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Mathematics Analysis and Approaches (AA) IA Exemplar: Infinite… | RevisionDojo
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IB Mathematics Analysis and Approaches (AA) HL Internal Assessment Example
Scores
Rubric
Similar Examples
10
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Exploring the Convergence and Divergence of Different Infinite Series Using Various Convergence Tests
HL
A
B
C
D
E
6
Official IB Result
15/20
Verified
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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
Good
Criteria Feedback
Clear logical progression through introduction, body sections and conclusion
Well-structured with headings, sub-headings and table of contents
Mostly concise and relevant material with minimal digressions
Occasional minor lapses in logic when justifying test applicability
Missing page numbers and inconsistent TOC entries hinder navigation
Some redundant sentences and unnecessary standalone lines interrupt flow
Comments
1.1
·
Weakness
Page 1
• Click to view
The inclusion of a standalone “Page Count” line interrupts the academic flow and is unnecessary within the main body.
1.2
·
Strength
Page 1
• Click to view
The title prominently identifies the subject and level of inquiry, providing clear context for the reader.
1.3
·
Suggestion
Page 1
• Click to view
Consider adding a brief abstract or aim statement on the title page to outline objectives and scope.
1.4
·
Weakness
Page 2
• Click to view
The first TOC entry reads “In traditional action,” which appears unrelated to the investigation’s content—review for accuracy.
1.5
·
Weakness
Page 2
• Click to view
The table of contents provides section names but omits page references, making navigation cumbersome.
1.6
·
Suggestion
Page 2
• Click to view
Consider aligning all TOC entries in a consistent format and include page numbers for each section.
1.7
·
Suggestion
Page 3
• Click to view
Footnotes interrupt readability; integrate key references in-text or use endnotes to enhance conciseness.
1.8
·
Suggestion
Page 4
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Repeating the list of series tested adds redundancy; consolidate into one concise paragraph.
1.9
·
Weakness
Page 4
• Click to view
The final sentence trails off mid–thought; complete the aim statement to clarify the scope of series under study.
1.10
·
Suggestion
Page 10
• Click to view
The harmonic series section repeats the definition style; consider referring back to the standard form to avoid redundancy.
1.11
·
Weakness
Page 18
• Click to view
Bibliography entries vary in style and are missing access dates; adopt a consistent citation convention.
Criteria B: Mathematical Communication
3/4
0
2
4
Criteria Strands
View Full Rubric
B.1
Mathematical language and notation
Good
B.2
Multiple representations
Moderate
B.3
Logical structure and clarity
Good
Criteria Feedback
Mostly consistent and accurate use of mathematical language and notation
Step-by-step derivations with clear verbal explanations
Good logical structure enabling the reader to follow arguments
Limited variety of representations—no self-generated tables or CAS outputs
Occasional notation slips (e.g. “ar2” instead of exponent format)
Some omitted intermediate steps reduce absolute clarity
Comments
2.1
·
Strength
Page 3
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The introduction clearly defines infinite sequences and series, establishing foundational concepts effectively.
2.2
·
Suggestion
Page 5
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Consider summarizing the four limit comparison outcomes in a small table to enhance multiple representations.
2.3
·
Weakness
Page 5
• Click to view
The statement of limit comparison test conditions is conflated—L=0 and L=∞ clauses need clearer separation.
2.4
·
Weakness
Page 7
• Click to view
The generalised geometric series’ formula uses “ar2” instead of proper exponent notation
a
r
2
—adjust for consistency.
2.5
·
Suggestion
Page 7
• Click to view
Including a small table of values of
a
n
versus
n
would improve clarity of how
∣
r
∣
controls term size.
2.6
·
Suggestion
Page 9
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The graph visually supports divergence reasoning, but it is a stock image; generating your own CAS plot would be more authentic.
2.7
·
Strength
Page 9
• Click to view
The explanation of how the area under
f
(
x
)
bounds the series is clear and logically structured.
2.8
·
Strength
Page 10
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The conditions for the integral test on
f
(
x
)
=
1/
x
are systematically verified, demonstrating clear methodical communication.
2.9
·
Weakness
Page 10
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In the limit calculation, the step “ln 1=0” is omitted; include explicit evaluation to maintain rigor.
Criteria C: Personal Engagement
2/3
0
2
3
Criteria Strands
View Full Rubric
C.1
Independent thinking
Good
C.2
Personal approach
Good
C.3
Creativity and initiative
Poor
Criteria Feedback
Genuine personal connection to finance and perpetuity valuation
Clear personal voice in introduction and topic choice
Limited creativity—the exploration follows standard convergence tests
Independent thinking is evident but not fully developed into innovative approach
Comments
3.1
·
Strength
Page 3
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The personal connection to finance in perpetuity valuation demonstrates genuine engagement with real-world applications.
3.2
·
Strength
Page 3
• Click to view
The exploration shows clear personal interest in finance, linking theory to real‐world motivation effectively.
Criteria D: Reflection
2/3
0
2
3
Criteria Strands
View Full Rubric
D.1
Depth of reflection
Good
D.2
Critical analysis
Poor
D.3
Evaluation of outcomes
Poor
Criteria Feedback
Meaningful reflections on choice and applicability of tests
Acknowledgment of limitations and learning outcomes
Surface-level critical analysis with limited probing of error sources
Brief evaluation of outcomes without detailed future implications
Comments
4.1
·
Weakness
Page 16
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Reflection on why certain tests were inapplicable is noted but would benefit from deeper critical analysis.
4.2
·
Suggestion
Page 16
• Click to view
Describing how each test complements others in the evaluation section would deepen reflection on methodology.
4.3
·
Weakness
Page 17
• Click to view
The evaluation acknowledges limitations but lacks discussion on error sources or sensitivity of tests.
4.4
·
Suggestion
Page 17
• Click to view
Suggest extending to p-series or root test as noted, and specify expected outcomes to sharpen future directions.
Criteria E: Use of Mathematics
5/6
0
3
6
Criteria Strands
View Full Rubric
E.1
Relevance of mathematics
Good
E.2
Level appropriateness
Good
E.3
Understanding and accuracy
Good
Criteria Feedback
Effective and varied selection of convergence tests (integral, ratio, limit comparison, alternating)
Mathematics fully commensurate with HL course level
Correct derivations with sound conceptual understanding
Minor omissions in justifying continuity and monotonicity conditions
Typographical and notation slips do not undermine overall validity
Comments
5.1
·
Strength
Page 5
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The definition of the generalised arithmetic series is accurately presented with summation notation.
5.2
·
Suggestion
Page 6
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The conclusion that integral test cannot apply due to an increasing derivative needs referencing derivative sign tests.
5.3
·
Strength
Page 6
• Click to view
The limit calculation correctly shows that L=d, a constant >0, proving divergence via limit comparison.
5.4
·
Strength
Page 7
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Use of both ratio and integral tests demonstrates effective selection of HL convergence techniques.
5.5
·
Weakness
Page 8
• Click to view
The integral test application correctly computes
∫
1
∞
a
r
x
d
x
, but justification for continuity on
[
1
,
∞
)
is minimal.
5.6
·
Suggestion
Page 13
• Click to view
In the alternating series test section, rationale is sound but could be improved by referencing Leibniz’s original theorem source.
