Edexcel Further Maths Decision Maths 1 QP: Full Topic Guide | Edexcel 高等数学决策数学 1 真题全解

📚 Edexcel Further Maths Decision Maths 1 QP: Full Topic Guide | Edexcel 高等数学决策数学 1 真题全解

Decision Maths 1 (D1) is a very practical module in Edexcel Further Mathematics. Unlike pure mathematics, it focuses on algorithms, optimisation, and discrete structures such as graphs and networks. Many students find the ideas easier to understand, but exam papers require precise working, clear tables, and efficient use of notation. This guide breaks down the most common Question Paper topics, the methods you need to demonstrate, and the typical pitfalls to avoid in the Edexcel D1 exam.

决策数学 1（D1）是 Edexcel 高等数学中一门非常实用的模块。与纯数学不同，它关注算法、优化以及图与网络等离散结构。很多学生觉得这些概念更容易理解，但考试要求精确的过程书写、清晰的表格以及规范的符号使用。本指南将解析 D1 真题中最常见的考点、你需要展示的方法，以及考试中要避免的典型失分点。

1. D1 Exam Paper Structure | D1 试卷结构概览

The Edexcel D1 Question Paper is usually a single paper lasting 1 hour 30 minutes with 75 raw marks. It contains about 7 to 8 structured questions. You must show your working in the answer booklet, and many questions require explicit tables, lists, or updated diagrams. The paper is designed to test both routine algorithm use and the ability to interpret a problem in a new context.

Edexcel D1 真题通常为一份 1 小时 30 分钟、75 分的试卷，包含 7 至 8 道结构化题目。考生需要在答题册中写出完整过程，很多题目要求明确列出表格、列表或更新图形。试卷既考查常规算法的使用，也考查在新情境中解读问题的能力。

常见考点包括算法与排序、装箱问题、图与网络、最小生成树、Dijkstra 最短路径、路径检查、关键路径分析、线性规划和匹配问题。考题通常采用结构化分步设问，所以即使最终答案错误，清晰的中间步骤仍然可以获得大量方法分。

2. Algorithms and Sorting | 算法与排序

D1 papers often start with sorting algorithms and binary search. For bubble sort, you compare adjacent elements and swap them if they are in the wrong order. You keep making passes until a full pass produces no swaps. For quick sort, choose a pivot, partition the list into numbers smaller than the pivot and numbers larger than the pivot, then repeat on each sublist. Binary search works on an ordered list by repeatedly comparing the target with the middle value and discarding the half that cannot contain the target.

D1 试卷常以排序算法和二分查找开头。冒泡排序通过比较相邻元素并在顺序错误时交换，持续进行若干趟，直到某一趟没有发生交换。快速排序先选取基准值，将列表分成小于基准和大于基准的两部分，然后递归处理每个子列表。二分查找适用于已排序列表，通过不断与中间值比较，舍弃不可能包含目标值的一半。

Bubble sort maximum comparisons = n(n − 1) / 2

冒泡排序的最多比较次数为 n(n − 1) / 2。考试中需要正确计算比较和交换次数，尤其是当题目给出具体列表并要求展示每一趟排序后的结果时。

3. Bin Packing | 装箱问题

Bin packing questions give items with known sizes and bins with fixed capacity. The three heuristic methods are first-fit, first-fit decreasing, and full-bin. First-fit places each item into the first bin that has enough space. First-fit decreasing sorts items into decreasing order before applying first-fit. Full-bin looks for groups of items that exactly fill a bin. You also need to calculate a lower bound by dividing the total item size by the bin capacity and rounding up.

装箱问题给出已知大小的物品和固定容量的箱子。三种常用启发式算法是首次适应、降序首次适应和满箱策略。首次适应将每个物品放入第一个有足够空间的箱子；降序首次适应先将物品按大小降序排列；满箱策略寻找恰好填满一个箱子的组合。考生还需要用总物品大小除以箱子容量并向上取整来计算下界。

Lower bound = ⌈ total item size / bin capacity ⌉

下界计算公式为总物品大小除以箱子容量并向上取整。它给出了理想情况下所需箱子的最小数量，但启发式算法不一定总达到这个下界。题目常要求比较不同启发式算法的结果，并指出哪种方法使用了更少的箱子。

4. Graphs and Networks: Minimum Spanning Trees | 图与网络：最小生成树

A minimum spanning tree connects all vertices of a network with the minimum total weight and no cycles. Kruskal’s algorithm chooses the shortest unused edge that does not form a cycle, repeating until n

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