📚 Year 11 Eduqas Maths: Case Study Practical Walkthroughs | Eduqas 数学案例分析实战演练
Case studies in Eduqas GCSE Maths test your ability to apply mathematical concepts to real-life scenarios. This article provides a structured approach, from reading the problem to verifying your answer, using worked examples across topics like percentages, geometry, and statistics.
Eduqas GCSE 数学中的案例分析题考查你将数学概念应用于实际情境的能力。本文将提供一种结构化的解题方法，从阅读问题到验证答案，并配合百分比、几何和统计等主题的实例讲解。
1. Understanding the Case Study Context | 理解案例背景
Start by reading the entire problem statement slowly. Underline key information: numbers, units, and what exactly is being asked. Is the final answer expected in pounds, metres, or as a percentage? Identify the 'story'—it might be about shopping, travel, or a school event.
先慢慢通读整个问题陈述。划出关键信息：数字、单位以及最终要求什么。答案是英镑、米还是百分比？识别'故事'背景——可能是购物、旅行或学校活动。
2. Extracting Data and Units | 提取数据和单位
List all given values with their units. Common units in Eduqas case studies include £, kg, m, cm, minutes, and km. Watch out for mixed units—you may need to convert everything to the same unit before calculating. For example, 1.5 km and 800 m should both be in metres.
列出所有给定的值及其单位。Eduqas 案例中常见的单位有 £、kg、m、cm、分钟和 km。注意混合单位——你可能需要先统一单位再计算。例如 1.5 km 和 800 m 都应转换为米。
3. Identifying the Maths Topics | 确定数学知识点
down the formulas you might need, such as speed = distance ÷ time, or percentage change = (difference ÷ original) × 100.
判断需要哪些数学技能。一个案例分析通常会混合多个主题：百分比、比例、面积、平均值或读图。写下可能需要的公式，如速度 = 距离 ÷ 时间，或百分比变化 =（差值 ÷ 原值）× 100。
4. Planning a Step-by-step Strategy | 制定分步策略
Break the problem into smaller tasks. For instance, if you need to find the total cost of tiling a floor, first calculate the floor area, then the number of tiles, then the number of boxes, and finally the total price. Number each step to stay organised.
将问题分解为更小的任务。例如，如果需要计算铺设地板的总费用，先算地板面积，再算所需地砖数量，再算要多少箱，最后算总价。给每一步编号，保持条理。
5. Case Study 1: Best Value Shopping | 案例分析1：最佳购物性价比
A shop sells the same brand of rice in three different packs. Pack A: 500 g for £1.20. Pack B: 750 g for £1.70. Pack C: 2 kg for £4.50, with a 'buy one get one half price' offer on Pack C. Which pack gives the lowest price per 100 g when you buy two Pack C bags?
一家商店以三种不同包装出售同一个品牌的大米。A 包：500 g 售价 £1.20。B 包：750 g 售价 £1.70。C 包：2 kg 售价 £4.50，且 C 包有'买一送一半价'优惠。如果购买两包 C，哪种包装每 100 g 的单价最低？
Step 1: Calculate price per gram for Pack A. 500 g costs £1.20, so cost per gram = 1.20 ÷ 500 = £0.0024. Per 100 g = 0.0024 × 100 = £0.24.
步骤1：计算 A 包每克价格。500 g 花费 £1.20，所以每克成本 = 1.20 ÷ 500 = £0.0024。每 100 g = 0.0024 × 100 = £0.24。
Step 2: Pack B: 1.70 ÷ 750 = £0.002267 per gram, so per 100 g = £0.2267 (about 22.7 pence).
步骤2：B 包：1.70 ÷ 750 = £0.002267 每克，所以每 100 g = £0.2267（约 22.7 便士）。
Step 3: Pack C offer: two packs cost £4.50 + (50% of £4.50) = £4.50 + £2.25 = £6.75 for 2 × 2 kg = 4 kg. Cost per gram = 6.75 ÷ 4000 = £0.0016875, per 100 g = £0.16875. This is the best value.
步骤3：C 包优惠：两包价格 = £4.50 + (50% × £4.50) = £4.50 + £2.25 = £6.75，总重 2 × 2 kg = 4 kg。每克成本 = 6.75 ÷ 4000 = £0.0016875，每 100 g = £0.16875。这是最划算的。
Comparative table:
对比表格：
| Pack | Weight (g) | Total cost (£) | Price per 100 g (£) |
|---|---|---|---|
| A | 500 | 1.20 | 0.240 |
| B | 750 | 1.70 | 0.227 |
| C (offer) | 4000 | 6.75 | 0.169 |
6. Case Study 2: Floor Tiling Project | 案例分析2：地板铺砖工程
A rectangular room measures 4.8 m by 3.5 m. Square tiles of side 40 cm are to be laid. Tiles are sold in boxes of 12, priced at £28.80 per box. The shop recommends buying 5% extra to allow for cutting and breakages. Calculate the total cost of tiles needed.
一个长方形房间尺寸为 4.8 m × 3.5 m，需要铺设边长为 40 cm 的正方形地砖。地砖每箱 12 块，价格 £28.80。商店建议多买 5% 以预留切割和破损。计算所需地砖的总费用。
Convert all to the same unit. Room dimensions in cm: 480 cm by 350 cm. Tile side = 40 cm.
步骤1：统一单位。房间尺寸以厘米计：480 cm × 350 cm。地砖边长 = 40 cm。
one tile = 40 × 40 = 1600 cm². Number of tiles without waste = 168,000 ÷ 1600 = 105 tiles.
步骤2：房间面积 = 480 × 350 = 168,000 cm²。一块地砖面积 = 40 × 40 = 1600 cm²。不计损耗所需地砖数 = 168,000 ÷ 1600 = 105 块。
Step 3: Add 5% extra
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