Year 7 CIE Maths: Interdisciplinary Problem-Solving Practice | Year 7 CIE 数学：跨学科综合题型训练

📚 Year 7 CIE Maths: Interdisciplinary Problem-Solving Practice | Year 7 CIE 数学：跨学科综合题型训练

In Year 7, mathematics is not just about numbers and algebra – it connects to science, geography, economics, sports, and many other subjects. Interdisciplinary problems challenge you to apply your maths skills in real-world contexts. This revision guide will help you practise these mixed-topic questions that appear in CIE assessments.

在七年级，数学不仅仅是关于数字和代数——它还与科学、地理、经济、体育等许多学科相联系。跨学科问题要求你将数学技能应用到现实世界场景中。这份复习指南将帮助你练习CIE评估中出现的这类综合题型。

1. Science and Measurement | 科学与测量

In science lessons, you often record measurements such as length, mass, temperature, and time. You need to convert units, calculate averages, and plot graphs. For example, if you measure the temperature of a cooling liquid every minute, you can find the temperature drop per minute.

在科学课上，你经常记录长度、质量、温度和时间等测量数据。你需要转换单位、计算平均值并绘制图表。例如，如果你每分钟测量一次冷却液体的温度，你可以求出每分钟的温度下降量。

A typical question might give you a table: at time 0 min, temperature is 80°C; after 5 min, it is 50°C. The average rate of cooling is (80 − 50) ÷ 5 = 6°C per minute.

一个典型问题可能会给你一张表格：在0分钟时，温度为80°C；5分钟后，温度为50°C。平均冷却速率为（80 − 50）÷ 5 = 每分钟6°C。

Remember to use the correct unit: degrees Celsius per minute (°C/min). If you need to convert to seconds, divide by 60.

记住使用正确的单位：摄氏度每分钟（°C/min）。如果你需要转换为秒，则除以60。

Average rate of change = (Final value − Initial value) ÷ Time

平均变化率 = (最终值 − 初始值) ÷ 时间

2. Geography: Maps and Scale | 地理：地图与比例尺

Geography uses map scales frequently. A scale of 1 : 50,000 means that 1 cm on the map represents 50,000 cm in real life, which is 500 m or 0.5 km. You must be able to convert between map distances and actual distances.

地理中经常使用地图比例尺。比例尺1：50,000意味着地图上的1厘米代表实际生活中的50,000厘米，即500米或0.5公里。你必须能够在地图距离和实际距离之间进行转换。

Example: On a map with a scale of 1 : 25,000, two villages are 8 cm apart. The real distance is 8 × 25,000 = 200,000 cm = 2 km. To find the map distance from a real distance of 5 km, first convert 5 km to 500,000 cm, then divide by 25,000 to get 20 cm.

例如：在一幅比例尺为1:25,000的地图上，两个村庄相距8厘米。实际距离为8 × 25,000 = 200,000厘米 = 2公里。要从实际距离5公里求地图距离，先将5公里转换为500,000厘米，然后除以25,000，得到20厘米。

• Always convert to the same unit before calculating.

  计算前始终转换为相同单位。

• Large scale maps (e.g., 1:10,000) show more detail; small scale maps (e.g., 1:1,000,000) show less detail.

  大比例尺地图（例如1:10,000）显示更多细节；小比例尺地图（例如1:1,000,000）显示较少细节。

3. Statistics and Population Data | 统计与人口数据

In human geography or social studies, you may be given population data in tables or bar charts. You might need to calculate the total population, the range, the median, or create a pie chart showing the distribution of age groups.

在人文地理或社会研究中，你可能会在表格或条形图中得到人口数据。你可能需要计算总人口、范围、中位数，或制作显示年龄组分布的饼图。

For instance, the populations of five towns are: 12,400, 8,700, 15,200, 9,800, and 11,300. To find the mean, add them (57,400) and divide by 5: 11,480.

例如，五个城镇的人口分别为：12,400、8,700、15,200、9,800和11,300。要计算平均值，将它们相加（57,400）再除以5，得到11,480。

When interpreting a pie chart, remember that the full circle is 360°. If 20% of the population is aged 60 and over, the sector angle is 20% × 360° = 72°.

在解读饼图时，记住整个圆是360°。如果20%的人口年龄在60岁及以上，那么扇区角度为20% × 360° = 72°。

Sector angle =