Report an issue
This site uses cookie tracking technologies. Learn more in our
Cookie Policy
.
Opt out
Allow
Mathematics Analysis and Approaches (AA) IA Exemplar: Synodic Period… | RevisionDojo
Loading document preview...
View file
Back
IB Mathematics Analysis and Approaches (AA) HL Internal Assessment Example
Scores
Rubric
Similar Examples
10
Chat
Determining the synodic period of Mars using an abstracted model
HL
Loading scores...
A
B
C
D
E
4
Official IB Result
9/20
Verified
Moderated
Was this exemplar helpful?
Want a report just like this?
Free mini report for your own coursework
Fast feedback on what to improve next
Annotated highlights on your writing
Review my coursework for free
General feedback
9/20
0
10
20
5.1
·
Suggestion
Page 1
• Click to view
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
• Click to view
The list of references is comprehensive and correctly formatted, strengthening the investigation’s academic grounding.
Criteria A: Presentation
3/4
0
2
4
Criteria Strands
View Full Rubric
A.1
Coherence and logical development
Good
A.2
Organization and structure
Good
A.3
Conciseness 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
Comments
1.1
·
Strength
Page 1
• Click to view
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
• Click to view
The list of model assumptions is concise and clear; however, grouping them into numbered subsections would improve structure.
1.3
·
Strength
Page 2
• Click to view
The definition of “total planetary alignment” is explicit and well-placed, providing clear scope for the investigation.
1.4
·
Weakness
Page 2
• Click to view
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
• Click to view
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
• Click to view
The repetition of algebraic manipulations across multiple cases leads to unnecessary length; consolidate shared steps to improve conciseness.
1.7
·
Suggestion
Page 5
• Click to view
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
• Click to view
Equation (16) clusters multiple lines without explanation; break into separate numbered equations and add commentary on each transformation.
1.9
·
Weakness
Page 8
• Click to view
Section headings mix lower- and uppercase styling (“Step 1” vs “Step 2”); standardize formatting to improve visual coherence.
1.10
·
Weakness
Page 10
• Click to view
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 Strands
View Full Rubric
B.1
Mathematical language and notation
Moderate
B.2
Multiple representations
Moderate
B.3
Logical 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
Comments
2.1
·
Weakness
Page 3
• Click to view
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
• Click to view
Assumptions list is thorough, but adding a table summarizing these assumptions could enhance readability and quick reference.
2.3
·
Weakness
Page 4
• Click to view
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
• Click to view
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
• Click to view
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
• Click to view
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 Strands
View Full Rubric
C.1
Independent thinking
Poor
C.2
Personal approach
Poor
C.3
Creativity 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 Strands
View Full Rubric
D.1
Depth of reflection
Poor
D.2
Critical analysis
Poor
D.3
Evaluation 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
Comments
3.1
·
Suggestion
Page 7
• Click to view
The general opposition formula is elegant; linking it algebraically to the standard synodic period formula would deepen mathematical insight.
3.2
·
Weakness
Page 9
• Click to view
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 Strands
View Full Rubric
E.1
Relevance of mathematics
Poor
E.2
Level appropriateness
Poor
E.3
Understanding 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
Comments
4.1
·
Weakness
Page 4
• Click to view
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
• Click to view
There is no discussion of the valid integer range for k when interpreting physical occurrences; specifying k bounds ensures meaningful solutions.
