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IB Mathematics · Complete topic list
373 topic ideas for the Mathematics IA and Extended Essay.
A mixed, filterable one-page list with guidance for IA or EE, Mathematics AA or AI, SL or HL, plus codes for independent direction, equipment and safety.
One page · 373 suggestions
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The list mixes calculus, statistics, modelling, geometry, number theory, computer science, sport, environmental topics and other areas. On a phone, every table row automatically becomes a compact card.
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.
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| No. | Topic idea | A | C | P | M | S |
|---|---|---|---|---|---|---|
| 1 | Game theory & decision-makingNash equilibria in extended rock-paper-scissors games | 3 | 9 | 1811 | 0 | 0 |
| 2 | Biomathematics & medicineModelling blood-glucose levels after meals with the Bergman minimal model | 2 | 8 | 111 | 1319 | 3 |
| 3 | Environmental mathematics & sustainabilityCalculating a family's ecological footprint using geometric means | 1 | 6 | 15 | 13 | 0 |
| 4 | Sports biomechanics & movementCalculating the optimal approach speed in long jump | 3 | 9 | 1311 | 13 | 1 |
| 5 | Data science & introductory algorithmsBenford's law in financial data and election results | 3 | 6 | 19 | 0 | 0 |
| 6 | Chaos & dynamical systemsThe logistic map and the transition to chaos | 2 | 2 | 1 | 13 | 0 |
| 7 | Music, acoustics & wavesCalculating optimal room acoustics for a music studio | 3 | 9 | 1811 | 913 | 0 |
| 8 | Art, design & architectureProportions in the human face and claims about the golden ratio | 3 | 9 | 12 | 17 | 0 |
| 9 | Astronomy & spaceflightCalculating satellite orbits with Kepler's laws | 2 | 2 | 1 | 1317 | 0 |
| 10 | Psychology & cognitionReaction-time distributions within a class | 1 | 6 | 14 | 619 | 3 |
| 11 | Probability & riskCalculating expected loss for different insurance types | 1 | 6 | 5 | 13 | 0 |
| 12 | Culinary mathematicsCalculating the best-value pizza size by area and price | 1 | 9 | 159 | 113 | 0 |
| 13 | ThermodynamicsNewton's law of cooling for coffee in ceramic, glass, metal and paper cups | 1 | 9 | 15 | 3 | 0 |
| 14 | Material propertiesEvaporation rates of water, ethanol, acetone and salt water under controlled conditions | 1 | 9 | 112 | 2616 | 2 |
| 15 | ElectricityDischarge curves of AA batteries from different brands under a constant load | 1 | 9 | 112 | 5613 | 1 |
| 16 | Combined experimentsDensity of water and ethanol at temperatures from 10°C to 60°C | 1 | 3 | 1 | 23113 | 0 |
| 17 | Kitchen & everyday lifeOptimising coffee brewing: extraction rate versus temperature profile | 1 | 9 | 1511 | 2316 | 0 |
| 18 | EnvironmentParticulate-filter residue mass across different locations | 1 | 6 | 112 | 2 | 0 |
| 19 | PhysiologySurface heat loss from the human head with and without a hat after exercise | 1 | 6 | 1312 | 4313 | 3 |
| 20 | MaterialsWater absorption of brick, wood, concrete and plaster over time | 1 | 9 | 1 | 2618 | 0 |
| 21 | Algebra & number theoryThe golden ratio in architectural proportions across different cultures | 1 | 9 | 12 | 17 | 0 |
| 22 | Analysis & calculusOptimising container dimensions under cost and surface-area constraints | 3 | 3 | 1211 | 120 | 0 |
| 23 | Statistics & probabilityChi-squared tests: study habits, screen time and sleep | 1 | 6 | 14 | 14 | 3 |
| 24 | Mathematical modellingAn SIR model for the spread of disease | 2 | 8 | 1 | 0 | 0 |
| 25 | Geometry & topologyTessellations: which regular polygons tile the plane? | 1 | 3 | 1211 | 20 | 0 |
| 26 | Financial mathematicsCompound interest versus simple interest over different periods | 1 | 6 | 15 | 0 | 0 |
| 27 | Logic, set theory & proofMathematical induction for sums and divisibility identities | 2 | 2 | 10 | 13 | 0 |
| 28 | Discrete mathematics & computer scienceGraph-colouring problems | 3 | 3 | 1 | 0 | 0 |
| 29 | Applied & interdisciplinary mathematicsThe mathematics of recipes: ratios and scaling | 1 | 9 | 15 | 0 | 0 |
| 30 | Biomathematics & medicineModelling medication concentration and dosage over time with pharmacokinetics | 2 | 2 | 1911 | 613 | 3 |
| 31 | Environmental mathematics & sustainabilityOptimising waste separation with probability models | 1 | 6 | 1611 | 13 | 3 |
| 32 | Sports biomechanics & movementMathematical analysis of rotation in figure skating using angular momentum | 3 | 2 | 13 | 715 | 0 |
| 33 | Data science & introductory algorithmsA basic Fourier-based classification of music genres | 2 | 2 | 178 | 913 | 0 |
| 34 | Chaos & dynamical systemsModelling the double pendulum and its unpredictability | 2 | 2 | 1711 | 13 | 0 |
| 35 | Music, acoustics & wavesOvertone series in different musical instruments | 3 | 3 | 18 | 913 | 0 |
| 36 | Art, design & architectureCalculating perspective in painting using one-point perspective | 3 | 3 | 12 | 1713 | 0 |
| 37 | Astronomy & spaceflightModelling tidal forces and their mathematical periodicity | 3 | 9 | 1611 | 613 | 0 |
| 38 | Psychology & cognitionModelling the Ebbinghaus forgetting curve with exponential decay | 1 | 6 | 1411 | 13 | 3 |
| 39 | Probability & riskModelling smoking risk with life-expectancy data | 3 | 6 | 12 | 0 | 3 |
| 40 | Culinary mathematicsModelling coffee brewing through extraction rates and temperature | 3 | 9 | 1511 | 31316 | 0 |
| 41 | ThermodynamicsInsulating performance of cup materials: time taken to approach room temperature | 1 | 9 | 112 | 3416 | 0 |
| 42 | Material propertiesDetermining the density of different woods from mass and volume | 1 | 3 | 1 | 211314 | 3 |
| 43 | ElectricitySolar-cell power at different light angles and distances | 1 | 9 | 111 | 511013 | 1 |
| 44 | Combined experimentsElectrolysis of water: electrode mass change versus applied voltage | 1 | 2 | 1 | 251621 | 2 |
| 45 | Kitchen & everyday lifeWhich teapot material retains heat longest: cast iron, glass or porcelain? | 1 | 9 | 15 | 34113 | 0 |
| 46 | EnvironmentRainwater: precipitation amount, temperature and electrical conductivity | 1 | 6 | 16 | 2351 | 1 |
| 47 | PhysiologySkin-surface temperature recovery after a safe cold-water exposure | 1 | 6 | 1 | 41319 | 3 |
| 48 | MaterialsHeat distribution around skateboard or longboard axles after riding | 1 | 9 | 13 | 43813 | 0 |
| 49 | Algebra & number theoryModelling population growth: logistic versus exponential models | 1 | 6 | 1611 | 13 | 1 |
| 50 | Analysis & calculusNewton's law of cooling: modelling with differential equations | 3 | 2 | 111 | 313 | 0 |
| 51 | Statistics & probabilityThe birthday paradox: simulation versus theoretical probability | 1 | 9 | 145 | 1314 | 3 |
| 52 | Mathematical modellingPredator-prey dynamics: the Lotka-Volterra equations | 2 | 2 | 6 | 0 | 0 |
| 53 | Geometry & topologyThe Seven Bridges of Königsberg and graph theory | 3 | 2 | 10 | 13 | 0 |
| 54 | Financial mathematicsMortgage repayment: how much can an extra payment save? | 1 | 6 | 5 | 0 | 0 |
| 55 | Logic, set theory & proofBoolean algebra and logic gates: De Morgan's laws | 2 | 2 | 17 | 0 | 0 |
| 56 | Discrete mathematics & computer scienceAnalysing sorting algorithms: running time and comparisons | 3 | 9 | 1712 | 613 | 0 |
| 57 | Applied & interdisciplinary mathematicsOptimising how to pack a suitcase or backpack | 1 | 6 | 111 | 0 | 0 |
| 58 | Game theory & decision-makingOptimal blackjack hand strategy using probability | 3 | 8 | 178 | 13 | 0 |
| 59 | Environmental mathematics & sustainabilityModelling seasonal water levels in local lakes | 1 | 6 | 1611 | 13 | 0 |
| 60 | Sports biomechanics & movementModelling force distribution while climbing on different wall angles | 3 | 3 | 1311 | 1315 | 1 |
| 61 | Data science & introductory algorithmsAnalysing sentiment trends on social media over time | 3 | 6 | 1 | 6 | 0 |
| 62 | Chaos & dynamical systemsSensitivity to initial conditions and the butterfly effect | 2 | 2 | 17 | 13 | 0 |
| 63 | Music, acoustics & wavesModelling dissonance with interval-frequency ratios | 3 | 3 | 1811 | 913 | 0 |
| 64 | Art, design & architectureMathematical analysis of Escher tessellations and symmetry groups | 3 | 3 | 148 | 0 | 0 |
| 65 | Astronomy & spaceflightLight curves of variable stars | 3 | 6 | 1 | 1017 | 0 |
| 66 | Psychology & cognitionAnalysing mathematical patterns in sleep and REM cycles | 3 | 6 | 1 | 6 | 3 |
| 67 | Probability & riskModelling the failure probability of technical devices | 3 | 6 | 11112 | 13 | 0 |
| 68 | Culinary mathematicsThe geometry of pasta shapes and their cooking times | 3 | 3 | 15 | 6 | 0 |
| 69 | ThermodynamicsHeating surfaces of different colours in sunlight: black, white, red and silver | 1 | 9 | 1 | 341 | 0 |
| 70 | Material propertiesWater content of fruits and vegetables measured by oven drying | 1 | 6 | 15 | 2 | 1 |
| 71 | ElectricityInternal resistance of alkaline, NiMH and lithium batteries | 1 | 2 | 112 | 513 | 1 |
| 72 | Combined experimentsSpecific heat capacity of different liquids under equal energy input | 1 | 3 | 1 | 23 | 0 |
| 73 | Kitchen & everyday lifeIce-cream melting rate: mass loss and surface temperature across different formulations | 1 | 6 | 112 | 2413 | 1 |
| 74 | EnvironmentCompost: mass loss and core temperature over four weeks | 1 | 6 | 16 | 236 | 0 |
| 75 | PhysiologySweat-related body-mass change during exercise under different ambient conditions | 1 | 6 | 13 | 231319 | 3 |
| 76 | MaterialsMoisture absorption by three-dimensional printing filaments | 1 | 3 | 1 | 261318 | 0 |
| 77 | Algebra & number theoryRSA encryption and prime number theory | 2 | 2 | 10 | 13 | 0 |
| 78 | Analysis & calculusCalculating work done by a variable force in sport | 3 | 2 | 13 | 13 | 0 |
| 79 | Statistics & probabilityRegression: carbon dioxide emissions and global temperatures | 1 | 6 | 9 | 313 | 0 |
| 80 | Mathematical modellingThe trajectory of a basketball or tennis shot | 1 | 9 | 13 | 7 | 0 |
| 81 | Geometry & topologyFractal geometry and the coastline paradox | 3 | 2 | 110 | 0 | 0 |
| 82 | Financial mathematicsThe true cost of minimum credit-card payments | 1 | 4 | 15 | 13 | 0 |
| 83 | Logic, set theory & proofCantor's infinities: countability and the diagonal argument | 2 | 2 | 10 | 0 | 0 |
| 84 | Discrete mathematics & computer scienceHuffman coding and data compression | 3 | 9 | 17 | 0 | 0 |
| 85 | Applied & interdisciplinary mathematicsRoom acoustics and reverberation time | 3 | 9 | 18 | 9 | 0 |
| 86 | Game theory & decision-makingThe mathematics of auction systems: English versus Dutch auctions | 3 | 6 | 178 | 13 | 0 |
| 87 | Biomathematics & medicineHeart-rate variability analysed with statistical methods | 3 | 6 | 13 | 819 | 3 |
| 88 | Sports biomechanics & movementOptimising swimming technique through drag models | 3 | 8 | 1311 | 613 | 1 |
| 89 | Data science & introductory algorithmsTesting the predictive accuracy of weather apps with regression | 3 | 6 | 16 | 13 | 0 |
| 90 | Chaos & dynamical systemsJulia sets and their dependence on parameters | 2 | 2 | 1711 | 0 | 0 |
| 91 | Music, acoustics & wavesMathematical analysis of rhythm patterns across music genres | 3 | 9 | 18 | 9 | 0 |
| 92 | Art, design & architectureCurves in typeface design: Bézier curves | 3 | 3 | 18 | 0 | 0 |
| 93 | Astronomy & spaceflightCalculating stellar distances by parallax | 3 | 3 | 111 | 11317 | 0 |
| 94 | Psychology & cognitionOptimising break intervals in study sessions with a Pomodoro model | 1 | 6 | 111 | 13 | 3 |
| 95 | Probability & riskCalculating optimal diversification in an investment portfolio | 3 | 5 | 1711 | 13 | 0 |
| 96 | Culinary mathematicsCalculating optimal lasagne layering with heat-conduction models | 3 | 3 | 1511 | 313 | 0 |
| 97 | ThermodynamicsHeat distribution across a laptop under CPU load | 1 | 9 | 110 | 437 | 0 |
| 98 | Material propertiesCarbon dioxide loss from fizzy drinks over 48 hours under different storage conditions | 1 | 9 | 1 | 26 | 0 |
| 99 | ElectricityVoltage drop along copper cables of different lengths and cross-sections | 1 | 3 | 1 | 513 | 1 |
| 100 | Combined experimentsSolar-cell voltage loss as temperature increases | 1 | 8 | 1 | 4513 | 1 |
| 101 | Kitchen & everyday lifeBread baking: water loss and core temperature over time | 1 | 9 | 15 | 23 | 1 |
| 102 | EnvironmentSolar cooker: water temperature and evaporation mass at different angles | 1 | 9 | 111 | 23110 | 1 |
| 103 | PhysiologyHand-surface temperature before and after a low-risk cognitive task | 1 | 6 | 14 | 4319 | 3 |
| 104 | MaterialsThermal response of granite, wood and stainless-steel worktops | 1 | 3 | 15 | 341 | 0 |
| 105 | Algebra & number theoryPascal's triangle: patterns, binomial coefficients and combinatorics | 1 | 9 | 1 | 0 | 0 |
| 106 | Analysis & calculusConvergence of series: the harmonic series, Basel problem and geometric series | 2 | 2 | 10 | 0 | 0 |
| 107 | Statistics & probabilityThe Monty Hall problem: simulation versus theory | 1 | 7 | 17 | 13 | 0 |
| 108 | Mathematical modellingLogistic growth in social-media followers and viral trends | 1 | 9 | 1 | 0 | 1 |
| 109 | Geometry & topologyPlatonic solids: Euler's formula and why there are exactly five | 3 | 3 | 2 | 20 | 0 |
| 110 | Financial mathematicsSaving strategies: lump-sum investment versus regular deposits | 1 | 4 | 1511 | 0 | 0 |
| 111 | Logic, set theory & proofArrow's impossibility theorem and voting systems | 2 | 2 | 10 | 0 | 0 |
| 112 | Discrete mathematics & computer scienceModelling networks with adjacency matrices | 3 | 3 | 111 | 13 | 0 |
| 113 | Applied & interdisciplinary mathematicsModelling an optimal running pace | 1 | 9 | 1311 | 13 | 0 |
| 114 | Game theory & decision-makingThe prisoner's dilemma in repeated games | 3 | 9 | 1411 | 0 | 0 |
| 115 | Biomathematics & medicineModelling tumour growth: Gompertz versus exponential models | 2 | 8 | 11 | 13 | 3 |
| 116 | Environmental mathematics & sustainabilityStatistical analysis of the effectiveness of recycling programmes | 1 | 6 | 167 | 13 | 0 |
| 117 | Data science & introductory algorithmsCalculating text similarity with introductory vector models | 2 | 2 | 1712 | 13 | 0 |
| 118 | Chaos & dynamical systemsCalculating Lyapunov exponents for simple functions | 2 | 2 | 710 | 13 | 0 |
| 119 | Music, acoustics & wavesCalculating string lengths for alternative tuning systems | 3 | 3 | 18 | 91314 | 3 |
| 120 | Art, design & architectureCalculating optimal stage lighting through angle analysis | 3 | 3 | 1811 | 11013 | 0 |
| 121 | Astronomy & spaceflightModelling a rocket trajectory with air resistance | 2 | 2 | 1711 | 13 | 1 |
| 122 | Psychology & cognitionThe Stroop effect analysed with statistical hypothesis tests | 1 | 6 | 14 | 0 | 3 |
| 123 | Probability & riskPerceived risk versus measured risk: air travel and driving | 3 | 6 | 1412 | 14 | 3 |
| 124 | Culinary mathematicsAnalysing bubble distributions in bread and sparkling drinks with a Poisson model | 3 | 6 | 125 | 7 | 0 |
| 125 | ThermodynamicsTemperature gradients in a classroom from floor to desk height and ceiling over a day | 1 | 6 | 14 | 3416 | 0 |
| 126 | Material propertiesAbsorption rates of toilet paper, kitchen roll and newspaper | 1 | 6 | 15 | 26 | 0 |
| 127 | ElectricityCharging and discharging capacitors of different capacitances | 1 | 2 | 1 | 5 | 0 |
| 128 | Combined experimentsEvaporation: mass loss versus surface temperature in wind, sun and shade | 1 | 9 | 1 | 2413 | 0 |
| 129 | Kitchen & everyday lifeYoghurt fermentation: temperature profile and mass change | 1 | 6 | 15 | 2316 | 1 |
| 130 | EnvironmentHeat loss from buildings using facade surface-temperature measurements | 1 | 6 | 26 | 413 | 0 |
| 131 | PhysiologyReaction time and naturally observed body-temperature variation | 1 | 6 | 110 | 31319 | 3 |
| 132 | MaterialsElectrical conductivity of pencil lines with grades from 2H to 6B | 1 | 3 | 12 | 513 | 1 |
| 133 | Algebra & number theoryFibonacci numbers and the limiting ratio of consecutive terms | 3 | 3 | 16 | 13 | 0 |
| 134 | Analysis & calculusThe mathematics of rainbow formation: Snell's law, refraction and optimisation | 3 | 2 | 611 | 0 | 0 |
| 135 | Statistics & probabilityStatistical bias in media reporting | 1 | 6 | 912 | 0 | 0 |
| 136 | Mathematical modellingTraffic flow at roundabouts or traffic lights | 1 | 2 | 16 | 0 | 1 |
| 137 | Geometry & topologyUsing vectors to model three-dimensional reflections in a kaleidoscope | 3 | 2 | 124 | 1320 | 0 |
| 138 | Financial mathematicsAn introduction to the Black-Scholes model for option pricing | 2 | 5 | 1 | 13 | 0 |
| 139 | Logic, set theory & proofTruth tables and their minimisation | 1 | 2 | 127 | 20 | 0 |
| 140 | Discrete mathematics & computer scienceHeuristics for the travelling salesperson problem | 2 | 8 | 111 | 8 | 0 |
| 141 | Applied & interdisciplinary mathematicsAnalysing the efficiency of water pumps | 1 | 6 | 111 | 0 | 0 |
| 142 | Game theory & decision-makingOptimal positioning in penalty kicks using mixed strategies | 3 | 8 | 1311 | 7 | 0 |
| 143 | Biomathematics & medicineMathematical analysis of mosquito-population spread | 3 | 9 | 6 | 12 | 0 |
| 144 | Environmental mathematics & sustainabilityCalculating optimal home insulation using heat conduction | 3 | 3 | 1211 | 313 | 0 |
| 145 | Sports biomechanics & movementOptimising launch angles in archery | 3 | 3 | 1311 | 1 | 1 |
| 146 | Chaos & dynamical systemsModelling population fluctuations with discrete dynamical systems | 1 | 8 | 111 | 13 | 0 |
| 147 | Music, acoustics & wavesSound propagation through different materials | 3 | 3 | 1 | 9 | 0 |
| 148 | Art, design & architectureModelling wave patterns in textile design | 3 | 9 | 1211 | 13 | 0 |
| 149 | Astronomy & spaceflightMathematical patterns in planetary resonances | 2 | 2 | 9 | 9 | 0 |
| 150 | Psychology & cognitionModelling decision fatigue with probability models | 1 | 5 | 111 | 13 | 3 |
| 151 | Probability & riskThe probability of natural disasters at a particular location | 3 | 6 | 6 | 13 | 0 |
| 152 | Culinary mathematicsModelling fermentation in bread and yoghurt with exponential growth | 3 | 9 | 1511 | 13 | 1 |
| 153 | ThermodynamicsCooling curves of aluminium, copper and iron from the same starting temperature | 1 | 3 | 112 | 3 | 0 |
| 154 | Material propertiesOsmosis: mass change of potato slices in salt solutions from 0% to 20% | 1 | 9 | 15 | 21316 | 0 |
| 155 | ElectricityElectrical conductivity of water, juice, cola and salt water | 1 | 9 | 1 | 5111316 | 1 |
| 156 | Combined experimentsFreezing-point depression: dissolved salt or sugar mass versus minimum temperature | 1 | 3 | 1 | 231316 | 0 |
| 157 | Kitchen & everyday lifeWater and mass loss from cheese or cured food during refrigerated storage | 1 | 6 | 15 | 213 | 0 |
| 158 | EnvironmentAlgal growth: biomass and aquarium-water temperature over time | 1 | 6 | 1 | 23613 | 1 |
| 159 | Algebra & number theoryNumber systems and modular arithmetic in computer science | 3 | 2 | 7 | 13 | 0 |
| 160 | Analysis & calculusModelling roller-coaster curves with cubic and quintic functions | 3 | 3 | 1211 | 20 | 0 |
| 161 | Statistics & probabilityCorrelation between study time and predicted IB grades | 1 | 4 | 110 | 14 | 3 |
| 162 | Mathematical modellingThe mathematics of music: frequency ratios and overtones | 3 | 3 | 18 | 9 | 0 |
| 163 | Geometry & topologyNon-Euclidean geometry: angle sums on a sphere and a hyperbolic surface | 2 | 2 | 10 | 1 | 0 |
| 164 | Financial mathematicsReturns across different types of investment | 1 | 6 | 159 | 0 | 0 |
| 165 | Logic, set theory & proofDifferent proofs that there are infinitely many primes | 2 | 3 | 10 | 13 | 0 |
| 166 | Discrete mathematics & computer scienceHash functions and collisions | 2 | 2 | 17 | 0 | 0 |
| 167 | Applied & interdisciplinary mathematicsThe mathematics of photography: exposure and aperture | 3 | 9 | 128 | 710 | 0 |
| 168 | Game theory & decision-makingThe mathematics behind bidding strategies in The Price Is Right | 3 | 6 | 178 | 13 | 0 |
| 169 | Biomathematics & medicineBMI and its statistical validity across different populations | 1 | 6 | 1412 | 1314 | 3 |
| 170 | Environmental mathematics & sustainabilityCorrelation between air quality and asthma incidence | 3 | 6 | 6910 | 12 | 3 |
| 171 | Sports biomechanics & movementMathematical analysis of the Magnus effect in a football free kick | 3 | 2 | 13 | 7 | 0 |
| 172 | Data science & introductory algorithmsModelling Netflix-style recommendations with simple distance measures | 3 | 6 | 138 | 13 | 0 |
| 173 | Music, acoustics & wavesModelling vibrato frequency and its perception | 3 | 9 | 11112 | 91314 | 0 |
| 174 | Art, design & architectureAnalysing proportions in fashion: clothing sizes and golden-ratio claims | 3 | 6 | 189 | 1 | 0 |
| 175 | Astronomy & spaceflightCalculating optimal launch windows with Hohmann transfers | 2 | 2 | 111 | 13 | 0 |
| 176 | Psychology & cognitionCorrelation between music genre and mathematical performance | 1 | 6 | 148 | 914 | 3 |
| 177 | Probability & riskModelling cafeteria queues with a Poisson process | 3 | 6 | 1411 | 13 | 0 |
| 178 | Culinary mathematicsCalculating an optimal chocolate-melting temperature | 3 | 3 | 1511 | 313 | 1 |
| 179 | ThermodynamicsHeat storage in sand, clay and humus under equal energy input | 1 | 9 | 16 | 341 | 0 |
| 180 | Material propertiesCorrosion of iron nails in water, salt water, cola and vinegar | 1 | 3 | 111 | 2613 | 1 |
| 181 | ElectricityVoltage from homemade galvanic cells using lemons, potatoes, cola and apples | 1 | 3 | 15 | 5 | 2 |
| 182 | Combined experimentsConductivity versus salt concentration in aqueous solutions | 1 | 9 | 1 | 251113 | 1 |
| 183 | Kitchen & everyday lifePackaging fruit: mass loss under cling film, vacuum storage and wax wrap | 1 | 6 | 1512 | 26 | 1 |
| 184 | EnvironmentPaving stones versus grass: daytime surface temperature and night-time cooling | 1 | 6 | 6 | 34113 | 0 |
| 185 | Algebra & number theoryMagic squares: algebraic construction methods | 1 | 3 | 1211 | 20 | 0 |
| 186 | Analysis & calculusRiemann sums and numerical integration | 3 | 2 | 12 | 13 | 0 |
| 187 | Statistics & probabilityThe normal distribution in sports performance data | 1 | 6 | 13 | 0 | 0 |
| 188 | Mathematical modellingModelling the spread of rumours in a school community | 1 | 8 | 1 | 0 | 0 |
| 189 | Geometry & topologyThe golden spiral in selected natural forms | 3 | 9 | 126 | 7 | 0 |
| 190 | Financial mathematicsCalculating the effective annual percentage rate on consumer loans | 1 | 4 | 5 | 13 | 0 |
| 191 | Logic, set theory & proofParadoxes in set theory | 2 | 2 | 10 | 0 | 0 |
| 192 | Discrete mathematics & computer scienceBinary trees and their properties | 3 | 3 | 1211 | 20 | 0 |
| 193 | Applied & interdisciplinary mathematicsModelling optimal lighting in a room | 1 | 6 | 111 | 1013 | 0 |
| 194 | Game theory & decision-makingZero-sum games in classic board games | 3 | 3 | 18 | 0 | 0 |
| 195 | Biomathematics & medicineCorrelation between sleep duration and cognitive performance | 1 | 6 | 110 | 19 | 3 |
| 196 | Environmental mathematics & sustainabilityModelling plastic degradation in oceans with exponential decay | 3 | 6 | 6911 | 13 | 0 |
| 197 | Sports biomechanics & movementModelling an optimal stride pattern for the 100-metre sprint | 3 | 9 | 111 | 813 | 0 |
| 198 | Data science & introductory algorithmsCluster formation in friendship networks | 3 | 6 | 14 | 14 | 3 |
| 199 | Chaos & dynamical systemsArnold tongues in the circle map | 2 | 2 | 810 | 914 | 3 |
| 200 | Art, design & architectureThe mathematics of three-dimensional printing structures and infill patterns | 3 | 3 | 12 | 20 | 0 |
| 201 | Astronomy & spaceflightThe distribution of asteroids in the Solar System | 3 | 6 | 1 | 17 | 0 |
| 202 | Psychology & cognitionCalculating an optimal group size for effective learning | 1 | 6 | 1411 | 13 | 3 |
| 203 | Probability & riskCalculating the risk of base-rate errors in everyday decisions | 3 | 9 | 112 | 1319 | 0 |
| 204 | Culinary mathematicsThe mathematics of laminated dough folds | 3 | 3 | 1 | 0 | 0 |
| 205 | ThermodynamicsMelting rate of ice shapes: volume, surface area and form | 1 | 3 | 1 | 231 | 0 |
| 206 | Material propertiesFermentation: carbon dioxide loss from yeast-sugar solutions of different concentrations | 1 | 9 | 1 | 216 | 0 |
| 207 | ElectricityPhotovoltaic power loss under partial shading in series and parallel circuits | 1 | 8 | 1311 | 571013 | 1 |
| 208 | Combined experimentsHeat capacity of coins made from different alloys | 1 | 3 | 112 | 2316 | 0 |
| 209 | Kitchen & everyday lifeSurface-temperature patterns after different forms of exercise | 1 | 6 | 1312 | 319 | 3 |
| 210 | EnvironmentHousehold waste separation: mass of different fractions per week | 1 | 6 | 15 | 2 | 0 |
| 211 | Algebra & number theoryThe Collatz conjecture: convergence behaviour for different starting values | 2 | 2 | 710 | 0 | 0 |
| 212 | Analysis & calculusParameter changes in the logistic function | 3 | 8 | 911 | 0 | 0 |
| 213 | Statistics & probabilityBayes' theorem and the reliability of medical tests | 3 | 2 | 1012 | 0 | 3 |
| 214 | Mathematical modellingModelling the spread of wildfires | 2 | 8 | 679 | 13 | 0 |
| 215 | Geometry & topologyCalculating sightlines in a theatre or concert hall | 1 | 3 | 268 | 113 | 0 |
| 216 | Financial mathematicsModelling the effect of inflation on purchasing power | 1 | 6 | 11 | 13 | 0 |
| 217 | Logic, set theory & proofModelling logic puzzles with propositional logic | 1 | 3 | 111 | 13 | 0 |
| 218 | Discrete mathematics & computer scienceModelling game strategies with game trees | 3 | 9 | 1811 | 13 | 0 |
| 219 | Applied & interdisciplinary mathematicsThe mathematics of perfume: evaporation and diffusion | 3 | 9 | 18 | 16 | 0 |
| 220 | Game theory & decision-makingModelling negotiation strategies with cooperative game theory | 3 | 5 | 1811 | 13 | 0 |
| 221 | Biomathematics & medicineModelling the spread of antibiotic resistance in bacterial populations | 2 | 2 | 1711 | 13 | 3 |
| 222 | Environmental mathematics & sustainabilityOptimising solar-panel orientation for maximum energy yield | 3 | 9 | 1611 | 10 | 0 |
| 223 | Sports biomechanics & movementCalculating stability in different yoga poses using centre of mass | 3 | 3 | 123 | 171315 | 0 |
| 224 | Data science & introductory algorithmsTime-series analysis: forecasting share prices with moving averages | 3 | 6 | 1 | 0 | 0 |
| 225 | Music, acoustics & wavesAnalysing the mathematical structure of canons and fugues | 3 | 3 | 18 | 9 | 0 |
| 226 | ThermodynamicsThermal conductivity of metal rods measured by the time taken for wax to melt | 1 | 3 | 112 | 3613 | 1 |
| 227 | Material propertiesSublimation of dry ice: mass loss over time at constant conditions | 1 | 3 | 1 | 23621 | 2 |
| 228 | ElectricityThermoelectric voltage as a function of temperature difference using a Peltier element | 1 | 2 | 1 | 3513 | 1 |
| 229 | Combined experimentsThermocouple voltage as a function of hot-to-cold water-bath temperature difference | 1 | 2 | 16 | 351316 | 1 |
| 230 | Kitchen & everyday lifeHand surface-temperature recovery after a safe cold-water exposure | 1 | 6 | 1 | 4136 | 3 |
| 231 | EnvironmentWater mass loss from plastic and glass containers over time | 1 | 3 | 1 | 216 | 0 |
| 232 | Algebra & number theoryPerfect numbers and their rarity | 3 | 3 | 10 | 13 | 0 |
| 233 | Analysis & calculusOptimising the flight path of a paper aeroplane | 1 | 9 | 1311 | 17 | 0 |
| 234 | Statistics & probabilityGrade distributions across different school subjects | 1 | 6 | 1 | 0 | 0 |
| 235 | Mathematical modellingOptimising seating arrangements in a classroom | 1 | 6 | 1411 | 14 | 3 |
| 236 | Geometry & topologySymmetry in Islamic art | 1 | 3 | 128 | 7 | 0 |
| 237 | Financial mathematicsInsurance models and premium calculations | 1 | 6 | 5 | 13 | 0 |
| 238 | Logic, set theory & proofAn introduction to Gödel's incompleteness theorems | 2 | 2 | 1 | 0 | 0 |
| 239 | Discrete mathematics & computer scienceError-detecting codes and Hamming distance | 2 | 2 | 138 | 0 | 0 |
| 240 | Applied & interdisciplinary mathematicsAnalysing the stability of towers built from blocks | 1 | 9 | 1211 | 1520 | 0 |
| 241 | Biomathematics & medicineThe geometry and optimisation of leaf-vein networks | 3 | 3 | 1611 | 0 | 0 |
| 242 | Environmental mathematics & sustainabilityMathematical analysis of wind-energy potential at a location | 3 | 6 | 6 | 12 | 0 |
| 243 | Sports biomechanics & movementMathematical patterns in dance choreography | 3 | 9 | 138 | 7 | 0 |
| 244 | Data science & introductory algorithmsIntroductory image compression with singular value decomposition | 2 | 2 | 17 | 0 | 0 |
| 245 | Music, acoustics & wavesCalculating the resonant frequencies of glasses in a glass harmonica | 3 | 3 | 1 | 913 | 0 |
| 246 | Art, design & architectureCalculating tension in tent structures based on hyperbolic paraboloids | 2 | 2 | 1211 | 51320 | 1 |
| 247 | ThermodynamicsTemperature change while baking a muffin: core versus surface temperature | 1 | 9 | 1511 | 3 | 1 |
| 248 | Material propertiesHygroscopicity of salts and sugars: mass gain from moisture in air | 1 | 3 | 112 | 261318 | 0 |
| 249 | ElectricityTemperature-dependent resistance of an incandescent lamp | 1 | 3 | 1 | 35 | 1 |
| 250 | Combined experimentsCalorimetry: determining the specific heat capacity of a metal | 1 | 3 | 112 | 2316 | 0 |
| 251 | Kitchen & everyday lifeTemperature change in a vacuum flask over 24 hours | 1 | 3 | 1 | 3613 | 0 |
| 252 | EnvironmentWater samples: dissolved-solid mass and electrical conductivity | 1 | 6 | 16 | 2513 | 1 |
| 253 | Algebra & number theoryThe relationship between continued fractions and irrational numbers | 2 | 2 | 1 | 0 | 0 |
| 254 | Analysis & calculusSpeed and acceleration while cycling | 1 | 3 | 13 | 8 | 3 |
| 255 | Statistics & probabilityComparing mean, median and mode in salary data | 1 | 6 | 1912 | 0 | 0 |
| 256 | Mathematical modellingModelling water supply in a city | 1 | 6 | 611 | 13 | 0 |
| 257 | Geometry & topologyModelling shadows cast by sundials | 1 | 3 | 123 | 7101320 | 0 |
| 258 | Financial mathematicsComparing vehicle leasing with purchasing | 1 | 6 | 1512 | 0 | 0 |
| 259 | Logic, set theory & proofProof methods: direct proof, contraposition and contradiction | 2 | 2 | 10 | 13 | 0 |
| 260 | Discrete mathematics & computer scienceRecurrence relations and the Tower of Hanoi | 2 | 3 | 17 | 0 | 0 |
| 261 | Applied & interdisciplinary mathematicsModelling an optimal racket length in sport | 1 | 9 | 1311 | 13 | 0 |
| 262 | Biomathematics & medicineMathematical modelling of visual acuity and corrective-lens power | 3 | 3 | 111 | 1319 | 3 |
| 263 | Environmental mathematics & sustainabilityCalculating carbon dioxide emissions per kilometre for different forms of transport | 1 | 6 | 16 | 813 | 0 |
| 264 | Sports biomechanics & movementAnalysing the optimal riding position on a road bicycle | 3 | 3 | 1311 | 0 | 0 |
| 265 | Data science & introductory algorithmsPassword-strength patterns through combinatorics | 3 | 3 | 1 | 0 | 0 |
| 266 | ThermodynamicsHeating of asphalt, grass and water in midday sun | 1 | 6 | 6 | 341 | 0 |
| 267 | Material propertiesBurning rates of candles with different diameters and wax types | 1 | 9 | 19 | 21613 | 1 |
| 268 | ElectricityVoltage and capacity change of a lithium-ion battery over repeated charge cycles | 1 | 9 | 1 | 5613 | 1 |
| 269 | Combined experimentsElectroplating: cathode mass gain versus voltage and time | 1 | 2 | 1 | 251321 | 2 |
| 270 | Algebra & number theoryEuler's totient function and its properties | 3 | 3 | 1 | 0 | 0 |
| 271 | Analysis & calculusModelling breathing with sinusoidal functions | 1 | 9 | 111 | 13 | 0 |
| 272 | Statistics & probabilityWaiting times in the school cafeteria | 1 | 6 | 14 | 6 | 0 |
| 273 | Mathematical modellingThe propagation of sound waves in rooms | 3 | 8 | 1 | 9 | 0 |
| 274 | Geometry & topologySphere-packing density in three dimensions | 3 | 2 | 1 | 220 | 0 |
| 275 | Financial mathematicsCalculating the break-even point for a small business | 1 | 6 | 1 | 13 | 0 |
| 276 | Logic, set theory & proofEquivalence relations and partitions | 2 | 2 | 10 | 0 | 0 |
| 277 | Applied & interdisciplinary mathematicsThe mathematics of origami folds | 3 | 3 | 128 | 20 | 0 |
| 278 | ThermodynamicsHeat loss through single, double and triple glazing in winter | 1 | 6 | 1 | 413 | 0 |
| 279 | Material propertiesWater loss from cut flowers in different solutions | 1 | 6 | 112 | 2616 | 0 |
| 280 | ElectricityPower output of a small wind turbine at simulated wind speeds | 1 | 6 | 1 | 512 | 1 |
| 281 | Combined experimentsCorrosion and conductivity: metal mass loss versus electrical response of the solution | 1 | 3 | 1 | 251316 | 1 |
| 282 | Algebra & number theoryDiophantine equations and their solvability | 2 | 2 | 10 | 13 | 0 |
| 283 | Analysis & calculusCalculating the volume of irregular objects by integration | 3 | 3 | 12 | 11320 | 0 |
| 284 | Statistics & probabilityAnalysing success rates in basketball or throwing tasks | 1 | 6 | 13 | 0 | 0 |
| 285 | Mathematical modellingModelling the growth of bacterial cultures | 1 | 9 | 111 | 1321 | 1 |
| 286 | Geometry & topologyReflection geometry in architecture | 1 | 3 | 268 | 7 | 0 |
| 287 | Financial mathematicsLottery probabilities and expected value | 3 | 9 | 110 | 13 | 0 |
| 288 | Logic, set theory & proofModelling circuits with Karnaugh-Veitch maps | 1 | 2 | 1811 | 13 | 0 |
| 289 | Applied & interdisciplinary mathematicsComparing the efficiency of stairs and lifts | 1 | 6 | 111 | 0 | 0 |
| 290 | ThermodynamicsSurface-temperature recovery after ten minutes of exercise | 1 | 6 | 1312 | 319 | 3 |
| 291 | Material propertiesMass change caused by adsorption onto activated carbon | 1 | 3 | 112 | 216 | 0 |
| 292 | ElectricityElectrical conductivity of soil samples at different moisture levels | 1 | 6 | 16 | 251318 | 1 |
| 293 | Combined experimentsHeat-storage capacity of equal masses of stone, metal and wood | 1 | 3 | 1 | 2313 | 0 |
| 294 | Algebra & number theoryProperties of Mersenne primes | 3 | 3 | 10 | 0 | 0 |
| 295 | Analysis & calculusLimits and L'Hôpital's rule | 2 | 2 | 10 | 13 | 0 |
| 296 | Statistics & probabilityTesting the randomness of music shuffle functions | 1 | 6 | 18 | 9 | 0 |
| 297 | Mathematical modellingOptimising routes to school or work | 1 | 6 | 1411 | 813 | 0 |
| 298 | Geometry & topologyCurves of constant width and the Reuleaux triangle | 3 | 3 | 1211 | 20 | 0 |
| 299 | Financial mathematicsModelling exchange-rate fluctuations | 1 | 6 | 11 | 13 | 0 |
| 300 | Logic, set theory & proofProperties of relations: reflexivity, symmetry and transitivity | 1 | 3 | 110 | 0 | 0 |
| 301 | Applied & interdisciplinary mathematicsModelling the amount of coffee needed to maximise caffeine extraction | 1 | 9 | 1511 | 13 | 0 |
| 302 | Material propertiesFiltration efficiency measured by suspended-solid mass in different water samples | 1 | 6 | 1611 | 2 | 0 |
| 303 | ElectricityVoltage distribution in series and parallel circuits with identical lamps | 1 | 3 | 11012 | 5 | 1 |
| 304 | Combined experimentsBattery discharge across different temperatures using safe manufacturer-approved conditions | 1 | 3 | 112 | 235 | 2 |
| 305 | Algebra & number theoryThe mathematics of ISBN and IBAN check digits | 1 | 7 | 1 | 13 | 0 |
| 306 | Analysis & calculusAreas between curves and their meaning in economics | 1 | 3 | 1 | 1 | 0 |
| 307 | Statistics & probabilityComparing probabilities in different games of chance | 1 | 9 | 112 | 13 | 0 |
| 308 | Mathematical modellingModelling climate change with simple climate models | 3 | 5 | 6911 | 13 | 0 |
| 309 | Geometry & topologyCalculating areas with Pick's theorem | 3 | 3 | 1210 | 11320 | 0 |
| 310 | Financial mathematicsCalculating economic order quantity with the EOQ model | 1 | 6 | 111 | 13 | 0 |
| 311 | Logic, set theory & proofA proof of the fundamental theorem of arithmetic | 2 | 2 | 10 | 13 | 0 |
| 312 | Applied & interdisciplinary mathematicsThe mathematics of soap bubbles and minimal surfaces | 3 | 3 | 1 | 1 | 0 |
| 313 | ThermodynamicsTemperature changes in chemical hot and cold packs | 1 | 3 | 111 | 34113 | 2 |
| 314 | ElectricitySurface resistance of wood, metal, plastic and water | 1 | 3 | 1 | 51 | 1 |
| 315 | Combined experimentsDrying curves of wet clay or paper: mass loss and surface temperature | 1 | 6 | 112 | 2413 | 0 |
| 316 | Algebra & number theoryNumber sequences and their explicit formulae | 1 | 3 | 110 | 0 | 0 |
| 317 | Analysis & calculusModelling oscillations with damped harmonic oscillators | 3 | 2 | 111 | 13 | 0 |
| 318 | Statistics & probabilityCorrelation between weather and mood | 1 | 6 | 1610 | 1214 | 3 |
| 319 | Mathematical modellingThe propagation of light through different media | 3 | 3 | 1 | 10 | 0 |
| 320 | Geometry & topologyVoronoi diagrams in natural structures | 3 | 9 | 16 | 0 | 0 |
| 321 | Financial mathematicsDepreciation methods in accounting | 1 | 6 | 1 | 0 | 0 |
| 322 | Logic, set theory & proofAxiom systems through the example of geometry | 2 | 2 | 10 | 0 | 0 |
| 323 | Applied & interdisciplinary mathematicsAnalysing the distribution of stars in the night sky | 3 | 6 | 1 | 17 | 0 |
| 324 | ThermodynamicsThermal radiation from matte black and shiny metal surfaces at the same temperature | 1 | 3 | 1 | 413 | 0 |
| 325 | Material propertiesComparing fat content in crisps by supervised solvent extraction | 1 | 3 | 112 | 21621 | 2 |
| 326 | Combined experimentsBaking soda and vinegar: carbon dioxide mass loss and temperature change | 1 | 3 | 1511 | 2313 | 1 |
| 327 | Algebra & number theoryThe mathematics behind Sudoku-solving strategies | 1 | 7 | 178 | 1316 | 0 |
| 328 | Analysis & calculusOptimising a vehicle's fuel consumption | 1 | 8 | 1511 | 0 | 0 |
| 329 | Statistics & probabilityStatistical analysis of election results and forecasts | 1 | 6 | 9 | 13 | 0 |
| 330 | Mathematical modellingModelling population change in a city | 1 | 6 | 6911 | 13 | 0 |
| 331 | Geometry & topologyGeometric constructions of ellipses and parabolas | 3 | 3 | 1211 | 0 | 0 |
| 332 | Financial mathematicsComparing fixed-term and instant-access savings rates over ten years | 1 | 6 | 159 | 0 | 0 |
| 333 | ThermodynamicsTemperature change inside a compost heap over fourteen days | 1 | 6 | 6 | 36 | 1 |
| 334 | Material propertiesSalt content of water samples measured by evaporation and residue mass | 1 | 9 | 16 | 2111316 | 0 |
| 335 | ElectricityPower output of a bicycle dynamo at different rotational speeds | 1 | 9 | 1311 | 58913 | 1 |
| 336 | Algebra & number theoryPalindromic numbers in different bases | 3 | 3 | 17 | 13 | 0 |
| 337 | Analysis & calculusCurvature in bridges and arches | 3 | 3 | 6 | 0 | 0 |
| 338 | Statistics & probabilityBattery life across different brands | 1 | 6 | 1512 | 5 | 1 |
| 339 | Mathematical modellingThe trajectory of a frisbee or boomerang | 1 | 9 | 13 | 7 | 0 |
| 340 | Geometry & topologyProperties of torus knots | 2 | 2 | 1 | 0 | 0 |
| 341 | Financial mathematicsModelling retirement savings under different scenarios | 1 | 6 | 1511 | 13 | 0 |
| 342 | ThermodynamicsCooling molten wax or chocolate: phase transition and solidification | 1 | 3 | 1511 | 3413 | 1 |
| 343 | Material propertiesBiomass growth of cress or sprouts over fourteen days | 1 | 6 | 111 | 26 | 1 |
| 344 | ElectricityBioelectric voltages in selected fruits, vegetables and plant tissues | 1 | 3 | 156 | 5 | 1 |
| 345 | Combined experimentsResistance change as a resistor heats during current flow | 1 | 3 | 16 | 4513 | 1 |
| 346 | Algebra & number theoryThe distribution and density of prime numbers | 2 | 2 | 10 | 0 | 0 |
| 347 | Analysis & calculusCalculating the centroid of irregular regions | 3 | 3 | 1211 | 11320 | 0 |
| 348 | Statistics & probabilityWaiting times on public transport | 1 | 6 | 16 | 68 | 0 |
| 349 | Mathematical modellingModelling household water consumption | 1 | 6 | 1511 | 13 | 0 |
| 350 | Geometry & topologyGreat-circle distances on Earth | 3 | 3 | 1 | 13 | 0 |
| 351 | ThermodynamicsSurface heating of smartphone batteries during gaming, streaming and standby | 1 | 9 | 1 | 3415 | 1 |
| 352 | Material propertiesDensity and air fraction in different chocolate bars measured by water displacement | 1 | 3 | 1512 | 2 | 0 |
| 353 | ElectricityPiezoelectric voltage under different applied forces | 1 | 3 | 1 | 515 | 2 |
| 354 | Combined experimentsPlant growth: biomass versus leaf-surface temperature | 1 | 6 | 110 | 243 | 1 |
| 355 | Algebra & number theoryRepeating patterns in decimal expansions | 1 | 3 | 110 | 13 | 0 |
| 356 | Analysis & calculusTaylor series and their convergence | 2 | 2 | 1012 | 0 | 0 |
| 357 | Statistics & probabilityThe normal distribution of student heights in a class | 1 | 4 | 14 | 14 | 3 |
| 358 | Mathematical modellingLight propagation in optical fibres | 3 | 2 | 111 | 1013 | 0 |
| 359 | Geometry & topologyPenrose tilings | 2 | 2 | 1211 | 20 | 0 |
| 360 | ThermodynamicsHeat output of LED, halogen and incandescent lamps at comparable brightness | 1 | 9 | 11112 | 41310 | 1 |
| 361 | Material propertiesSugar solubility in water from 20°C to 80°C | 1 | 3 | 1 | 231316 | 0 |
| 362 | ElectricityThermocouple voltage for different metal pairs and junction temperatures | 1 | 2 | 16 | 3513 | 2 |
| 363 | Combined experimentsComparing coffee cups using mass, surface temperature and core temperature | 1 | 9 | 1511 | 2341 | 0 |
| 364 | Algebra & number theoryThe mathematics of barcodes and QR codes | 1 | 7 | 1 | 0 | 0 |
| 365 | Analysis & calculusModelling plant growth rates | 1 | 9 | 1611 | 13 | 1 |
| 366 | Statistics & probabilityComparing box plots across different school grading systems | 1 | 6 | 412 | 0 | 0 |
| 367 | Mathematical modellingModelling the efficiency of solar-energy systems | 1 | 6 | 111 | 13 | 0 |
| 368 | ThermodynamicsA temperature map of a hotplate: centre-to-edge variation | 1 | 6 | 15 | 43 | 1 |
| 369 | Material propertiesDrying rates of cotton, polyester, wool and microfibre textiles | 1 | 6 | 112 | 26 | 0 |
| 370 | ElectricityBattery discharge at different ambient temperatures | 1 | 9 | 1 | 35 | 1 |
| 371 | Combined experimentsIce formation: frost mass gain and surface temperature over time | 1 | 3 | 1 | 2413 | 0 |
| 372 | Analysis & calculusAnalysing speed distributions in traffic flow | 1 | 8 | 6 | 0 | 0 |
| 373 | Statistics & probabilityThe probability of twin births | 1 | 6 | 9 | 13 | 3 |
No topic ideas match this combination.
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.
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 requirementsFrequently 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 373 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.