IB Mathematics · Complete topic list

900 topic ideas – page 25 of 36.

Topics 601 to 625 with explanations, methods, course and equipment guidance.

Mathematics and applications

Compare 900 ideas clearly.

The list mixes calculus, statistics, modelling, geometry, number theory, computer science, sport, environmental topics and other areas. Each entry includes a short explanation and visible methods such as differential calculus, integral calculus, statistics or regression.

Planning guidance, not official topic approvalThe IA, EE, AA, Math AI, SL and HL classifications are editorial guidance. The current subject guide, assessment session, mathematical depth, focus and school approval remain decisive.
1

Select an idea. Titles and areas are starting points, not finished research questions.

2

Check A and C. These codes give an initial indication of assessment type, course and level.

3

Read P, M and S. They show possible independent direction, tools, and safety or data-protection needs.

Work
Course
Level

Showing 25 of 25 topic ideas

Mixed topic list for the Mathematics IA and Mathematics Extended Essay
No. Topic idea A C P M S
601 Batteries and energyWi-Fi versus mobile data

Transfer the same amount of data or stream the same content over Wi-Fi and mobile data. Use paired measurements on the same device.

Functions & modelling
3 9 181112 35 2
602 Batteries and energyRefresh rate and energy consumption

Compare battery loss at different screen refresh rates while keeping displayed content and brightness constant.

Functions & modelling
3 9 11112 57 2
603 Batteries and energyLocal AI computation and battery load

Run a fixed number of local AI inferences using models of different sizes. Compare energy per inference, runtime, and device temperature.

Functions & modelling
3 9 1361112 235620 2
604 Batteries and energyPower-bank efficiency

Measure input and output energy at different load currents. Determine the load at which efficiency is greatest.

Functions & modellingDifferential calculusOptimisation
3 9 11112 25 2
605 Sound and acousticsSpeed of sound in air and temperature

Determine travel time between two microphones or by echo at several temperatures. Compare linear and square-root-type models.

Functions & modellingGeometry
3 9 131112 369111220 0
606 Sound and acousticsSpeed of sound in water and temperature

Use waterproof transmitters and receivers in a container of constant length. Because of the more demanding measurement, this topic is especially suitable for an EE.

Proof
3 2 16101112 1391216 1
607 Sound and acousticsSalinity and sound speed

Measure the travel time of an acoustic or ultrasonic signal through solutions with different salt concentrations at constant temperature.

Functions & modelling
3 9 131112 369111216 0
608 Sound and acousticsHumidity and speed of sound

Vary humidity in a controlled experimental space without human exposure in a sealed environment, while simultaneously controlling temperature.

Functions & modelling
3 9 161112 3691218 0
609 Sound and acousticsTube length and resonance frequency

Measure resonant frequencies of open and one-end-closed tubes of different lengths. Investigate the relationship between frequency and inverse tube length.

Functions & modellingTrigonometry
3 9 11112 16916 0
610 Sound and acousticsWater level in a bottle and pitch

Vary the air or water volume in identical bottles. Compare different geometric models for the resulting frequency.

Functions & modellingTrigonometryGeometry
3 9 161112 13691620 0
611 Sound and acousticsMaterial and sound attenuation

Place materials of different types and thicknesses between a speaker and microphone. Model attenuation in decibels as a function of thickness and frequency.

Functions & modellingTrigonometryAlgebra
3 9 181112 691120 0
612 Sound and acousticsFurnishing and reverberation time

Measure room reverberation time with different amounts of absorbing material. Compare measurements with an acoustic room model.

Functions & modelling
3 9 1361112 6920 0
613 Magnetic fields and electromagnetic inductionMagnetic field strength and distance

Measure magnetic-field strength along a fixed axis at increasing distances. Determine the exponent of a power model.

Functions & modellingVector mathematicsProofAlgebra
3 2 1101112 151720 1
614 Magnetic fields and electromagnetic inductionMagnetic-field component and angle

Rotate the sensor in fixed angular steps relative to the magnet. Test whether the measured field component follows a trigonometric model.

Functions & modellingVector mathematicsTrigonometryProof
3 2 1101112 1520 1
615 Magnetic fields and electromagnetic inductionNumber and spacing of magnets

Compare stacked magnets and magnets separated by different gaps. Investigate field strength and spatial uniformity.

Vector mathematicsGeometryProof
3 2 16101112 1517 1
616 Magnetic fields and electromagnetic inductionMaterial between magnet and sensor

Place equal-thickness layers of plastic, aluminium, steel, or other materials between magnet and sensor. Investigate changes and redirection of the field.

Vector mathematicsProof
3 2 138101112 25 1
617 Magnetic fields and electromagnetic inductionCurrent and magnetic field of a coil

Vary the current through a fixed coil within safe limits. Measure the magnetic field at the centre and at several external points.

Vector mathematicsProof
3 2 1101112 517 1
618 Magnetic fields and electromagnetic inductionNumber of turns and magnetic field

Build coils of equal length with different numbers of turns. Keep current constant and investigate the relationship with field strength.

Functions & modellingVector mathematicsProof
3 2 12101112 15121720 1
619 Magnetic fields and electromagnetic inductionMagnet speed and induced voltage

Move the same magnet through a coil at different speeds. Compare peak voltage and total voltage–time area.

Functions & modellingDifferential calculusVector mathematicsGeometryProof
3 2 1101112 5612 1
620 Magnetic fields and electromagnetic inductionEddy-current braking and magnet distance

Allow a magnet to swing past an aluminium or copper plate. Model oscillation decay time as a function of separation distance.

Functions & modellingDifferential equationsVector mathematicsProofAlgebra
3 2 1101112 15620 1
621 Mobile reception, Wi-Fi, and radio attenuationWi-Fi signal strength and distance

Measure signal strength along a straight line with clear line of sight. Fit a logarithmic distance model and examine residuals.

Functions & modellingRegressionAlgebra
3 6 11112 1131720 1
622 Mobile reception, Wi-Fi, and radio attenuationWall material and signal attenuation

Compare wood, glass, plasterboard, brick, and concrete under similar geometry. Calculate additional loss relative to a clear line of sight.

GeometryProof
3 2 18101112 2 1
623 Mobile reception, Wi-Fi, and radio attenuationMaterial thickness and signal attenuation

Stack several identical panels or layers. Test whether loss in decibels increases approximately linearly with thickness.

Functions & modelling
3 9 131112 3 1
624 Mobile reception, Wi-Fi, and radio attenuationWet and dry material

Compare controlled wet and dry samples of the same material. Record mass, moisture level, and signal loss.

Functions & modelling
3 9 11112 218 1
625 Mobile reception, Wi-Fi, and radio attenuationDevice orientation and hand position

Rotate the smartphone through fixed angles or change a standardized hand position. Analyse the mean and variation of signal strength.

Statistics & probabilityTrigonometry
3 6 181112 131117 1
Code legend

What A, C, P, M and S mean.

The table stays narrow on a phone by replacing long descriptions with numeric codes. Entries may contain several P and M codes.

AAssessment type
1
Internal Assessment (IA)
2
Mathematics Extended Essay (EE)
3
Potentially suitable for an IA or EE, depending on focus and mathematical depth
CCourse and level
1
Mathematics AA SL
2
Mathematics AA HL
3
Mathematics AA at SL or HL
4
Mathematics AI SL
5
Mathematics AI HL
6
Mathematics AI at SL or HL
7
Mathematics AA or AI at SL
8
Mathematics AA or AI at HL
9
Mathematics AA or AI at SL or HL
PWays to demonstrate independent direction and personal engagement
1
Own data, measurements, observations or experiment
2
Own photographs, drawings, constructions or models
3
Own sport, video, GPS or tracker context
4
Own school or class survey or observation
5
Own everyday, household, consumer or financial data
6
Local context: environment, buildings, traffic, climate or nature
7
Own programming, simulation or algorithm
8
Personal interest: music, art, games, design or another hobby
9
Public data selected, prepared and analysed independently
10
Own conjecture, proof idea, generalisation or theoretical comparison
11
Own modelling decision, construction, optimisation or adaptation
12
Critical comparison of assumptions, errors, limitations or ethical issues
MMeasuring instruments, tools or data access
0
No specialist physical instrument; a calculator, CAS, spreadsheet or open data may be sufficient
1
Ruler, tape measure, calliper or protractor
2
Balance or precision scale
3
Contact thermometer or temperature data logger
4
Infrared thermometer or thermal camera
5
Multimeter or another electrical measuring instrument
6
Stopwatch or timer
7
Camera or smartphone for photographic and video analysis
8
GPS device or fitness tracker
9
Microphone, sound-level meter or audio-analysis software
10
Light meter, light sensor or solar sensor
11
Conductivity, pH or salinity meter
12
Weather instruments, such as an anemometer or rain gauge
13
Computer, spreadsheet, CAS, GeoGebra, Desmos or Python
14
Survey form, data sheet or observation record
15
Force sensor or spring balance
16
Laboratory glassware, measuring cylinder or pipette
17
Telescope, binoculars or a suitable camera
18
Humidity or material-moisture sensor
19
Non-invasive physiology sensor, such as heart-rate or reaction-time measurement
20
Physical model, 3D printer or material samples
21
Specialist school laboratory equipment
SSafety and data protection
0
Likely to be low risk within normal school practice
1
Supervision recommended, for example for heat, electricity, sport or traffic observation
2
Carry out only in a school laboratory or with qualified supervision
3
Sensitive personal or health data: consent, anonymisation and preferably secondary data; no medical self-intervention
From heading to investigation

A topic becomes workable only through independent decisions.

The table is designed to speed up the first step. The actual research question emerges through focus, mathematical choice and critical checking.

Focus the object

Define the object, dataset, time period, variable or mathematical structure as precisely as possible.

Select the mathematics

Decide which models, proofs, statistical procedures or optimisation steps can genuinely answer the question.

Plan independent direction

Use your own data, comparisons, modelling choices, extensions or proof ideas rather than reproducing a standard procedure.

Reflect on limitations

Examine assumptions, sources of error, data quality, model limitations, safety and possible improvements.

Personal engagement and independent direction

A personal connection is more than one sentence in the introduction.

The P codes indicate possible ways to shape an investigation independently. Independent thinking becomes visible through justified decisions, appropriate data selection, personal model variants, meaningful comparisons and critical reflection. A code does not guarantee a particular mark.

Review the IA requirements
Frequently asked questions

Use the topic list correctly.

Are the titles finished research questions?

No. They name a possible direction. A question for assessed work must be focused more narrowly, matched to the course and level, and connected to a clear mathematical method.

What does A = 3 mean?

The broad direction could be developed as an IA or Mathematics EE, depending on focus and depth. An EE will normally require a substantially deeper mathematical argument and an appropriate research scope.

Is C an official IB classification?

No. C is editorial guidance for Mathematics AA or Math AI and SL or HL. Final suitability depends on the specific research question and the current requirements.

Do I need to own the listed instruments?

No. M indicates typical or possible tools. Many topics can use open data, a spreadsheet, CAS, GeoGebra, Desmos or Python. Adapt the topic to resources that are genuinely available.

How should topics involving health or personal data be handled?

Prefer anonymised or publicly available secondary data. Original data collection needs consent, data protection, school approval and a low-risk method. Diagnosis, medication changes and invasive self-experimentation do not belong in a Mathematics project.

The complete list is also machine-readable.

The same 900 entries are available as plain text and bilingual JSON for search, accessibility and AI systems.

Authoritative foundations

Check the current curriculum version before starting.

The catalogue complements the PreLearning explanations. Current official IB documents and the school's instructions remain authoritative.

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