📚 Year 7 Cambridge Advanced Mathematics: Case Study Practical Exercises | Year 7 Cambridge 进阶数学：案例分析实战演练
Advanced mathematics in Year 7 goes beyond routine calculations by applying concepts to real-world scenarios. This article presents ten case studies that integrate number, algebra, geometry, and data handling, encouraging you to think critically and solve problems creatively.
7 年级的进阶数学不仅仅停留在常规计算上，更注重将概念应用于实际情境。本文提供了十个案例分析，融合了数、代数、几何和数据处理，鼓励你进行批判性思考并创造性地解决问题。
1. Designing a Rectangular Garden | 案例一：设计矩形花园
metres. You want to maximise the area for planting. How do you choose the length and width? = 10, w = 2, A = 20 m². The maximum area occurs when l = w = 6 m, forming a square. This demonstrates that for a given perimeter, a square encloses the largest area.
假设你要设计一个周长为 24 米的矩形花园，并希望种植面积最大。应该怎样选择长和宽呢？设长 l m，宽 w m，周长 2(l + w) = 24，所以 l + w = 12。面积 A = l × w。尝试整数解：若 l = 6, w = 6，A = 36 m²；若 l = 8, w = 4，A = 32 m²；若 l = 10, w = 2，A = 20 m²。当 l = w = 6 米时面积最大，成为正方形。这说明给定周长时，正方形所围面积最大。
0.5 m wide path inside the perimeter. What is the new planting area for the square design? , so the planting region is a smaller square with side 6 − 2×0.5 = 5 m. Area = 5² = 25 m².
园丁决定在边界内侧修建一条 0.5 米宽的小路。正方形边长为 6 米，因此种植区是一个边长为 6 − 2×0.5 = 5 米的小正方形。面积 = 5² = 25 m²。
If the path is paved with stones costing £ nd the cost. Area of path = total area − planting area = 36 − 25 = 11 m². Cost = 11 × 12 = £132.
如果小路用每平方米 12 英镑的石头铺设，求费用。小路面积 = 总面积 − 种植面积 = 36 − 25 = 11 m²。费用 = 11 × 12 = 132 英镑。
2. Budgeting a School Trip | 案例二：学校旅行预算
A school plans a trip for 120 students. The cost per student is £15.50, which includes transport and lunch. However, if more than 100 students attend, a 10% discount applies to the total cost. What is the final bill? The total cost without discount is 120 × 15.50 = £1860. A 10% discount means they pay 90% of £1860 = 0.9 × 1860 = £1674. How much does each student actually pay? £1674 ÷ 120 ≈ £13.95. This exercise uses multiplication of decimals and percentage decrease.
学校计划组织 120 名学生旅行，每名学生费用为 15.50 英镑，包含交通和午餐。如果超过 100 名学生参加，总费用可享 10% 折扣。最终账单是多少？不打折的总费用为 120 × 15.50 = 1860 英镑。10% 折扣后，需支付 1860 的 90% = 0.9 × 1860 = 1674 英镑。每名学生实际支付多少？1674 ÷ 120 ≈ 13.95 英镑。该练习运用了小数乘法和百分比递减计算。
If the school's budget is £1700, they can afford the trip and have £1700 − £1674 = £26 left. This introduces checking against a budget.
如果学校预算为 1700 英镑，他们可以负担此次旅行，并剩余 1700 − 1674 = 26 英镑。这引入了与预算进行比较的方法。
The museum charges an additional £2.50 per student for a guided tour. What is the new total cost? With 120 students, extra cost = 120 × 2.50 = £300. New total = £1674 + £300 = £1974. Average cost per student = £1974 ÷ 120 = £16.45.
博物馆对每名学生收取 2.50 英镑的导览附加费。新的总费用是多少？120 名学生附加费 = 120 × 2.50 = 300 英镑。新总费用 = 1674 + 300 = 1974 英镑。每名学生平均费用 = 1974 ÷ 120 = 16.45 英镑。
3. Analysing Sports Statistics | 案例三：体育统计分析
15, 10, 18, 22, 14, 10, 19. Find the mean, median, mode, and range. Mean = (12+15+10+18+22
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