Focus the object
Define the object, dataset, time period, variable or mathematical structure as precisely as possible.
Topics 551 to 575 with explanations, methods, course and equipment guidance.
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.
Select an idea. Titles and areas are starting points, not finished research questions.
Check A and C. These codes give an initial indication of assessment type, course and level.
Read P, M and S. They show possible independent direction, tools, and safety or data-protection needs.
| No. | Topic idea | A | C | P | M | S |
|---|---|---|---|---|---|---|
| 551 | Water and flowWater temperature and flow velocity Measure the flow rate through a narrow tube at constant pressure head and different temperatures. Compare linear, polynomial, and viscosity-based models. |
3 | 9 | 161112 | 35121620 | 0 |
| 552 | Water and flowStreambed roughness and velocity Use smooth plastic, sandpaper, sand, and gravel as interchangeable beds. Investigate how a defined roughness index relates to velocity and discharge. |
3 | 9 | 1361112 | 25121620 | 0 |
| 553 | Water and flowChannel slope and discharge Vary the slope of a model channel while keeping other conditions constant. Test whether a power model describes the relationship between slope and discharge. |
3 | 9 | 161112 | 51620 | 0 |
| 554 | Water and flowBend radius and velocity distribution Build channels with different bend radii and film floating tracer particles. Compare velocities along the inner and outer sides of each bend. |
3 | 6 | 1236811 | 15121620 | 0 |
| 555 | Water and flowChannel sinuosity and travel time Compare straight and meandering channels with the same elevation drop. Model travel time as a function of path length and number of bends. |
3 | 6 | 1361112 | 1561620 | 0 |
| 556 | Water and flowCross-sectional shape and discharge Compare rectangular, triangular, and semicircular channels with similar cross-sectional areas. Include wetted perimeter and hydraulic radius in the model. |
3 | 9 | 161112 | 1351620 | 1 |
| 557 | Water and flowWater depth and wave speed Generate small waves in a long shallow tray and determine their speed using video analysis. Compare a linear model with a square-root model. |
3 | 9 | 1261112 | 157121620 | 0 |
| 558 | Water and flowObstacle density and flow loss Place different numbers of equal-sized stones or rods in the channel. Measure travel time, upstream water level, and discharge. |
3 | 9 | 1361112 | 5616 | 0 |
| 559 | Water and flowArtificial aquatic plants and flow Simulate aquatic plants using flexible strips or stems. Separately investigate the effects of plant density, height, or flexibility. |
3 | 9 | 1681112 | 1516 | 0 |
| 560 | Water and flowGrain size and onset of sediment transport Gradually increase the flow until sand or gravel grains of different sizes begin to move. Model critical velocity as a function of grain diameter. |
3 | 9 | 1361112 | 135121620 | 1 |
| 561 | Water and flowParticle size and settling velocity Allow spherical particles or sorted sand grains to settle through a water column. Compare linear, quadratic, and other power models. |
3 | 9 | 168101112 | 511121620 | 0 |
| 562 | Water and flowTemperature and dye dispersion Place an equal-sized dye drop into still water at different temperatures. Use image analysis to measure coloured area or colour variance over time. |
3 | 6 | 161112 | 35671316 | 0 |
| 563 | Water and flowSolution concentration and flow rate Compare water containing different proportions of sugar or glycerol in a narrow tube. Investigate how concentration changes the flow rate. |
3 | 9 | 161112 | 516 | 0 |
| 564 | Water and flowWater head and jet range Allow water to leave through a side opening in a container. Vary the water height above the opening and model the horizontal range. |
3 | 9 | 161112 | 151620 | 0 |
| 565 | Water and flowOutlet area and drainage time Drain identical containers through openings of different sizes. Also record water level over time and develop a differential-equation model. |
3 | 2 | 136101112 | 5612131620 | 0 |
| 566 | Water and flowHeight difference and siphon performance Vary the height difference between two water containers while using the same tube. Measure flow rate and drainage time. |
3 | 9 | 1361112 | 13561112 | 0 |
| 567 | Water and flowSoil composition and infiltration Compare defined mixtures of sand, soil, and clay. Record cumulative water infiltration as a function of time. |
3 | 9 | 13681112 | 561618 | 0 |
| 568 | Water and flowFilter grain size and filtration performance Investigate how the grain size and layer depth of a sand filter affect flow time and turbidity. |
3 | 9 | 161112 | 13561216 | 0 |
| 569 | Water and flowDecay of a water vortex Create a reproducible vortex and film the angular velocity of a marker. Test exponential and power-decay models. |
3 | 9 | 1361112 | 15121620 | 0 |
| 570 | Water and flowWater-wheel blade angle Build water wheels with different blade angles. Measure rotational speed, torque, or electrical output and determine an optimal angle. |
3 | 9 | 1261112 | 135151620 | 1 |
| 571 | Ice, freezing, and strengthAir-bubble fraction and flexural strength Photograph equal-sized ice samples before loading and calculate the visible bubble-area fraction. Compare it with maximum breaking load. |
3 | 9 | 121112 | 2371115 | 1 |
| 572 | Ice, freezing, and strengthBubble size and fracture strength Determine mean bubble diameter, variation, and bubble count using image analysis. Use multiple regression to predict strength. |
3 | 6 | 1101112 | 13713 | 0 |
| 573 | Ice, freezing, and strengthFreezing rate and trapped air Freeze identical amounts of water at different rates, for example using different insulation layers. Measure bubble content, transparency, and strength. |
3 | 9 | 1681112 | 31216 | 0 |
| 574 | Ice, freezing, and strengthIce temperature and breaking stress Test standardized ice beams at several temperatures below 0 °C. Calculate a comparable breaking stress from failure load and sample geometry. |
3 | 9 | 11112 | 2351520 | 1 |
| 575 | Ice, freezing, and strengthSalinity and ice strength Produce ice samples with different accurately measured salt concentrations. Investigate strength, density, and fracture behaviour. |
3 | 9 | 11112 | 31116 | 0 |
No topic ideas match this combination.
The table stays narrow on a phone by replacing long descriptions with numeric codes. Entries may contain several P and M codes.
The table is designed to speed up the first step. The actual research question emerges through focus, mathematical choice and critical checking.
Define the object, dataset, time period, variable or mathematical structure as precisely as possible.
Decide which models, proofs, statistical procedures or optimisation steps can genuinely answer the question.
Use your own data, comparisons, modelling choices, extensions or proof ideas rather than reproducing a standard procedure.
Examine assumptions, sources of error, data quality, model limitations, safety and possible improvements.
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 requirementsNo. 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.
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.
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.
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.
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 same 900 entries are available as plain text and bilingual JSON for search, accessibility and AI systems.
The catalogue complements the PreLearning explanations. Current official IB documents and the school's instructions remain authoritative.