📚 Interdisciplinary Problem Solving for WJEC Mathematics Year 11 | 跨学科综合题型训练
In the WJEC Year 11 Mathematics curriculum, applying mathematical skills to interdisciplinary contexts is a key component of exam success. Real-world problems often combine ideas from physics, economics, biology, and other subjects, requiring you to translate a situation into equations, graphs, or statistical measures. This article provides a structured training session with nine worked examples that mirror the style of WJEC questions. Work through each section carefully; English and Chinese explanations are paired to reinforce understanding.
在 WJEC 11 年级数学课程中，将数学技能应用于跨学科情境是考试成功的关键要素。现实世界的问题往往结合了物理、经济、生物和其他学科的思想，要求你把实际情况转化为方程、图形或统计量。本文提供了一个结构化的训练，包含九个例题，模拟了 WJEC 题目的风格。请仔细学习每一节；中英文解释配对呈现，以加深理解。
1. Distance–Time Graphs and Kinematics | 距离–时间图与运动学
Physics and mathematics frequently overlap when analysing motion. A distance–time graph shows how far an object has moved over a period. The slope (gradient) of the line represents the speed. For a straight line from the origin to (10 s, 200 m), the speed is constant: v = Δd / Δt = 200/10 = 20 m/s. A horizontal segment indicates the object is stationary. To find the average speed over a journey that includes stationary periods, use total distance divided by total time. WJEC exam questions may ask you to interpret such graphs and calculate distance, speed, or time intervals.
物理和数学在分析运动时经常交叉。距离–时间图显示了物体在一段时间内移动了多远。线的斜率（梯度）表示速度。对于从原点到 (10 s, 200 m) 的一条直线，速度是恒定的：v = Δd / Δt = 200/10 = 20 m/s。水平段表明物体静止。要计算包含静止时段的整个行程的平均速度，用总距离除以总时间。WJEC 试题可能会要求你解读这种图并计算距离、速度或时间间隔。
Key skills:
- Identify linear segments: constant speed; horizontal: zero speed.
- Approach: calculate gradient as rise ÷ run for each sloping part.
- For average speed, sum all distances and divide by the total time taken.
关键技能：
- 识别线段：斜线表示匀速；水平线表示静止。
- 方法：对每个倾斜部分，用上升量 ÷ 水平量计算梯度。
- 对于平均速度，总距离除以总时间。
2. Supply and Demand Equations in Economics | 经济学中的供求方程
In economics, supply and demand can be modelled by linear equations. For example, the supply of a product might be P = 2Q + 10 and the demand as P = −3Q + 50, where P is price (£ lds P = 26. The equilibrium point is (8, 26). WJEC mathematics papers often feature such contextual algebra tasks, testing your ability to set up and solve linear equations.
在经济学中，供给与需求可以用线性方程建模。例如，某种商品的供给可能是 P = 2Q + 10，需求为 P = −3Q + 50，其中 P 是价格（英镑），Q 是数量。市场均衡出现在供给等于需求时：解方程 2Q + 10 = −3Q + 50。得到 5Q = 40，因此 Q = 8，代入后 P = 26。均衡点为 (8, 26)。WJEC 数学试卷中经常出现这类情境代数题，考察你建立和求解线性方程的能力。
Tip: After finding the equilibrium quantity, always substitute back to confirm the price is consistent in both equations. Making a quick table of values can help you sketch the two lines and visualise the intersection.
提示：求出均衡数量后，务必回代确认价格在两个方程中一致。做一个简单的数值表可以帮助你画出两条线并想象交点。
3. Geometry in Architecture: Composite Areas | 建筑几何：组合面积
s width 2 m and height 1.5 m, and the semicircle’s diameter equals the width, the total area is the sum of the rectangle’s area and half the area of a circle: Area = (2 × 1.5) + ½ × π × (1)². Using π ≈ 3.14, we get 3 + 1.57 = 4.57 m². WJEC questions may require you to combine area formulas and manage units carefully.
建筑师使用几何来计算组合形状的面积。一扇窗户可能
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