The IB maths internal assessment, known as the exploration, is a written piece of mathematics on a topic the student chooses, worth 20% of the final grade at SL and HL. This guide covers the criteria, topic ideas, structure and the academic-honesty line every family should know.
The maths is taught. The exploration stays theirs.
The exploration must be the student's own work — a tutor explains the maths and the process, nothing more
What is ClassArc?
ClassArc is live one-to-one online maths tutoring for school-age children.
One teacher and one child, for 55 minutes. The same teacher every week.
Classes run inside our own classroom software, not a video call: a shared
worksheet you both write on, a shared whiteboard, and answers that sync live.
The IB maths IA is a 12–20 page exploration worth 20% of the grade
The exploration is a report in which the student investigates an area of mathematics and shows they understand it. The same five criteria apply in AA SL, AA HL, AI SL and AI HL, for 20 marks in total. The school's maths teacher marks it, and the IB moderates a sample.
The IB's guidance is 12 to 20 pages, double-spaced, counting graphs and diagrams but not the bibliography. The level of mathematics is judged against the course the student takes, so an HL exploration needs HL-standard mathematics to reach the top marks.
This page describes the current course, examined for the last time in November 2028. The school sets the timeline, and the teacher gives feedback on a draft within limits set by the IB.
Criteria
Five criteria mark the IB maths IA, and criterion E carries the most
The summaries below are in our words. Your child's teacher will share the official descriptors, and those are the ones to work from.
Criterion
Marks
What it rewards
A. Presentation
4
A clear aim, a logical structure and a conclusion that answers the aim, with nothing irrelevant
B. Mathematical communication
4
Correct notation and terminology, defined variables, labelled graphs and tables
C. Personal engagement
3
Independent thinking: the student's own questions, examples and way of presenting ideas
D. Reflection
3
Critical comment throughout on what results mean, their limits and whether the method suited the task
E. Use of mathematics
6
Relevant, correct mathematics at the level of the course, with understanding shown, not just stated
Criterion E is capped by the level of the mathematics. An exploration built on maths well below the course struggles on E however well it is written, so the topic choice matters more than anything else.
Topic ideas
A good IA topic needs course-level maths, a narrow question and genuine interest
These are starting questions, not finished plans. Each one needs narrowing and making personal, and a topic that grows out of the student's own hobby or data makes criterion C far easier.
Starting points for Analysis and Approaches
The lightest drinks can: for a fixed volume, which radius and height minimise surface area, and why do real cans differ?
A curved building façade: model its profile from a photograph with polynomial or trigonometric functions, and compare the fits
How fast does a series for π converge? Compare how many terms different series need for a given accuracy
Great-circle routes: why long-haul flights from Dubai curve towards the poles, using spherical trigonometry
Cooling a cup of karak chai: collect temperatures and compare Newton's law of cooling with a fitted exponential
A number pattern the student noticed: investigate it, then prove it (by induction at HL)
Starting points for Applications and Interpretation
A metro network as a graph: shortest routes between stations, with graph algorithms at HL
Used-car prices: a regression model of price against age and mileage, comparing linear and exponential depreciation
Queues at the school canteen: model arrival times with a probability distribution and test the fit
Goals in a football season: a Poisson model for match outcomes, checked against real results
Household water use: model it against temperature from the family's own bills, with permission
Follower growth on an account: logistic or exponential, and where each model breaks down
Well-worn topics such as the golden ratio or the Monty Hall problem are not banned, but moderators have read many of them, and personal engagement is harder to show.
Structure
Most strong explorations follow a six-part shape
This is a guide rather than a rule; the teacher may suggest a different outline for a particular topic.
Introduction and aim (about half a page): why this topic, the question it answers, the mathematics it will use.
Background: only the context and definitions a reader needs.
The mathematics, making up most of the report: logical steps, each introduced with a sentence on what it does and why.
Reflection as you go: after each key result, does it make sense, what does it mean, where are its limits?
Conclusion: answer the aim directly, evaluate the method, suggest one realistic extension.
Bibliography: every source, cited consistently and at the point of use.
Mistakes
Eight IA mistakes that cost marks
A question that is too broad. “Maths in music” cannot be finished in 20 pages; “can guitar fret spacing be modelled exponentially?” can.
Maths below the course level, such as only averages and a bar chart in an HL piece, which limits criterion E.
Derivations copied without understanding. Moderators reward explanation of why each step applies.
Reflection saved for the last page instead of running through the whole piece.
Undefined variables and unlabelled graphs, which give away easy marks on criterion B.
Calculator or software output with no commentary. Technology is welcome, especially in AI, but the student must say what the output means.
Writing before the mathematics is planned. Weak explorations are often written first and calculated second.
Running far past 20 pages. Length earns nothing and usually costs marks on presentation.
Academic honesty
The IA must be the student's own work, so a tutor teaches, never writes
Work written, rewritten or substantially directed by someone else, or generated by an AI tool, and handed in as the student's own breaches the IB's academic integrity rules and can put the subject grade and the Diploma at risk. This is where ClassArc draws the line.
A tutor may
A tutor may not
Teach the mathematics the topic needs, such as how regression or optimisation works
Write, rewrite or edit any part of the exploration
Explain what each criterion rewards, using the official descriptors
Choose the topic or hand over a ready-made plan
Ask questions that help the student narrow their own idea
Do the calculations, draw the graphs or run the software
Check the student understands mathematics they plan to use
Mark up the draft or say what to change in it
Cover general skills: notation, labelling graphs, citing sources
Replace the school teacher's feedback on the draft
Read your school's academic integrity policy too. If the school asks students to declare outside help, declare the tutoring; there is nothing to hide when the help is teaching.
Revised course
Students starting the Diploma from August 2027 should use their teacher's criteria
The IB's revised maths courses are first taught in August 2027 and first examined in May 2029, and the assessment is being revised alongside them. The A–E criteria on this page belong to the current course.
If your child starts the Diploma in August 2027 or later, work from the IA criteria their teacher provides under the new subject guide, not from this table. For the wider picture of the change, see our IB maths parent guide.
With ClassArc
We teach the mathematics inside the IA so your child can explain it themselves
Criterion E rewards understanding that is shown, and that is exactly what one-to-one teaching builds. A ClassArc teacher can teach the regression, calculus or probability a topic needs, work through similar problems that are not from the exploration, and explain what the criteria are asking for.
The exploration itself is never opened for editing in class. The same teacher works with your child every week on the wider AA or AI course, and the first 55-minute class is free, with no card required.
6/20
marks sit in criterion E, use of mathematics, the one that rewards understanding shown on the page
The IB suggests 12 to 20 pages, double-spaced, counting graphs and diagrams but not the bibliography. An exploration that runs well past 20 pages tends to lose marks on presentation.
Can my child pick a topic from an online list?
An online list is fine as a starting point, but the question has to be narrowed and made the student's own. A popular topic followed closely from an online example scores poorly on personal engagement and can raise academic-honesty concerns.
Is the IA marked differently at HL and SL?
The five criteria are identical at both levels. The difference is in criterion E, where HL students need mathematics at HL standard to reach the top marks.
Can a tutor check my child's IA draft?
No. A tutor should not annotate, edit or rewrite the draft; feedback on the draft belongs to the school's teacher. A tutor can teach the mathematics the student is using and explain what the criteria reward.
How do we ask ClassArc about IA support?
WhatsApp us on +91 78781 48026 with your child's course, AA or AI at SL or HL, and the topic area they are considering. We will explain how our teachers support the mathematics and where they stop.
free
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1
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3
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