📚 Interdisciplinary Mixed Practice for Edexcel Year 11 Further Maths | Edexcel 十一年级进阶数学跨学科综合题型训练
Further Mathematics is not just a collection of abstract topics – it is the language that connects engineering, computer science, biology, finance and navigation. This article brings together core Year 11 Edexcel Further Maths skills and shows how they are applied in real-world, cross-disciplinary contexts. Each section presents a concise scenario followed by dual-language explanation and worked example, helping you master mixed problem-solving techniques required for top exam performance.
进阶数学并非一系列抽象专题的堆砌，它是贯通工程、计算机科学、生物学、金融和导航等学科的语言。本文汇集了 Edexcel 十一年级进阶数学的核心技能，并展示它们如何在跨学科的真实情境中应用。每个小节给出一个简洁场景，再配以双语讲解和例题，助你掌握考试高分所需的综合解题技巧。
1. Calculus in Kinematics | 运动学中的微积分应用
celeration a(t) = dv/dt = d²s/dt². Conversely, integrating acceleration gives velocity, and integrating velocity yields displacement.
微积分能够描述运动物体的位移、速度和加速度之间的关系。若位置为 s(t)，则速度 v(t) = ds/dt，加速度 a(t) = dv/dt = d²s/dt²。反过来，对加速度积分得速度，对速度积分得位移。
4 m s⁻². Find its velocity function and the distance travelled during the first 5 seconds.
例题：一枚火箭从静止开始在测试轨道上加速，加速度 a(t) = 12t - 4 m s⁻²。求其速度函数以及前5秒行驶的距离。
e v(0) = 0, C = 0, so v = 6t² - 4t. Then s(t) = ∫(6t² - 4t)dt = 2t³ - 2t² + D, with s(0)=0 ⇒ D=0. Distance at t=5: s(5) = 2×125 - 2×25 = 200 m.
v(t) = ∫(12t - 4)dt = 6t² - 4t + C。由 v(0)=0 得 C=0，故 v = 6t² - 4t。接着 s(t) = ∫(6t² - 4t)dt = 2t³ - 2t²
Published by TutorHao | Year 11 进阶数学 Revision Series | aleveler.com
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