📚 Case Study Practical Exercises for WJEC Year 13 Further Maths | WJEC 进阶数学Year 13案例分析实战演练
The WJEC A2 Case Studies in Mathematics unit challenges you to apply pure, mechanics, statistics and decision mathematics to realistic scenarios. Success depends on reading the context carefully, building appropriate models, and communicating your reasoning clearly. This article provides a structured revision guide with worked examples and practice tasks to sharpen your case‑study skills.
WJEC A2 数学案例分析单元要求你把纯数、力学、统计和决策数学知识综合运用于真实情境。成功的关键在于仔细阅读背景材料、建立恰当的数学模型，并清晰地表达推理过程。本文提供结构化的复习指南，包括详尽的解答示例和练习题，帮助你提升案例分析能力。
1. Understanding Case Studies | 认识案例分析
Case studies in WJEC Further Maths are extended problems set in real‑life contexts such as engineering, medicine, logistics or finance. You will be given a booklet containing data, graphs and descriptions. Questions then guide you through simplifying assumptions, formulating equations, solving them and interpreting the results in the original context. It is essential to connect the mathematics back to the scenario.
WJEC 进阶数学中的案例分析是设定在工程、医学、物流或金融等真实情境中的拓展问题。你会拿到一本包含数据、图表和描述的小册子，题目会引导你作出简化假设、建立方程、求解并回到原始情境解释结果。把数学与场景联系起来至关重要。
2. The Modelling Cycle | 建模循环
A successful case‑study solution follows the modelling cycle: (1) define the real‑world problem; (2) make simplifying assumptions; (3) represent the situation mathematically; (4) analyse the model; (5) obtain a mathematical solution; (6) interpret the solution back into the real world; (7) validate the model by checking against data or common sense. Always state assumptions explicitly – for instance, neglecting air resistance, treating a rope as light and inextensible, or assuming a population follows a normal distribution.
成功的案例分析解答应遵循建模循环：(1) 界定现实问题；(2) 作出简化假设；(3) 用数学语言表述情境；(4) 分析模型；(5) 求得数学解；(6) 将解还原到现实世界进行解释；(7) 对照数据或常理验证模型。务必明确陈述假设——例如忽略空气阻力、视绳索为轻质且不可伸长，或者假设总体服从正态分布。
3. Mechanics Case: Towing a Caravan with Air Resistance | 力学案例：考虑空气阻力的房车牵引
s wheels. The car experiences air resistance proportional to its speed, given by R = 15v N, where v is the speed in m coupling between car and caravan is light and rigid. The system starts from rest at t = 0.
一辆质量为 1200 kg 的汽车沿平直水平道路牵引一辆 800 kg 的房车。发动机对车轮施加恒定的 2500 N 牵引力。汽车受到与速度成正比的空气阻力 R =
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