How to Score Well on Your Mathematical Exploration
This page is designed to give you an overview of the five assessment criteria used to mark your mathematical exploration and, more importantly, to help you understand what you should do to achieve the best possible score. For each criterion, you will find a short summary of the key things to remember, followed by practical advice based on recent IB subject reports. If you follow this guidance carefully as you plan, write and review your exploration, you will give yourself the strongest possible chance of reaching the top mark bands.
Criterion A: Presentation — 4 marks
Clear aim • Logical structure • Concise • Easy to follow
Your exploration should tell a clear mathematical story from beginning to end. State a clear and manageable aim early, give enough context for the reader to understand what you are investigating, develop the mathematics in a logical order, and finish with a conclusion that answers your aim. Write for another Maths AA student at your level: explain unfamiliar ideas or subject-specific terminology, but do not waste space explaining basic mathematics they are already expected to know. Be concise—remove repeated calculations, enormous data tables and unnecessary background information, and make sure every section contributes to your investigation. Proofread the final document carefully so that graphs and tables are sensibly positioned and the document is easy to follow. Cite any information or ideas taken from sources properly. The strongest explorations are not necessarily long; they are focused, coherent and easy to read.
Criterion B: Mathematical Communication — 4 marks
Correct notation • Define variables • Label graphs • Consistent accuracy
Make your mathematics look like mathematics, not calculator or computer output. Use an equation editor, define every variable when it first appears, use notation consistently, include subscripts where needed, use appropriate mathematical symbols such as ≈ when a value is approximate, and give answers to a sensible and consistent degree of accuracy. Every graph should have clearly labelled axes, appropriate units and readable text; tables should also be clearly organised. Do not simply insert a graph, diagram or table—introduce it and explain what the reader should learn from it. Avoid programming notation such as * for multiplication or other calculator/computer conventions in your mathematical writing. Most of the problems identified by examiners are small, avoidable details, so carefully checking notation, graphs, units, rounding and formatting before submitting can make a significant difference.
Criterion C: Personal Engagement — 3 marks
Your choices • Your ideas • Initiative • Explore alternatives
Personal engagement is about what you do with the mathematics, not simply saying that you like the topic, choosing something connected to a hobby, collecting your own data or describing how hard you worked. To reach the highest level, make the exploration genuinely yours by making mathematical decisions independently. Ask your own questions, make and test predictions, decide which methods are appropriate, adapt your approach when something interesting happens, compare alternative methods or investigate the problem from more than one perspective. Look for opportunities to make choices rather than simply following a standard procedure or template. Creative presentation of mathematical ideas, an original approach, or a thoughtful decision about how to continue the investigation can all provide evidence of engagement. The examiner should be able to see throughout the exploration that you are driving the mathematics rather than simply carrying out somebody else's method.
Criterion D: Reflection — 3 marks
Question results • Evaluate methods • Identify limitations • Adapt and improve
Do not leave reflection until the conclusion and simply write a paragraph about your strengths, weaknesses and possible improvements. Instead, reflect as the exploration develops. After obtaining an important result, ask what it means, whether it is reasonable, how it relates to your aim and whether it changes what you should do next. Question your assumptions, data and mathematical methods; identify limitations that genuinely affect your conclusions; notice unexpected results or inconsistencies and investigate them rather than ignoring them. If a method or model does not work well, explain why and use that reflection to justify trying something different. You can also compare methods, discuss how a modelling choice affects the result and consider meaningful alternative approaches or extensions. The strongest reflection is therefore not an extra section added afterwards—it actually influences the direction of your investigation and shows that you are thinking critically about your mathematics.
Criterion E: Use of Mathematics — SL — 6 marks
Appropriate maths • Show understanding • Explain choices • Interpret results
Choose mathematics that is appropriate for your aim and that you genuinely understand; using mathematics beyond the SL course will not help if you cannot explain it. Show your reasoning rather than simply substituting values into formulas, repeating calculations or copying software output. Explain why you have chosen a method, what the mathematics means and what your results tell you in the context of your investigation. If you use technology for regression or modelling, first examine the data, justify why the type of function is appropriate, interpret important parameters and consider the behaviour and limitations of the model rather than choosing it simply because it has the largest R². Technology should support your mathematical thinking, not replace it. Explain important concepts in your own words where this demonstrates understanding, check your mathematics carefully for errors, and avoid adding unnecessarily advanced techniques just to make the exploration appear sophisticated. Depth of understanding is much more valuable than quantity or complexity of calculation.
Criterion E: Use of Mathematics — HL — 6 marks
HL-level maths • Show understanding • Be rigorous • Show sophistication
Choose mathematics that is relevant to your aim and appropriate for HL, and make sure you genuinely understand everything you use. You do not need university-level mathematics: mathematics from the HL syllabus is entirely appropriate, and even mathematics from the SL syllabus can contribute to a high mark if you use it in a sufficiently complex and sophisticated way. Show the development of your mathematics clearly, explain why methods work, justify important steps and claims, and interpret your results in the context of your exploration. For the highest marks, your mathematics should demonstrate both sophistication and rigour: sophistication comes from using mathematics thoughtfully, making connections, recognising underlying structures or approaching a problem in an insightful way; rigour means that your reasoning is logical and your mathematical claims are properly justified. Your mathematics should also be precise, with appropriate accuracy and very few errors. Technology can perform calculations, but it cannot demonstrate understanding for you—explain and, where appropriate, check the results it produces. Advanced mathematics is not automatically sophisticated: deep understanding and rigorous mathematical reasoning are much more important than complexity.