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IB Mathematics Applications & Interpretation (AI) SL Internal Assessment Example

Is it financially more viable for a student to pay for their education and living expenses by working while studying or is it necessary to take out the student loan, and analyse how this decision will affect their financial stability in future?SL

Official IB Result

9/20

Criteria A: Presentation

2/4

Criteria Strands

A.1Coherence and logical development

Moderate

A.2Organization and structure

Good

A.3Conciseness and relevance

Moderate

Criteria Feedback

Clear articulation of the research question providing a strong foundation for coherence
Well‐structured table of contents and consistent use of headings enhancing navigation
Conclusion synthesizes quantitative findings and directly addresses the research question
Logical progression in data‐collection section from assumptions to methodology

Abrupt transitions between sections (e.g., from interest results to time‐budget discussion) interrupt the flow
Misplaced digressions (IB learner profile references) dilute mathematical focus
Inconsistent citation formatting reduces presentation quality
Extended non‐mathematical commentary (detailed time‐budget paragraph) inflates length without adding insight

1.1·Strength

Page 1• Click to view

The research question is clearly articulated and focused, providing a strong foundation for the exploration’s coherence and logical progression.

1.2·Strength

Page 2• Click to view

The table of contents is well structured with clear headings and page references, enhancing navigation and overall organization.

1.3·Suggestion

Page 3• Click to view

The introduction mentions the IB learner profile, which adds narrative context but dilutes the mathematical focus. Consider refining this to emphasize the specific mathematical aims and models used.

1.4·Weakness

Page 4• Click to view

Citations for tuition and supply costs lack consistent formatting (e.g., access dates, authors). Adopt a standard style to enhance presentation quality.

1.5·Strength

Page 4• Click to view

The data-collection section is clearly sectioned and provides a logical progression from assumptions to methodology.

1.6·Suggestion

Page 13• Click to view

This detailed time-budget paragraph interrupts the mathematical flow. Consider summarizing it or relocating to a reflective section to maintain coherence.

1.7·Strength

Page 15• Click to view

The conclusion concisely synthesizes the quantitative findings and directly addresses the research question, demonstrating strong logical development.

Criteria B: Mathematical Communication

2/4

Criteria Strands

B.1Mathematical language and notation

Moderate

B.2Multiple representations

Moderate

B.3Clarity and consistency

Moderate

Criteria Feedback

Comprehensive and well‐formatted inflation data table supporting analysis
Effective Table 1 presenting scenarios clearly and enabling comparison across representations

Graphical representations lack labeled axes and units, reducing clarity
Inconsistent and incorrect currency symbols throughout calculations
Mixed notation (boldface vs. standard symbols) and unexplained models (exponential inflation) undermine precision

2.1·Suggestion

Page 3• Click to view

The aim statement is broadly worded. Specify precisely how compound-interest formulas and linear models will address the research question to clarify the methodology.

2.2·Weakness

Page 7• Click to view

The calculation shows €10404 but uses the sterling symbol. Ensure consistent and correct currency notation to avoid confusion.

2.3·Weakness

Page 7• Click to view

Notation for living costs uses the Greek epsilon and the euro symbol interchangeably, which reduces clarity. Standardize currency notation (e.g., “€1000”).

2.4·Weakness

Page 9• Click to view

The SF35 monthly repayment is shown as £340.3; currency symbol and rounding should match earlier sections and be clearly defined.

2.5·Suggestion

Page 10• Click to view

Breaking the multi-step wage/working-hours calculation into separate lines would improve readability and reduce potential arithmetic confusion.

2.6·Strength

Page 12• Click to view

Table 1 presents scenarios effectively, allowing clear comparison across multiple representations. The layout supports easy interpretation.

2.7·Strength

Page 13• Click to view

The inflation data table is comprehensive and well formatted, providing a solid basis for subsequent analysis.

2.8·Weakness

Page 14• Click to view

The best-fit line graph lacks axis labels and units, which reduces clarity and interpretability. Include clearly labeled axes and scales.

Criteria C: Personal Engagement

2/3

Criteria Strands

C.1Independent thinking

Good

C.2Personal approach

Good

C.3Creativity and initiative

Poor

Criteria Feedback

Problem choice and data gathering reflect significant independent thinking beyond textbook examples
Clear personal approach: investigation framed around the student’s own upcoming studies and priorities

Creativity and initiative are limited to standard models without deeper extension or novel applications

Criteria D: Reflection

1/3

Criteria Strands

D.1Depth of reflection

Poor

D.2Critical analysis

Poor

D.3Connection to understanding

Poor

Criteria Feedback

Includes brief personal insights linking deflation and stress considerations to decision making

Reflection is brief and not woven through the exploration, lacking depth or reevaluation of earlier assumptions
No critical analysis of mathematical models or their limitations
Connections to enhanced understanding are only partially developed

3.1·Weakness

Page 14• Click to view

The narrative on deflation and wage effects provides personal insight but lacks critical analysis of the model’s validity and limitations.

3.2·Weakness

Page 16• Click to view

The evaluation mentions practical challenges but omits critique of key assumptions (e.g., constant rates). Include analysis of model limitations to deepen reflection.

3.3·Suggestion

Page 17• Click to view

The final conclusion restates findings nicely but could strengthen the link by referencing specific numerical results from the analysis.

Criteria E: Use of Mathematics

2/6

Criteria Strands

E.1Relevance and level

Moderate

E.2Accuracy and correctness

Poor

E.3Knowledge and understanding

Poor

Criteria Feedback

Uses compound-interest, linear income and regression models appropriate to the SL syllabus
Calculations demonstrate partial correctness in several sections, indicating some technical competence

Key errors in applying amortisation versus compound-interest formulas
Unit inconsistencies (months vs. years) and rounding mismatches lead to incorrect totals
Assumptions lack sensitivity analysis, indicating conceptual gaps

4.1·Weakness

Page 5• Click to view

The assumptions list simplifies the scenario but neglects potential variability in costs. Incorporate a sensitivity analysis to assess the impact of fluctuating expenses.

4.2·Suggestion

Page 5• Click to view

Clarify whether the stated hourly wage is gross or net of taxes and deductions, as this will affect actual take-home pay and loan reduction calculations.

4.3·Weakness

Page 6• Click to view

The compound-interest formula

A = Pigl(1+{rig/ n}igr)^{nt}

is misapplied for loan amortisation. Use the standard amortisation formula

M=P rac{r(1+r)^N}{(1+r)^N-1}

for accurate monthly repayments.

4.4·Weakness

Page 8• Click to view

The monthly repayment calculation divides by 180 months but labels

t

in years, leading to unit inconsistency. Revise to clarify the period or recalculate correctly.

4.5·Suggestion

Page 8• Click to view

The formula for monthly repayment uses

M = \frac{A}{t}

without clarifying that

t

is in months. State units explicitly to maintain consistency.

4.6·Weakness

Page 10• Click to view

The monthly cost sum uses 221 for tuition instead of 216.75; this rounding mismatch leads to an incorrect total of €1216.75. Ensure precise calculations and rounding.

4.7·Suggestion

Page 10• Click to view

The average hourly wage is calculated by a simple mean, but working hours may not split evenly between €13.50 and €15. Consider weighting by expected work distribution.

Loading scores...

Official IB Result

9/20

Criteria A: Presentation

2/4

Criteria Strands

A.1Coherence and logical development

Moderate

A.2Organization and structure

Good

A.3Conciseness and relevance

Moderate

Criteria Feedback

Clear articulation of the research question providing a strong foundation for coherence
Well‐structured table of contents and consistent use of headings enhancing navigation
Conclusion synthesizes quantitative findings and directly addresses the research question
Logical progression in data‐collection section from assumptions to methodology

Abrupt transitions between sections (e.g., from interest results to time‐budget discussion) interrupt the flow
Misplaced digressions (IB learner profile references) dilute mathematical focus
Inconsistent citation formatting reduces presentation quality
Extended non‐mathematical commentary (detailed time‐budget paragraph) inflates length without adding insight

1.1·Strength

Page 1• Click to view

The research question is clearly articulated and focused, providing a strong foundation for the exploration’s coherence and logical progression.

1.2·Strength

Page 2• Click to view

The table of contents is well structured with clear headings and page references, enhancing navigation and overall organization.

1.3·Suggestion

Page 3• Click to view

The introduction mentions the IB learner profile, which adds narrative context but dilutes the mathematical focus. Consider refining this to emphasize the specific mathematical aims and models used.

1.4·Weakness

Page 4• Click to view

Citations for tuition and supply costs lack consistent formatting (e.g., access dates, authors). Adopt a standard style to enhance presentation quality.

1.5·Strength

Page 4• Click to view

The data-collection section is clearly sectioned and provides a logical progression from assumptions to methodology.

1.6·Suggestion

Page 13• Click to view

This detailed time-budget paragraph interrupts the mathematical flow. Consider summarizing it or relocating to a reflective section to maintain coherence.

1.7·Strength

Page 15• Click to view

The conclusion concisely synthesizes the quantitative findings and directly addresses the research question, demonstrating strong logical development.

Criteria B: Mathematical Communication

2/4

Criteria Strands

B.1Mathematical language and notation

Moderate

B.2Multiple representations

Moderate

B.3Clarity and consistency

Moderate

Criteria Feedback

Comprehensive and well‐formatted inflation data table supporting analysis
Effective Table 1 presenting scenarios clearly and enabling comparison across representations

Graphical representations lack labeled axes and units, reducing clarity
Inconsistent and incorrect currency symbols throughout calculations
Mixed notation (boldface vs. standard symbols) and unexplained models (exponential inflation) undermine precision

2.1·Suggestion

Page 3• Click to view

The aim statement is broadly worded. Specify precisely how compound-interest formulas and linear models will address the research question to clarify the methodology.

2.2·Weakness

Page 7• Click to view

The calculation shows €10404 but uses the sterling symbol. Ensure consistent and correct currency notation to avoid confusion.

2.3·Weakness

Page 7• Click to view

Notation for living costs uses the Greek epsilon and the euro symbol interchangeably, which reduces clarity. Standardize currency notation (e.g., “€1000”).

2.4·Weakness

Page 9• Click to view

The SF35 monthly repayment is shown as £340.3; currency symbol and rounding should match earlier sections and be clearly defined.

2.5·Suggestion

Page 10• Click to view

Breaking the multi-step wage/working-hours calculation into separate lines would improve readability and reduce potential arithmetic confusion.

2.6·Strength

Page 12• Click to view

Table 1 presents scenarios effectively, allowing clear comparison across multiple representations. The layout supports easy interpretation.

2.7·Strength

Page 13• Click to view

The inflation data table is comprehensive and well formatted, providing a solid basis for subsequent analysis.

2.8·Weakness

Page 14• Click to view

The best-fit line graph lacks axis labels and units, which reduces clarity and interpretability. Include clearly labeled axes and scales.

Criteria C: Personal Engagement

2/3

Criteria Strands

C.1Independent thinking

Good

C.2Personal approach

Good

C.3Creativity and initiative

Poor

Criteria Feedback

Problem choice and data gathering reflect significant independent thinking beyond textbook examples
Clear personal approach: investigation framed around the student’s own upcoming studies and priorities

Creativity and initiative are limited to standard models without deeper extension or novel applications

Criteria D: Reflection

1/3

Criteria Strands

D.1Depth of reflection

Poor

D.2Critical analysis

Poor

D.3Connection to understanding

Poor

Criteria Feedback

Includes brief personal insights linking deflation and stress considerations to decision making

Reflection is brief and not woven through the exploration, lacking depth or reevaluation of earlier assumptions
No critical analysis of mathematical models or their limitations
Connections to enhanced understanding are only partially developed

3.1·Weakness

Page 14• Click to view

The narrative on deflation and wage effects provides personal insight but lacks critical analysis of the model’s validity and limitations.

3.2·Weakness

Page 16• Click to view

The evaluation mentions practical challenges but omits critique of key assumptions (e.g., constant rates). Include analysis of model limitations to deepen reflection.

3.3·Suggestion

Page 17• Click to view

The final conclusion restates findings nicely but could strengthen the link by referencing specific numerical results from the analysis.

Criteria E: Use of Mathematics

2/6

Criteria Strands

E.1Relevance and level

Moderate

E.2Accuracy and correctness

Poor

E.3Knowledge and understanding

Poor

Criteria Feedback

Uses compound-interest, linear income and regression models appropriate to the SL syllabus
Calculations demonstrate partial correctness in several sections, indicating some technical competence

Key errors in applying amortisation versus compound-interest formulas
Unit inconsistencies (months vs. years) and rounding mismatches lead to incorrect totals
Assumptions lack sensitivity analysis, indicating conceptual gaps

4.1·Weakness

Page 5• Click to view

The assumptions list simplifies the scenario but neglects potential variability in costs. Incorporate a sensitivity analysis to assess the impact of fluctuating expenses.

4.2·Suggestion

Page 5• Click to view

Clarify whether the stated hourly wage is gross or net of taxes and deductions, as this will affect actual take-home pay and loan reduction calculations.

4.3·Weakness

Page 6• Click to view

The compound-interest formula

A = Pigl(1+{rig/ n}igr)^{nt}

is misapplied for loan amortisation. Use the standard amortisation formula

M=P rac{r(1+r)^N}{(1+r)^N-1}

for accurate monthly repayments.

4.4·Weakness

Page 8• Click to view

The monthly repayment calculation divides by 180 months but labels

t

in years, leading to unit inconsistency. Revise to clarify the period or recalculate correctly.

4.5·Suggestion

Page 8• Click to view

The formula for monthly repayment uses

M = \frac{A}{t}

without clarifying that

t

is in months. State units explicitly to maintain consistency.

4.6·Weakness

Page 10• Click to view

The monthly cost sum uses 221 for tuition instead of 216.75; this rounding mismatch leads to an incorrect total of €1216.75. Ensure precise calculations and rounding.

4.7·Suggestion

Page 10• Click to view

The average hourly wage is calculated by a simple mean, but working hours may not split evenly between €13.50 and €15. Consider weighting by expected work distribution.