📚 Year 10 CIE Maths: Case Study Practice Walkthrough | 案例分析实战演练
In the IGCSE 0580 Mathematics syllabus, case study questions bridge classroom theory and real‑world applications. This article walks you through four carefully selected case studies — journey planning, business break‑even analysis, probability games, and geometric design — showing exactly how to approach multi‑step problems, extract data, choose the right maths and communicate your reasoning clearly.
在IGCSE 0580数学大纲中，案例分析题连接了课堂理论与实际应用。本文将带你走过四个精心挑选的案例——旅程规划、商业盈亏分析、概率游戏和几何设计——一一展示如何应对多步问题、提取数据、选择合适的数学工具并清晰表达推理过程。
1. Understanding Case Studies in CIE Maths | 理解CIE数学中的案例分析题
Case study questions present a scenario — often with a table, graph or diagram — and ask several connected questions. They test your ability to identify what mathematics to use rather than just perform a routine calculation. Start by reading the entire scenario, underlining key numbers and units. Decide which topic (e.g., algebra, geometry, probability) is involved and note any given formulas. Always show your working, and make sure your final answer is in the correct units and form requested.
案例分析题会给出一个情境——常带有表格、图像或示意图——然后提出几个相互关联的问题。这类题考查的是你识别该用哪种数学的能力，而不仅仅是完成常规计算。先通读整个情境，划出关键数字和单位。判断涉及哪个知识领域（如代数、几何、概率），并记下已给的公式。展示所有解题步骤，并确保最终答案的单位和形式符合题目要求。
2. Case Study 1: Journey Planning – Using Distance, Speed, Time | 案例一：旅程规划 – 距离、速度、时间
Sarah cycles a 36 km route. She rides for 1 hour at an average speed of 15 km/h, rests for 15 minutes, then completes the remaining distance at 12 km/h. What is her total journey time, and at what time does she finish if she starts at 09:00? First, find the distance covered in the first part: d₁ = 15 km/h × 1 h = 15 km 21 km. The time for the second part is t₂ = 21 km ÷ 12 km/h = 1.75 h = 1 hour 45 minutes.
莎拉骑自行车走完36公里路线。她以平均速度15公里/小时骑行1小时，休息15分钟，然后以12公里/小时完成剩余距离。她的总行程时间是多少？如果她在09:00出发，什么时间到达？首先，计算第一阶段行驶距离：d₁ = 15 km/h × 1 h = 15 km。剩余距离为36 − 15 = 21 km。第二阶段时间 t₂ = 21 km ÷ 12 km/h = 1.75 h = 1小时45分钟。
Total riding time = 1 h + 1.75 h = 2.75 h = 2 h 45 min. Add the 15‑ ectly: 15 min = 0.25 h, and 45 min = 0.75 h. Using decimals avoids common fraction errors.
总骑行时间 = 1 h + 1.75 h = 2.75 h = 2小时45分钟。加上15分钟休息，总耗时为3小时。09:00出发，到达时间为12:00（中午）。始终正确换算分钟为小时：15 min = 0.25 h，45 min = 0.75 h。使用小数可避免常见的分数错误。
3. Interpreting Travel Graphs | 解读行程图
If we plot Sarah's journey on a distance–time graph, the first section (steep slope) represents the faster speed of 15 km/h. The flat horizontal section shows the rest — distance stays constant at 15 km for 0
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