Year 7 CCEA Geography: Quick Reference Formula & Theorem Handbook | CCEA 七年级地理：公式定理速查手册

📚 Year 7 CCEA Geography: Quick Reference Formula & Theorem Handbook | CCEA 七年级地理：公式定理速查手册

This handbook provides a concise summary of essential geographical formulas and concepts for Year 7 students following the CCEA curriculum. Master these to boost your map skills, data analysis, and understanding of physical and human geography.

本手册为学习 CCEA 课程的七年级学生总结了基本的地理公式与概念。掌握这些内容，可提升你的地图技能、数据分析能力以及对自然与人文地理的理解。

1. Map Scale and Distance | 地图比例尺与距离

A map scale shows the relationship between a distance on the map and the corresponding distance on the ground. There are three common types: statement scale (e.g., 1 cm to 1 km), linear scale (a bar line), and representative fraction (e.g., 1:50,000).

地图比例尺表示图上距离与实地距离的比值。常见类型有三种：文字比例尺（如 1 厘米代表 1 千米）、直线比例尺（线段式）和数字比例尺（如 1:50,000）。

To calculate the real-world distance, use the scale factor. Always convert units correctly. From centimetres to kilometres, divide by 100,000.

要计算实际距离，需使用比例尺因子。务必将单位正确转换。从厘米转换为千米，需除以 100,000。

Real Distance (km) = Map Distance (cm) × Scale Denominator ÷ 100,000

For example, on a 1:25,000 map, a distance of 4 cm represents 4 × 25,000 = 100,000 cm = 1 km.

例如，在一幅 1:25,000 的地图上，图上距离 4 厘米代表 4 × 25,000 = 100,000 厘米 = 1 千米。

Scale (Representative Fraction)	1 cm on map equals
1:10,000	100 m
1:25,000	250 m
1:50,000	500 m (0.5 km)
1:100,000	1 km

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2. Area Calculation on Maps | 地图上的面积计算

Geographers often need to estimate the area of features such as lakes, forests, or fields from a map. For regular shapes like rectangles, multiply length by width.

地理学者常需从地图上估算湖泊、森林或田地等要素的面积。对于像矩形这样的规则形状，用长乘以宽。

Area (cm² on map) = Length (cm) × Width (cm)

Then convert to real-world area using the scale squared. If the scale is 1:50,000, then 1 cm² on the map equals (50,000 × 50,000) cm² = 2,500,000,000 cm². To get m², divide by 10,000; to get km², divide by 10,000,000,000.

然后使用比例尺的平方转换为实际面积。若比例尺为 1:50,000，则图上 1 平方厘米等于（50,000 × 50,000）平方厘米 = 2,500,000,000 平方厘米。要得到平方米，除以 10,000；要得到平方千米，除以 10,000,000,000。

For irregular shapes, use a grid method: count full squares and combine part-squares to estimate total area in cm², then apply the scale conversion.

对于不规则形状，使用网格法：数出完整的格子，并估算部分格子相加得到总面积（平方厘米），再运用比例尺换算。

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3. Gradient and Slope | 梯度与坡度

Gradient describes the steepness of a slope. It is the ratio of vertical rise to horizontal distance. Often expressed as a fraction, ratio, or percentage.

梯度描述坡度的陡峭程度。它是垂直升高与水平距离的比值。通常以分数、比或百分数表示。

Gradient = Vertical Rise (m) ÷ Horizontal Distance (m)

For example, if a hill rises 30 metres over a horizontal distance of 200 metres, the gradient is 30 ÷ 200 = 0.15, which can be written as 1:6.67 (approximately) or 15%.

例如，若一座山在 200 米的水平距离上升高 30 米，梯度为 30 ÷ 200 = 0.15，可写作 1:6.67（约）或 15%。

Ensure both measurements are in the same unit. Use the contour lines to find rise, and measure the horizontal distance on the map.

确保两项测量使用相同单位。用等高线求升高，在图上量取水平距离。

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4. Contour Lines and Vertical Interval | 等高线与等高距

Contour lines join points of equal height above sea level. The vertical interval (VI) is the difference in height between two adjacent contours. It remains constant on a given map.

等高线连接海平面以上高度相等的点。等高距（垂直间隔）是相邻两条等高线之间的高度差。在一幅给定地图上，它是恒定的。

Closely spaced contours indicate a steep slope; widely spaced contours indicate a gentle slope. When contours form a V shape pointing uphill, it denotes a valley; a V pointing downhill suggests a ridge.

密集的等高线表示陡坡；稀疏的等高线表示缓坡。当等高线形成指向上坡的 V 形时，表示山谷；指向下坡的 V 形表示山脊。

Slope Steepness ∝ 1 ÷ Spacing of Contours

There is no direct numeric formula, but the smaller the horizontal gap between contours, the greater the gradient.

虽无直接数值公式，但等高线之间的水平间距越小，梯度越大。

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5. Population Density | 人口密度

Population density measures how crowded an area is. It is the number of people per unit area, usually per square kilometre (km²).

人口密度衡量一个地区的拥挤程度。它是每单位面积上的人口数量，通常以每平方千米（km²）为单位。

Population Density = Total Population ÷ Area (km²)

For instance, if a city has 2,000,000 people and covers 500 km², the density is 2,000,000 ÷ 500 = 4,000 people/km².

例如，一座城市有 2,000,000 人口，占地 500 平方千米，则密度为 2,000,000 ÷ 500 = 4,000 人/平方千米。

High density is found in urban areas, while low density occurs in rural or mountainous regions. Always check that area is in km² before calculating.

高密度见于城区，低密度出现在农村或山区。计算前始终确保面积单位为平方千米。

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6. Birth Rate and Death Rate | 出生率与死亡率

These rates help analyse population change. They are usually calculated per 1,000 people per year.

这些比率有助于分析人口变化。它们通常按每年每千人计算。

Birth Rate = (Number of Live Births ÷ Total Population) × 1,000

Death Rate = (Number of Deaths ÷ Total Population) × 1,000

If a country has a population of 10 million and records 150,000 births in a year, its birth rate is (150,000 ÷ 10,000,000) × 1,000 = 15 per 1,000.

若某国人口为 1,000 万，一年记录出生 15 万，则其出生率为（150,000 ÷ 10,000,000）× 1,000 = 每千人 15。

The natural increase rate can be found by subtracting death rate from birth rate (and often dividing by 10 to get a percentage).

自然增长率可由出生率减去死亡率得出（常再除以 10 得到百分比）。

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7. Temperature: Range and Mean | 气温：较差与平均值

Temperature data is essential for climate studies. The daily or monthly temperature range shows the variation, while the mean gives the average.

气温数据对气候研究至关重要。日或月气温较差显示变化幅度，而平均值给出平均水平。

Temperature Range = Maximum Temperature – Minimum Temperature

Mean Temperature = Sum of All Recorded Temperatures ÷ Number of Readings

For example, if the highest temperature in a day is 24 °C and the lowest is 12 °C, the daily range is 12 °C. To find the mean monthly temperature, add all daily means and divide by the number of days in the month.

例如，某日最高气温为 24 °C，最低为 12 °C，则日较差为 12 °C。求月平均气温时，将全月每日均温相加，除以该月天数。

Always include the degree Celsius symbol (°C) in your answer. Range is always a positive value.

作答时务必包含摄氏度符号（°C）。较差总是正值。

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8. Rainfall Measurement and Average | 降雨量测量与平均降雨量

Rainfall is measured in millimetres (mm) using a rain gauge. One millimetre of rainfall is equivalent to 1 litre of water per square metre.

降雨量使用雨量计以毫米（mm）为单位测量。1 毫米降雨量相当于每平方米 1 升水。

Total Monthly Rainfall = Sum of Daily Rainfalls in the Month

Mean Annual Rainfall = Total Rainfall in a Year ÷ Number of Years

To calculate average monthly rainfall over several years, add the rainfall for that month across all years and divide by the number of years.

要计算多年平均月降雨量，将该月份各年降雨量相加，再除以年数。

Climate graphs often display monthly temperature as a line and rainfall as bars, requiring accurate data plotting.

气候图常以折线表示月气温，以柱状表示月降雨量，这需要准确的数据绘制。

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9. River Cross-sectional Area | 河流横截面积

To estimate the amount of water a river carries, geographers measure its channel dimensions. The cross-sectional area (CSA) is the area of the slice across the river.

为估算河流的输水量，地理学者测量河道尺寸。横截面积是河流横切面的面积。

Cross-sectional Area (m²) = Width (m) × Average Depth (m)

This is a simplification assuming a rectangular channel. The average depth is found by taking several depth readings along a cross-section and dividing the sum by the number of readings.

这是假设河道为矩形时的简化公式。平均深度通过沿横断面多次测量水深，求和再除以测量次数得出。

River discharge (not always required at Year 7) would multiply CSA by the velocity of water, but simply understanding CSA helps later work.

河流流量（七年级不常要求）等于横截面积乘以流速，但理解横截面积本身对后续学习十分有益。

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10. Compass Bearings and Grid References | 罗盘方位与网格坐标

Direction on maps is given using compass points (N, NE, E, SE, S, SW, W, NW) or bearings in degrees measured clockwise from north.

地图上的方向使用罗盘点（北、东北、东、东南、南、西南、西、西北）或从北按顺时针测量的方位角（以度为单位）。

A bearing is always a three‑digit number (e.g., 045°, 180°, 315°). To find a bearing, draw a north line at your starting point and measure the angle clockwise to the target.

方位角始终为三位数（如 045°、180°、315°）。求方位角时，在起点画一条北线，顺时针量测至目标的夹角。

Four‑figure grid references locate a grid square (e.g., 1532). The first two digits are the easting (along the bottom), the last two are the northing (up the side). Remember: ‘along the corridor and up the stairs’.

四位网格坐标用于定位一个方格（如 1532）。前两位是东距（沿底部横向走），后两位是北距（沿侧边向上走）。记住：’先横后纵，如同沿走廊走再上楼梯’。

Six‑figure grid references pinpoint an exact location inside a grid square. Divide the square into tenths mentally to get the extra digit for easting and northing.

六位网格坐标可精确定位方格内的确切地点。想象将方格十等分，为东距和北距各添加一位数字。

Grid Reference Rule: Eastings then Northings (E N)

This consistent order prevents confusion and is a fundamental map‑reading theorem.

这一固定顺序避免混淆，是基础的读图规则。

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