Interdisciplinary Integrated Question Training for Year 12 WJEC Mathematics | WJEC 12年级数学跨学科综合题型训练

📚 Interdisciplinary Integrated Question Training for Year 12 WJEC Mathematics | WJEC 12年级数学跨学科综合题型训练

Year 12 WJEC Mathematics lays the groundwork for applying pure, mechanics and statistics across a wide range of subjects. This article presents a series of integrated question exercises that connect calculus, algebra, probability and vectors to real-world scenarios in physics, economics, biology, finance and beyond. By working through these cross-disciplinary problems, you will strengthen your modelling skills and see how mathematical techniques are used outside the classroom.

12 年级 WJEC 数学为纯数学、力学和统计学的跨学科应用打下基础。本文提供了一系列综合题型训练，将微积分、代数、概率和向量与物理学、经济学、生物学、金融等真实情境联系起来。通过解决这些跨学科问题，你将强化建模能力，并体会数学方法在课堂之外的广泛应用。

1. Kinematics in Physics: SUVAT and Calculus | 物理学中的运动学：匀加速运动与微积分

In mechanics, motion with constant acceleration is a perfect arena to integrate differentiation and integration. Displacement s, velocity v and acceleration a are connected by v = ds/dt and a = dv/dt. The reverse process uses area under curves: s = ∫ v dt and v = ∫ a dt.

在力学中，匀加速运动是结合微分与积分的绝佳场景。位移 s、速度 v 和加速度 a 通过 v = ds/dt 与 a = dv/dt 相互关联，反过程使用曲线下方面积：s = ∫ v dt，v = ∫ a dt。

Starting from constant acceleration a and integrating gives v = u + at. A second integration yields s = ut + ½at². Combining these with s = ½(u+v)t and v² = u² + 2as forms the SUVAT suite, each missing one kinematic variable.

从恒定加速度 a 出发，积分得 v = u + at，再次积分得 s = ut + ½at²。将这两个方程与 s = ½(u+v)t、v² = u² + 2as 组合，即构成 SUVAT 方程组，每个方程都缺失一个运动学变量。

Example: A particle starts from rest and accelerates at 2 m s⁻². Find its displacement after 5 s using SUVAT and then verify using integral calculus.

例题：一质点从静止开始以 2 m s⁻² 加速。用 SUVAT 求 5 s 后的位移，然后用积分法验证。

Solution with SUVAT: u = 0, a = 2, t = 5. Substituting into s = ut + ½at² gives s = 0×5 + ½×2×5² = 25 m.

用 SUVAT 求解：u = 0，a = 2，t = 5

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