Investigating the shortest and safest path to take between 4 Los Angeles Neighbourhoods during the COVID-19 pandemic to minimise the risk of contagion and distance travelled using graph theorySL
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4
Official IB Result
11/20
General feedback
11/20
0
10
20
No overall summary is available for this report.
5.1·Weakness
Page 11
Skipping the worked Dijkstra steps in the safer-route section weakens the reflection because the reader cannot check how the result emerged. The student should show at least one representative iteration or a verification step to support confidence in the conclusion.
5.2·Weakness
Page 13
The justification that risk is more important than distance is stated, but it is not critically examined against the outcomes. The student should compare the distance-only, risk-only, and combined results more explicitly to evaluate whether the chosen weights actually achieved the intended balance.
5.3·Question
Page 18
Do the three route sets actually support the claim that the model finds the “quickest and safest” path, or do they reveal a trade-off between the two aims? Addressing that directly would make the evaluation much more convincing.
5.4·Strength
Page 18
The evaluation now acknowledges a key modelling simplification: treating each neighbourhood as one coordinate. That is a useful reflective step because it shows awareness that the model is an approximation rather than a perfect representation.
5.5·Suggestion
Page 18
A stronger evaluation would compare the stated future improvements with the actual limitations of the model. For example, the student could explain which extra factor would matter most and why it would improve the realism of the route decisions.
5.6·Weakness
Page 18
The reflection is still mostly descriptive and does not test how sensitive the results are to the modelling assumptions. The student should discuss, for example, whether changing the coefficient ratio or the risk aggregation rule would alter the chosen route.
Criteria A: Presentation
3/4
0
2
4
Criteria Strands
A.1Coherence and logical development
Good
A.2Organization and structure
Good
A.3Conciseness and relevance
Moderate
Criteria Feedback
- Your exploration has a clear sequence that is easy to follow from the original graph model through to the final route comparisons.
- You use a well-organized structure with labelled sections, tables, and graphs that support the reader’s understanding.
- Most of the material stays relevant to the investigation and keeps the focus on route modelling and decision-making.
- Some sections include more context than the mathematics needs, which makes the exploration longer than necessary.
- A few transitions between steps are described more procedurally than reasoned out in detail.
- Several large tables could be condensed or moved out of the main body to improve readability.
1.1·Weakness
Page 2
This historical background on COVID-19 is still much longer than the mathematical setup requires. The student should condense it to only the details needed to justify the risk model, so the exploration stays tightly centred on the graph optimisation.
1.2·Strength
Page 2
The introduction now gives the investigation a clearer opening than the previous draft by moving quickly into the COVID-19 context and then into the aim. This helps the reader understand why the route model matters before the graph theory content begins.
1.3·Weakness
Page 3
The list of 12 neighbourhoods and coordinates is extensive, but the later calculations only use a subset of routes. The student should trim or relocate the full dataset so the main body is less crowded and the most relevant nodes are easier to follow.
1.4·Strength
Page 4
The phrase “Finding the shortest route between 6 locations” signals the task clearly and keeps the exploration focused on the mathematical objective. This explicit signposting helps the overall structure feel purposeful rather than descriptive.
1.5·Suggestion
Page 6
Consider summarising the large adjacency tables with only the connected edges that are actually used in the route calculations. That would improve conciseness while keeping the essential mathematical information visible.
1.6·Question
Page 18
Which of the many modelling choices had the biggest effect on the final routes: the graph connectivity, the risk scaling, or the coefficient choice? A brief comparison here would make the evaluation feel more analytical.
Criteria B: Mathematical Communication
3/4
0
2
4
Criteria Strands
B.1Mathematical language and notation
Good
B.2Multiple representations
Excellent
B.3Logical structure and clarity
Good
Criteria Feedback
- You use graph language, matrices, and algorithm terminology appropriately and mostly consistently.
- You include multiple mathematical representations, such as maps, adjacency matrices, Dijkstra tables, and permutations, to support the same investigation.
- Your communication is generally clear and the reader can usually follow how each part connects to the next.
- Some calculations are not shown in enough detail, especially in the later shortest-path work.
- A few notations are not fully defined early enough, which can make the combined-weight section harder to interpret.
- Some symbols and conventions could be made more consistent throughout the write-up.
2.1·Strength
Page 3
The notation and the later use of adjacency matrices show a solid grasp of graph language. This makes the model easy to interpret and gives the exploration a mathematically appropriate framework.
2.2·Strength
Page 10
The normalization formula is clearly defined and the variables are explained immediately afterwards. This is strong mathematical communication because the reader can see exactly how the density values are transformed before being turned into risk factors.
2.3·Weakness
Page 11
The statement “The average of the risk factors was chosen” is still too brief for a key modelling decision. The student should explain why averaging the two endpoint risks is a reasonable edge model, and whether another rule might better represent exposure along a route.
2.4·Weakness
Page 12
The combined-weight formula is stated clearly, but the notation does not fully show whether and are raw values or normalized values at this point. The student should make that distinction explicit to avoid ambiguity in later calculations.
2.5·Suggestion
Page 16
The total-path expression would be stronger if the student renamed the path total with a different symbol, since already refers to the route itself. Using separate symbols for the route and its weight would improve clarity.
2.6·Question
Page 17
What would change if the invalidity check were replaced by a penalty instead of a full rejection? Thinking about that distinction could sharpen the student’s understanding of how the brute-force search is filtering routes.
Criteria C: Personal Engagement
2/3
0
2
3
Criteria Strands
C.1Independent thinking
Good
C.2Personal approach
Good
C.3Creativity and initiative
Good
Criteria Feedback
- You show clear ownership of the investigation by choosing a real-world travel context that matters to the model.
- You make purposeful modelling decisions, such as balancing distance and risk rather than treating the problem as purely geometric.
- You extend the work beyond a standard shortest-path task by adding a constrained route variant.
- Some of your modelling choices are presented as preferences rather than deeply justified decisions.
- The investigation stays fairly close to familiar methods and does not explore many alternative approaches.
- The personal angle comes more from the chosen context than from a highly distinctive mathematical framework.
3.1·Strength
Page 4
Mapping real neighbourhood coordinates onto Desmos shows initiative because the student is not only applying a template, but building a location-based model from chosen data. That personal selection gives the exploration a clear real-world anchor.
3.2·Weakness
Page 13
The statement is sensible, but it is still presented as a preference rather than a justified modelling choice. The student should briefly explain why this weighting best matches the real-world goal instead of simply asserting it.
3.3·Strength
Page 13
The decision to make risk more important than distance and then assign and shows the student is making modelling choices rather than merely following a fixed procedure. This is a genuine sign of ownership over the investigation.
3.4·Weakness
Page 15
The TSP extension is a good idea, but the setup remains quite conventional because it mainly applies brute force to a reduced route list. The student could show stronger independent thinking by comparing this method with another optimisation strategy or by justifying the chosen intermediate nodes.
3.5·Question
Page 18
How might the final routes change if neighbourhoods were represented by multiple access points instead of one coordinate each? That question would push the investigation beyond a standard graph model and deepen the sense of initiative.
3.6·Suggestion
Page 18
To strengthen the personal approach, the student could evaluate whether the chosen neighbourhoods reflect a realistic travel pattern in Los Angeles. Linking the model back to a more specific personal or practical scenario would make the investigation feel more distinctive.
Criteria D: Reflection
1/3
0
2
3
Criteria Strands
D.1Depth of reflection
Poor
D.2Critical analysis
Poor
D.3Evaluation of outcomes
Poor
Criteria Feedback
- You do reflect on the practicality of the methods and mention some limitations of the model.
- You show awareness that the investigation could be extended with additional real-world factors.
- You provide some commentary on what the route results mean in the context of the problem.
- Your reflection is mostly descriptive rather than deeply analytical.
- You do not examine how strongly the outcomes depend on key modelling choices.
- The implications of the route comparisons are not developed in enough detail.
Criteria E: Use of Mathematics
2/6
0
3
6
Criteria Strands
E.1Relevance of mathematics
Good
E.2Level appropriateness
Moderate
E.3Understanding and accuracy
Moderate
Criteria Feedback
- You use relevant mathematics appropriately for the problem, especially graphs, weighted networks, normalization, and shortest-path methods.
- Your risk calculation from population density shows real mathematical processing rather than simple description.
- You demonstrate a solid grasp of how different mathematical ideas can be combined into one model.
- Some calculations are not shown fully, which limits how easy it is to verify the results.
- A few modelling steps, such as the combined-weight setup and permutation checking, need clearer justification.
- There are some minor inconsistencies in notation and explanation that affect precision.
4.1·Strength
Page 6
The initialization step is now explained clearly, including the role of the starting node and the meaning of tentative distances. This improves mathematical transparency and addresses the earlier issue of unexplained setup.
4.2·Weakness
Page 8
The instruction to “repeat this process for every node” leaves too much of the calculation hidden. Even if the full table is large, the student should show at least one more intermediate iteration so the shortest-path result can be checked rather than merely accepted.
4.3·Strength
Page 10
The worked normalization example for Westchester is a strong addition because it shows the student can carry a real data point through the full modelling process. That makes the risk-factor table much easier to trust and follow.
4.4·Strength
Page 12
The separate formulas for and are a clear improvement in communication and accuracy. The student now distinguishes the two quantities explicitly, which helps prevent the earlier confusion between raw and transformed values.
4.5·Weakness
Page 12
The formula still needs a stronger justification, especially for the factor of 100. The student should explain why this scaling is necessary and what it changes mathematically, rather than presenting it as a simple convention.
4.6·Weakness
Page 16
The permutation count contains a mathematical error: does not equal as written. The student should correct the counting logic by clearly identifying how many intermediate cities are being permuted and then computing the factorial from that value.
4.7·Weakness
Page 17
The exemplar permutation calculation is not transparent enough because the path is immediately marked invalid without showing each consecutive edge check in detail. The student should show the route segment by segment so the invalidity comes from the matrix rather than from assertion.
4.8·Suggestion
Page 18
The final route claim would be stronger if the student briefly compared it with the next-best valid permutation. That would demonstrate that the chosen route is optimal, not just one acceptable output from the brute-force search.