D1 Decision Mathematics 1 is an IAS applied unit in Pearson Edexcel International A Level Mathematics. It covers algorithms, networks, project planning and linear programming. For the full Mathematics award, D1 can be paired with M1 Mechanics 1 or S1 Statistics 1, alongside compulsory P1 to P4.
Use this page as an independent revision note for the current Issue 3 specification. It is not Pearson's solution bank or a reproduced mark scheme. D1 can also be used in some Further Mathematics routes, but the qualification rules and result use are separate.
Official unit scope
Algorithms and graph terminology.
Minimum spanning trees and shortest paths.
Route inspection and travelling-salesperson bounds.
Critical path analysis.
Linear programming and simplex ideas.
Sorting, packing and matching algorithms.
Where D1 fits
Level: IAS applied unit.
Full IAL Mathematics routes: M1 + D1 or S1 + D1.
Revise first:
Check this topic from memory
Attempt the matching topic bank before reopening the notes. Use each missed idea to decide what to review next.
The specification assumes prerequisite knowledge stated for the unit, so later-unit questions may combine earlier methods without re-teaching them. Treat the list above as an integrated toolkit. A question can begin in one topic and finish in another, such as using algebra to form a model, calculus to optimise it and a graph to interpret the result.
Core reasoning and methods
Follow an algorithm's tie-breaking and labelling rules visibly so the final answer can be audited.
Distinguish a minimum spanning tree, which connects all vertices cheaply, from a shortest path between two named vertices.
In critical path analysis, use forward and backward passes to identify zero-float activities and project duration.
Write mathematical arguments so another reader can reproduce every transition. Define symbols that are introduced, preserve exact values until a decimal is requested, and place restrictions beside the step that creates them. Calculator use can support arithmetic, graph exploration and checking, but it does not replace a proof, derivation or required chain of working.
When a model is used, state the simplifying assumptions and interpret the answer in the original setting. A mathematically valid root may be inadmissible because it lies outside a time interval, represents a negative length, violates a probability range or conflicts with a geometric domain. The final check is therefore both algebraic and contextual.
Worked example
For a network with edges AB = 2, AC = 5, BC = 1, BD = 4 and CD = 3, Kruskal's algorithm orders edges by weight. Select BC = 1, AB = 2, then CD = 3. These three edges connect all four vertices without a cycle, so the minimum spanning tree has weight 6. Edge BD = 4 is not needed, and AC = 5 would create a cycle after the tree is complete. Recording rejected edges and the reason for rejection demonstrates the algorithm rather than presenting only a final sketch.
The transferable method is to identify the target, select a representation that exposes it, carry out a justified procedure and then check the result independently. If the question gives a result to prove, work from known information toward it rather than assuming the displayed result in an intermediate step.
Connections across the unit
Build a revision map with one row per official content heading. For each row, record a trigger phrase, a standard representation, one method, one condition and one frequent error. Then add links between rows. Algebra supports every unit; graphs reveal roots and rates; trigonometric or probability models impose domain restrictions; calculus or algorithms produce results that still need interpretation.
The formula booklet is a resource, not a substitute for recognition. Practise deciding which formula applies, rearranging it safely and checking that the required assumptions hold. Also distinguish formulae supplied in the booklet from results the specification expects students to know.
How D1 functions in this award
D1 completes either the M1 + D1 or S1 + D1 applied pair for IAL Mathematics. The same official D1 content can appear in a Further Mathematics pathway, but that does not mean one result can automatically be counted in two cash-ins. Ask your centre which qualification will use the unit.
D1 rewards a visible process. Name the algorithm, show each label or table update, apply the stopping rule and interpret the result. A final network or number without the prescribed steps may not demonstrate the method the question asks for.
Common misconceptions and corrections
Using shortest-path logic to answer a minimum-spanning-tree problem. A shortest-path algorithm minimises one route between specified vertices; a minimum spanning tree connects every vertex with minimum total edge weight and no cycle.
Stopping an algorithm once a plausible answer appears. The stopping rule is part of the method
Assuming a lower bound for a travelling-salesperson problem is itself a tour. The bound proves that no tour can be cheaper than that value, but the bound itself need not be a closed route visiting every vertex.
Copying calculator output without validation. Give the requested exact form or accuracy, and use substitution, estimation, dimensions or a second method to check it.
Ignoring the qualification route. Unit content may be shared across awards, but the result cannot automatically be counted in every cash-in combination.
Assessment guidance
The D1 paper is 1 hour 30 minutes and carries 75 marks. Answer all questions and show the mathematical structure that earns method marks. Use diagrams for mechanics, geometry, vectors and networks; label probability events; and state hypotheses or modelling assumptions precisely. Keep exact values through intermediate work unless the question directs otherwise. For numerical answers, round only at the end and state units where relevant. If an answer is rejected by a domain, explain why. When an algorithm, proof or iterative method is requested, display the prescribed steps rather than reporting only the final calculator value.
Retrieval practice
Create five mixed questions that collectively use every official content heading listed above. For each, write the trigger, method, condition, final check and one plausible wrong turn. Complete one question without notes, mark the exact step where your reasoning first diverged, and redo it using a different representation. Finally, explain aloud how D1 contributes to International A Level Mathematics and ask your centre to verify the intended unit combination before cash-in.
