：12 个月的月降水量之和。
Mean = Σx ÷ n
平均值 = 总和 ÷ 项数
Range = Max value – Min value
变幅 = 最大值 – 最小值
These calculations allow you to construct climate graphs, which display temperature as a line graph and rainfall as bar chart for each month. Always label axes clearly and use consistent scales.
这些计算能帮你绘制气候图，通常用折线图表示温度，用条形图表示每月的降水量。务必清楚标注坐标轴，并使用一致的刻度。
12. Geographic Information Systems (GIS) and Data Interpretation | 地理信息系统与数据解读
GIS is used to store, analyse, and display geographic data. While not a formula handbook, you need to be able to interpret graphs, charts, and map layers. Simple concepts like interpolation and density mapping are often used.
地理信息系统用于存储、分析和显示地理数据。虽然这不是一本公式手册，但你需要能够解读图表、统计图和地图图层。诸如插值和密度制图等简单概念经常用到。
ibute value ÷ Number of dots. If a dot map shows 500 dots for a region with 1,000,000 people, each dot represents 2,000 people. This is a key skill in interpreting thematic maps.
例如，点密度图使用一个公式来确定每个点代表的值：点值 = 总属性值 ÷ 点数量。如果一幅点密度图用 500 个点表示一个有 1,000,000 人口的区域，那么每个点代表 2,000 人。这是解读专题地图的一项关键技能。
. For circles, Area = π × r², so to make one symbol twice the value, you multiply the radius by √2 (approximately 1.414).
类似地，使用比例符号地图时，符号的面积与数据值成正比。简单方法采用正方形或圆形。对于圆形，面积 = π × r²，因此若要使一个符号代表的值为另一个的两倍，应将半径乘以 √2（约 1.414）。
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