📚 Year 7 CAIE Maths: Case Study Practice Drills | Year 7 CAIE 数学：案例分析实战演练
Case studies are a powerful way to apply your mathematical knowledge to real-life situations. In Year 7 CAIE Mathematics, you will encounter problems that require logical thinking, number operations, geometry, and data handling. This article provides a series of practical case studies designed to sharpen your problem-solving skills and boost exam confidence.
案例分析是将数学知识应用于现实情境的强大方式。在 Year 7 CAIE 数学中，你会遇到需要逻辑思维、数字运算、几何和数据处理的问题。本文提供一系列实用的案例分析，旨在提升你的解题能力并增强考试信心。
1. Why Case Studies Matter | 为什么案例分析很重要
Case studies bridge the gap between textbook exercises and the world around you. Instead of simply calculating 20% of 30, you learn to think: "I have a 20% discount on a £30 item – how much do I save?" This practical lens makes mathematics meaningful and strengthens your ability to interpret questions under exam conditions.
案例分析弥合了课本练习与周围世界之间的差距。你不再只是计算 30 的 20%，而是学会思考：“一件 30 英镑的商品打八折，我能省多少钱？”这种实践视角让数学变得有意义，并增强了你在考试条件下解读题目的能力。
Key habits for success include: reading the problem twice, underlining important numbers and units, deciding which operation to use, and checking whether the answer makes sense.
成功的关键习惯包括：仔细读题两遍，划出重要数字和单位，决定使用哪种运算，并检查答案是否合理。
2. Shopping Discounts | 购物折扣
Scenario: Emma goes to a store with £60. She wants to buy a jacket originally priced at £45. The store is offering a 15% discount on the jacket. She also picks up a pair of socks for £4.50. How much change will she get after paying for both items?
情景：Emma 带着 60 英镑去商店。她想买一件原价 45 英镑的夹克，商店正提供 15% 的折扣。她还拿了一双 4.50 英镑的袜子。她支付这两件商品后会得到多少找零？
Step 1: Calculate the discount amount. 15% of £45 = 0.15 × 45 = £6.75.
步骤 1：计算折扣金额。45 英镑的 15% = 0.15 × 45 = 6.75 英镑。
Step 2: Find the sale price of the jacket: £45 – £6.75 = £38.25.
步骤 2：求出夹克的售价：£45 – £6.75 = £38.25。
Step 3: Add the socks: £38.25 + £4.50 = £42.75 total spent.
步骤 3：加上袜子：总花费 £38.25 + £4.50 = £42.75。
Step 4: Subtract from Emma's money: £60 – £42.75 = £17.25 change.
步骤 4：从 Emma 的钱中减去：£60 – £42.75 = £17.25 找零。
Always convert percentages to decimals or fractions, and double-check your subtraction.
始终将百分比转换为小数或分数，并仔细检查减法运算。
3. Journey Planning | 行程规划
Scenario: A cyclist plans to ride from town A to town B, a distance of 36 km. She cycles at a steady speed of 12 km per hour. She leaves at 09:30 and takes a 20-minute break halfway. At what time does she arrive?
情景：一位自行车骑手计划从 A 镇骑到 B 镇，距离 36 公里。她以 12 公里/小时的稳定速度骑行。她在 09:30 出发，中途休息 20 分钟。她将在什么时间到达？
Time spent cycling = Distance ÷ Speed = 36 km ÷ 12 km/h = 3 hours.
骑行时间 = 距离 ÷ 速度 = 36 公里 ÷ 12 公里/小时 = 3 小时。
Total time including break = 3 hours + 20 minutes = 3 hours 20 minutes.
包括休息的总时间 = 3 小时 + 20 分钟 = 3 小时 20 分钟。
Adding 3h 20min to 09:30 gives 12:50. So the cyclist arrives at 12:50.
将 3 小时 20 分钟加到 09:30 上得到 12:50。因此骑手在 12:50 到达。
When working with time, be careful with 60-minute hours. Drawing a timeline can prevent mistakes.
处理时间问题时，要当心 60 分钟为一小时。画一条时间线可以避免出错。
4. Garden Area and Perimeter | 花园的面积与周长
Scenario: A rectangular garden measures 8 m in length and 5 m in width. The owner wants to put a fence around it and then lay grass over the entire area. Fencing costs £6 per metre, and grass seed costs £2 per square metre. Find the total cost.
情景：一个矩形花园长 8 米，宽 5 米。主人想围上篱笆，然后在整片区域铺上草坪。篱笆每米 6 英镑，草籽每平方米 2 英镑。求总费用。
Perimeter of rectangle = 2 × (length + width) = 2 × (8 m + 5 m) = 2 × 13 m = 26 m.
矩形周长 = 2 × (长 + 宽) = 2 × (8 m + 5 m) = 2 × 13 m = 26 m。
Cost of fencing = 26 m × £6/m = £156.
篱笆费用 = 26 m × £6/m = £156。
Area of rectangle = length × width = 8 m × 5 m = 40 m².
矩形面积 = 长 × 宽 = 8 m × 5 m = 40 m²。
Cost of grass seed = 40 m² × £2/m² = £80.
草籽费用 = 40 m² × £2/m² = £80。
Total cost = £156 + £80 = £236.
总费用 = £156 + £80 = £236。
Remember: perimeter uses the distance around the edge, while area measures the space inside.
请记住：周长使用边缘的距离，而面积测量内部的空间。
5. Interpreting Bar Charts | 解读条形图
Scenario: A class of Year 7 students recorded their favourite fruit. The results are shown in the table below.
情景：一个 Year 7 班级的学生记录了各自最喜欢的水果。结果如下表所示。
| Fruit | Number of students |
|---|---|
| Apple | 12 |
| Banana | 8 |
| Orange | 10 |
| Grapes | 6 |
| Strawberry | 4 |
Use the data to answer: a) Which fruit is the mode? b) How many students took part? c) Calculate the mean number of students per fruit category.
使用数据回答：a) 哪种水果是众数？b) 有多少学生参与？c) 计算每类水果的平均学生人数。
a) The mode is the category with the highest frequency. Apple has 12 students, so the mode is Apple.
a) 众数是频率最高的类别。苹果有 12 名学生，因此众数是苹果。
b) Total students = 12 + 8 + 10 + 6 + 4 = 40 students.
b) 学生总数 = 12 + 8 + 10 + 6 + 4 = 40 名学生。
c) Mean = Total students ÷ Number of categories = 40 ÷ 5 = 8 students per category.
c) 平均 = 学生总数 ÷ 类别数量 = 40 ÷ 5 = 每类 8 名学生。
When you present a bar chart, remember to label axes and use an appropriate scale.
当你要呈现条形图时，记得标明坐标轴并使用合适的刻度。
6. Recipe Ratios | 食谱中的比例
Scenario: A pancake recipe for 4 people requires 200 g of flour, 2 eggs, 300 ml of milk and 50 g of sugar. You need to make pancakes for 10 people. What quantity of each ingredient is needed?
情景：一份供 4 人食用的煎饼食谱需要 200 克面粉、2 个鸡蛋、300 毫升牛奶和 50 克糖。你需要为 10 人制作煎饼。每种配料需要多少量？
The ratio of people is 10 : 4, which simplifies to 2.5 : 1. Multiply each quantity by 2.5.
人数比为 10 : 4，化简为 2.5 : 1。将每种配料的数量乘以 2.5。
5 = 500 g. Eggs: 2 × 2.5 = 5 eggs. Milk: 300 ml × 2.5 = 750 ml. Sugar: 50 g × 2.5 = 125 g.
面粉：200 g × 2.5 = 500 g。鸡蛋：2 × 2.5 = 5 个。牛奶：300 ml × 2.5 = 750 ml。糖：50 g × 2.5 = 125 g。
You can also use the unitary method: find the amount for one person first (divide by 4), then multiply by 10.
你也可以使用归一法：先求出每人的量（除以 4），再乘以 10。
Proportions appear in many everyday contexts – scaling up or down is a valuable skill.
比例出现在许多日常情境中——按比例放大或缩小是一项宝贵的技能。
7. Spinner Probability | 转盘概率
Scenario: A fair spinner is divided into 4 equal sections coloured red, blue, yellow and green. If you spin it once, what is the probability of landing on a primary colour (red, blue or yellow)?
情景：一个公平的转盘被分成 4 个相等的区域，分别涂上红色、蓝色、黄色和绿色。如果转动一次，落到原色（红色、蓝色或黄色）的概率是多少？
sible outcomes = 4 (red, blue, yellow, green). Favorable outcomes = 3 (red, blue, yellow).
所有可能的结果 = 4（红、蓝、黄、绿）。有利结果 = 3（红、蓝、黄）。
Probability = Favorable outcomes / Total outcomes = 3/4.
概率 = 有利结果 / 所有可能结果 = 3/4。
The spinner is spun twice. What is the probability that it lands on green both times?
转盘转动两次。两次都落到绿色的概率是多少？
ability of green on one spin = 1/4. For two independent spins, multiply: 1/4 × 1/4 = 1/16.
单次落到绿色的概率 = 1/4。对于两次独立转动，相乘：1/4 × 1/4 = 1/16。
Always ensure the spinner is fair, meaning each section has an equal chance.
务必确保转盘是公平的，即每个区域都有相同的机会。
8. Unit Conversions in Cooking | 烹饪中的单位换算
Scenario: A recipe calls for 1.5 kg of flour and 750 ml of water. The kitchen scale measures in grams, and the measuring jug shows litres. Convert both amounts to the units shown on the tools. Then, state the flour in grams and water in litres.
情景：一份食谱要求 1.5 公斤面粉和 750 毫升水。厨房秤以克为单位计量，量杯以升为单位显示。将两个数量都转换为工具上显示的单位。然后，说出面粉的克数和水的升数。
1 kg = 1000 g, so 1.5 kg = 1.5 × 1000 = 1500 g of flour.
1 公斤 = 1000 克，因此 1.5 公斤 = 1.5 × 1000 = 1500 克面粉。
1000 ml = 1 litre, so 750 ml = 750 ÷ 1000 = 0.75 litres of water.
1000 毫升 = 1 升，因此 750 毫升 = 750 ÷ 1000 = 0.75 升水。
Now the baker also needs 0.4 kg of butter. Express that in grams: 0.4 × 1000 = 400 g.
现在面包师还需要 0.4 公斤黄油。以克表示：0.4 × 1000 = 400 克。
Memorise common metric prefixes: kilo- means thousand, milli- means thousandth, centi- means hundredth.
记住常用的公制前缀：kilo- 表示千，milli- 表示千分之一，centi- 表示百分之一。
9. Budgeting a School Trip | 学校旅行的预算
Scenario: A group of 28 students and 2 teachers plan a museum visit. Entry costs £7.50 per student and £10 per teacher. The coach hire is £180 in total, to be shared equally among all 30 people. Find the total cost per person.
情景：一个由 28 名学生和 2 名老师组成的小组计划参观博物馆。学生门票每人 7.50 英镑，老师每人 10 英镑。大巴总租金为 180 英镑，由全部 30 人平均分摊。求每人总费用。
Student entry total: 28 × £7.50 = £210. Teacher entry total: 2 × £10 = £20. Total entry = £230.
学生门票总额：28 × £7.50 = £210。老师门票总额：2 × £10 = £20。门票总额 = £230。
Coach cost per person = £180 ÷
Published by TutorHao | Year 7 Mathematics Revision Series | aleveler.com
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