The inside of a convex 19-gon is colored using two colors. Prove that there will always exist four vertices such that the centroids of any three of them have the same color.HL
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7
Official IB Result
IB Grade: 7
Criteria A: Presentation
0/4
0
2
4
Criteria StrandsPro
A.1Coherence and logical development
Moderate
A.2Organization and structure
Good
A.3Conciseness and relevance
Moderate
Criteria Feedback
- The student presents their investigation in a recognizable sequence with headings, sections, and a clear mathematical topic.
- The student's choice of graph theory and Ramsey ideas gives the work a coherent academic direction.
- The student's writing is generally easy to navigate because the structure signals where the reader should look next.
- The main line of reasoning does not successfully lead from the graph construction to the geometric conclusion.
- Some sections take up more space than they contribute to the final argument.
- Several diagrams and explanations do not clearly show the exact mathematical claim being used.
Criteria B: Mathematical Communication
0/4
0
2
4
Criteria StrandsPro
B.1Mathematical language and notation
Moderate
B.2Multiple representations
Moderate
B.3Clarity and consistency
Moderate
Criteria Feedback
- The student uses appropriate terms from graph theory such as complete graphs, vertices, edges, and Ramsey notation.
- The student includes several mathematical representations, including symbolic notation and diagrams.
- The student's formatting and sectioning make the work reasonably readable.
- Some definitions and statements are not precise enough to support later arguments.
- The diagrams do not always make clear which objects are being represented or how they relate to the proof.
- At several points the wording blurs important distinctions, which makes the logic harder to verify.
Criteria C: Personal Engagement
0/3
0
2
3
Criteria StrandsPro
C.1Independent thinking
Poor
C.2Personal approach
Poor
C.3Creativity and initiative
Poor
Criteria Feedback
- Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
- Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
- Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur.
- Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
Criteria D: Reflection
0/3
0
2
3
Criteria StrandsPro
D.1Depth of reflection
Poor
D.2Critical analysis
Poor
D.3Connection to understanding
Poor
Criteria Feedback
- Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
- Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
- Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur.
- Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
Criteria F: Use of Mathematics (HL)
0/6
0
3
6
Criteria StrandsPro
F.1Relevance and level
Moderate
F.2Accuracy and correctness
Poor
F.3Knowledge and understanding
Poor
Criteria Feedback
- Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
- Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
- Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur.
- Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.