Edexcel进阶数学D1决策数学评分标准全解析 | Edexcel Further Maths D1 Decision Maths: Mark Scheme Guide

Edexcel进阶数学D1决策数学评分标准全解析

一、评分标准中的M分、A分与B分 | M Marks, A Marks and B Marks in the Mark Scheme

Edexcel进阶数学的Decision Maths 1（决策数学1，简称D1）试卷，评分标准围绕三种标记展开：M分是方法分，只要考生展示了正确的解题思路，即使最后答案算错，方法分依然保留；A分是准确分，必须建立在正确方法的基础上，通常要求答案以指定形式给出，比如保留两位小数或者写成某个精确值；B分是独立分，不依赖其他步骤，例如直接写出正确的初始状态或图论中的术语。读懂这三种标记的差别，是正确使用评分标准的第一步。

The Edexcel Further Maths Decision Maths 1 paper, known as D1, uses a mark scheme built on three types of annotation. An M mark is a method mark: it is awarded as soon as the candidate shows a valid approach, even if the final answer is wrong. An A mark is an accuracy mark, which is only awarded on top of a correct method and normally requires the answer in a specified form, such as two decimal places or an exact value. A B mark is an independent mark, given for a correct statement, diagram or value that does not depend on earlier working, for example writing down the correct initial state of an algorithm or a correct graph theory term. Understanding the difference between these three mark types is the first step in using any D1 mark scheme properly.

二、方法分M1的判定规则 | How Method Marks M1 Are Awarded

在D1评分标准中，M1分通常对应"正确的算法步骤开始执行"。例如冒泡排序中完整写出第一趟比较，或者Prim算法中正确选择第一条最小边，都构成M1。阅卷时只看步骤痕迹是否出现，不追究数值是否完美。特别要注意：算法中途出错但思路正确，后续的M分仍然可以拿到，这就是"方法分独立于准确分"的含义。因此答题时务必保留每一步过程，哪怕涂改，也不要整段划掉，因为痕迹本身就是分数。

In the D1 mark scheme, an M1 mark usually corresponds to the start of a correct algorithmic procedure. For example, writing out the first complete pass of a bubble sort, or selecting the correct first edge in Prim's algorithm, both earn an M1. Examiners look only for the trace of the step, not for perfect arithmetic. A key point is that if the approach is right but a numerical error occurs midway, later method marks can still be awarded, because method marks are independent of accuracy marks. This is why candidates should keep every line of working visible, and never cross out a whole section even after a mistake, since the trace itself is worth marks.

三、准确分A1与答案书写要求 | Accuracy Marks A1 and Answer Presentation

A1分的要求比M分严格得多。评分标准中常见两种标注：awrt表示"在此范围内均可接受"，通常用于四舍五入的数值；cao表示"仅此一个正确答案"，多用于排序的最终序列或最短路的总距离。要拿稳A1分，最终答案必须写在显眼位置，比如画框或者另起一行单独写出。很多考生过程全对，却把最终答案藏在草稿般的过程里，阅卷人找不到，A分就丢了。养成"答案单独成行"的习惯，是性价比最高的提分动作。

A1 marks are far stricter than M marks. The mark scheme uses two common annotations: awrt means any value within the given range is accepted, usually applied to rounded numbers; cao means only the exact correct answer is accepted, typically used for the final sequence of a sort or the total distance of a shortest path. To secure the A1 mark, the final answer must be placed prominently, for example boxed or written on its own line. Many candidates complete the working correctly but bury the answer among messy steps, so the examiner cannot find it and the accuracy mark is lost. Making it a habit to present the final answer on a separate line is the most cost-effective way to raise marks.

四、排序算法题的得分点 | Scoring Points in Sorting Algorithm Questions

排序题是D1的送分题，但失分也最冤枉。评分标准通常按"趟数分"和"最终顺序分"分开给：冒泡排序每一趟的比较结果都要完整写出，漏写一趟就丢一趟的M分；快速排序要求标明pivot（基准值）的选择，并展示划分过程；穿梭排序（shuttle sort）则要求每趟后圈出已经就位的元素。最终顺序必须按cao标准精确匹配。建议用表格逐趟记录，既清晰又不易漏步。

Sorting questions are the easiest marks on the D1 paper, yet they are also where marks are lost most carelessly. The mark scheme typically splits marks between the passes and the final order. For bubble sort, every pass must be written out in full, and a missing pass loses that pass's method mark. Quicksort requires the pivot to be stated and the partition steps shown. Shuttle sort expects each pass to ring the elements already in their final positions. The final order must match exactly under the cao rule. Recording each pass in a small table keeps the working clear and prevents skipped steps.

五、装箱问题的评分陷阱 | Marking Traps in Bin Packing Questions

装箱问题（bin packing）的评分标准有三个陷阱。第一，first-fit decreasing算法必须先按降序排列物品，这个排序步骤本身就占M分，跳过排序直接装箱会丢分；第二，每个物品放入哪只箱子必须标注清楚，评分标准按"物品分配是否正确"逐件给分，部分正确就部分得分；第三，题目若要求"最少箱子数"，单纯给出数字往往不够，还需一句简短说明，例如"9个箱子可以装下，8个箱子容量不足"，这属于B分。答题时逐件写清分配，不要心算后只写总数。

Bin packing questions hide three traps in the mark scheme. First, the first-fit decreasing algorithm requires the items to be sorted into descending order first, and this sorting step itself carries a method mark; packing without sorting loses it. Second, the box assigned to each item must be clearly recorded, because marks are awarded item by item according to whether the allocation is correct, so partial answers still earn partial credit. Third, when the question asks for the minimum number of bins, a bare number is often not enough; a short justification is expected, such as noting that nine bins suffice while eight do not have enough capacity, and this earns a B mark. Candidates should write the allocation item by item instead of calculating mentally and writing only the total.

六、最小生成树题目的答题规范 | Answering Conventions for Minimum Spanning Trees

最小生成树（minimum spanning tree）考查Kruskal算法和Prim算法。评分标准的给分点是"边的选择顺序"：Kruskal按权重从小到大逐条加边，遇到成环的边要明确跳过；Prim从起始顶点出发，每次选择连接已选集合与未选集合的最小权边。两类算法的M分都按"选对的边数"累计，A分则要求最终树的总权重正确。阅卷时若只看图不看过程，很容易丢分，所以必须写出每一步选择的边的编号或权重，形成可追踪的边序列。

Minimum spanning tree questions test Kruskal's algorithm and Prim's algorithm. The mark scheme focuses on the order in which edges are selected. Kruskal's algorithm adds edges in increasing order of weight and explicitly skips any edge that would create a cycle. Prim's algorithm starts from a chosen vertex and repeatedly selects the smallest-weight edge joining the selected set to the remaining vertices. Method marks accumulate for each correctly chosen edge, while the accuracy mark requires the total weight of the final tree to be correct. Since an examiner cannot follow a diagram alone, candidates must list every chosen edge, by label or weight, producing a traceable sequence of selections.

七、Dijkstra最短路题的表格分 | Table Marks in Dijkstra's Algorithm Questions

Dijkstra最短路算法以"表格分"著称，评分标准逐行给分。每处理一个顶点，临时值、圈出值和前驱顶点都要正确填写；一行出错不影响其他行的得分，这就是表格题的宽容之处。最终答案部分通常分两问：最短距离和最短路径，前者按数值给A分，后者按路径经过的顶点序列给分，路径必须从头写起。常见失分点是圈出顶点后忘记划掉旧临时值，以及最终路径漏写起点。考前用三张真题表格练手，能显著提高这类题的正确率。

Dijkstra's shortest path algorithm is famous for table marks, with the mark scheme awarding marks row by row. For each vertex processed, the temporary values, the ringed value and the predecessor must all be filled in correctly; an error in one row does not affect the marks of other rows, which is why table questions are relatively forgiving. The final answer usually has two parts: the shortest distance and the shortest route. The distance earns an accuracy mark for its value, while the route earns marks for the sequence of vertices, which must be listed from the start. Common mark losses include forgetting to cross out old temporary values after ringing a vertex, and omitting the starting vertex in the final route. Practising three past-paper tables before the exam improves accuracy significantly.

八、中国邮路问题的配对分 | Pairing Marks in Route Inspection Problems

路线检查问题（route inspection，又称中国邮路问题）的评分标准集中在"奇点配对"上。第一步找出所有奇数度顶点，每个奇点本身占分；第二步将奇点两两配对，评分标准会列出所有可接受配对及其最短路径距离，正确配对给M分；第三步把配对距离相加得到重复行走的总长度，再与原始路径总长相加得到最终答案。配对方案不唯一，只要距离和最小即可。答题时先画奇点列表，再写配对和距离，最后汇总，结构清晰能保证每一步的分数落袋。

The route inspection problem, also called the Chinese postman problem, is marked mainly on the pairing of odd vertices. The first step is to identify all vertices of odd degree, and each odd vertex found earns a mark. The second step pairs these vertices, and the mark scheme lists all acceptable pairings with their shortest-path distances; a correct pairing earns a method mark. The third step sums the paired distances to find the total duplicated length, then adds it to the original route length for the final answer. The pairing is not unique, so any combination giving the minimum total distance is accepted. Writing the odd-vertex list first, then the pairings with distances, and finally the total, guarantees that every stage of the marks is secured.

九、线性规划作图的得分要求 | Drawing Requirements for Linear Programming

线性规划（linear programming）题在D1中分值较高，评分标准按"约束线、可行域、目标线"三块给分。每条约束线都要正确画出，直线方程写在图旁；可行域必须清晰标出，常用阴影或箭头表示；目标线的位置和移动方向要正确，最优解交点要圈出。整数解问题额外要求"检验相邻整数点"，每检验一个点就给一个B分，最终答案取使目标函数最大的可行整数点。作图题最忌"差不多"，交点在网格交叉点附近时，必须代入验证。

Linear programming carries significant marks in D1, and the mark scheme awards them in three blocks: constraint lines, the feasible region and the objective line. Every constraint must be drawn correctly with its equation written beside the line; the feasible region must be clearly identified, usually by shading or arrows; and the objective line must be positioned and shifted in the correct direction, with the optimal vertex ringed. Integer programming questions additionally require testing neighbouring integer points, and each tested point earns a B mark, with the final answer being the feasible integer point that maximises the objective function. Drawing questions punish approximate work, so when the optimal vertex lies near a grid intersection, substitution is essential to confirm it.

十、关键路径分析的浮动时间分 | Float Marks in Critical Path Analysis

关键路径分析（critical path analysis）的评分标准围绕最早开始时间、最晚开始时间、浮动时间和关键路径展开。活动网络图中，每个活动的两个时间值都要计算正确，这是M分的来源；浮动时间（float）等于最晚开始减最早开始，公式套对即得分；总浮动为零的活动串成关键路径，标出关键路径有专门的B分。Gantt图（甘特图）题目按活动条的位置和长度给分，错一位就丢A分。建议先用表格列出每个活动的时间，再画图，能减少低级错误。

The mark scheme for critical path analysis revolves around earliest start times, latest start times, float and the critical path. In the activity network, both time values for every activity must be computed correctly, which provides the method marks. The float equals the latest start minus the earliest start, so applying the formula correctly earns the marks. Activities with zero total float form the critical path, and identifying it carries a dedicated B mark. Gantt chart questions award marks for the position and length of each activity bar, so a one-cell shift loses the accuracy mark. Listing all activities with their times in a table before drawing the chart is a reliable way to avoid careless errors.

十一、D1备考的失分点与对策 | Common Mark Losses and How to Avoid Them

结合多年评分标准，D1最常见的失分点有四类：一是过程痕迹不完整，算法步骤跳步导致M分丢失；二是最终答案位置不显眼，A分找不到；三是单位、保留位数不符合awrt要求；四是整数解问题漏检验。对策也很明确：每道真题做完后，对照评分标准逐条核对M、A、B分的落点，统计自己在哪类题目上丢分最重，再针对性重做。D1题型高度固定，吃透近五年真题的评分标准，分数提升比刷十套新题更快。

Across many years of mark schemes, four mark losses dominate in D1. First, incomplete working traces: skipping algorithm steps loses method marks. Second, an inconspicuous final answer: accuracy marks cannot be awarded if the examiner cannot find the result. Third, ignoring units or the required degree of rounding, which fails the awrt condition. Fourth, missing the integer-point check in integer programming questions. The remedy is equally clear: after each past paper, check every M, A and B mark against the mark scheme, identify the question types where marks are lost most heavily, and redo those specific questions. D1 has a highly fixed question structure, so mastering the mark schemes of the last five years of past papers improves scores faster than grinding through ten new papers.

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