Maths IA structure: sections, criteria and page length

At a glance

The structure, section by section

1. Cover page

Required by the IB (the guide lists the title and the page count as the cover's contents) · No criterion (formal requirement) · Outside the word count

The exploration's title and its page count.

1. Enter a working title.
2. Let the counter fill in the page count.
3. Confirm the count after your final edit.

2. Introduction: aim and rationale

Rewarded by a criterion (Presentation expects an introduction that states the aim, and Personal engagement rewards a personal link to the topic) · Criterion: Presentation, Personal engagement

What you explore, why it matters to you, and how the work is organised.

1. State the aim in 1 or 2 sentences.
2. Explain your personal link to the topic with specific detail.
3. Outline the order of the sections.
4. Name the technology you will use.

3. Background, definitions and assumptions

Rewarded by a criterion (Mathematical communication rewards defined terms and variables) · Criterion: Mathematical communication, Use of mathematics

Only the theory the aim needs, with every symbol defined.

1. Introduce only the concepts the aim needs.
2. Define each variable and symbol on first use.
3. Cite the source of any formula you did not derive.
4. List your assumptions and justify each one.

4. Data collection or model set-up

Rewarded by a criterion (applies to modelling and statistics topics) · Criterion: Mathematical communication, Personal engagement, Use of mathematics · Only when it applies

How you collected your data or built the model, and why.

1. Describe how you collected your own data.
2. Put the data in a numbered table, and move large sets to an appendix.
3. Justify the method or model you chose.
4. Note the limits of the data.
5. If you pooled data with classmates, explain how.

5. Mathematical development

Rewarded by a criterion (Use of mathematics and Mathematical communication reward the working) · Criterion: Use of mathematics, Mathematical communication, Personal engagement

The working, step by step, in 1 or more subsections, with each graph and table placed where you discuss it.

1. Split the work into subsections that follow the aim.
2. Justify each step as you take it.
3. Discuss every graph and table where it appears.
4. Explain the reasoning behind any technology output.
5. Cut repeated calculations.
6. At HL, justify or prove each claim.

6. Interpretation and reflection

Rewarded by a criterion (Reflection can be earned anywhere in the work) · Criterion: Reflection

What the results mean, how you checked them, their limits and implications, first in the body and then in a closing discussion.

1. Interpret each result against the aim when you reach it.
2. Check key results another way, by hand or with technology.
3. Discuss the limitations and how they affect the results.
4. Say what you would explore next.

7. Conclusion

Rewarded by a criterion (Presentation expects a conclusion) · Criterion: Presentation, Reflection

A direct answer to the aim.

1. Answer the aim directly.
2. Summarise the key results.
3. Link back to your reflection.
4. Add no new mathematics.

8. Bibliography

Required by the IB (the guide asks for a detailed bibliography) · No criterion (not marked) · Outside the word count

Every source, including the sources of images, graphs and formulae.

1. Log each source when you first use it.
2. Record where each borrowed image, graph and formula came from.
3. Use 1 style throughout.
4. Check that every citation has an entry.

9. Appendices

Common practice (the guide allows appendices for bulky material) · No criterion · Outside the word count · Only when it applies

Large raw data sets and extra graphs.

1. Move only bulky material here.
2. Keep anything that earns marks in the body.
3. Refer to each appendix in the text.

What counts toward the limit

Counts pages at double line spacing: the whole exploration, with graphs, diagrams and tables included. The bibliography is outside the count, and the guide is silent on the cover and appendices, so they are left out here too.

The limit: About 12 to 20 pages at double line spacing, with no word limit. There is no fixed penalty for going over; length is judged through the conciseness strand of Presentation.

Graphs and visuals

• Function graphs (GeoGebra, Desmos or GDC style) Plotted, very common
  Several functions on 1 set of axes; labelled axes and curves; marked intercepts, turning points and intersections; placed beside the discussion. Unlabelled graphs are the guide's own example of weak communication.
• Tables of data, iterations or values Table, very common
  Numbered title and headed columns; raw data longer than about a page goes to an appendix.
• Equations and derivations Math, very common
  Mathematical notation throughout; the symbols *, ^ and E appear only inside output that software produced; key equations numbered.
• Scatter plot with regression line, equation and r or R², plus a residual plot Plotted, common
  More common in AI. Fitted equation and r or R² on the chart; a residual view; axis titles with units. Bivariate data leaves AA from May 2029.
• Geometric diagrams (triangles, circles, vectors, proof figures) Drawn, common
  Labelled vertices, angles and lengths; dynamic geometry software is named course technology.
• Statistical charts (histogram, box plot, bar chart) Plotted, common
  Common in statistics topics. Axis titles, units and class widths.
• Photo with a fitted curve overlaid (modelling a real object) Image, common
  Common in modelling topics. Image import with axes laid over it; credit any image that is not your own.
• 3D surfaces and solids of revolution Plotted, occasional
  x, y and z axis labels; mostly HL calculus and volume topics.
• Probability trees and sample-space diagrams Drawn, occasional
  Labelled branch probabilities.
• Networks, graph-theory and Voronoi diagrams Drawn, occasional
  Mostly AI and mostly HL. Labelled vertices, edges and weights; both topics are AI content.
• Screenshots of software output (spreadsheet, GDC, code) Image, occasional
  Evidence only; the mathematics is still explained in the text.

The frequencies are our estimates, from what the IB guide expects and what teachers advise. We did not count them in marked work.

Citations

The IB prescribes no style; it asks for a detailed bibliography and a citation wherever a picture, diagram, graph or formula comes from a source. MLA, APA or Harvard all work if used consistently.

The workspace keeps your sources and writes the bibliography in APA 7th to start with. You can switch to MLA 9th, Chicago author-date, Chicago notes (footnotes) or Harvard at any point.

Pitfalls

• Label every graph and define every variable, and keep calculator notation out of the text, since gaps here weaken Mathematical communication.
• Place the graphs and tables your argument needs beside the discussion, discuss each one, and keep them out of the appendix.
• Cut repetitive calculations and long description, since conciseness counts under Presentation.
• Show your own reasoning for known mathematics, and reflect on the results as well as describing them.
• Explain every technology output in your own words, and choose mathematics that the aim needs.

The workspace is free with an account, and it never writes or rewrites your text. What we will and will not do with your coursework →

Sources

• Mathematics: analysis and approaches guide, first assessment 2021
• Mathematics: applications and interpretation guide, first assessment 2021
• IB, Examiner Instructions 2027: Mathematics: analysis and approaches
• IB, "Read curriculum updates" (page last updated 24 March 2026)
• IB, "DP mathematics: analysis and approaches updates" (last updated 3 April 2026)
• IB, "DP mathematics: applications and interpretation updates" (last updated 23 March 2026)
• Subject brief: Mathematics: analysis and approaches, first assessment 2029
• Subject brief: Mathematics: applications and interpretation, first assessment 2029

The IB documents behind this page, checked 29 October 2026. The linked ones are on ibo.org; the others are IB documents we read in copies hosted elsewhere, so we name them without a link. Everything above is in our own words: the official wording is in your subject guide, which your coordinator can give you. LimeAdmissions is independent of the International Baccalaureate Organization, which has not endorsed this page. Every coursework structure →