📚 Year 10 SQA Maths: Interdisciplinary Problem-Solving Practice | 跨学科综合题型训练
Interdisciplinary problems in SQA Mathematics require you to apply mathematical skills to real-world contexts from science, economics, and technology. These questions test not only your calculation ability but also your understanding of how mathematics models other subjects. This article provides practice across a range of topics.
在 SQA 数学的跨学科问题中，你需要将数学技能应用于科学、经济和技术等现实世界场景。这些问题不仅考察计算能力，还检验你对数学如何模拟其他学科的理解。本文将提供一系列主题的训练。
1. Physics: Speed, Distance and Time | 物理：速度、距离与时间
In physics, the relationship between speed, distance and time is fundamental: speed = distance ÷ time. SQA integrated questions may ask you to find any unknown, unit conversion or interpret a distance-time graph. For example, a plane flies 1500 km in 3 hours. Find its speed in km/h and m/s.
在物理学中，速度、距离和时间的关系是基本公式：速度 = 距离 ÷ 时间。SQA 综合题可能要求你求未知量、转换单位或解读距离-时间图。例如，一架飞机 3 小时飞行 1500 km，求其速度（km/h 和 m/s）。
3600) = 500 × (5/18) ≈ 138.89 m/s. These conversions are common in SQA exams.
计算：速度 = 1500 ÷ 3 = 500 km/h。转换为 m/s：500 × (1000 ÷ 3600) = 500 × (5/18) ≈ 138.89 m/s。这些换算是 SQA 考试中的常见内容。
2. Chemistry: Concentration and Mixtures | 化学：浓度与混合物
Concentration is mass of solute per unit volume: C = m / V. You might need to calculate the concentration when dissolving salt in water, or find the volume needed for a certain mass. For instance, 40 g of sodium chloride is dissolved in 500 cm³ of water. Express the concentration in g/cm³ and in g/L.
浓度是单位体积溶剂中的溶质质量：C = m / V。你可能要计算将盐溶于水后的浓度，或求特定质量所需的体积。例如，将 40 g 氯化钠溶于 500 cm³ 水中，请以 g/cm³ 和 g/L 表示浓度。
/L: 0.08 × 1000 = 80 g/L. These problems reinforce unit conversion and ratio skills.
1 L = 1000 cm³;。浓度以 g/cm³ 表示：40 ÷ 500 = 0.08 g/cm³;。以 g/L 表示：0.08 × 1000 = 80 g/L。这些问题强化了单位换算和比例技能。
3. Biology: Bacterial Growth | 生物：细菌种群增长
Exponential growth models in biology follow the formula N = N₀ × 2t/d, where N₀ is initial count, t is time, d is doubling period. A culture starts with 200 bacteria and doubles every 30 minutes. How many bacteria after 3 hours?
生物学中的指数增长模型遵循公式 N = N₀ × 2t/d，其中 N₀ 为初始数量，t 为时间，d 为倍增周期。一个培养物初始有 200 个细菌，每 30 分钟翻倍。3 小时后有多少细菌？
3 hours = 6 doubling periods (180 min ÷ 30 min). So N = 200 × 2⁶ = 200 × 64 = 12,800 bacteria. Understanding exponential indices is key here.
3 小时 = 6 个倍增周期（180 min ÷ 30 min）。因此 N = 200 × 2⁶ = 200 × 64 = 12,800 个细菌。这里的关键是理解指数运算。
4. Economics: Profit and Break-even | 经济：利润与盈亏平衡点
Businesses calculate profit using Profit = Revenue - Cost shirts: fixed cost £200, variable cost £5 per shirt, selling price £15. Find break-even quantity and profit for 50 shirts.
企业使用 利润 = 收入 - 成本 计算利润。盈亏平衡点出现在收入等于成本时。某公司销售 T 恤：固定成本 £200，每件可变成本 £5，售价 £15。求盈亏平衡产量以及 50 件时的利润。
e number of shirts. Revenue = 15x, Total cost = 200 + 5x. Break-even: 15x = 200 + 5x &rarr
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