Interactive guide to understanding the assessment criteria
A short report where you explore a mathematical topic of your choice in depth.
Your exploration should be guided by a focused research question. This question drives everything you do.
Tip: Sometimes it helps to simplify the problem first — start with a specific case, understand it fully, then build towards the general. A simpler question explored deeply beats a complex one done superficially.
Don't just calculate — explain what you're doing and why. Show your reasoning at every step.
Link different mathematical ideas together. Show the same concept algebraically, graphically, and numerically.
What do your results mean? Relate back to your original question. Are there limitations?
| Criterion | Marks | Focus |
|---|---|---|
| A: Communication | 4 | Is it coherent, organized, and complete? |
| B: Mathematical Presentation | 4 | Notation, diagrams, graphs — professional quality? |
| C: Personal Engagement | 3 | Independent thinking, creativity, your own tools? |
| D: Reflection | 3 | Critical analysis of validity and limitations? |
| E: Use of Mathematics | 6 | Correct, sophisticated, rigorous understanding? |
| Total | 20 |
The exploration is difficult to follow with no clear structure
To avoid: Create clear sections with headings, write a clear introduction stating your aim, summarize findings at the end
Some structure exists but organization is weak
Basic headings present, but transitions between sections are unclear, rationale is vague, ideas not connected
Use clear section titles, connect ideas between sections, state why you chose this topic, discuss relationships between concepts
The work has structure and reasonable organization
Clear sections (intro, methods, results), rationale is stated, some summarizing of results, beginning to discuss and connect ideas
Ensure each section flows logically, clearly state your aim and rationale, summarize key findings, start connecting mathematical ideas
Well-structured, coherent, and logically organized throughout
Logical flow from introduction through to conclusion, ideas are discussed and connected, results are interpreted clearly, concise writing without repetition
DISCUSS findings (not just state them), CONNECT different mathematical ideas, INTERPRET what results mean - avoid repetition, focus on quality over quantity
Excellently structured, concise, complete, and highly coherent
Professional presentation where ideas are deeply discussed, meaningfully connected, and insightfully interpreted. Concise - every sentence adds value, no repetition or padding. A clear research question guides the entire exploration
Start with a focused research question that guides your investigation. Consider simplifying the problem first — explore a specific case deeply, then build towards the general. Master DISCUSS-CONNECT-INTERPRET: discuss each idea thoroughly, connect to broader mathematics, interpret significance. Quality over quantity: every sentence should add value
Mathematical notation is absent or incorrect
To avoid: Learn proper notation for your topic, define all variables, use mathematical symbols correctly, create clear diagrams
Some appropriate mathematical notation is used
Basic notation present but inconsistent, some graphs/tables without labels, variables mostly defined, basic presentation
Be consistent with notation, label all axes and tables, define variables at first use, improve visual quality
Mathematical presentation is mostly appropriate
Generally correct notation, most graphs and tables are labeled, terminology mostly accurate, reasonably professional appearance
Check all notation is standard, ensure all visuals are properly labeled, use correct terminology. Consider using graphing software (Desmos, GeoGebra) for clearer visuals
Mathematical presentation is appropriate throughout
Correct notation consistently used, all diagrams/tables well-presented and labeled, proper terminology, professional-looking presentation
Review notation standards, double-check all labels and legends, use precise mathematical language. Use professional tools: graphing software (Desmos, GeoGebra, Python), consider LaTeX for equations
Mathematical presentation is precise, concise, and exemplary
Flawless notation (LaTeX-quality), publication-quality graphs created with professional software, perfect terminology, elegant and polished mathematical writing
Use professional tools: LaTeX for equations, Python/Desmos/GeoGebra for graphs, Excel/Sheets for data tables. Polish all mathematical writing to publication standard. Ask yourself: "Does this look professional enough for a mathematics journal?"
No evidence of independent mathematical development
To avoid: Take ownership of your exploration - develop your own approach, create your own tools, connect ideas independently
Limited independent mathematical engagement
Mostly follows given examples, minimal development of own methods or tools, limited mathematical connections
Start creating your own approach: try building a simple spreadsheet model, make your own variations, explore connections
Some evidence of independent mathematical engagement
Some independent exploration, beginning to develop own tools (basic spreadsheet/code), making some mathematical connections
Develop your own tools: create spreadsheet models, write code, build physical models. Start connecting different mathematical areas to answer your question
Significant independent mathematical engagement
Developed own sophisticated tools (complex spreadsheets, programs, models), connected multiple mathematical areas for genuine purpose, taken exploration significantly further than initial scope
Take it FURTHER: develop sophisticated tools (advanced Excel models, Python code, physical/digital simulations), meaningfully connect multiple areas of mathematics (algebra+geometry, calculus+statistics) to truly answer your question. This is NOT about personal interest stories - it's about independent mathematical development
No mathematical reflection on validity or limitations
To avoid: Question your results: Are they valid? Under what conditions? What are the limitations?
Limited mathematical reflection
Mentions validity or limitations superficially, but doesn't explore or act on them. May include irrelevant personal reflections (enjoyed it, should have started earlier)
Question validity critically: Test your results, identify specific mathematical limitations, consider what conditions make results invalid. Avoid personal feelings - focus on mathematics
Meaningful mathematical reflection
Questions validity of results, identifies mathematical limitations, discusses extensions, begins to act on limitations (tests alternatives)
Critically examine: When are results valid/invalid? What mathematical limitations exist? Test different models/approaches when you find limitations. Discuss how extendable your work is
Substantial critical mathematical reflection with action
Rigorously questions validity, identifies specific mathematical limitations AND acts on them (tries different models, tests alternatives, explores variations), discusses sophisticated extensions with mathematical justification
REFLECT → ACT cycle: Identify "this is not valid because X" → DO something (test different model, adjust approach, try variations). Show: validity testing, limitation analysis, AND concrete action taken. This is NOT about enjoyment/effort - it's about mathematical rigor and responsive investigation
Replicating impressive topics
without understanding
Simpler mathematics done WELL
with precise, clear explanations
Substitution into a formula rarely passes Level 3 (often Level 2)
Justify why your chosen method is appropriate, and explore the problem with multiple tools to demonstrate you understand the logic of your investigation.
To reach Level 5-6: You need both Sophistication (multiple representations, cross-connected ideas) AND Rigour (clear logical arguments)
Error-free mathematics using appropriate accuracy at all times
Multiple representations, different perspectives, linking areas of mathematics
Clarity of logic and language in arguments and calculations
Very basic or irrelevant mathematics, not appropriate for DP level
Use mathematics at least at your course level, ensure it's relevant to your question
Basic mathematics present but limited understanding shown. WARNING: Replicating impressive-sounding topics (Fourier analysis, curved surface area) without understanding scores poorly here
Use mathematics you actually UNDERSTAND. Don't just copy advanced formulas - explain them clearly. Better to use simpler math well than complex math poorly
Appropriate level mathematics used but with gaps in understanding. Imprecise/vague explanations reveal incomplete understanding despite research
Ensure mathematics matches your course (HL/SL), show you understand concepts through PRECISE explanations, apply correctly. Quality of explanation reveals depth of understanding
Mathematics at right level, some understanding shown, some correct work but errors reveal incomplete grasp. May have researched but not fully understood
Use mathematics commensurate with HL/SL, demonstrate understanding through CLEAR, PRECISE explanations, minimize errors. Examiners can tell if you've researched but not understood
Correct mathematics at course level, good understanding demonstrated through precise explanations, mostly accurate work. Understanding is evident, not just replication
Use sophisticated course-level mathematics that you genuinely understand. Explain precisely and concisely - vague explanations lose marks even with correct results
Advanced mathematics appropriate to course, very good understanding shown through precise, clear explanations. Application is sophisticated and well-understood
Use challenging mathematics for your level, show deep understanding through crystal-clear explanations. IMPORTANT: Known outcomes (deriving well-known formulas) rarely score here - you need original application
Sophisticated mathematics appropriate to your course level, flawless execution, deep understanding evident through precise, insightful explanations. Original application, not replication of known results. You can draw inspiration from other IB syllabi (e.g., SL students using matrices or Poisson distribution from HL) - what matters is HOW WELL you understand and apply it
WARNING: You do NOT need mathematics well beyond your syllabus - using topics from other IB syllabi is perfectly acceptable (SL students can use HL topics like matrices, differential equations, etc.). What matters is ORIGINAL APPLICATION with THOROUGH UNDERSTANDING shown through precise, concise explanations. Replication of known outcomes rarely scores well, no matter how impressive the mathematics sounds. Examiners spot researched-but-not-understood work instantly through imprecise explanations