Determining the synodic period of Mars using an abstracted modelHL
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4
Official IB Result
9/20
General feedback
9/20
0
10
20
No overall summary is available for this report.
5.1·Suggestion
Page 1
The word count and page count are administrative details and do not contribute to the academic content; they could be moved to an appendix or removed.
5.2·Strength
Page 11
The list of references is comprehensive and correctly formatted, strengthening the investigation’s academic grounding.
Criteria A: Presentation
3/4
0
2
4
Criteria StrandsPro
A.1Coherence and logical development
Good
A.2Organization and structure
Good
A.3Conciseness and relevance
Moderate
Criteria Feedback
- Overall narrative is coherent and logically developed
- Clear numbering of major headings and placement of figures close to relevant text
- Exploration stays within the word limit and covers all key sections
- Abrupt transitions between some sections (e.g., LCM discussion to simultaneous equations)
- Inconsistent figure and heading numbering and formatting
- Repetition of algebraic steps leads to unnecessary length
1.1·Strength
Page 1
The title is clear and indicates the investigation topic effectively, but consider specifying the synodic period focus to enhance precision.
1.2·Suggestion
Page 2
The list of model assumptions is concise and clear; however, grouping them into numbered subsections would improve structure.
1.3·Strength
Page 2
The definition of “total planetary alignment” is explicit and well-placed, providing clear scope for the investigation.
1.4·Weakness
Page 2
The opening anecdote is engaging but digresses into planetary trivia never referenced later; focus strictly on model rationale to maintain relevance.
1.5·Weakness
Page 3
The transition from model description to introducing functions in Solution 3 is abrupt; insert a brief bridging paragraph to improve coherence.
1.6·Weakness
Page 5
The repetition of algebraic manipulations across multiple cases leads to unnecessary length; consolidate shared steps to improve conciseness.
1.7·Suggestion
Page 5
The heading “3.1 Solving for Opposition” is clear, but the sub-subsections lack consistent numbering; align numbering style throughout.
1.8·Suggestion
Page 6
Equation (16) clusters multiple lines without explanation; break into separate numbered equations and add commentary on each transformation.
1.9·Weakness
Page 8
Section headings mix lower- and uppercase styling (“Step 1” vs “Step 2”); standardize formatting to improve visual coherence.
1.10·Weakness
Page 10
The caption “Figure 3: Figure 3:” is redundant; remove duplication and ensure captions are concise and unique.
Criteria B: Mathematical Communication
2/4
0
2
4
Criteria StrandsPro
B.1Mathematical language and notation
Moderate
B.2Multiple representations
Moderate
B.3Logical structure and clarity
Moderate
Criteria Feedback
- Use of standard mathematical notation (θ, subscripts, π) throughout
- Inclusion of unit-circle sketches, sine-wave graphs, and external reference plots
- Most algebraic explanations precede the manipulations
- Some notation inconsistencies (calling 365 and 687 the 'lowest common factor', inconsistent boldface)
- Axes and scales are missing in graphs; variables defined after first use
- Transitions between general solutions and numerical results are terse
2.1·Weakness
Page 3
Figure 1 lacks axis labels and scale markers; include x- and y-axis labels on the unit circle diagram to clarify coordinate definitions.
2.2·Suggestion
Page 3
Assumptions list is thorough, but adding a table summarizing these assumptions could enhance readability and quick reference.
2.3·Weakness
Page 4
Notation in equations (1)–(4) uses an argument (x) but then refers to θ in text; unify variable symbols to reduce confusion.
2.4·Weakness
Page 5
The integer k is introduced but its domain is not explicitly stated until later; define k ∈ ℤ at first mention for clarity.
2.5·Weakness
Page 7
Expressions for θₒ use Eₜ and Mₜ before these symbols are defined; introduce their definition earlier to maintain logical flow.
2.6·Weakness
Page 10
Axes and data points on the theoretical synodic period graph are unlabeled; include axis titles and scale ticks for clarity.
Criteria C: Personal Engagement
1/3
0
2
3
Criteria StrandsPro
C.1Independent thinking
Poor
C.2Personal approach
Poor
C.3Creativity and initiative
Poor
Criteria Feedback
- Opening anecdote provides a brief personal voice
- Choice of Earth–Mars model shows some initiative
- Use of colour-coded graphs reflects minimal personal approach
- Mathematics largely follows a standard textbook derivation
- No novel techniques or extensions are attempted
- Limited independent thinking beyond selecting the planetary case
Criteria D: Reflection
1/3
0
2
3
Criteria StrandsPro
D.1Depth of reflection
Poor
D.2Critical analysis
Poor
D.3Evaluation of outcomes
Poor
Criteria Feedback
- Basic comparison of calculated vs. theoretical synodic period
- Reporting of percentage error provides elementary evaluation
- No discussion of model limitations or error sources
- Lacks depth in critical analysis and no suggestions for future work
- Reflection confined to noting numerical closeness without insight
3.1·Suggestion
Page 7
The general opposition formula is elegant; linking it algebraically to the standard synodic period formula would deepen mathematical insight.
3.2·Weakness
Page 9
Combining the frequencies of opposition and conjunction by simply adding counts lacks justification; explain why summation yields an average period.
Criteria E: Use of Mathematics
2/6
0
3
6
Criteria StrandsPro
E.1Relevance of mathematics
Poor
E.2Level appropriateness
Poor
E.3Understanding and accuracy
Poor
Criteria Feedback
- Trigonometric model directly addresses the exploration question
- Mathematics is at the appropriate SL level (trig identities, LCM, period conversion)
- Derivations are generally correct and relevant
- Mislabeling the LCM as 'lowest common factor'
- Conceptual slips in rounding and no domain specified for integer k
- Scope is narrow (circular orbits only), with missed opportunities for extension
4.1·Weakness
Page 4
Calling 365 and 687 their “lowest common factor” is incorrect; replace with “product” or clarify that you mean LCM of the periods.
4.2·Weakness
Page 8
There is no discussion of the valid integer range for k when interpreting physical occurrences; specifying k bounds ensures meaningful solutions.