GCSE Edexcel Maths: Critical Path Analysis | 关键路径分析 考点精讲

📚 GCSE Edexcel Maths: Critical Path Analysis | 关键路径分析 考点精讲

Critical Path Analysis (CPA) is a fundamental topic in the Edexcel GCSE Mathematics syllabus, particularly within the ‘Decision Mathematics’ component. It equips you with tools to model complex projects, determine the minimum completion time, and identify which tasks must not be delayed. This revision guide covers all essential concepts including activity networks, forward and backward passes, float calculations, cascade charts, and common pitfalls in exams.

关键路径分析（CPA）是Edexcel GCSE数学大纲中的一个基础主题，尤其在’决策数学’部分。它为你提供工具来模拟复杂项目，确定最短完工时间，并识别哪些任务不可延迟。本复习指南涵盖所有重要概念，包括活动网络、正向与反向遍历、浮动时间计算、级联图及考试中的常见陷阱。

1. Introduction to Critical Path Analysis | 关键路径分析简介

Critical Path Analysis (CPA) is a project management technique developed in the 1950s to schedule and coordinate large-scale projects. In GCSE Edexcel Maths, you apply it to model a project as a network of activities. The network shows the order in which tasks must be completed, and the analysis reveals the critical path – the sequence of activities that dictates the overall project duration. Understanding CPA helps answer questions such as: “What is the earliest time the project can finish?” and “Which activities can be delayed without affecting the overall deadline?”

关键路径分析是一种项目管理技术，始于20世纪50年代，用于安排和协调大型项目。在GCSE Edexcel数学中，你将应用它把项目建模为活动网络。该网络展示了任务必须完成的顺序，通过分析可以揭示关键路径——即决定整个项目工期的活动序列。理解关键路径分析有助于回答诸如”项目最早何时能完成？”以及”哪些活动可以延迟而不影响最终期限？”等问题。

2. Activities and Precedence Tables | 活动与前序关系表

An activity is any task that consumes time and resources. For instance, “paint walls” or “lay carpet” are activities. A precedence table (or dependence table) summarises all activities, their durations, and which other activities must be finished first. Here is a simple example:

活动是指任何消耗时间和资源的任务。例如，”粉刷墙壁”或”铺设地毯”都是活动。前序关系表（或称依赖表）概括

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