# 1037 IB Mathematics topic ideas for IA and EE

Canonical HTML: https://www.prelearning.de/en/ib-mathematics-ia-ee-topic-list/
Updated: 2026-09-11
Entries: 1037

## A: Assessment type
1 = Internal Assessment (IA)
2 = Mathematics Extended Essay (EE)
3 = Potentially suitable for an IA or EE, depending on focus and mathematical depth

## C: Course 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

## P: Ways 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

## M: Measuring 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

## S: Safety 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

## Topic entries
1 | Game theory & decision-making | Nash equilibria in extended rock-paper-scissors games | A=3 | C=9 | P=1,8,11 | M=0 | S=0
2 | Transport & mobility mathematics | Modelling delay propagation along a bus route | A=3 | C=9 | P=1,6,11,12 | M=6,8,13 | S=0
3 | Biomathematics & medicine | Modelling blood-glucose levels after meals with the Bergman minimal model | A=2 | C=8 | P=1,11 | M=13,19 | S=3
4 | Operations research & logistics | Route optimisation for school deliveries with capacity constraints | A=3 | C=9 | P=4,6,7,11 | M=13 | S=0
5 | Environmental mathematics & sustainability | Calculating a family's ecological footprint using geometric means | A=1 | C=6 | P=1,5 | M=13 | S=0
6 | Networks & social systems | Centrality measures in an anonymised school collaboration network | A=3 | C=9 | P=4,7,12 | M=13,14 | S=3
7 | Sports biomechanics & movement | Calculating the optimal approach speed in long jump | A=3 | C=9 | P=1,3,11 | M=13 | S=1
8 | Information & coding theory | Shannon entropy across different written languages | A=3 | C=8 | P=8,9,10 | M=13 | S=0
9 | Data science & introductory algorithms | Benford's law in financial data and election results | A=3 | C=6 | P=1,9 | M=0 | S=0
10 | Robotics, control & sensing | Optimising PID control for a line-following robot | A=2 | C=8 | P=2,7,11,12 | M=5,7,13,20 | S=1
11 | Chaos & dynamical systems | The logistic map and the transition to chaos | A=2 | C=2 | P=1 | M=13 | S=0
12 | Image processing & computer graphics | Choosing thresholds for edge detection on personal photographs | A=3 | C=9 | P=2,7,12 | M=7,13 | S=0
13 | Music, acoustics & waves | Calculating optimal room acoustics for a music studio | A=3 | C=9 | P=1,8,11 | M=9,13 | S=0
14 | Language & text mathematics | Heaps’ law and vocabulary growth in long texts | A=3 | C=9 | P=8,9,10,12 | M=13 | S=0
15 | Art, design & architecture | Proportions in the human face and claims about the golden ratio | A=3 | C=9 | P=1,2 | M=1,7 | S=0
16 | Education & learning analytics | Estimating forgetting curves from personal flashcard logs | A=1 | C=9 | P=1,4,7,11,12 | M=13 | S=3
17 | Astronomy & spaceflight | Calculating satellite orbits with Kepler's laws | A=2 | C=2 | P=1 | M=13,17 | S=0
18 | Economic models & markets | Estimating price elasticity from public retail data | A=3 | C=6 | P=5,9,11,12 | M=13 | S=0
19 | Psychology & cognition | Reaction-time distributions within a class | A=1 | C=6 | P=1,4 | M=6,19 | S=3
20 | Time series & forecasting | Comparing exponential smoothing and autoregressive models for electricity demand | A=2 | C=8 | P=7,9,11,12 | M=13 | S=0
21 | Probability & risk | Calculating expected loss for different insurance types | A=1 | C=6 | P=5 | M=13 | S=0
22 | Geospatial & cartographic mathematics | Distortion in different map projections as a function of latitude | A=2 | C=8 | P=6,9,10,12 | M=13 | S=0
23 | Culinary mathematics | Calculating the best-value pizza size by area and price | A=1 | C=9 | P=1,5,9 | M=1,13 | S=0
24 | Engineering design & optimisation | Minimising truss weight under load constraints | A=2 | C=2 | P=2,7,10,11 | M=13,20 | S=0
25 | Thermodynamics | Newton's law of cooling for coffee in ceramic, glass, metal and paper cups | A=1 | C=9 | P=1,5 | M=3 | S=0
26 | Epidemiology & public health | An age-structured vaccination model with different contact matrices | A=2 | C=8 | P=7,9,11,12 | M=13 | S=0
27 | Material properties | Evaporation rates of water, ethanol, acetone and salt water under controlled conditions | A=1 | C=9 | P=1,12 | M=2,6,16 | S=2
28 | Sports analytics & tactics | An expected-goals model using shot location and angle | A=3 | C=9 | P=3,7,9,11 | M=7,13 | S=0
29 | Electricity | Discharge curves of AA batteries from different brands under a constant load | A=1 | C=9 | P=1,12 | M=5,6,13 | S=1
30 | Recreational games & mathematics | Monopoly landing probabilities using a transition matrix | A=3 | C=9 | P=7,8,10 | M=13 | S=0
31 | Combined experiments | Density of water and ethanol at temperatures from 10°C to 60°C | A=1 | C=3 | P=1 | M=2,3,1,13 | S=0
32 | Combinatorics & discrete probability | Derangements in Secret Santa without self-assignment | A=3 | C=9 | P=4,8,10 | M=13 | S=0
33 | Kitchen & everyday life | Optimising coffee brewing: extraction rate versus temperature profile | A=1 | C=9 | P=1,5,11 | M=2,3,16 | S=0
34 | Climate, Earth & ocean mathematics | Sea-level trends with measurement uncertainty and confidence intervals | A=3 | C=6 | P=9,11,12 | M=13 | S=0
35 | Environment | Particulate-filter residue mass across different locations | A=1 | C=6 | P=1,12 | M=2 | S=0
36 | Physiology | Surface heat loss from the human head with and without a hat after exercise | A=1 | C=6 | P=1,3,12 | M=4,3,13 | S=3
37 | Materials | Water absorption of brick, wood, concrete and plaster over time | A=1 | C=9 | P=1 | M=2,6,18 | S=0
38 | Algebra & number theory | The golden ratio in architectural proportions across different cultures | A=1 | C=9 | P=1,2 | M=1,7 | S=0
39 | Analysis & calculus | Optimising container dimensions under cost and surface-area constraints | A=3 | C=3 | P=1,2,11 | M=1,20 | S=0
40 | Statistics & probability | Chi-squared tests: study habits, screen time and sleep | A=1 | C=6 | P=1,4 | M=14 | S=3
41 | Mathematical modelling | An SIR model for the spread of disease | A=2 | C=8 | P=1 | M=0 | S=0
42 | Geometry & topology | Tessellations: which regular polygons tile the plane? | A=1 | C=3 | P=1,2,11 | M=20 | S=0
43 | Financial mathematics | Compound interest versus simple interest over different periods | A=1 | C=6 | P=1,5 | M=0 | S=0
44 | Logic, set theory & proof | Mathematical induction for sums and divisibility identities | A=2 | C=2 | P=10 | M=13 | S=0
45 | Discrete mathematics & computer science | Graph-colouring problems | A=3 | C=3 | P=1 | M=0 | S=0
46 | Applied & interdisciplinary mathematics | The mathematics of recipes: ratios and scaling | A=1 | C=9 | P=1,5 | M=0 | S=0
47 | Game theory & decision-making | Optimal blackjack hand strategy using probability | A=3 | C=8 | P=1,7,8 | M=13 | S=0
48 | Transport & mobility mathematics | Optimal bike-sharing station locations using weighted Voronoi diagrams | A=3 | C=9 | P=6,9,11 | M=8,13 | S=0
49 | Biomathematics & medicine | Modelling medication concentration and dosage over time with pharmacokinetics | A=2 | C=2 | P=1,9,11 | M=6,13 | S=3
50 | Operations research & logistics | Reorder points and safety stock under variable demand | A=1 | C=6 | P=5,9,11,12 | M=13 | S=0
51 | Environmental mathematics & sustainability | Optimising waste separation with probability models | A=1 | C=6 | P=1,6,11 | M=13 | S=3
52 | Networks & social systems | Community detection in a network of music artists | A=3 | C=9 | P=8,9,7 | M=13 | S=0
53 | Sports biomechanics & movement | Mathematical analysis of rotation in figure skating using angular momentum | A=3 | C=2 | P=1,3 | M=7,15 | S=0
54 | Information & coding theory | Arithmetic coding compared with Huffman coding | A=2 | C=8 | P=7,10,12 | M=13 | S=0
55 | Data science & introductory algorithms | A basic Fourier-based classification of music genres | A=2 | C=2 | P=1,7,8 | M=9,13 | S=0
56 | Robotics, control & sensing | Using a Kalman filter to smooth a noisy distance sensor | A=2 | C=8 | P=2,7,11,12 | M=13,20,21 | S=1
57 | Chaos & dynamical systems | Modelling the double pendulum and its unpredictability | A=2 | C=2 | P=1,7,11 | M=13 | S=0
58 | Image processing & computer graphics | Perspective correction of a photograph using a homography | A=2 | C=2 | P=2,7,10 | M=7,13 | S=0
59 | Music, acoustics & waves | Overtone series in different musical instruments | A=3 | C=3 | P=1,8 | M=9,13 | S=0
60 | Language & text mathematics | Modelling letter sequences with Markov chains | A=3 | C=9 | P=7,8,10 | M=13 | S=0
61 | Art, design & architecture | Calculating perspective in painting using one-point perspective | A=3 | C=3 | P=1,2 | M=1,7,13 | S=0
62 | Education & learning analytics | Simplified item response theory for estimating item difficulty | A=2 | C=8 | P=4,7,10,12 | M=13,14 | S=3
63 | Astronomy & spaceflight | Modelling tidal forces and their mathematical periodicity | A=3 | C=9 | P=1,6,11 | M=6,13 | S=0
64 | Economic models & markets | Lorenz curves and decomposition of the Gini coefficient | A=2 | C=8 | P=9,10,12 | M=13 | S=0
65 | Psychology & cognition | Modelling the Ebbinghaus forgetting curve with exponential decay | A=1 | C=6 | P=1,4,11 | M=13 | S=3
66 | Time series & forecasting | Seasonal decomposition of bicycle-rental data | A=3 | C=6 | P=6,9,11 | M=13 | S=0
67 | Probability & risk | Modelling smoking risk with life-expectancy data | A=3 | C=6 | P=12 | M=0 | S=3
68 | Geospatial & cartographic mathematics | Comparing great-circle and rhumb-line routes for long journeys | A=3 | C=9 | P=6,9,10 | M=8,13 | S=0
69 | Culinary mathematics | Modelling coffee brewing through extraction rates and temperature | A=3 | C=9 | P=1,5,11 | M=3,13,16 | S=0
70 | Engineering design & optimisation | Optimising a beam cross-section under bending | A=2 | C=2 | P=2,10,11 | M=13,20 | S=0
71 | Thermodynamics | Insulating performance of cup materials: time taken to approach room temperature | A=1 | C=9 | P=1,12 | M=3,4,1,6 | S=0
72 | Epidemiology & public health | Estimating the effective reproduction number from a public case series | A=2 | C=8 | P=9,11,12 | M=13 | S=0
73 | Material properties | Determining the density of different woods from mass and volume | A=1 | C=3 | P=1 | M=2,1,13,14 | S=3
74 | Sports analytics & tactics | Entropy of serve placement in tennis | A=3 | C=9 | P=1,3,8,12 | M=7,13 | S=0
75 | Electricity | Solar-cell power at different light angles and distances | A=1 | C=9 | P=1,11 | M=5,1,10,13 | S=1
76 | Recreational games & mathematics | Optimal Nim strategy using binary representation | A=2 | C=2 | P=7,8,10 | M=13 | S=0
77 | Combined experiments | Electrolysis of water: electrode mass change versus applied voltage | A=1 | C=2 | P=1 | M=2,5,16,21 | S=2
78 | Combinatorics & discrete probability | The coupon collector problem for trading cards | A=3 | C=9 | P=5,7,8,10 | M=13 | S=0
79 | Kitchen & everyday life | Which teapot material retains heat longest: cast iron, glass or porcelain? | A=1 | C=9 | P=1,5 | M=3,4,1,13 | S=0
80 | Climate, Earth & ocean mathematics | Decomposing tides with harmonic analysis | A=2 | C=8 | P=6,9,10,11 | M=13 | S=0
81 | Environment | Rainwater: precipitation amount, temperature and electrical conductivity | A=1 | C=6 | P=1,6 | M=2,3,5,1 | S=1
82 | Physiology | Skin-surface temperature recovery after a safe cold-water exposure | A=1 | C=6 | P=1 | M=4,1,3,19 | S=3
83 | Materials | Heat distribution around skateboard or longboard axles after riding | A=1 | C=9 | P=1,3 | M=4,3,8,13 | S=0
84 | Algebra & number theory | Modelling population growth: logistic versus exponential models | A=1 | C=6 | P=1,6,11 | M=13 | S=1
85 | Analysis & calculus | Newton's law of cooling: modelling with differential equations | A=3 | C=2 | P=1,11 | M=3,13 | S=0
86 | Statistics & probability | The birthday paradox: simulation versus theoretical probability | A=1 | C=9 | P=1,4,5 | M=13,14 | S=3
87 | Mathematical modelling | Predator-prey dynamics: the Lotka-Volterra equations | A=2 | C=2 | P=6 | M=0 | S=0
88 | Geometry & topology | The Seven Bridges of Königsberg and graph theory | A=3 | C=2 | P=10 | M=13 | S=0
89 | Financial mathematics | Mortgage repayment: how much can an extra payment save? | A=1 | C=6 | P=5 | M=0 | S=0
90 | Logic, set theory & proof | Boolean algebra and logic gates: De Morgan's laws | A=2 | C=2 | P=1,7 | M=0 | S=0
91 | Discrete mathematics & computer science | Analysing sorting algorithms: running time and comparisons | A=3 | C=9 | P=1,7,12 | M=6,13 | S=0
92 | Applied & interdisciplinary mathematics | Optimising how to pack a suitcase or backpack | A=1 | C=6 | P=1,11 | M=0 | S=0
93 | Game theory & decision-making | The mathematics of auction systems: English versus Dutch auctions | A=3 | C=6 | P=1,7,8 | M=13 | S=0
94 | Transport & mobility mathematics | Shortest route versus fastest route under time-dependent traffic | A=3 | C=9 | P=1,6,7,11 | M=8,13 | S=0
95 | Biomathematics & medicine | Heart-rate variability analysed with statistical methods | A=3 | C=6 | P=1,3 | M=8,19 | S=3
96 | Operations research & logistics | Staff scheduling with integer linear optimisation | A=2 | C=8 | P=7,9,11 | M=13 | S=0
97 | Environmental mathematics & sustainability | Modelling seasonal water levels in local lakes | A=1 | C=6 | P=1,6,11 | M=13 | S=0
98 | Networks & social systems | Epidemic thresholds in networks with different degree distributions | A=2 | C=8 | P=7,11,12 | M=13 | S=0
99 | Sports biomechanics & movement | Modelling force distribution while climbing on different wall angles | A=3 | C=3 | P=1,3,11 | M=13,15 | S=1
100 | Information & coding theory | Error correction with Hamming codes under simulated channel noise | A=3 | C=8 | P=7,10,11 | M=13 | S=0
101 | Data science & introductory algorithms | Analysing sentiment trends on social media over time | A=3 | C=6 | P=1 | M=6 | S=0
102 | Robotics, control & sensing | Inverse kinematics of a two-link robot arm | A=2 | C=2 | P=2,7,10,11 | M=1,13,20 | S=1
103 | Chaos & dynamical systems | Sensitivity to initial conditions and the butterfly effect | A=2 | C=2 | P=1,7 | M=13 | S=0
104 | Image processing & computer graphics | Comparing median and Gaussian filters under different image noise | A=3 | C=9 | P=2,7,12 | M=7,13 | S=0
105 | Music, acoustics & waves | Modelling dissonance with interval-frequency ratios | A=3 | C=3 | P=1,8,11 | M=9,13 | S=0
106 | Language & text mathematics | Comparing readability formulas and sentence-length distributions | A=1 | C=6 | P=8,9,12 | M=13 | S=0
107 | Art, design & architecture | Mathematical analysis of Escher tessellations and symmetry groups | A=3 | C=3 | P=1,4,8 | M=0 | S=0
108 | Education & learning analytics | Modelling learning curves in typing or mental arithmetic practice | A=1 | C=9 | P=1,4,11,12 | M=6,13 | S=3
109 | Astronomy & spaceflight | Light curves of variable stars | A=3 | C=6 | P=1 | M=10,17 | S=0
110 | Economic models & markets | Stability of the cobweb model under delayed supply response | A=2 | C=8 | P=7,10,11 | M=13 | S=0
111 | Psychology & cognition | Analysing mathematical patterns in sleep and REM cycles | A=3 | C=6 | P=1 | M=6 | S=3
112 | Time series & forecasting | Sensitivity of different forecast-error metrics | A=3 | C=9 | P=7,10,12 | M=13 | S=0
113 | Probability & risk | Modelling the failure probability of technical devices | A=3 | C=6 | P=1,11,12 | M=13 | S=0
114 | Geospatial & cartographic mathematics | GPS error in dense urban areas and open spaces | A=1 | C=9 | P=1,6,12 | M=8,13 | S=0
115 | Culinary mathematics | The geometry of pasta shapes and their cooking times | A=3 | C=3 | P=1,5 | M=6 | S=0
116 | Engineering design & optimisation | Modelling heat-sink fin shape for heat transfer | A=2 | C=8 | P=2,7,11,12 | M=3,4,13,20,21 | S=2
117 | Thermodynamics | Heating surfaces of different colours in sunlight: black, white, red and silver | A=1 | C=9 | P=1 | M=3,4,1 | S=0
118 | Epidemiology & public health | Optimal pool size in pooled diagnostic testing | A=2 | C=8 | P=7,9,10,11 | M=13 | S=0
119 | Material properties | Water content of fruits and vegetables measured by oven drying | A=1 | C=6 | P=1,5 | M=2 | S=1
120 | Sports analytics & tactics | Passing-network centrality and match outcome | A=3 | C=9 | P=3,7,9,12 | M=7,13 | S=0
121 | Electricity | Internal resistance of alkaline, NiMH and lithium batteries | A=1 | C=2 | P=1,12 | M=5,13 | S=1
122 | Recreational games & mathematics | Clue density and uniqueness in Sudoku puzzles | A=3 | C=9 | P=7,8,10,11 | M=13 | S=0
123 | Combined experiments | Specific heat capacity of different liquids under equal energy input | A=1 | C=3 | P=1 | M=2,3 | S=0
124 | Combinatorics & discrete probability | Occupancy problems in random seating arrangements | A=3 | C=9 | P=4,7,10 | M=13 | S=0
125 | Kitchen & everyday life | Ice-cream melting rate: mass loss and surface temperature across different formulations | A=1 | C=6 | P=1,12 | M=2,4,1,3 | S=1
126 | Climate, Earth & ocean mathematics | Investigating urban heat islands with spatial regression | A=3 | C=9 | P=1,6,9,11,12 | M=3,4,8,12,13 | S=0
127 | Environment | Compost: mass loss and core temperature over four weeks | A=1 | C=6 | P=1,6 | M=2,3,6 | S=0
128 | Physiology | Sweat-related body-mass change during exercise under different ambient conditions | A=1 | C=6 | P=1,3 | M=2,3,13,19 | S=3
129 | Materials | Moisture absorption by three-dimensional printing filaments | A=1 | C=3 | P=1 | M=2,6,13,18 | S=0
130 | Algebra & number theory | RSA encryption and prime number theory | A=2 | C=2 | P=10 | M=13 | S=0
131 | Analysis & calculus | Calculating work done by a variable force in sport | A=3 | C=2 | P=1,3 | M=13 | S=0
132 | Statistics & probability | Regression: carbon dioxide emissions and global temperatures | A=1 | C=6 | P=9 | M=3,13 | S=0
133 | Mathematical modelling | The trajectory of a basketball or tennis shot | A=1 | C=9 | P=1,3 | M=7 | S=0
134 | Geometry & topology | Fractal geometry and the coastline paradox | A=3 | C=2 | P=1,10 | M=0 | S=0
135 | Financial mathematics | The true cost of minimum credit-card payments | A=1 | C=4 | P=1,5 | M=13 | S=0
136 | Logic, set theory & proof | Cantor's infinities: countability and the diagonal argument | A=2 | C=2 | P=10 | M=0 | S=0
137 | Discrete mathematics & computer science | Huffman coding and data compression | A=3 | C=9 | P=1,7 | M=0 | S=0
138 | Applied & interdisciplinary mathematics | Room acoustics and reverberation time | A=3 | C=9 | P=1,8 | M=9 | S=0
139 | Game theory & decision-making | The prisoner's dilemma in repeated games | A=3 | C=9 | P=1,4,11 | M=0 | S=0
140 | Transport & mobility mathematics | A queueing model for airport security lanes | A=3 | C=6 | P=9,11,12 | M=13 | S=0
141 | Biomathematics & medicine | Modelling tumour growth: Gompertz versus exponential models | A=2 | C=8 | P=11 | M=13 | S=3
142 | Operations research & logistics | Efficient parcel packing with the bin-packing problem | A=3 | C=9 | P=2,5,7,11 | M=1,13,20 | S=0
143 | Environmental mathematics & sustainability | Statistical analysis of the effectiveness of recycling programmes | A=1 | C=6 | P=1,6,7 | M=13 | S=0
144 | Networks & social systems | Power-grid robustness under targeted node removal | A=2 | C=8 | P=7,9,11 | M=13 | S=0
145 | Sports biomechanics & movement | Optimising swimming technique through drag models | A=3 | C=8 | P=1,3,11 | M=6,13 | S=1
146 | Information & coding theory | Reed–Solomon codes and the damage tolerance of QR codes | A=2 | C=8 | P=2,7,10,11 | M=7,13 | S=0
147 | Data science & introductory algorithms | Testing the predictive accuracy of weather apps with regression | A=3 | C=6 | P=1,6 | M=13 | S=0
148 | Robotics, control & sensing | A* and Dijkstra algorithms for path planning on grid maps | A=3 | C=9 | P=7,10,12 | M=13 | S=0
149 | Chaos & dynamical systems | Julia sets and their dependence on parameters | A=2 | C=2 | P=1,7,11 | M=0 | S=0
150 | Image processing & computer graphics | Fractal dimension of natural image textures | A=3 | C=8 | P=2,6,7,10 | M=7,13 | S=0
151 | Music, acoustics & waves | Mathematical analysis of rhythm patterns across music genres | A=3 | C=9 | P=1,8 | M=9 | S=0
152 | Language & text mathematics | Stylometry using function-word frequencies | A=2 | C=8 | P=7,9,10,12 | M=13 | S=0
153 | Art, design & architecture | Curves in typeface design: Bézier curves | A=3 | C=3 | P=1,8 | M=0 | S=0
154 | Education & learning analytics | The relationship between response time and answer accuracy | A=1 | C=6 | P=1,4,12 | M=6,13,14 | S=3
155 | Astronomy & spaceflight | Calculating stellar distances by parallax | A=3 | C=3 | P=1,11 | M=1,13,17 | S=0
156 | Economic models & markets | Simulating Cournot and Bertrand duopoly models | A=2 | C=8 | P=7,10,11 | M=13 | S=0
157 | Psychology & cognition | Optimising break intervals in study sessions with a Pomodoro model | A=1 | C=6 | P=1,11 | M=13 | S=3
158 | Time series & forecasting | Detecting structural breaks in long-term temperature series | A=2 | C=8 | P=9,11,12 | M=13 | S=0
159 | Probability & risk | Calculating optimal diversification in an investment portfolio | A=3 | C=5 | P=1,7,11 | M=13 | S=0
160 | Geospatial & cartographic mathematics | Position finding by bearings and triangulation | A=3 | C=9 | P=1,2,6,11 | M=1,7,13 | S=0
161 | Culinary mathematics | Calculating optimal lasagne layering with heat-conduction models | A=3 | C=3 | P=1,5,11 | M=3,13 | S=0
162 | Engineering design & optimisation | Wind-turbine blade pitch and theoretical power | A=2 | C=8 | P=2,7,9,11 | M=12,13,20 | S=0
163 | Thermodynamics | Heat distribution across a laptop under CPU load | A=1 | C=9 | P=1,10 | M=4,3,7 | S=0
164 | Epidemiology & public health | Survival analysis of waiting times using public health data | A=2 | C=8 | P=9,11,12 | M=13 | S=0
165 | Material properties | Carbon dioxide loss from fizzy drinks over 48 hours under different storage conditions | A=1 | C=9 | P=1 | M=2,6 | S=0
166 | Sports analytics & tactics | Predictive accuracy of different Elo-rating variants | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
167 | Electricity | Voltage drop along copper cables of different lengths and cross-sections | A=1 | C=3 | P=1 | M=5,13 | S=1
168 | Recreational games & mathematics | The group structure of the Rubik’s Cube | A=2 | C=2 | P=2,8,10 | M=13,20 | S=0
169 | Combined experiments | Solar-cell voltage loss as temperature increases | A=1 | C=8 | P=1 | M=4,5,1,3 | S=1
170 | Combinatorics & discrete probability | The connectivity threshold in random graphs | A=2 | C=2 | P=7,10,12 | M=13 | S=0
171 | Kitchen & everyday life | Bread baking: water loss and core temperature over time | A=1 | C=9 | P=1,5 | M=2,3 | S=1
172 | Climate, Earth & ocean mathematics | Comparing drought indices using moving windows | A=3 | C=6 | P=9,11,12 | M=13 | S=0
173 | Environment | Solar cooker: water temperature and evaporation mass at different angles | A=1 | C=9 | P=1,11 | M=2,3,1,10 | S=1
174 | Physiology | Hand-surface temperature before and after a low-risk cognitive task | A=1 | C=6 | P=1,4 | M=4,3,19 | S=3
175 | Materials | Thermal response of granite, wood and stainless-steel worktops | A=1 | C=3 | P=1,5 | M=3,4,1 | S=0
176 | Algebra & number theory | Pascal's triangle: patterns, binomial coefficients and combinatorics | A=1 | C=9 | P=1 | M=0 | S=0
177 | Analysis & calculus | Convergence of series: the harmonic series, Basel problem and geometric series | A=2 | C=2 | P=10 | M=0 | S=0
178 | Statistics & probability | The Monty Hall problem: simulation versus theory | A=1 | C=7 | P=1,7 | M=13 | S=0
179 | Mathematical modelling | Logistic growth in social-media followers and viral trends | A=1 | C=9 | P=1 | M=0 | S=1
180 | Geometry & topology | Platonic solids: Euler's formula and why there are exactly five | A=3 | C=3 | P=2 | M=20 | S=0
181 | Financial mathematics | Saving strategies: lump-sum investment versus regular deposits | A=1 | C=4 | P=1,5,11 | M=0 | S=0
182 | Logic, set theory & proof | Arrow's impossibility theorem and voting systems | A=2 | C=2 | P=10 | M=0 | S=0
183 | Discrete mathematics & computer science | Modelling networks with adjacency matrices | A=3 | C=3 | P=1,11 | M=13 | S=0
184 | Applied & interdisciplinary mathematics | Modelling an optimal running pace | A=1 | C=9 | P=1,3,11 | M=13 | S=0
185 | Game theory & decision-making | Optimal positioning in penalty kicks using mixed strategies | A=3 | C=8 | P=1,3,11 | M=7 | S=0
186 | Transport & mobility mathematics | Reliability of train headways using coefficients of variation and outliers | A=1 | C=6 | P=1,6,9,12 | M=6,13 | S=0
187 | Biomathematics & medicine | Mathematical analysis of mosquito-population spread | A=3 | C=9 | P=6 | M=12 | S=0
188 | Operations research & logistics | Location optimisation for public defibrillators under response-time constraints | A=3 | C=9 | P=6,9,11,12 | M=8,13 | S=0
189 | Environmental mathematics & sustainability | Calculating optimal home insulation using heat conduction | A=3 | C=3 | P=1,2,11 | M=3,13 | S=0
190 | Networks & social systems | Small-world properties of a regional transport network | A=3 | C=9 | P=6,9,7 | M=13 | S=0
191 | Sports biomechanics & movement | Optimising launch angles in archery | A=3 | C=3 | P=1,3,11 | M=1 | S=1
192 | Information & coding theory | Mutual information between weather variables and forecast accuracy | A=2 | C=8 | P=9,11,12 | M=13 | S=0
193 | Data science & introductory algorithms | Calculating text similarity with introductory vector models | A=2 | C=2 | P=1,7,12 | M=13 | S=0
194 | Robotics, control & sensing | Sensor fusion for accelerometer and gyroscope data | A=2 | C=8 | P=2,7,11,12 | M=7,13,20 | S=1
195 | Chaos & dynamical systems | Calculating Lyapunov exponents for simple functions | A=2 | C=2 | P=7,10 | M=13 | S=0
196 | Image processing & computer graphics | Colour segmentation using k-means clustering | A=3 | C=9 | P=2,7,11 | M=7,13 | S=0
197 | Music, acoustics & waves | Calculating string lengths for alternative tuning systems | A=3 | C=3 | P=1,8 | M=9,13,14 | S=3
198 | Language & text mathematics | Uncertainty in sentiment scores from different lexicons | A=3 | C=6 | P=7,9,12 | M=13 | S=0
199 | Art, design & architecture | Calculating optimal stage lighting through angle analysis | A=3 | C=3 | P=1,8,11 | M=1,10,13 | S=0
200 | Education & learning analytics | Optimising test-item order under fatigue | A=3 | C=8 | P=4,7,11,12 | M=13,14 | S=3
201 | Astronomy & spaceflight | Modelling a rocket trajectory with air resistance | A=2 | C=2 | P=1,7,11 | M=13 | S=1
202 | Economic models & markets | How basket weights affect a consumer price index | A=3 | C=6 | P=5,9,12 | M=13 | S=0
203 | Psychology & cognition | The Stroop effect analysed with statistical hypothesis tests | A=1 | C=6 | P=1,4 | M=0 | S=3
204 | Time series & forecasting | Cross-correlation between search trends and sales | A=3 | C=6 | P=9,11,12 | M=13 | S=0
205 | Probability & risk | Perceived risk versus measured risk: air travel and driving | A=3 | C=6 | P=1,4,12 | M=14 | S=3
206 | Geospatial & cartographic mathematics | Interpolating local temperatures with inverse-distance weighting | A=3 | C=9 | P=1,6,7,11 | M=3,8,12,13 | S=0
207 | Culinary mathematics | Analysing bubble distributions in bread and sparkling drinks with a Poisson model | A=3 | C=6 | P=1,2,5 | M=7 | S=0
208 | Engineering design & optimisation | Optimising bottle shape for material use and stability | A=3 | C=9 | P=2,5,11,12 | M=1,13,20 | S=0
209 | Thermodynamics | Temperature gradients in a classroom from floor to desk height and ceiling over a day | A=1 | C=6 | P=1,4 | M=3,4,1,6 | S=0
210 | Epidemiology & public health | Covering a contact-tracing network with a minimum number of tests | A=2 | C=8 | P=7,9,11 | M=13 | S=0
211 | Material properties | Absorption rates of toilet paper, kitchen roll and newspaper | A=1 | C=6 | P=1,5 | M=2,6 | S=0
212 | Sports analytics & tactics | Optimal substitution timing using a hazard model | A=2 | C=8 | P=7,9,11,12 | M=13 | S=0
213 | Electricity | Charging and discharging capacitors of different capacitances | A=1 | C=2 | P=1 | M=5 | S=0
214 | Recreational games & mathematics | Wordle strategies using entropy and information gain | A=3 | C=9 | P=7,8,10,11 | M=13 | S=0
215 | Combined experiments | Evaporation: mass loss versus surface temperature in wind, sun and shade | A=1 | C=9 | P=1 | M=2,4,1,3 | S=0
216 | Combinatorics & discrete probability | Catalan numbers in parenthesisations and lattice paths | A=2 | C=2 | P=7,10 | M=13 | S=0
217 | Kitchen & everyday life | Yoghurt fermentation: temperature profile and mass change | A=1 | C=6 | P=1,5 | M=2,3,16 | S=1
218 | Climate, Earth & ocean mathematics | River rating curves from water level and discharge | A=3 | C=9 | P=1,6,11,12 | M=1,6,8,12,13 | S=1
219 | Environment | Heat loss from buildings using facade surface-temperature measurements | A=1 | C=6 | P=2,6 | M=4,1,3 | S=0
220 | Physiology | Reaction time and naturally observed body-temperature variation | A=1 | C=6 | P=1,10 | M=3,13,19 | S=3
221 | Materials | Electrical conductivity of pencil lines with grades from 2H to 6B | A=1 | C=3 | P=1,2 | M=5,13 | S=1
222 | Algebra & number theory | Fibonacci numbers and the limiting ratio of consecutive terms | A=3 | C=3 | P=1,6 | M=13 | S=0
223 | Analysis & calculus | The mathematics of rainbow formation: Snell's law, refraction and optimisation | A=3 | C=2 | P=6,11 | M=0 | S=0
224 | Statistics & probability | Statistical bias in media reporting | A=1 | C=6 | P=9,12 | M=0 | S=0
225 | Mathematical modelling | Traffic flow at roundabouts or traffic lights | A=1 | C=2 | P=1,6 | M=0 | S=1
226 | Geometry & topology | Using vectors to model three-dimensional reflections in a kaleidoscope | A=3 | C=2 | P=1,2,4 | M=13,20 | S=0
227 | Financial mathematics | An introduction to the Black-Scholes model for option pricing | A=2 | C=5 | P=1 | M=13 | S=0
228 | Logic, set theory & proof | Truth tables and their minimisation | A=1 | C=2 | P=1,2,7 | M=20 | S=0
229 | Discrete mathematics & computer science | Heuristics for the travelling salesperson problem | A=2 | C=8 | P=1,11 | M=8 | S=0
230 | Applied & interdisciplinary mathematics | Analysing the efficiency of water pumps | A=1 | C=6 | P=1,11 | M=0 | S=0
231 | Game theory & decision-making | The mathematics behind bidding strategies in The Price Is Right | A=3 | C=6 | P=1,7,8 | M=13 | S=0
232 | Transport & mobility mathematics | Propagation of traffic waves in stop-and-go congestion | A=2 | C=8 | P=6,9,11 | M=13 | S=0
233 | Biomathematics & medicine | BMI and its statistical validity across different populations | A=1 | C=6 | P=1,4,12 | M=13,14 | S=3
234 | Operations research & logistics | Investigating project completion times with PERT and Monte Carlo simulation | A=3 | C=9 | P=7,11,12 | M=13 | S=0
235 | Environmental mathematics & sustainability | Correlation between air quality and asthma incidence | A=3 | C=6 | P=6,9,10 | M=12 | S=3
236 | Networks & social systems | Applying PageRank to a scientific citation network | A=2 | C=8 | P=7,9,12 | M=13 | S=0
237 | Sports biomechanics & movement | Mathematical analysis of the Magnus effect in a football free kick | A=3 | C=2 | P=1,3 | M=7 | S=0
238 | Information & coding theory | Image complexity and achievable compression ratio | A=3 | C=9 | P=2,7,11 | M=7,13 | S=0
239 | Data science & introductory algorithms | Modelling Netflix-style recommendations with simple distance measures | A=3 | C=6 | P=1,3,8 | M=13 | S=0
240 | Robotics, control & sensing | Position estimation by trilateration with ultrasonic sensors | A=3 | C=9 | P=1,2,7,11 | M=1,13,20,21 | S=1
241 | Chaos & dynamical systems | Modelling population fluctuations with discrete dynamical systems | A=1 | C=8 | P=1,11 | M=13 | S=0
242 | Image processing & computer graphics | Investigating facial-landmark symmetry with anonymised images | A=1 | C=9 | P=2,7,12 | M=7,13 | S=3
243 | Music, acoustics & waves | Sound propagation through different materials | A=3 | C=3 | P=1 | M=9 | S=0
244 | Language & text mathematics | Levenshtein distances between regional spelling variants | A=3 | C=9 | P=7,8,10 | M=13 | S=0
245 | Art, design & architecture | Modelling wave patterns in textile design | A=3 | C=9 | P=1,2,11 | M=13 | S=0
246 | Education & learning analytics | A mathematical comparison of grade-normalisation methods | A=3 | C=9 | P=4,9,10,12 | M=13 | S=3
247 | Astronomy & spaceflight | Mathematical patterns in planetary resonances | A=2 | C=2 | P=9 | M=9 | S=0
248 | Economic models & markets | Optimal bidding in a first-price auction under risk aversion | A=2 | C=8 | P=7,10,11 | M=13 | S=0
249 | Psychology & cognition | Modelling decision fatigue with probability models | A=1 | C=5 | P=1,11 | M=13 | S=3
250 | Time series & forecasting | Autocorrelation of heart rate during interval training | A=1 | C=6 | P=1,3,11,12 | M=8,13,19 | S=3
251 | Probability & risk | The probability of natural disasters at a particular location | A=3 | C=6 | P=6 | M=13 | S=0
252 | Geospatial & cartographic mathematics | Investigating Voronoi service areas for fire stations | A=3 | C=9 | P=6,9,11,12 | M=8,13 | S=0
253 | Culinary mathematics | Modelling fermentation in bread and yoghurt with exponential growth | A=3 | C=9 | P=1,5,11 | M=13 | S=1
254 | Engineering design & optimisation | Optimising the placement of acoustic panels in a room | A=3 | C=9 | P=1,2,8,11 | M=1,9,13 | S=0
255 | Thermodynamics | Cooling curves of aluminium, copper and iron from the same starting temperature | A=1 | C=3 | P=1,12 | M=3 | S=0
256 | Epidemiology & public health | A queueing model for hospital beds | A=2 | C=8 | P=9,11,12 | M=13 | S=0
257 | Material properties | Osmosis: mass change of potato slices in salt solutions from 0% to 20% | A=1 | C=9 | P=1,5 | M=2,13,16 | S=0
258 | Sports analytics & tactics | Residual errors in a mathematical model of baseball pitches | A=2 | C=8 | P=1,3,7,11,12 | M=7,13 | S=0
259 | Electricity | Electrical conductivity of water, juice, cola and salt water | A=1 | C=9 | P=1 | M=5,11,13,16 | S=1
260 | Recreational games & mathematics | The combinatorial structure of the card game SET | A=2 | C=8 | P=2,8,10 | M=13,20 | S=0
261 | Combined experiments | Freezing-point depression: dissolved salt or sugar mass versus minimum temperature | A=1 | C=3 | P=1 | M=2,3,13,16 | S=0
262 | Combinatorics & discrete probability | Computational investigation of small Ramsey numbers | A=2 | C=2 | P=7,10,12 | M=13 | S=0
263 | Kitchen & everyday life | Water and mass loss from cheese or cured food during refrigerated storage | A=1 | C=6 | P=1,5 | M=2,13 | S=0
264 | Climate, Earth & ocean mathematics | The Gutenberg–Richter law for earthquake frequencies | A=2 | C=8 | P=9,10,12 | M=13 | S=0
265 | Environment | Algal growth: biomass and aquarium-water temperature over time | A=1 | C=6 | P=1 | M=2,3,6,13 | S=1
266 | Algebra & number theory | Number systems and modular arithmetic in computer science | A=3 | C=2 | P=7 | M=13 | S=0
267 | Analysis & calculus | Modelling roller-coaster curves with cubic and quintic functions | A=3 | C=3 | P=1,2,11 | M=20 | S=0
268 | Statistics & probability | Correlation between study time and predicted IB grades | A=1 | C=4 | P=1,10 | M=14 | S=3
269 | Mathematical modelling | The mathematics of music: frequency ratios and overtones | A=3 | C=3 | P=1,8 | M=9 | S=0
270 | Geometry & topology | Non-Euclidean geometry: angle sums on a sphere and a hyperbolic surface | A=2 | C=2 | P=10 | M=1 | S=0
271 | Financial mathematics | Returns across different types of investment | A=1 | C=6 | P=1,5,9 | M=0 | S=0
272 | Logic, set theory & proof | Different proofs that there are infinitely many primes | A=2 | C=3 | P=10 | M=13 | S=0
273 | Discrete mathematics & computer science | Hash functions and collisions | A=2 | C=2 | P=1,7 | M=0 | S=0
274 | Applied & interdisciplinary mathematics | The mathematics of photography: exposure and aperture | A=3 | C=9 | P=1,2,8 | M=7,10 | S=0
275 | Game theory & decision-making | Zero-sum games in classic board games | A=3 | C=3 | P=1,8 | M=0 | S=0
276 | Transport & mobility mathematics | Optimising signal phases at a four-way intersection | A=3 | C=9 | P=1,6,7,11 | M=6,7,13 | S=1
277 | Biomathematics & medicine | Correlation between sleep duration and cognitive performance | A=1 | C=6 | P=1,10 | M=19 | S=3
278 | Operations research & logistics | Multi-objective optimisation of delivery time and carbon emissions | A=2 | C=8 | P=6,9,11,12 | M=13 | S=0
279 | Environmental mathematics & sustainability | Modelling plastic degradation in oceans with exponential decay | A=3 | C=6 | P=6,9,11 | M=13 | S=0
280 | Networks & social systems | Assortativity in passing networks from team sports | A=3 | C=9 | P=3,7,9 | M=7,13 | S=0
281 | Sports biomechanics & movement | Modelling an optimal stride pattern for the 100-metre sprint | A=3 | C=9 | P=1,11 | M=8,13 | S=0
282 | Information & coding theory | Collision probabilities for simple checksums | A=3 | C=9 | P=7,10,12 | M=13 | S=0
283 | Data science & introductory algorithms | Cluster formation in friendship networks | A=3 | C=6 | P=1,4 | M=14 | S=3
284 | Robotics, control & sensing | Stability of a simplified self-balancing robot model | A=2 | C=2 | P=2,7,10,11 | M=13,20 | S=1
285 | Chaos & dynamical systems | Arnold tongues in the circle map | A=2 | C=2 | P=8,10 | M=9,14 | S=3
286 | Image processing & computer graphics | The discrete cosine transform in JPEG compression | A=2 | C=2 | P=7,10,12 | M=13 | S=0
287 | Music, acoustics & waves | Modelling vibrato frequency and its perception | A=3 | C=9 | P=1,11,12 | M=9,13,14 | S=0
288 | Language & text mathematics | N-gram entropy in texts by different authors | A=2 | C=8 | P=7,8,9,10 | M=13 | S=0
289 | Art, design & architecture | Analysing proportions in fashion: clothing sizes and golden-ratio claims | A=3 | C=6 | P=1,8,9 | M=1 | S=0
290 | Education & learning analytics | Bootstrap confidence intervals for small learning groups | A=3 | C=6 | P=4,7,12 | M=13 | S=3
291 | Astronomy & spaceflight | Calculating optimal launch windows with Hohmann transfers | A=2 | C=2 | P=1,11 | M=13 | S=0
292 | Economic models & markets | Investigating volatility clustering in exchange-rate data | A=2 | C=8 | P=9,11,12 | M=13 | S=0
293 | Psychology & cognition | Correlation between music genre and mathematical performance | A=1 | C=6 | P=1,4,8 | M=9,14 | S=3
294 | Time series & forecasting | Bootstrap prediction intervals for short time series | A=2 | C=8 | P=7,10,12 | M=13 | S=0
295 | Probability & risk | Modelling cafeteria queues with a Poisson process | A=3 | C=6 | P=1,4,11 | M=13 | S=0
296 | Geospatial & cartographic mathematics | Spatial autocorrelation of house prices using Moran’s I | A=2 | C=8 | P=6,9,11,12 | M=13 | S=0
297 | Culinary mathematics | Calculating an optimal chocolate-melting temperature | A=3 | C=3 | P=1,5,11 | M=3,13 | S=1
298 | Engineering design & optimisation | A daily angle schedule for a single-axis solar tracker | A=3 | C=9 | P=6,7,11 | M=5,10,13,20 | S=1
299 | Thermodynamics | Heat storage in sand, clay and humus under equal energy input | A=1 | C=9 | P=1,6 | M=3,4,1 | S=0
300 | Epidemiology & public health | Modelling seasonal influenza with harmonic functions | A=2 | C=8 | P=9,11,12 | M=13 | S=0
301 | Material properties | Corrosion of iron nails in water, salt water, cola and vinegar | A=1 | C=3 | P=1,11 | M=2,6,13 | S=1
302 | Sports analytics & tactics | Cycling power as a function of gradient and speed | A=1 | C=9 | P=1,3,6,11 | M=8,13,19 | S=1
303 | Electricity | Voltage from homemade galvanic cells using lemons, potatoes, cola and apples | A=1 | C=3 | P=1,5 | M=5 | S=2
304 | Recreational games & mathematics | Probability inference in Minesweeper | A=3 | C=9 | P=7,8,10,11 | M=13 | S=0
305 | Combined experiments | Conductivity versus salt concentration in aqueous solutions | A=1 | C=9 | P=1 | M=2,5,11,13 | S=1
306 | Combinatorics & discrete probability | Constructing and counting Latin squares | A=2 | C=8 | P=2,7,10 | M=13,20 | S=0
307 | Kitchen & everyday life | Packaging fruit: mass loss under cling film, vacuum storage and wax wrap | A=1 | C=6 | P=1,5,12 | M=2,6 | S=1
308 | Climate, Earth & ocean mathematics | Wave energy from a simplified ocean-wave spectrum | A=2 | C=8 | P=9,10,11 | M=13 | S=0
309 | Environment | Paving stones versus grass: daytime surface temperature and night-time cooling | A=1 | C=6 | P=6 | M=3,4,1,13 | S=0
310 | Algebra & number theory | Magic squares: algebraic construction methods | A=1 | C=3 | P=1,2,11 | M=20 | S=0
311 | Analysis & calculus | Riemann sums and numerical integration | A=3 | C=2 | P=12 | M=13 | S=0
312 | Statistics & probability | The normal distribution in sports performance data | A=1 | C=6 | P=1,3 | M=0 | S=0
313 | Mathematical modelling | Modelling the spread of rumours in a school community | A=1 | C=8 | P=1 | M=0 | S=0
314 | Geometry & topology | The golden spiral in selected natural forms | A=3 | C=9 | P=1,2,6 | M=7 | S=0
315 | Financial mathematics | Calculating the effective annual percentage rate on consumer loans | A=1 | C=4 | P=5 | M=13 | S=0
316 | Logic, set theory & proof | Paradoxes in set theory | A=2 | C=2 | P=10 | M=0 | S=0
317 | Discrete mathematics & computer science | Binary trees and their properties | A=3 | C=3 | P=1,2,11 | M=20 | S=0
318 | Applied & interdisciplinary mathematics | Modelling optimal lighting in a room | A=1 | C=6 | P=1,11 | M=10,13 | S=0
319 | Game theory & decision-making | Modelling negotiation strategies with cooperative game theory | A=3 | C=5 | P=1,8,11 | M=13 | S=0
320 | Transport & mobility mathematics | A capacity model for pedestrian flow in school corridors | A=1 | C=6 | P=1,4,11,12 | M=6,7,14 | S=3
321 | Biomathematics & medicine | Modelling the spread of antibiotic resistance in bacterial populations | A=2 | C=2 | P=1,7,11 | M=13 | S=3
322 | Operations research & logistics | Maximum flow for distributing meals in a school canteen | A=3 | C=9 | P=4,7,11 | M=13 | S=0
323 | Environmental mathematics & sustainability | Optimising solar-panel orientation for maximum energy yield | A=3 | C=9 | P=1,6,11 | M=10 | S=0
324 | Networks & social systems | The size of information cascades in social networks | A=3 | C=6 | P=9,11,12 | M=13 | S=0
325 | Sports biomechanics & movement | Calculating stability in different yoga poses using centre of mass | A=3 | C=3 | P=1,2,3 | M=1,7,13,15 | S=0
326 | Information & coding theory | Lempel–Ziv complexity of public DNA sequences | A=2 | C=8 | P=7,9,12 | M=13 | S=0
327 | Data science & introductory algorithms | Time-series analysis: forecasting share prices with moving averages | A=3 | C=6 | P=1 | M=0 | S=0
328 | Robotics, control & sensing | Modelling PWM duty cycle and motor speed | A=1 | C=9 | P=1,2,7,11 | M=5,6,13,20 | S=1
329 | Image processing & computer graphics | Aliasing and sampling frequency in digital patterns | A=3 | C=9 | P=2,7,10 | M=7,13 | S=0
330 | Music, acoustics & waves | Analysing the mathematical structure of canons and fugues | A=3 | C=3 | P=1,8 | M=9 | S=0
331 | Language & text mathematics | Building topic clusters with cosine similarity | A=3 | C=9 | P=7,9,11 | M=13 | S=0
332 | Art, design & architecture | The mathematics of three-dimensional printing structures and infill patterns | A=3 | C=3 | P=1,2 | M=20 | S=0
333 | Education & learning analytics | Modelling mastery development with a Markov chain | A=2 | C=8 | P=4,7,11 | M=13 | S=3
334 | Astronomy & spaceflight | The distribution of asteroids in the Solar System | A=3 | C=6 | P=1 | M=17 | S=0
335 | Economic models & markets | Limitations of simple Laffer-curve models | A=2 | C=8 | P=9,10,12 | M=13 | S=0
336 | Psychology & cognition | Calculating an optimal group size for effective learning | A=1 | C=6 | P=1,4,11 | M=13 | S=3
337 | Time series & forecasting | Fourier analysis of daily traffic patterns | A=2 | C=8 | P=6,9,11 | M=13 | S=0
338 | Probability & risk | Calculating the risk of base-rate errors in everyday decisions | A=3 | C=9 | P=1,12 | M=13,19 | S=0
339 | Geospatial & cartographic mathematics | Fractal dimension of local road networks | A=2 | C=8 | P=6,7,9,10 | M=13 | S=0
340 | Culinary mathematics | The mathematics of laminated dough folds | A=3 | C=3 | P=1 | M=0 | S=0
341 | Engineering design & optimisation | Modelling thrust and power consumption of small drone propellers | A=2 | C=8 | P=1,2,7,11,12 | M=5,6,13,15,20 | S=1
342 | Thermodynamics | Melting rate of ice shapes: volume, surface area and form | A=1 | C=3 | P=1 | M=2,3,1 | S=0
343 | Epidemiology & public health | Comparing diagnostic-test thresholds using ROC curves | A=3 | C=8 | P=9,10,12 | M=13 | S=0
344 | Material properties | Fermentation: carbon dioxide loss from yeast-sugar solutions of different concentrations | A=1 | C=9 | P=1 | M=2,16 | S=0
345 | Sports analytics & tactics | Optimising pacing strategies using swimming split times | A=1 | C=9 | P=1,3,11,12 | M=6,13 | S=0
346 | Electricity | Photovoltaic power loss under partial shading in series and parallel circuits | A=1 | C=8 | P=1,3,11 | M=5,7,10,13 | S=1
347 | Recreational games & mathematics | Mathematically balancing a self-designed dice game | A=3 | C=9 | P=2,7,8,11,12 | M=13,20 | S=0
348 | Combined experiments | Heat capacity of coins made from different alloys | A=1 | C=3 | P=1,12 | M=2,3,16 | S=0
349 | Combinatorics & discrete probability | The inclusion–exclusion principle in password policies | A=3 | C=9 | P=7,10,12 | M=13 | S=0
350 | Kitchen & everyday life | Surface-temperature patterns after different forms of exercise | A=1 | C=6 | P=1,3,12 | M=3,19 | S=3
351 | Environment | Household waste separation: mass of different fractions per week | A=1 | C=6 | P=1,5 | M=2 | S=0
352 | Algebra & number theory | The Collatz conjecture: convergence behaviour for different starting values | A=2 | C=2 | P=7,10 | M=0 | S=0
353 | Analysis & calculus | Parameter changes in the logistic function | A=3 | C=8 | P=9,11 | M=0 | S=0
354 | Statistics & probability | Bayes' theorem and the reliability of medical tests | A=3 | C=2 | P=10,12 | M=0 | S=3
355 | Mathematical modelling | Modelling the spread of wildfires | A=2 | C=8 | P=6,7,9 | M=13 | S=0
356 | Geometry & topology | Calculating sightlines in a theatre or concert hall | A=1 | C=3 | P=2,6,8 | M=1,13 | S=0
357 | Financial mathematics | Modelling the effect of inflation on purchasing power | A=1 | C=6 | P=11 | M=13 | S=0
358 | Logic, set theory & proof | Modelling logic puzzles with propositional logic | A=1 | C=3 | P=1,11 | M=13 | S=0
359 | Discrete mathematics & computer science | Modelling game strategies with game trees | A=3 | C=9 | P=1,8,11 | M=13 | S=0
360 | Applied & interdisciplinary mathematics | The mathematics of perfume: evaporation and diffusion | A=3 | C=9 | P=1,8 | M=16 | S=0
361 | Transport & mobility mathematics | Ride sharing as a weighted bipartite matching problem | A=3 | C=8 | P=5,6,7,11 | M=13 | S=0
362 | Biomathematics & medicine | The geometry and optimisation of leaf-vein networks | A=3 | C=3 | P=1,6,11 | M=0 | S=0
363 | Operations research & logistics | Minimising waste in a cutting-stock problem for sheet material | A=3 | C=9 | P=2,7,11 | M=1,13,20 | S=0
364 | Environmental mathematics & sustainability | Mathematical analysis of wind-energy potential at a location | A=3 | C=6 | P=6 | M=12 | S=0
365 | Networks & social systems | A minimum spanning tree for a campus cable network | A=3 | C=9 | P=2,6,7,11 | M=1,13 | S=0
366 | Sports biomechanics & movement | Mathematical patterns in dance choreography | A=3 | C=9 | P=1,3,8 | M=7 | S=0
367 | Information & coding theory | Channel capacity of a binary symmetric channel | A=2 | C=2 | P=7,10 | M=13 | S=0
368 | Data science & introductory algorithms | Introductory image compression with singular value decomposition | A=2 | C=2 | P=1,7 | M=0 | S=0
369 | Robotics, control & sensing | Optimising Bézier curves for smooth robot turns | A=3 | C=9 | P=2,7,11 | M=13,20 | S=0
370 | Image processing & computer graphics | 3D projection matrices and camera field of view | A=2 | C=2 | P=2,7,10 | M=1,7,13 | S=0
371 | Music, acoustics & waves | Calculating the resonant frequencies of glasses in a glass harmonica | A=3 | C=3 | P=1 | M=9,13 | S=0
372 | Language & text mathematics | Analysing character networks in a novel | A=3 | C=9 | P=7,8,11 | M=13 | S=0
373 | Art, design & architecture | Calculating tension in tent structures based on hyperbolic paraboloids | A=2 | C=2 | P=1,2,11 | M=5,13,20 | S=1
374 | Education & learning analytics | Attendance and performance while accounting for possible confounders | A=1 | C=6 | P=4,9,12 | M=13 | S=3
375 | Economic models & markets | Network effects and adoption curves for digital platforms | A=3 | C=9 | P=9,11,12 | M=13 | S=0
376 | Time series & forecasting | Comparing random-walk and mean-reversion models for exchange rates | A=2 | C=8 | P=9,10,12 | M=13 | S=0
377 | Geospatial & cartographic mathematics | Approximating watersheds from a digital elevation model | A=2 | C=8 | P=7,9,11 | M=13 | S=0
378 | Engineering design & optimisation | Comparing catenary, parabolic and circular-arc bridge models | A=2 | C=2 | P=2,6,10,12 | M=1,7,13 | S=0
379 | Thermodynamics | Thermal conductivity of metal rods measured by the time taken for wax to melt | A=1 | C=3 | P=1,12 | M=3,6,13 | S=1
380 | Epidemiology & public health | Herd immunity under heterogeneous contact rates | A=2 | C=8 | P=7,10,11,12 | M=13 | S=0
381 | Material properties | Sublimation of dry ice: mass loss over time at constant conditions | A=1 | C=3 | P=1 | M=2,3,6,21 | S=2
382 | Sports analytics & tactics | Analysing volleyball rotations as Markov transitions | A=3 | C=9 | P=1,3,7,11 | M=7,13 | S=0
383 | Electricity | Thermoelectric voltage as a function of temperature difference using a Peltier element | A=1 | C=2 | P=1 | M=3,5,13 | S=1
384 | Recreational games & mathematics | Designing escape-room routes as a directed graph | A=3 | C=9 | P=2,7,8,11 | M=13,20 | S=0
385 | Combined experiments | Thermocouple voltage as a function of hot-to-cold water-bath temperature difference | A=1 | C=2 | P=1,6 | M=3,5,13,16 | S=1
386 | Combinatorics & discrete probability | Testing the Poisson approximation for rare events | A=3 | C=9 | P=7,9,10,12 | M=13 | S=0
387 | Kitchen & everyday life | Hand surface-temperature recovery after a safe cold-water exposure | A=1 | C=6 | P=1 | M=4,1,3,6 | S=3
388 | Environment | Water mass loss from plastic and glass containers over time | A=1 | C=3 | P=1 | M=2,16 | S=0
389 | Algebra & number theory | Perfect numbers and their rarity | A=3 | C=3 | P=10 | M=13 | S=0
390 | Analysis & calculus | Optimising the flight path of a paper aeroplane | A=1 | C=9 | P=1,3,11 | M=1,7 | S=0
391 | Statistics & probability | Grade distributions across different school subjects | A=1 | C=6 | P=1 | M=0 | S=0
392 | Mathematical modelling | Optimising seating arrangements in a classroom | A=1 | C=6 | P=1,4,11 | M=14 | S=3
393 | Geometry & topology | Symmetry in Islamic art | A=1 | C=3 | P=1,2,8 | M=7 | S=0
394 | Financial mathematics | Insurance models and premium calculations | A=1 | C=6 | P=5 | M=13 | S=0
395 | Logic, set theory & proof | An introduction to Gödel's incompleteness theorems | A=2 | C=2 | P=1 | M=0 | S=0
396 | Discrete mathematics & computer science | Error-detecting codes and Hamming distance | A=2 | C=2 | P=1,3,8 | M=0 | S=0
397 | Applied & interdisciplinary mathematics | Analysing the stability of towers built from blocks | A=1 | C=9 | P=1,2,11 | M=15,20 | S=0
398 | Transport & mobility mathematics | An accessibility index for public-transport stops using weighted distances | A=1 | C=6 | P=6,9,11 | M=8,13 | S=0
399 | Biomathematics & medicine | Mathematical modelling of visual acuity and corrective-lens power | A=3 | C=3 | P=1,11 | M=13,19 | S=3
400 | Operations research & logistics | Conflict-minimising exam timetabling with graph colouring | A=3 | C=9 | P=4,7,11 | M=13 | S=0
401 | Environmental mathematics & sustainability | Calculating carbon dioxide emissions per kilometre for different forms of transport | A=1 | C=6 | P=1,6 | M=8,13 | S=0
402 | Networks & social systems | Network motifs in a public food-web dataset | A=2 | C=8 | P=7,9,12 | M=13 | S=0
403 | Sports biomechanics & movement | Analysing the optimal riding position on a road bicycle | A=3 | C=3 | P=1,3,11 | M=0 | S=0
404 | Information & coding theory | Password entropy and common human choice patterns | A=3 | C=9 | P=5,7,12 | M=13 | S=0
405 | Data science & introductory algorithms | Password-strength patterns through combinatorics | A=3 | C=3 | P=1 | M=0 | S=0
406 | Robotics, control & sensing | Error propagation at the endpoint of a robot arm | A=2 | C=2 | P=2,7,10,12 | M=1,13,20 | S=1
407 | Image processing & computer graphics | Estimating optical flow in short video sequences | A=2 | C=8 | P=2,7,11,12 | M=7,13 | S=0
408 | Language & text mathematics | Investigating periodic structures in poetic metre | A=3 | C=9 | P=8,10,12 | M=13 | S=0
409 | Education & learning analytics | Reliability of peer assessment using inter-rater correlation | A=1 | C=6 | P=4,12 | M=13,14 | S=3
410 | Economic models & markets | Association rules in anonymised market-basket data | A=3 | C=6 | P=5,7,9,12 | M=13 | S=3
411 | Time series & forecasting | How different imputation methods affect time-series trends | A=3 | C=6 | P=7,9,12 | M=13 | S=0
412 | Geospatial & cartographic mathematics | Choosing an optimal map scale for a hiking route | A=1 | C=9 | P=2,6,11 | M=8,13 | S=0
413 | Engineering design & optimisation | Optimising pallet stacking for mixed package sizes | A=3 | C=9 | P=2,5,7,11 | M=1,13,20 | S=0
414 | Thermodynamics | Temperature change while baking a muffin: core versus surface temperature | A=1 | C=9 | P=1,5,11 | M=3 | S=1
415 | Epidemiology & public health | Lag between wastewater signals and reported cases | A=3 | C=6 | P=9,11,12 | M=13 | S=0
416 | Material properties | Hygroscopicity of salts and sugars: mass gain from moisture in air | A=1 | C=3 | P=1,12 | M=2,6,13,18 | S=0
417 | Sports analytics & tactics | Basketball shot selection using expected points | A=3 | C=9 | P=1,3,7,11,12 | M=7,13 | S=0
418 | Electricity | Temperature-dependent resistance of an incandescent lamp | A=1 | C=3 | P=1 | M=3,5 | S=1
419 | Recreational games & mathematics | Investigating first-player advantage in a board game | A=3 | C=9 | P=1,7,8,12 | M=13 | S=0
420 | Combined experiments | Calorimetry: determining the specific heat capacity of a metal | A=1 | C=3 | P=1,12 | M=2,3,16 | S=0
421 | Combinatorics & discrete probability | Load distribution in the balls-into-bins model | A=2 | C=8 | P=7,10,11 | M=13 | S=0
422 | Kitchen & everyday life | Temperature change in a vacuum flask over 24 hours | A=1 | C=3 | P=1 | M=3,6,13 | S=0
423 | Environment | Water samples: dissolved-solid mass and electrical conductivity | A=1 | C=6 | P=1,6 | M=2,5,13 | S=1
424 | Algebra & number theory | The relationship between continued fractions and irrational numbers | A=2 | C=2 | P=1 | M=0 | S=0
425 | Analysis & calculus | Speed and acceleration while cycling | A=1 | C=3 | P=1,3 | M=8 | S=3
426 | Statistics & probability | Comparing mean, median and mode in salary data | A=1 | C=6 | P=1,9,12 | M=0 | S=0
427 | Mathematical modelling | Modelling water supply in a city | A=1 | C=6 | P=6,11 | M=13 | S=0
428 | Geometry & topology | Modelling shadows cast by sundials | A=1 | C=3 | P=1,2,3 | M=7,10,13,20 | S=0
429 | Financial mathematics | Comparing vehicle leasing with purchasing | A=1 | C=6 | P=1,5,12 | M=0 | S=0
430 | Logic, set theory & proof | Proof methods: direct proof, contraposition and contradiction | A=2 | C=2 | P=10 | M=13 | S=0
431 | Discrete mathematics & computer science | Recurrence relations and the Tower of Hanoi | A=2 | C=3 | P=1,7 | M=0 | S=0
432 | Applied & interdisciplinary mathematics | Modelling an optimal racket length in sport | A=1 | C=9 | P=1,3,11 | M=13 | S=0
433 | Transport & mobility mathematics | E-bike energy consumption as a function of gradient and speed | A=1 | C=9 | P=1,3,6,11 | M=5,8,13 | S=1
434 | Operations research & logistics | Budget selection as a knapsack problem using dynamic programming | A=3 | C=9 | P=5,7,11 | M=13 | S=0
435 | Networks & social systems | Simplified influence maximisation under a limited campaign budget | A=2 | C=8 | P=7,9,11,12 | M=13 | S=0
436 | Information & coding theory | Secret sharing using polynomial interpolation | A=2 | C=2 | P=7,10,11 | M=13 | S=0
437 | Robotics, control & sensing | Discrete feedback control for room temperature | A=3 | C=8 | P=1,7,11,12 | M=3,13 | S=0
438 | Thermodynamics | Heating of asphalt, grass and water in midday sun | A=1 | C=6 | P=6 | M=3,4,1 | S=0
439 | Material properties | Burning rates of candles with different diameters and wax types | A=1 | C=9 | P=1,9 | M=2,1,6,13 | S=1
440 | Electricity | Voltage and capacity change of a lithium-ion battery over repeated charge cycles | A=1 | C=9 | P=1 | M=5,6,13 | S=1
441 | Combined experiments | Electroplating: cathode mass gain versus voltage and time | A=1 | C=2 | P=1 | M=2,5,13,21 | S=2
442 | Algebra & number theory | Euler's totient function and its properties | A=3 | C=3 | P=1 | M=0 | S=0
443 | Analysis & calculus | Modelling breathing with sinusoidal functions | A=1 | C=9 | P=1,11 | M=13 | S=0
444 | Statistics & probability | Waiting times in the school cafeteria | A=1 | C=6 | P=1,4 | M=6 | S=0
445 | Mathematical modelling | The propagation of sound waves in rooms | A=3 | C=8 | P=1 | M=9 | S=0
446 | Geometry & topology | Sphere-packing density in three dimensions | A=3 | C=2 | P=1 | M=2,20 | S=0
447 | Financial mathematics | Calculating the break-even point for a small business | A=1 | C=6 | P=1 | M=13 | S=0
448 | Logic, set theory & proof | Equivalence relations and partitions | A=2 | C=2 | P=10 | M=0 | S=0
449 | Applied & interdisciplinary mathematics | The mathematics of origami folds | A=3 | C=3 | P=1,2,8 | M=20 | S=0
450 | Transport & mobility mathematics | Predicting parking occupancy with a Markov chain | A=3 | C=6 | P=1,6,7,11 | M=6,13 | S=0
451 | Operations research & logistics | Checkout capacity planning with queueing theory | A=1 | C=6 | P=1,5,11,12 | M=6,13 | S=0
452 | Networks & social systems | Anonymising a friendship network and measuring changes in degree distribution | A=3 | C=8 | P=4,7,12 | M=13,14 | S=3
453 | Information & coding theory | Comparing run-length encoding for pixel art and photographs | A=1 | C=9 | P=2,7,8,12 | M=7,13 | S=0
454 | Robotics, control & sensing | Simplified SLAM geometry using known landmarks | A=2 | C=8 | P=2,7,10,11 | M=7,8,13,20 | S=1
455 | Thermodynamics | Heat loss through single, double and triple glazing in winter | A=1 | C=6 | P=1 | M=4,1,3 | S=0
456 | Material properties | Water loss from cut flowers in different solutions | A=1 | C=6 | P=1,12 | M=2,6,16 | S=0
457 | Electricity | Power output of a small wind turbine at simulated wind speeds | A=1 | C=6 | P=1 | M=5,12 | S=1
458 | Combined experiments | Corrosion and conductivity: metal mass loss versus electrical response of the solution | A=1 | C=3 | P=1 | M=2,5,13,16 | S=1
459 | Algebra & number theory | Diophantine equations and their solvability | A=2 | C=2 | P=10 | M=13 | S=0
460 | Analysis & calculus | Calculating the volume of irregular objects by integration | A=3 | C=3 | P=1,2 | M=1,13,20 | S=0
461 | Statistics & probability | Analysing success rates in basketball or throwing tasks | A=1 | C=6 | P=1,3 | M=0 | S=0
462 | Mathematical modelling | Modelling the growth of bacterial cultures | A=1 | C=9 | P=1,11 | M=13,21 | S=1
463 | Geometry & topology | Reflection geometry in architecture | A=1 | C=3 | P=2,6,8 | M=7 | S=0
464 | Financial mathematics | Lottery probabilities and expected value | A=3 | C=9 | P=1,10 | M=13 | S=0
465 | Logic, set theory & proof | Modelling circuits with Karnaugh-Veitch maps | A=1 | C=2 | P=1,8,11 | M=13 | S=0
466 | Applied & interdisciplinary mathematics | Comparing the efficiency of stairs and lifts | A=1 | C=6 | P=1,11 | M=0 | S=0
467 | Thermodynamics | Surface-temperature recovery after ten minutes of exercise | A=1 | C=6 | P=1,3,12 | M=3,19 | S=3
468 | Material properties | Mass change caused by adsorption onto activated carbon | A=1 | C=3 | P=1,12 | M=2,16 | S=0
469 | Electricity | Electrical conductivity of soil samples at different moisture levels | A=1 | C=6 | P=1,6 | M=2,5,13,18 | S=1
470 | Combined experiments | Heat-storage capacity of equal masses of stone, metal and wood | A=1 | C=3 | P=1 | M=2,3,13 | S=0
471 | Algebra & number theory | Properties of Mersenne primes | A=3 | C=3 | P=10 | M=0 | S=0
472 | Analysis & calculus | Limits and L'Hôpital's rule | A=2 | C=2 | P=10 | M=13 | S=0
473 | Statistics & probability | Testing the randomness of music shuffle functions | A=1 | C=6 | P=1,8 | M=9 | S=0
474 | Mathematical modelling | Optimising routes to school or work | A=1 | C=6 | P=1,4,11 | M=8,13 | S=0
475 | Geometry & topology | Curves of constant width and the Reuleaux triangle | A=3 | C=3 | P=1,2,11 | M=20 | S=0
476 | Financial mathematics | Modelling exchange-rate fluctuations | A=1 | C=6 | P=11 | M=13 | S=0
477 | Logic, set theory & proof | Properties of relations: reflexivity, symmetry and transitivity | A=1 | C=3 | P=1,10 | M=0 | S=0
478 | Applied & interdisciplinary mathematics | Modelling the amount of coffee needed to maximise caffeine extraction | A=1 | C=9 | P=1,5,11 | M=13 | S=0
479 | Thermodynamics | Temperature changes in chemical hot and cold packs | A=1 | C=3 | P=1,11 | M=3,4,1,13 | S=2
480 | Material properties | Filtration efficiency measured by suspended-solid mass in different water samples | A=1 | C=6 | P=1,6,11 | M=2 | S=0
481 | Electricity | Voltage distribution in series and parallel circuits with identical lamps | A=1 | C=3 | P=1,10,12 | M=5 | S=1
482 | Combined experiments | Battery discharge across different temperatures using safe manufacturer-approved conditions | A=1 | C=3 | P=1,12 | M=2,3,5 | S=2
483 | Algebra & number theory | The mathematics of ISBN and IBAN check digits | A=1 | C=7 | P=1 | M=13 | S=0
484 | Analysis & calculus | Areas between curves and their meaning in economics | A=1 | C=3 | P=1 | M=1 | S=0
485 | Statistics & probability | Comparing probabilities in different games of chance | A=1 | C=9 | P=1,12 | M=13 | S=0
486 | Mathematical modelling | Modelling climate change with simple climate models | A=3 | C=5 | P=6,9,11 | M=13 | S=0
487 | Geometry & topology | Calculating areas with Pick's theorem | A=3 | C=3 | P=1,2,10 | M=1,13,20 | S=0
488 | Financial mathematics | Calculating economic order quantity with the EOQ model | A=1 | C=6 | P=1,11 | M=13 | S=0
489 | Logic, set theory & proof | A proof of the fundamental theorem of arithmetic | A=2 | C=2 | P=10 | M=13 | S=0
490 | Applied & interdisciplinary mathematics | The mathematics of soap bubbles and minimal surfaces | A=3 | C=3 | P=1 | M=1 | S=0
491 | Thermodynamics | Thermal radiation from matte black and shiny metal surfaces at the same temperature | A=1 | C=3 | P=1 | M=4,1,3 | S=0
492 | Material properties | Comparing fat content in crisps by supervised solvent extraction | A=1 | C=3 | P=1,12 | M=2,16,21 | S=2
493 | Electricity | Surface resistance of wood, metal, plastic and water | A=1 | C=3 | P=1 | M=5,1 | S=1
494 | Combined experiments | Drying curves of wet clay or paper: mass loss and surface temperature | A=1 | C=6 | P=1,12 | M=2,4,1,3 | S=0
495 | Algebra & number theory | Number sequences and their explicit formulae | A=1 | C=3 | P=1,10 | M=0 | S=0
496 | Analysis & calculus | Modelling oscillations with damped harmonic oscillators | A=3 | C=2 | P=1,11 | M=13 | S=0
497 | Statistics & probability | Correlation between weather and mood | A=1 | C=6 | P=1,6,10 | M=12,14 | S=3
498 | Mathematical modelling | The propagation of light through different media | A=3 | C=3 | P=1 | M=10 | S=0
499 | Geometry & topology | Voronoi diagrams in natural structures | A=3 | C=9 | P=1,6 | M=0 | S=0
500 | Financial mathematics | Depreciation methods in accounting | A=1 | C=6 | P=1 | M=0 | S=0
501 | Logic, set theory & proof | Axiom systems through the example of geometry | A=2 | C=2 | P=10 | M=0 | S=0
502 | Applied & interdisciplinary mathematics | Analysing the distribution of stars in the night sky | A=3 | C=6 | P=1 | M=17 | S=0
503 | Thermodynamics | Temperature change inside a compost heap over fourteen days | A=1 | C=6 | P=6 | M=3,6 | S=1
504 | Material properties | Salt content of water samples measured by evaporation and residue mass | A=1 | C=9 | P=1,6 | M=2,11,13,16 | S=0
505 | Electricity | Power output of a bicycle dynamo at different rotational speeds | A=1 | C=9 | P=1,3,11 | M=5,8,9,13 | S=1
506 | Combined experiments | Baking soda and vinegar: carbon dioxide mass loss and temperature change | A=1 | C=3 | P=1,5,11 | M=2,3,13 | S=1
507 | Algebra & number theory | The mathematics behind Sudoku-solving strategies | A=1 | C=7 | P=1,7,8 | M=13,16 | S=0
508 | Analysis & calculus | Optimising a vehicle's fuel consumption | A=1 | C=8 | P=1,5,11 | M=0 | S=0
509 | Statistics & probability | Statistical analysis of election results and forecasts | A=1 | C=6 | P=9 | M=13 | S=0
510 | Mathematical modelling | Modelling population change in a city | A=1 | C=6 | P=6,9,11 | M=13 | S=0
511 | Geometry & topology | Geometric constructions of ellipses and parabolas | A=3 | C=3 | P=1,2,11 | M=0 | S=0
512 | Financial mathematics | Comparing fixed-term and instant-access savings rates over ten years | A=1 | C=6 | P=1,5,9 | M=0 | S=0
513 | Thermodynamics | Cooling molten wax or chocolate: phase transition and solidification | A=1 | C=3 | P=1,5,11 | M=3,4,13 | S=1
514 | Material properties | Biomass growth of cress or sprouts over fourteen days | A=1 | C=6 | P=1,11 | M=2,6 | S=1
515 | Electricity | Bioelectric voltages in selected fruits, vegetables and plant tissues | A=1 | C=3 | P=1,5,6 | M=5 | S=1
516 | Combined experiments | Resistance change as a resistor heats during current flow | A=1 | C=3 | P=1,6 | M=4,5,1,3 | S=1
517 | Algebra & number theory | Palindromic numbers in different bases | A=3 | C=3 | P=1,7 | M=13 | S=0
518 | Analysis & calculus | Curvature in bridges and arches | A=3 | C=3 | P=6 | M=0 | S=0
519 | Statistics & probability | Battery life across different brands | A=1 | C=6 | P=1,5,12 | M=5 | S=1
520 | Mathematical modelling | The trajectory of a frisbee or boomerang | A=1 | C=9 | P=1,3 | M=7 | S=0
521 | Geometry & topology | Properties of torus knots | A=2 | C=2 | P=1 | M=0 | S=0
522 | Financial mathematics | Modelling retirement savings under different scenarios | A=1 | C=6 | P=1,5,11 | M=13 | S=0
523 | Thermodynamics | Surface heating of smartphone batteries during gaming, streaming and standby | A=1 | C=9 | P=1 | M=3,4,1,5 | S=1
524 | Material properties | Density and air fraction in different chocolate bars measured by water displacement | A=1 | C=3 | P=1,5,12 | M=2 | S=0
525 | Electricity | Piezoelectric voltage under different applied forces | A=1 | C=3 | P=1 | M=5,15 | S=2
526 | Combined experiments | Plant growth: biomass versus leaf-surface temperature | A=1 | C=6 | P=1,10 | M=2,4,3 | S=1
527 | Algebra & number theory | The distribution and density of prime numbers | A=2 | C=2 | P=10 | M=0 | S=0
528 | Analysis & calculus | Calculating the centroid of irregular regions | A=3 | C=3 | P=1,2,11 | M=1,13,20 | S=0
529 | Statistics & probability | Waiting times on public transport | A=1 | C=6 | P=1,6 | M=6,8 | S=0
530 | Mathematical modelling | Modelling household water consumption | A=1 | C=6 | P=1,5,11 | M=13 | S=0
531 | Geometry & topology | Great-circle distances on Earth | A=3 | C=3 | P=1 | M=13 | S=0
532 | Thermodynamics | Heat output of LED, halogen and incandescent lamps at comparable brightness | A=1 | C=9 | P=1,11,12 | M=4,1,3,10 | S=1
533 | Material properties | Sugar solubility in water from 20°C to 80°C | A=1 | C=3 | P=1 | M=2,3,13,16 | S=0
534 | Electricity | Thermocouple voltage for different metal pairs and junction temperatures | A=1 | C=2 | P=1,6 | M=3,5,13 | S=2
535 | Combined experiments | Comparing coffee cups using mass, surface temperature and core temperature | A=1 | C=9 | P=1,5,11 | M=2,3,4,1 | S=0
536 | Algebra & number theory | Repeating patterns in decimal expansions | A=1 | C=3 | P=1,10 | M=13 | S=0
537 | Analysis & calculus | Taylor series and their convergence | A=2 | C=2 | P=10,12 | M=0 | S=0
538 | Statistics & probability | The normal distribution of student heights in a class | A=1 | C=4 | P=1,4 | M=14 | S=3
539 | Mathematical modelling | Light propagation in optical fibres | A=3 | C=2 | P=1,11 | M=10,13 | S=0
540 | Geometry & topology | Penrose tilings | A=2 | C=2 | P=1,2,11 | M=20 | S=0
541 | Thermodynamics | A temperature map of a hotplate: centre-to-edge variation | A=1 | C=6 | P=1,5 | M=4,3 | S=1
542 | Material properties | Drying rates of cotton, polyester, wool and microfibre textiles | A=1 | C=6 | P=1,12 | M=2,6 | S=0
543 | Electricity | Battery discharge at different ambient temperatures | A=1 | C=9 | P=1 | M=3,5 | S=1
544 | Combined experiments | Ice formation: frost mass gain and surface temperature over time | A=1 | C=3 | P=1 | M=2,4,1,3 | S=0
545 | Algebra & number theory | The mathematics of barcodes and QR codes | A=1 | C=7 | P=1 | M=0 | S=0
546 | Analysis & calculus | Modelling plant growth rates | A=1 | C=9 | P=1,6,11 | M=13 | S=1
547 | Statistics & probability | Comparing box plots across different school grading systems | A=1 | C=6 | P=4,12 | M=0 | S=0
548 | Mathematical modelling | Modelling the efficiency of solar-energy systems | A=1 | C=6 | P=1,11 | M=13 | S=0
549 | Analysis & calculus | Analysing speed distributions in traffic flow | A=1 | C=8 | P=6 | M=0 | S=0
550 | Statistics & probability | The probability of twin births | A=1 | C=6 | P=9 | M=13 | S=3
551 | Water and flow | Water temperature and flow velocity | A=3 | C=9 | P=1,6,11,12 | M=3,5,12,16,20 | S=0
552 | Water and flow | Streambed roughness and velocity | A=3 | C=9 | P=1,3,6,11,12 | M=2,5,12,16,20 | S=0
553 | Water and flow | Channel slope and discharge | A=3 | C=9 | P=1,6,11,12 | M=5,16,20 | S=0
554 | Water and flow | Bend radius and velocity distribution | A=3 | C=6 | P=1,2,3,6,8,11 | M=1,5,12,16,20 | S=0
555 | Water and flow | Channel sinuosity and travel time | A=3 | C=6 | P=1,3,6,11,12 | M=1,5,6,16,20 | S=0
556 | Water and flow | Cross-sectional shape and discharge | A=3 | C=9 | P=1,6,11,12 | M=1,3,5,16,20 | S=1
557 | Water and flow | Water depth and wave speed | A=3 | C=9 | P=1,2,6,11,12 | M=1,5,7,12,16,20 | S=0
558 | Water and flow | Obstacle density and flow loss | A=3 | C=9 | P=1,3,6,11,12 | M=5,6,16 | S=0
559 | Water and flow | Artificial aquatic plants and flow | A=3 | C=9 | P=1,6,8,11,12 | M=1,5,16 | S=0
560 | Water and flow | Grain size and onset of sediment transport | A=3 | C=9 | P=1,3,6,11,12 | M=1,3,5,12,16,20 | S=1
561 | Water and flow | Particle size and settling velocity | A=3 | C=9 | P=1,6,8,10,11,12 | M=5,11,12,16,20 | S=0
562 | Water and flow | Temperature and dye dispersion | A=3 | C=6 | P=1,6,11,12 | M=3,5,6,7,13,16 | S=0
563 | Water and flow | Solution concentration and flow rate | A=3 | C=9 | P=1,6,11,12 | M=5,16 | S=0
564 | Water and flow | Water head and jet range | A=3 | C=9 | P=1,6,11,12 | M=1,5,16,20 | S=0
565 | Water and flow | Outlet area and drainage time | A=3 | C=2 | P=1,3,6,10,11,12 | M=5,6,12,13,16,20 | S=0
566 | Water and flow | Height difference and siphon performance | A=3 | C=9 | P=1,3,6,11,12 | M=1,3,5,6,11,12 | S=0
567 | Water and flow | Soil composition and infiltration | A=3 | C=9 | P=1,3,6,8,11,12 | M=5,6,16,18 | S=0
568 | Water and flow | Filter grain size and filtration performance | A=3 | C=9 | P=1,6,11,12 | M=1,3,5,6,12,16 | S=0
569 | Water and flow | Decay of a water vortex | A=3 | C=9 | P=1,3,6,11,12 | M=1,5,12,16,20 | S=0
570 | Water and flow | Water-wheel blade angle | A=3 | C=9 | P=1,2,6,11,12 | M=1,3,5,15,16,20 | S=1
571 | Ice, freezing, and strength | Air-bubble fraction and flexural strength | A=3 | C=9 | P=1,2,11,12 | M=2,3,7,11,15 | S=1
572 | Ice, freezing, and strength | Bubble size and fracture strength | A=3 | C=6 | P=1,10,11,12 | M=1,3,7,13 | S=0
573 | Ice, freezing, and strength | Freezing rate and trapped air | A=3 | C=9 | P=1,6,8,11,12 | M=3,12,16 | S=0
574 | Ice, freezing, and strength | Ice temperature and breaking stress | A=3 | C=9 | P=1,11,12 | M=2,3,5,15,20 | S=1
575 | Ice, freezing, and strength | Salinity and ice strength | A=3 | C=9 | P=1,11,12 | M=3,11,16 | S=0
576 | Ice, freezing, and strength | Ice thickness and maximum load | A=3 | C=9 | P=1,11,12 | M=2,3,15,20 | S=1
577 | Ice, freezing, and strength | Freeze–thaw cycles and strength loss | A=3 | C=9 | P=1,11,12 | M=3,20 | S=0
578 | Ice, freezing, and strength | Crack length and breaking load | A=3 | C=9 | P=1,11,12 | M=1,2,3,15,20 | S=1
579 | CO₂, indoor air, plants, and respiration | Number of occupants and CO₂ increase | A=3 | C=9 | P=1,4,6,11,12 | M=13,14,16 | S=3
580 | CO₂, indoor air, plants, and respiration | CO₂ decay curve and air-exchange rate | A=3 | C=9 | P=1,4,6,11,12 | M=13,16,20 | S=0
581 | CO₂, indoor air, plants, and respiration | Window opening and ventilation effectiveness | A=3 | C=9 | P=1,6,11,12 | M=1,6,12 | S=0
582 | CO₂, indoor air, plants, and respiration | Single-sided and cross ventilation | A=3 | C=9 | P=1,6,11,12 | M=6,12 | S=0
583 | CO₂, indoor air, plants, and respiration | Fan position and CO₂ distribution | A=3 | C=6 | P=1,6,11,12 | M=6 | S=1
584 | CO₂, indoor air, plants, and respiration | Sensor height and measured concentration | A=3 | C=9 | P=1,4,6,11,12 | M=1,13,16,18,20 | S=3
585 | CO₂, indoor air, plants, and respiration | Speaking and CO₂ increase | A=3 | C=9 | P=1,4,6,11,12 | M=6,14 | S=3
586 | CO₂, indoor air, plants, and respiration | Light activity and CO₂ production | A=3 | C=9 | P=1,3,6,11,12 | M=7,10 | S=0
587 | CO₂, indoor air, plants, and respiration | Room volume and CO₂ rise rate | A=3 | C=9 | P=1,3,6,11,12 | M=3,12 | S=0
588 | CO₂, indoor air, plants, and respiration | Predicting occupancy from CO₂ data | A=3 | C=9 | P=1,3,4,6,10,11 | M=3,6,13,14,16,20 | S=3
589 | CO₂, indoor air, plants, and respiration | Light intensity and net CO₂ uptake | A=3 | C=9 | P=1,6,11,12 | M=10,20 | S=0
590 | CO₂, indoor air, plants, and respiration | Light colour and net CO₂ exchange | A=3 | C=9 | P=1,3,6,11,12 | M=10 | S=0
591 | CO₂, indoor air, plants, and respiration | Leaf area and CO₂ uptake | A=3 | C=9 | P=1,2,6,11,12 | M=7,10,11 | S=0
592 | CO₂, indoor air, plants, and respiration | Soil moisture and net CO₂ exchange | A=3 | C=9 | P=1,6,8,11,12 | M=13,18 | S=0
593 | CO₂, indoor air, plants, and respiration | Temperature and plant CO₂ exchange | A=3 | C=9 | P=1,6,11,12 | M=3,10,20 | S=0
594 | CO₂, indoor air, plants, and respiration | Plant day–night cycle | A=3 | C=6 | P=1,3,6,11,12 | M=3,6,10,12,13,18 | S=0
595 | CO₂, indoor air, plants, and respiration | Yeast fermentation and CO₂ production | A=3 | C=9 | P=1,6,8,11,12 | M=3,6,16 | S=0
596 | CO₂, indoor air, plants, and respiration | Soil respiration and CO₂ | A=3 | C=6 | P=1,6,11,12 | M=3,13,18,20 | S=0
597 | Batteries and energy | Battery runtime and ambient temperature | A=3 | C=9 | P=1,3,11,12 | M=2,3,5,6 | S=2
598 | Batteries and energy | Voltage drop and temperature | A=3 | C=9 | P=1,3,11,12 | M=2,3,5 | S=2
599 | Batteries and energy | Screen brightness and smartphone battery life | A=3 | C=9 | P=1,2,6,8,11,12 | M=5,6,7,11,20 | S=2
600 | Batteries and energy | Signal quality and battery drain | A=3 | C=9 | P=1,11,12 | M=5,6,12,17 | S=2
601 | Batteries and energy | Wi-Fi versus mobile data | A=3 | C=9 | P=1,8,11,12 | M=3,5 | S=2
602 | Batteries and energy | Refresh rate and energy consumption | A=3 | C=9 | P=1,11,12 | M=5,7 | S=2
603 | Batteries and energy | Local AI computation and battery load | A=3 | C=9 | P=1,3,6,11,12 | M=2,3,5,6,20 | S=2
604 | Batteries and energy | Power-bank efficiency | A=3 | C=9 | P=1,11,12 | M=2,5 | S=2
605 | Sound and acoustics | Speed of sound in air and temperature | A=3 | C=9 | P=1,3,11,12 | M=3,6,9,11,12,20 | S=0
606 | Sound and acoustics | Speed of sound in water and temperature | A=3 | C=2 | P=1,6,10,11,12 | M=1,3,9,12,16 | S=1
607 | Sound and acoustics | Salinity and sound speed | A=3 | C=9 | P=1,3,11,12 | M=3,6,9,11,12,16 | S=0
608 | Sound and acoustics | Humidity and speed of sound | A=3 | C=9 | P=1,6,11,12 | M=3,6,9,12,18 | S=0
609 | Sound and acoustics | Tube length and resonance frequency | A=3 | C=9 | P=1,11,12 | M=1,6,9,16 | S=0
610 | Sound and acoustics | Water level in a bottle and pitch | A=3 | C=9 | P=1,6,11,12 | M=1,3,6,9,16,20 | S=0
611 | Sound and acoustics | Material and sound attenuation | A=3 | C=9 | P=1,8,11,12 | M=6,9,11,20 | S=0
612 | Sound and acoustics | Furnishing and reverberation time | A=3 | C=9 | P=1,3,6,11,12 | M=6,9,20 | S=0
613 | Magnetic fields and electromagnetic induction | Magnetic field strength and distance | A=3 | C=2 | P=1,10,11,12 | M=1,5,17,20 | S=1
614 | Magnetic fields and electromagnetic induction | Magnetic-field component and angle | A=3 | C=2 | P=1,10,11,12 | M=1,5,20 | S=1
615 | Magnetic fields and electromagnetic induction | Number and spacing of magnets | A=3 | C=2 | P=1,6,10,11,12 | M=1,5,17 | S=1
616 | Magnetic fields and electromagnetic induction | Material between magnet and sensor | A=3 | C=2 | P=1,3,8,10,11,12 | M=2,5 | S=1
617 | Magnetic fields and electromagnetic induction | Current and magnetic field of a coil | A=3 | C=2 | P=1,10,11,12 | M=5,17 | S=1
618 | Magnetic fields and electromagnetic induction | Number of turns and magnetic field | A=3 | C=2 | P=1,2,10,11,12 | M=1,5,12,17,20 | S=1
619 | Magnetic fields and electromagnetic induction | Magnet speed and induced voltage | A=3 | C=2 | P=1,10,11,12 | M=5,6,12 | S=1
620 | Magnetic fields and electromagnetic induction | Eddy-current braking and magnet distance | A=3 | C=2 | P=1,10,11,12 | M=1,5,6,20 | S=1
621 | Mobile reception, Wi-Fi, and radio attenuation | Wi-Fi signal strength and distance | A=3 | C=6 | P=1,11,12 | M=1,13,17,20 | S=1
622 | Mobile reception, Wi-Fi, and radio attenuation | Wall material and signal attenuation | A=3 | C=2 | P=1,8,10,11,12 | M=2 | S=1
623 | Mobile reception, Wi-Fi, and radio attenuation | Material thickness and signal attenuation | A=3 | C=9 | P=1,3,11,12 | M=3 | S=1
624 | Mobile reception, Wi-Fi, and radio attenuation | Wet and dry material | A=3 | C=9 | P=1,11,12 | M=2,18 | S=1
625 | Mobile reception, Wi-Fi, and radio attenuation | Device orientation and hand position | A=3 | C=6 | P=1,8,11,12 | M=1,3,11,17 | S=1
626 | Mobile reception, Wi-Fi, and radio attenuation | Line of sight, corners, and walls | A=3 | C=9 | P=1,2,11,12 | M=1,20 | S=1
627 | Mobile reception, Wi-Fi, and radio attenuation | 2.4 GHz versus 5 GHz | A=3 | C=9 | P=1,11,12 | M=6 | S=1
628 | Mobile reception, Wi-Fi, and radio attenuation | Signal strength, throughput, and packet loss | A=3 | C=9 | P=1,11,12 | M=3,6,17 | S=1
629 | Rubik’s Cube, graph theory, and optimization | Scramble length and minimum solution distance | A=3 | C=9 | P=1,3,8,11,12 | M=1,11,13,16 | S=0
630 | Rubik’s Cube, graph theory, and optimization | Distribution of optimal solution distances | A=3 | C=9 | P=1,3,8,11,12 | M=1,11,13,16 | S=0
631 | Rubik’s Cube, graph theory, and optimization | Practice time and solving speed | A=3 | C=9 | P=1,3,4,8,11,12 | M=3,6,11,12,13,16 | S=0
632 | Rubik’s Cube, graph theory, and optimization | Comparing solving methods | A=3 | C=9 | P=1,3,8,11,12 | M=6,11,12,13,16 | S=1
633 | Rubik’s Cube, graph theory, and optimization | Heuristic quality and computational effort | A=3 | C=9 | P=1,3,7,8,11,12 | M=6,11,13,16,17 | S=0
634 | Rubik’s Cube, graph theory, and optimization | Half-turn and quarter-turn metrics | A=3 | C=9 | P=1,3,8,11,12 | M=1,11,13,16 | S=0
635 | Experiments with artificial intelligence | Prompt specificity and answer quality | A=3 | C=9 | P=1,3,8,11,12 | M=13 | S=0
636 | Experiments with artificial intelligence | Zero-shot versus few-shot prompting | A=3 | C=6 | P=1,8,11,12 | M=3,20 | S=0
637 | Experiments with artificial intelligence | German and English prompts | A=3 | C=2 | P=1,8,10,11,12 | M=1 | S=0
638 | Experiments with artificial intelligence | Irrelevant information in prompts | A=3 | C=9 | P=1,8,11,12 | M=3 | S=0
639 | Experiments with artificial intelligence | Typographical and linguistic noise | A=3 | C=2 | P=1,3,8,10,11,12 | M=11,20 | S=0
640 | Experiments with artificial intelligence | Repeatability of identical AI queries | A=3 | C=9 | P=1,3,8,11,12 | M=13 | S=0
641 | Experiments with artificial intelligence | Free response versus fixed output format | A=3 | C=9 | P=1,8,11,12 | M=13 | S=0
642 | Experiments with artificial intelligence | Source requirements and verifiable claims | A=3 | C=9 | P=1,3,8,11,12 | M=13 | S=0
643 | Experiments with artificial intelligence | Position bias in multiple-choice questions | A=3 | C=9 | P=1,3,8,11,12 | M=3 | S=0
644 | Experiments with artificial intelligence | Robustness to small numerical changes | A=3 | C=9 | P=1,3,6,8,11,12 | M=10,13 | S=0
645 | Experiments with artificial intelligence | Image brightness and classification accuracy | A=3 | C=6 | P=1,4,8,11,12 | M=7 | S=0
646 | Experiments with artificial intelligence | Rotation and partial occlusion | A=3 | C=9 | P=1,8,11,12 | M=1,3,7,20 | S=0
647 | Experiments with artificial intelligence | Training-set size and model accuracy | A=3 | C=2 | P=1,4,8,10,11,12 | M=12,20 | S=0
648 | Experiments with artificial intelligence | Class imbalance and evaluation metrics | A=3 | C=2 | P=1,4,8,10,11,12 | M=3,12,13 | S=0
649 | Experiments with artificial intelligence | Model size, accuracy, and speed | A=3 | C=6 | P=1,3,8,11,12 | M=6,12,20 | S=0
650 | Experiments with artificial intelligence | Classical regression versus AI models | A=3 | C=6 | P=1,4,6,7,8,11 | M=3,5,9,13,16,20 | S=2
651 | Further water-flow and hydraulic experiments | Nozzle shape and discharge coefficient | A=3 | C=6 | P=1,3,6,11,12 | M=3,5,13,16,20 | S=0
652 | Further water-flow and hydraulic experiments | Pipe diameter and volume flow rate | A=3 | C=6 | P=1,3,6,11,12 | M=1,5,13,16,20 | S=0
653 | Further water-flow and hydraulic experiments | Pipe length and pressure loss | A=3 | C=6 | P=1,6,11,12 | M=1,5,13,16,20 | S=0
654 | Further water-flow and hydraulic experiments | Number of pipe bends and flow loss | A=3 | C=6 | P=1,6,11,12 | M=1,5,13,16,20 | S=0
655 | Further water-flow and hydraulic experiments | Inlet shape and flow rate | A=3 | C=6 | P=1,3,6,11,12 | M=5,13,16,20 | S=0
656 | Further water-flow and hydraulic experiments | Uniformity of a perforated pipe | A=3 | C=9 | P=1,3,6,11,12 | M=1,5,16 | S=0
657 | Further water-flow and hydraulic experiments | Opening angle of a triangular weir | A=3 | C=6 | P=1,6,11,12 | M=1,5,13,16 | S=0
658 | Further water-flow and hydraulic experiments | Width of a rectangular weir | A=3 | C=9 | P=1,3,6,11,12 | M=1,5,16,20 | S=0
659 | Further water-flow and hydraulic experiments | Venturi constriction and pressure difference | A=3 | C=6 | P=1,2,3,6,11,12 | M=5,13,16,20 | S=0
660 | Further water-flow and hydraulic experiments | Pump head and pump performance | A=3 | C=9 | P=1,3,6,11,12 | M=1,3,5,16 | S=0
661 | Buoyancy, floating bodies, and water resistance | Salt concentration and immersion depth | A=3 | C=6 | P=1,3,6,11,12 | M=1,5,11,13,16,20 | S=0
662 | Buoyancy, floating bodies, and water resistance | Hull shape and maximum payload | A=3 | C=9 | P=1,2,3,6,11,12 | M=2,5,16,20 | S=0
663 | Buoyancy, floating bodies, and water resistance | Centre-of-mass height and stability | A=3 | C=9 | P=1,2,3,6,11,12 | M=1,2,5,15,16,20 | S=0
664 | Buoyancy, floating bodies, and water resistance | Draft and oscillation period of a floating body | A=3 | C=9 | P=1,3,6,11,12 | M=1,2,5,6,15,16 | S=0
665 | Buoyancy, floating bodies, and water resistance | Towing speed and hydrodynamic drag | A=3 | C=9 | P=1,3,6,11,12 | M=5,12,16,20 | S=0
666 | Buoyancy, floating bodies, and water resistance | Object shape and drag coefficient | A=3 | C=6 | P=1,3,6,11,12 | M=5,11,13,16,20 | S=0
667 | Buoyancy, floating bodies, and water resistance | Air volume in a Cartesian diver | A=3 | C=9 | P=1,3,6,8,11,12 | M=5,16,20 | S=0
668 | Buoyancy, floating bodies, and water resistance | Ballast position and trim angle | A=3 | C=9 | P=1,2,3,6,11,12 | M=1,2,5,16,20 | S=0
669 | Buoyancy, floating bodies, and water resistance | Bubble diameter and rise velocity | A=3 | C=9 | P=1,3,6,10,11,12 | M=1,3,5,12,16,20 | S=0
670 | Buoyancy, floating bodies, and water resistance | Hydrometer stem diameter and sensitivity | A=3 | C=9 | P=1,2,3,6,11,12 | M=1,5,16,20 | S=0
671 | Surface tension, capillarity, and droplets | Capillary radius and rise height | A=3 | C=6 | P=1,6,11,12 | M=1,5,13,16,20 | S=0
672 | Surface tension, capillarity, and droplets | Surfactant concentration and contact angle | A=3 | C=6 | P=1,6,11,12 | M=1,3,5,13,16,20 | S=0
673 | Surface tension, capillarity, and droplets | Surface coating and contact-angle hysteresis | A=3 | C=9 | P=1,8,11,12 | M=1,2,5,16 | S=0
674 | Surface tension, capillarity, and droplets | Nozzle diameter and droplet mass | A=3 | C=9 | P=1,11,12 | M=1,2,5,15,16,20 | S=1
675 | Surface tension, capillarity, and droplets | Drop height and spreading factor | A=3 | C=2 | P=1,6,10,11,12 | M=1,5,7,13,16 | S=0
676 | Surface tension, capillarity, and droplets | Initial radius and evaporation time | A=3 | C=2 | P=1,2,11,12 | M=1,5,6,7,11,13 | S=1
677 | Surface tension, capillarity, and droplets | Air speed and droplet evaporation | A=3 | C=6 | P=1,11,12 | M=5,12,16,18,20 | S=0
678 | Surface tension, capillarity, and droplets | Wetted perimeter and surface load capacity | A=3 | C=9 | P=1,6,11,12 | M=2,5,10,16,20 | S=1
679 | Surface tension, capillarity, and droplets | Frame geometry and minimum soap-film area | A=3 | C=9 | P=1,2,3,11,12 | M=5,7,13,16 | S=0
680 | Surface tension, capillarity, and droplets | Glycerol fraction and soap-bubble lifetime | A=3 | C=9 | P=1,11,12 | M=5,6,16,20 | S=0
681 | Water waves, resonance, and hydraulic transitions | Frequency and wavelength of water waves | A=3 | C=6 | P=1,6,11,12 | M=1,6,11,12,13,16 | S=0
682 | Water waves, resonance, and hydraulic transitions | Gap width and diffraction angle | A=3 | C=9 | P=1,3,6,11,12 | M=1,16,20 | S=0
683 | Water waves, resonance, and hydraulic transitions | Source separation and interference pattern | A=3 | C=9 | P=1,3,6,11,12 | M=1,6,16,20 | S=0
684 | Water waves, resonance, and hydraulic transitions | Fluid viscosity and wave damping | A=3 | C=9 | P=1,6,11,12 | M=13,16 | S=0
685 | Water waves, resonance, and hydraulic transitions | Container length and sloshing resonance | A=3 | C=2 | P=1,6,11,12 | M=1,3,6,13,16,20 | S=0
686 | Water waves, resonance, and hydraulic transitions | Fill level and sloshing modes | A=3 | C=9 | P=1,3,6,11,12 | M=3,6,16,20 | S=0
687 | Water waves, resonance, and hydraulic transitions | Initial water height and dam-break front | A=3 | C=9 | P=1,3,6,11,12 | M=1,6,16,20 | S=1
688 | Water waves, resonance, and hydraulic transitions | Discharge and hydraulic jump | A=3 | C=9 | P=1,3,6,11,12 | M=1,16,20 | S=0
689 | Water waves, resonance, and hydraulic transitions | Shore slope and wave run-up | A=3 | C=9 | P=1,2,3,6,11,12 | M=1,13,16,20 | S=0
690 | Water waves, resonance, and hydraulic transitions | Breakwater porosity and wave transmission | A=3 | C=9 | P=1,3,6,11,12 | M=13,16,20 | S=0
691 | Further ice, snow, and freezing experiments | Sugar concentration and freezing point | A=3 | C=9 | P=1,11,12 | M=3,16,20 | S=0
692 | Further ice, snow, and freezing experiments | Solute type and freezing-point depression | A=3 | C=6 | P=1,3,8,11,12 | M=3,13,16,20 | S=0
693 | Further ice, snow, and freezing experiments | Surface roughness and supercooling | A=3 | C=6 | P=1,6,11,12 | M=3,16 | S=0
694 | Further ice, snow, and freezing experiments | Insulation thickness and freezing time | A=3 | C=9 | P=1,6,11,12 | M=3,5,6,16,20 | S=0
695 | Further ice, snow, and freezing experiments | Container shape and freezing time | A=3 | C=6 | P=1,3,11,12 | M=3,6,13,20 | S=0
696 | Further ice, snow, and freezing experiments | Surface colour and ice melting | A=3 | C=9 | P=1,11,12 | M=3,10 | S=0
697 | Further ice, snow, and freezing experiments | Fragment size and melting time | A=3 | C=6 | P=1,11,12 | M=2,3,6,13 | S=0
698 | Further ice, snow, and freezing experiments | Salt pattern and melt-channel formation | A=3 | C=9 | P=1,11,12 | M=1,3,7,11,17 | S=0
699 | Further ice, snow, and freezing experiments | Snow compaction and thermal insulation | A=3 | C=9 | P=1,11,12 | M=3,5,13,17,20 | S=1
700 | Further ice, snow, and freezing experiments | Snow grain size and melting rate | A=3 | C=9 | P=1,4,11,12 | M=3,12 | S=0
701 | Further CO₂ experiments | Door-opening frequency and CO₂ decay | A=3 | C=6 | P=1,6,8,11,12 | M=6,13,20 | S=0
702 | Further CO₂ experiments | Ventilation setting and steady-state CO₂ level | A=3 | C=6 | P=1,6,11,12 | M=2,13,20 | S=0
703 | Further CO₂ experiments | Break schedule and peak CO₂ concentration | A=3 | C=2 | P=1,3,11,12 | M=3,6,16 | S=0
704 | Further CO₂ experiments | Lag between occupancy and CO₂ response | A=3 | C=6 | P=1,3,11,12 | M=6,13,14,20 | S=0
705 | Further CO₂ experiments | CO₂ sensor response time | A=3 | C=9 | P=1,3,6,11,12 | M=6,16,19 | S=0
706 | Further CO₂ experiments | Agreement between multiple CO₂ sensors | A=3 | C=6 | P=1,11,12 | M=1,6,13 | S=0
707 | Further CO₂ experiments | Distance from ventilation opening and CO₂ gradient | A=3 | C=9 | P=1,6,11,12 | M=1,3,6,13 | S=0
708 | Further CO₂ experiments | Plant species and normalized net CO₂ exchange | A=3 | C=6 | P=1,6,8,11,12 | M=2,10 | S=0
709 | Further CO₂ experiments | Germination stage and CO₂ release | A=3 | C=9 | P=1,11,12 | M=2,3,6,20 | S=0
710 | Further CO₂ experiments | Temperature and CO₂ degassing from a beverage | A=3 | C=9 | P=1,11,12 | M=3,6,20 | S=1
711 | Heat transfer and temperature profiles | Container material and cooling constant | A=3 | C=2 | P=1,3,8,11,12 | M=2,3,13,20 | S=1
712 | Heat transfer and temperature profiles | Surface-area-to-volume ratio and cooling | A=3 | C=2 | P=1,3,11,12 | M=3,13 | S=1
713 | Heat transfer and temperature profiles | Lid opening and heat loss | A=3 | C=2 | P=1,3,11,12 | M=3,20 | S=1
714 | Heat transfer and temperature profiles | Stirring speed and heat transfer | A=3 | C=9 | P=1,3,11,12 | M=3,12,20 | S=1
715 | Heat transfer and temperature profiles | Air speed and convective cooling | A=3 | C=6 | P=1,3,11,12 | M=3,12,13,20 | S=1
716 | Heat transfer and temperature profiles | Surface emissivity and radiative cooling | A=3 | C=2 | P=1,3,11,12 | M=3,4,20 | S=1
717 | Heat transfer and temperature profiles | Number of insulation layers | A=3 | C=2 | P=1,3,10,11,12 | M=3,5 | S=1
718 | Heat transfer and temperature profiles | Wet surface and evaporative cooling | A=3 | C=6 | P=1,3,11,12 | M=2,3,13,18 | S=1
719 | Heat transfer and temperature profiles | Mass of a phase-change material | A=3 | C=9 | P=1,3,11,12 | M=2,3,6,11 | S=1
720 | Heat transfer and temperature profiles | Temperature profile along a metal rod | A=3 | C=2 | P=1,3,6,11,12 | M=3,20 | S=1
721 | Oscillations, coupling, and chaos | Pendulum length and corrected period | A=3 | C=2 | P=1,11,12 | M=1,2,6,13,20 | S=0
722 | Oscillations, coupling, and chaos | Release angle and pendulum period | A=3 | C=2 | P=1,3,11,12 | M=1,6,13,20 | S=1
723 | Oscillations, coupling, and chaos | Pendulum-bob shape and air damping | A=3 | C=2 | P=1,11,12 | M=2 | S=0
724 | Oscillations, coupling, and chaos | Fluid viscosity and pendulum damping | A=3 | C=2 | P=1,11,12 | M=3 | S=0
725 | Oscillations, coupling, and chaos | Coupling strength and energy transfer between pendulums | A=3 | C=2 | P=1,11,12 | M=6,15,17 | S=0
726 | Oscillations, coupling, and chaos | Mass and spring period with spring-mass correction | A=3 | C=9 | P=1,6,11,12 | M=2,6 | S=0
727 | Oscillations, coupling, and chaos | Spring nonlinearity | A=3 | C=9 | P=1,11,12 | M=2,15 | S=0
728 | Oscillations, coupling, and chaos | Wire geometry and torsion pendulum | A=3 | C=2 | P=1,11,12 | M=1,13 | S=0
729 | Oscillations, coupling, and chaos | Platform mass and metronome synchronization | A=3 | C=2 | P=1,11,12 | M=2,6,11 | S=0
730 | Oscillations, coupling, and chaos | Initial difference and chaotic divergence of a double pendulum | A=3 | C=2 | P=1,6,8,11,12 | M=1,11,17 | S=1
731 | Friction, rolling, and granular materials | Moment of inertia and ramp acceleration | A=3 | C=9 | P=1,11,12 | M=13 | S=0
732 | Friction, rolling, and granular materials | Wheel radius and rolling resistance | A=3 | C=9 | P=1,3,11,12 | M=1,2,5,15,20 | S=0
733 | Friction, rolling, and granular materials | Tyre pressure and rolling resistance | A=3 | C=9 | P=1,3,11,12 | M=1,5,8,20 | S=0
734 | Friction, rolling, and granular materials | Normal force and coefficient of friction | A=3 | C=2 | P=1,10,11,12 | M=2,13,15 | S=0
735 | Friction, rolling, and granular materials | Apparent contact area and friction | A=3 | C=9 | P=1,11,12 | M=13,15 | S=0
736 | Friction, rolling, and granular materials | Measured roughness and friction | A=3 | C=6 | P=1,2,3,11,12 | M=7,13 | S=0
737 | Friction, rolling, and granular materials | Lubricant viscosity and bearing coast-down time | A=3 | C=9 | P=1,3,11,12 | M=1,3,6,12,20 | S=0
738 | Friction, rolling, and granular materials | Particle shape and angle of repose | A=3 | C=6 | P=1,8,11,12 | M=1,11,12 | S=0
739 | Friction, rolling, and granular materials | Outlet diameter and granular discharge | A=3 | C=9 | P=1,8,11,12 | M=1,3,20 | S=0
740 | Friction, rolling, and granular materials | Spin rate and precession of a top | A=3 | C=6 | P=1,11,12 | M=3,6,12,13,20 | S=0
741 | Flight, aerodynamic drag, and propellers | Paper-helicopter blade length | A=3 | C=9 | P=1,3,11,12 | M=1,2,5,6,10,20 | S=1
742 | Flight, aerodynamic drag, and propellers | Fold angle of a paper rotor | A=3 | C=9 | P=1,3,11,12 | M=1,5,10,20 | S=1
743 | Flight, aerodynamic drag, and propellers | Wing aspect ratio and glide ratio | A=3 | C=6 | P=1,2,11,12 | M=1,5,10,13,20 | S=1
744 | Flight, aerodynamic drag, and propellers | Centre-of-mass position and flight stability | A=3 | C=2 | P=1,10,11,12 | M=2,5,7,10,20 | S=1
745 | Flight, aerodynamic drag, and propellers | Launch angle and range with air resistance | A=3 | C=2 | P=1,11,12 | M=1,5,7,10,13,20 | S=1
746 | Flight, aerodynamic drag, and propellers | Spin and lateral flight deflection | A=3 | C=9 | P=1,8,11,12 | M=5,7,10,13,20 | S=1
747 | Flight, aerodynamic drag, and propellers | Parachute area and terminal velocity | A=3 | C=9 | P=1,2,11,12 | M=2,5,7,10,12,20 | S=1
748 | Flight, aerodynamic drag, and propellers | Vent diameter and parachute stability | A=3 | C=9 | P=1,3,11,12 | M=1,5,6,10 | S=1
749 | Flight, aerodynamic drag, and propellers | Propeller pitch and thrust | A=3 | C=9 | P=1,3,11,12 | M=1,3,5,10,20 | S=1
750 | Flight, aerodynamic drag, and propellers | Number of blades and propeller efficiency | A=3 | C=6 | P=1,11,12 | M=3,5,10 | S=1
751 | Structures, beams, and material geometry | Span length and beam deflection | A=3 | C=6 | P=1,11,12 | M=1,2,13,20 | S=0
752 | Structures, beams, and material geometry | Cross-section orientation and stiffness | A=3 | C=9 | P=1,3,11,12 | M=2,15,20 | S=0
753 | Structures, beams, and material geometry | Hollow-section wall thickness and buckling load | A=3 | C=9 | P=1,2,8,11,12 | M=2,16,20 | S=0
754 | Structures, beams, and material geometry | Load position and beam deflection | A=3 | C=9 | P=1,11,12 | M=2,3,20 | S=0
755 | Structures, beams, and material geometry | Truss angle and load capacity | A=3 | C=9 | P=1,2,3,11,12 | M=1,2,15,20 | S=0
756 | Structures, beams, and material geometry | Arch rise and load capacity | A=3 | C=9 | P=1,3,11,12 | M=1,2,15,20 | S=0
757 | Structures, beams, and material geometry | Corrugation wavelength and bending stiffness | A=3 | C=9 | P=1,11,12 | M=1,2,15,20 | S=0
758 | Structures, beams, and material geometry | Honeycomb cell size | A=3 | C=9 | P=1,2,3,11,12 | M=13,20 | S=0
759 | Structures, beams, and material geometry | Fibre orientation in a laminate | A=3 | C=9 | P=1,11,12 | M=1,13,15,20 | S=0
760 | Structures, beams, and material geometry | 3D-print infill and stiffness | A=3 | C=6 | P=1,2,11,12 | M=2,13,15,17,20 | S=0
761 | Electrical circuits and sensors | Wire length and electrical resistance | A=3 | C=9 | P=1,6,11,12 | M=1,5,20 | S=1
762 | Electrical circuits and sensors | Wire diameter and resistance | A=3 | C=6 | P=1,11,12 | M=1,5,13,20 | S=1
763 | Electrical circuits and sensors | Temperature and conductor resistance | A=3 | C=6 | P=1,3,11,12 | M=3,5,13 | S=1
764 | Electrical circuits and sensors | LED colour and current–voltage characteristic | A=3 | C=9 | P=1,3,11,12 | M=5 | S=1
765 | Electrical circuits and sensors | Resistance and RC charging time | A=3 | C=9 | P=1,11,12 | M=5,6 | S=1
766 | Electrical circuits and sensors | Capacitance and RC discharge time | A=3 | C=9 | P=1,3,11,12 | M=5,6 | S=1
767 | Electrical circuits and sensors | Capacitor type and leakage current | A=3 | C=9 | P=1,11,12 | M=5,6,20 | S=1
768 | Electrical circuits and sensors | Illuminance and LDR resistance | A=3 | C=6 | P=1,2,11,12 | M=5,7,10,13,17,20 | S=1
769 | Electrical circuits and sensors | Thermistor resistance and temperature | A=3 | C=6 | P=1,3,8,11,12 | M=3,5,13,20 | S=1
770 | Electrical circuits and sensors | Capacitance and RLC resonance frequency | A=3 | C=2 | P=1,11,12 | M=3,5,6,13,20 | S=1
771 | Light, optics, and image formation | Distance and illuminance | A=3 | C=6 | P=1,3,11,12 | M=1,2,7,10,13,17 | S=0
772 | Light, optics, and image formation | Polarizer angle and light intensity | A=3 | C=9 | P=1,11,12 | M=1,7,10,11,20 | S=0
773 | Light, optics, and image formation | Sugar concentration and refractive index | A=3 | C=6 | P=1,11,12 | M=1,7,10,13,16 | S=0
774 | Light, optics, and image formation | Prism geometry and minimum deviation | A=3 | C=9 | P=1,3,11,12 | M=1,7,10,21 | S=0
775 | Light, optics, and image formation | Object distance and image distance | A=3 | C=6 | P=1,3,11,12 | M=1,7,10,13 | S=0
776 | Light, optics, and image formation | Aperture and depth of field | A=3 | C=6 | P=1,2,11,12 | M=1,7,10,11,13,20 | S=0
777 | Light, optics, and image formation | Slit width and diffraction pattern | A=3 | C=9 | P=1,4,11,12 | M=7,10,20,21 | S=2
778 | Light, optics, and image formation | Grating spacing and diffraction angle | A=3 | C=9 | P=1,6,11,12 | M=1,7,10 | S=0
779 | Light, optics, and image formation | Dye concentration and light transmission | A=3 | C=6 | P=1,3,11,12 | M=7,10,13,16,20 | S=0
780 | Light, optics, and image formation | Optical-fibre bend radius and light loss | A=3 | C=9 | P=1,8,11,12 | M=1,2,3,7,10,20 | S=0
781 | Solar and renewable energy | Solar-panel tilt angle | A=3 | C=9 | P=1,3,11,12 | M=1,3,5,10,20 | S=0
782 | Solar and renewable energy | Azimuth angle and solar output | A=3 | C=9 | P=1,11,12 | M=1,3,5,10 | S=0
783 | Solar and renewable energy | Panel temperature and electrical power | A=3 | C=6 | P=1,11,12 | M=3,5,10,13 | S=1
784 | Solar and renewable energy | Shaded fraction and solar output | A=3 | C=9 | P=1,11,12 | M=3,5,10 | S=0
785 | Solar and renewable energy | Shading position and output | A=3 | C=6 | P=1,11,12 | M=3,5,10,13,20 | S=0
786 | Solar and renewable energy | Dust coverage and solar yield | A=3 | C=6 | P=1,11,12 | M=5,10,13 | S=0
787 | Solar and renewable energy | Reflector geometry and focal concentration | A=3 | C=6 | P=1,11,12 | M=3,5,10,16 | S=0
788 | Solar and renewable energy | Reflector angle in a model solar cooker | A=3 | C=9 | P=1,3,11,12 | M=1,3,5,10,20 | S=1
789 | Solar and renewable energy | Temperature difference and thermoelectric voltage | A=3 | C=6 | P=1,3,11,12 | M=3,5,10,13 | S=1
790 | Solar and renewable energy | Blade pitch of a small wind turbine | A=3 | C=9 | P=1,3,11,12 | M=1,3,5,10,12,20 | S=0
791 | Reaction rates, diffusion, and solutions | Temperature and effervescent-tablet dissolution | A=3 | C=9 | P=1,3,8,11,12 | M=2,3,6,7,12,16 | S=0
792 | Reaction rates, diffusion, and solutions | Tablet surface area and reaction rate | A=3 | C=9 | P=1,3,11,12 | M=2,12,16,20 | S=1
793 | Reaction rates, diffusion, and solutions | Initial concentration and reaction order | A=3 | C=9 | P=1,4,11,12 | M=11,12,16 | S=1
794 | Reaction rates, diffusion, and solutions | Catalyst amount and oxygen production | A=3 | C=9 | P=1,3,4,6,11,12 | M=12,16,20,21 | S=2
795 | Reaction rates, diffusion, and solutions | Concentration and titration-curve shape | A=3 | C=9 | P=1,3,11,12 | M=11,12,16,21 | S=2
796 | Reaction rates, diffusion, and solutions | Temperature and diffusion coefficient in agar | A=3 | C=9 | P=1,11,12 | M=1,3,12,16 | S=0
797 | Reaction rates, diffusion, and solutions | Supersaturation and crystal growth | A=3 | C=9 | P=1,2,10,11,12 | M=1,7,11,12,16,20 | S=1
798 | Reaction rates, diffusion, and solutions | Temperature and solubility | A=3 | C=9 | P=1,11,12 | M=3,12,16,20 | S=0
799 | Reaction rates, diffusion, and solutions | Salt concentration and conductivity | A=3 | C=6 | P=1,11,12 | M=11,12,13,16,20 | S=0
800 | Reaction rates, diffusion, and solutions | Illumination time and dye degradation | A=3 | C=6 | P=1,3,11,12 | M=6,10,12,13,16 | S=0
801 | Plant growth and plant geometry | Salinity and germination probability | A=3 | C=6 | P=1,6,11,12 | M=11,13,16 | S=0
802 | Plant growth and plant geometry | Temperature and germination-time distribution | A=3 | C=6 | P=1,6,11,12 | M=3,6,20 | S=0
803 | Plant growth and plant geometry | Light direction and phototropism | A=3 | C=9 | P=1,2,6,11,12 | M=1,6,7,10,11,20 | S=0
804 | Plant growth and plant geometry | Photoperiod and plant growth | A=3 | C=9 | P=1,2,3,6,11,12 | M=1,6,7,10,11,13 | S=0
805 | Plant growth and plant geometry | Air speed and transpiration | A=3 | C=6 | P=1,6,8,11,12 | M=2,3,6,12,13 | S=0
806 | Plant growth and plant geometry | Humidity and transpiration rate | A=3 | C=9 | P=1,6,11,12 | M=10,12,18,20 | S=0
807 | Plant growth and plant geometry | Leaf position and stomatal density | A=3 | C=6 | P=1,6,11,12 | M=13,20 | S=0
808 | Plant growth and plant geometry | Tilt angle and root curvature | A=3 | C=9 | P=1,6,11,12 | M=1,6,12 | S=0
809 | Plant growth and plant geometry | Planting density and biomass | A=3 | C=9 | P=1,6,11,12 | M=2,20 | S=0
810 | Plant growth and plant geometry | Leaf area, perimeter, and fractal structure | A=3 | C=9 | P=1,2,3,6,8,11 | M=7,11 | S=1
811 | Food and cooking processes | Cooking time and pasta water absorption | A=3 | C=9 | P=1,6,11,12 | M=1,6,16,20 | S=0
812 | Food and cooking processes | Temperature and rice water absorption | A=3 | C=9 | P=1,6,11,12 | M=3,6,16,20 | S=0
813 | Food and cooking processes | Salt concentration and potato osmosis | A=3 | C=6 | P=1,3,8,11,12 | M=2,11,13,16 | S=0
814 | Food and cooking processes | Acid concentration and apple browning | A=3 | C=6 | P=1,11,12 | M=6,13,16,20 | S=0
815 | Food and cooking processes | Gelatin concentration and gel stiffness | A=3 | C=9 | P=1,3,11,12 | M=1,2,6,15,16,20 | S=0
816 | Food and cooking processes | Brew time and coffee extraction | A=3 | C=9 | P=1,11,12 | M=2,6,11,20 | S=0
817 | Food and cooking processes | Grind size and coffee-bed flow time | A=3 | C=9 | P=1,3,11,12 | M=2,6,20 | S=0
818 | Food and cooking processes | Dough temperature and cookie spread | A=3 | C=9 | P=1,11,12 | M=1,3,6,20 | S=0
819 | Food and cooking processes | Kernel mass and popcorn expansion | A=3 | C=6 | P=1,10,11,12 | M=2,13 | S=0
820 | Food and cooking processes | Temperature and egg-white coagulation | A=3 | C=9 | P=1,2,3,11,12 | M=3,6,7 | S=1
821 | Safe human-participant investigations | Heart-rate recovery over time | A=3 | C=6 | P=1,3,8,11,12 | M=1,2,6,10,13,19 | S=3
822 | Safe human-participant investigations | Step cadence and heart rate | A=3 | C=9 | P=1,8,11,12 | M=6,19,20 | S=3
823 | Safe human-participant investigations | Breathing-rate recovery after light exercise | A=3 | C=9 | P=1,8,11,12 | M=2,6,10,19 | S=0
824 | Safe human-participant investigations | Warning interval and reaction time | A=3 | C=9 | P=1,8,11,12 | M=6,19,20 | S=0
825 | Safe human-participant investigations | Target size, distance, and selection time | A=3 | C=6 | P=1,4,8,11,12 | M=1,6,7,13 | S=3
826 | Safe human-participant investigations | Practice trials and typing speed | A=3 | C=9 | P=1,8,11,12 | M=3,12 | S=0
827 | Safe human-participant investigations | Stance width and postural sway | A=3 | C=2 | P=1,3,8,11,12 | M=1,6,13 | S=0
828 | Safe human-participant investigations | Wrist angle and grip force | A=3 | C=9 | P=1,3,8,11,12 | M=1,15,20 | S=0
829 | Safe human-participant investigations | Walking speed and step length | A=3 | C=9 | P=1,3,8,11,12 | M=1,3,12,20 | S=0
830 | Safe human-participant investigations | Metronome tempo and gait synchronization | A=3 | C=9 | P=1,8,11,12 | M=6,11 | S=0
831 | Sport and motion analysis | Basketball release and entry angles | A=3 | C=9 | P=1,3,11,12 | M=1,7 | S=1
832 | Sport and motion analysis | Football launch angle and range | A=3 | C=9 | P=1,3,8,11,12 | M=1,5,7,13,17,20 | S=1
833 | Sport and motion analysis | Ball temperature and rebound height | A=3 | C=9 | P=1,3,11,12 | M=1,3,7 | S=1
834 | Sport and motion analysis | Ball pressure and coefficient of restitution | A=3 | C=6 | P=1,3,11,12 | M=1,7,13 | S=1
835 | Sport and motion analysis | Spin and table-tennis rebound angle | A=3 | C=6 | P=1,2,3,8,11,12 | M=1,7,12,13 | S=1
836 | Sport and motion analysis | Gear ratio and cycling cadence | A=3 | C=9 | P=1,3,11,12 | M=6,7,8,12 | S=1
837 | Sport and motion analysis | Take-off angle and standing-jump distance | A=3 | C=9 | P=1,2,3,11,12 | M=1,7,20 | S=1
838 | Sport and motion analysis | Rope length and maximum skipping frequency | A=3 | C=9 | P=1,3,11,12 | M=1,3,6,7,20 | S=1
839 | Sport and motion analysis | Stroke rate and rowing-ergometer power | A=3 | C=9 | P=1,3,4,8,11,12 | M=3,6,7 | S=1
840 | Sport and motion analysis | Throwing distance and dart dispersion | A=3 | C=6 | P=1,3,8,11,12 | M=1,7,20 | S=1
841 | Further magnetic-field experiments | Three-dimensional field map of a bar magnet | A=3 | C=9 | P=1,6,8,11,12 | M=13,20 | S=0
842 | Further magnetic-field experiments | Axial and equatorial magnetic field | A=3 | C=9 | P=1,11,12 | M=1,17 | S=0
843 | Further magnetic-field experiments | Magnet temperature and field strength | A=3 | C=2 | P=1,11,12 | M=3,17 | S=1
844 | Further magnetic-field experiments | Core material and solenoid field | A=3 | C=9 | P=1,11,12 | M=5,17,20 | S=0
845 | Further magnetic-field experiments | Air gap in a magnetic circuit | A=3 | C=9 | P=1,11,12 | M=1,3,5,20 | S=0
846 | Further magnetic-field experiments | Hysteresis loop of a soft magnetic material | A=3 | C=9 | P=1,3,11,12 | M=5,13 | S=0
847 | Further magnetic-field experiments | Shield geometry and magnetic-field attenuation | A=3 | C=6 | P=1,11,12 | M=13 | S=0
848 | Further magnetic-field experiments | Coil spacing and Helmholtz-field uniformity | A=3 | C=9 | P=1,3,11,12 | M=1 | S=0
849 | Further magnetic-field experiments | Coil radius and magnetic-field strength | A=3 | C=9 | P=1,2,3,11,12 | M=1,5,12,17,20 | S=0
850 | Further magnetic-field experiments | Separation and magnetic attraction force | A=3 | C=9 | P=1,11,12 | M=1,15 | S=0
851 | Further sound and music experiments | String length and fundamental frequency | A=3 | C=2 | P=1,3,8,11,12 | M=1,6,9,13,20 | S=0
852 | Further sound and music experiments | String tension and frequency | A=3 | C=6 | P=1,8,11,12 | M=2,5,6,9,13,20 | S=0
853 | Further sound and music experiments | Linear density and string frequency | A=3 | C=9 | P=1,8,11,12 | M=1,2,5,6,9,20 | S=0
854 | Further sound and music experiments | Membrane tension and drum frequency | A=3 | C=2 | P=1,8,11,12 | M=5,6,9,13 | S=0
855 | Further sound and music experiments | Frequency and Chladni patterns | A=3 | C=9 | P=1,8,11,12 | M=6,9,13 | S=0
856 | Further sound and music experiments | Frequency difference and beat frequency | A=3 | C=2 | P=1,8,11,12 | M=6,9,13 | S=0
857 | Further sound and music experiments | Source speed and Doppler shift | A=3 | C=6 | P=1,8,11,12 | M=9,12,13,20 | S=0
858 | Further sound and music experiments | Neck geometry and Helmholtz resonance | A=3 | C=9 | P=1,8,11,12 | M=1,9,20 | S=0
859 | Further sound and music experiments | Distance and sound intensity | A=3 | C=9 | P=1,3,6,8,11,12 | M=1,3,9 | S=0
860 | Further sound and music experiments | Room dimensions and acoustic modes | A=3 | C=9 | P=1,3,6,8,11,12 | M=1,6,9 | S=0
861 | Environment, weather, and microclimate | Surface material and heating | A=3 | C=9 | P=1,6,11,12 | M=3,10,11,12,20 | S=1
862 | Environment, weather, and microclimate | Soil depth and temperature profile | A=3 | C=6 | P=1,3,6,11,12 | M=1,3,6,11,12,13 | S=0
863 | Environment, weather, and microclimate | Shade fraction and microtemperature | A=3 | C=6 | P=1,6,11,12 | M=3,6,12,13,17,20 | S=0
864 | Environment, weather, and microclimate | Wind speed and evaporation rate | A=3 | C=9 | P=1,6,11,12 | M=2,3,12,16,20 | S=0
865 | Environment, weather, and microclimate | Exposed water area and evaporation | A=3 | C=9 | P=1,6,11,12 | M=6,12,16 | S=0
866 | Environment, weather, and microclimate | Roof colour and model-building temperature | A=3 | C=2 | P=1,2,6,11,12 | M=3,12,20 | S=1
867 | Environment, weather, and microclimate | Green-roof substrate depth | A=3 | C=9 | P=1,3,6,11,12 | M=1,2,12,20 | S=0
868 | Environment, weather, and microclimate | Leaf-litter depth and soil moisture | A=3 | C=9 | P=1,6,11,12 | M=1,6,12,18,20 | S=0
869 | Environment, weather, and microclimate | Rain angle and collection accuracy | A=3 | C=6 | P=1,6,11,12 | M=1,12 | S=1
870 | Environment, weather, and microclimate | Turbidity and light penetration in water | A=3 | C=6 | P=1,3,6,8,11,12 | M=10,12,13,16 | S=0
871 | Further artificial-intelligence experiments | Sampling temperature and response behaviour | A=3 | C=2 | P=1,8,10,11,12 | M=3 | S=0
872 | Further artificial-intelligence experiments | Context length and information use | A=3 | C=9 | P=1,8,11,12 | M=1,20 | S=0
873 | Further artificial-intelligence experiments | Chunk size in a retrieval-augmented system | A=3 | C=9 | P=1,3,8,11,12 | M=3 | S=0
874 | Further artificial-intelligence experiments | Number of retrieved passages and answer quality | A=3 | C=9 | P=1,8,11,12 | M=13,20 | S=0
875 | Further artificial-intelligence experiments | Label noise and model performance | A=3 | C=6 | P=1,8,11,12 | M=3,12,13,20,21 | S=0
876 | Further artificial-intelligence experiments | Data-augmentation method and robustness | A=3 | C=9 | P=1,8,11,12 | M=13,20 | S=0
877 | Further artificial-intelligence experiments | Feature scaling and training convergence | A=3 | C=9 | P=1,3,7,8,11,12 | M=12,13 | S=0
878 | Further artificial-intelligence experiments | Decision threshold and error cost | A=3 | C=9 | P=1,4,8,11,12 | M=13,20 | S=0
879 | Further artificial-intelligence experiments | Ensemble size and prediction variance | A=3 | C=6 | P=1,8,10,11,12 | M=12,13,20 | S=0
880 | Further artificial-intelligence experiments | Human, AI, and human–AI collaboration | A=3 | C=2 | P=1,8,10,11,12 | M=13,20,21 | S=0
881 | Algorithms, digital measurement, and data quality | Input size and sorting runtime | A=3 | C=9 | P=1,3,7,11,12 | M=6,13,20 | S=0
882 | Algorithms, digital measurement, and data quality | Obstacle density and A\* versus Dijkstra efficiency | A=3 | C=9 | P=1,3,7,8,11,12 | M=1,6,11,13 | S=0
883 | Algorithms, digital measurement, and data quality | Interpolation method and spatial prediction error | A=3 | C=6 | P=1,3,6,7,8,10 | M=3,10,13 | S=0
884 | Algorithms, digital measurement, and data quality | Step size and numerical-integration error | A=3 | C=9 | P=1,7,11,12 | M=3,12,13 | S=0
885 | Algorithms, digital measurement, and data quality | Sampling rate and frequency estimation | A=3 | C=2 | P=1,7,11,12 | M=6,13 | S=0
886 | Algorithms, digital measurement, and data quality | Repeated calculations and rounding error | A=3 | C=6 | P=1,3,6,7,11,12 | M=13 | S=0
887 | Algorithms, digital measurement, and data quality | Occlusion and QR-code recognition | A=3 | C=6 | P=1,7,11,12 | M=13 | S=0
888 | Algorithms, digital measurement, and data quality | Image compression and information loss | A=3 | C=9 | P=1,3,7,11,12 | M=7,13 | S=0
889 | Algorithms, digital measurement, and data quality | Pseudorandom generator and statistical uniformity | A=3 | C=6 | P=1,3,7,8,11,12 | M=1,13,17 | S=0
890 | Algorithms, digital measurement, and data quality | Bit-error pattern and detection probability | A=3 | C=6 | P=1,7,11,12 | M=1,13 | S=0
891 | Geometry, probability, queues, and networks | Optimal cylinder proportions | A=3 | C=9 | P=1,2,3,8,11,12 | M=1,13,20 | S=0
892 | Geometry, probability, queues, and networks | Corner cut and maximum box volume | A=3 | C=9 | P=1,3,8,11,12 | M=1,13 | S=0
893 | Geometry, probability, queues, and networks | Circle packing and area efficiency | A=3 | C=9 | P=1,3,7,8,11,12 | M=1,3,13 | S=0
894 | Geometry, probability, queues, and networks | Folding pattern and paper compression strength | A=3 | C=6 | P=1,8,11,12 | M=1,2,13,20 | S=0
895 | Geometry, probability, queues, and networks | Geometric irregularity and die fairness | A=3 | C=6 | P=1,8,11,12 | M=1,3,13,20 | S=0
896 | Geometry, probability, queues, and networks | Number of shuffles and card disorder | A=3 | C=6 | P=1,8,11,12 | M=1,13 | S=0
897 | Geometry, probability, queues, and networks | Dimension and random-walk return time | A=3 | C=6 | P=1,8,11,12 | M=1,6,13 | S=0
898 | Geometry, probability, queues, and networks | Single versus multiple queues | A=3 | C=6 | P=1,8,11,12 | M=1,3,6,13,20 | S=0
899 | Geometry, probability, queues, and networks | Traffic-light cycle and average delay | A=3 | C=9 | P=1,3,6,7,8,11 | M=1,10,13 | S=1
900 | Geometry, probability, queues, and networks | Node failure and network robustness | A=3 | C=6 | P=1,8,11,12 | M=1,13,17,20 | S=0
901 | Baking & food models | Butter proportion and its effect on baking time, height, and surface of muffins | A=3 | C=9 | P=1,7,11 | M=2,3,6,7,13 | S=1
902 | Baking & food models | Sugar proportion and its effect on browning, diameter, and crispness of cookies | A=3 | C=9 | P=1,7,11 | M=2,3,6,7,13 | S=1
903 | Baking & food models | Flour type and its effect on cake volume and pore structure | A=3 | C=9 | P=1,7,11 | M=2,3,6,7,13 | S=1
904 | Baking & food models | Number of eggs and its effect on the height, elasticity, and mass loss of a sponge cake | A=3 | C=9 | P=1,7,11 | M=2,3,6,7,13 | S=1
905 | Baking & food models | Water-to-milk ratio and its effect on baking time and moisture loss in bread | A=3 | C=9 | P=1,7,11 | M=2,3,6,7,13 | S=1
906 | Baking & food models | Amount of baking powder and its effect on batter volume, pore size, and final height | A=3 | C=9 | P=1,7,11 | M=2,3,6,7,13 | S=1
907 | Baking & food models | Butter, margarine, or oil: comparing the spread and surface of baked goods | A=3 | C=9 | P=1,7,11 | M=2,3,6,7,13 | S=1
908 | Baking & food models | Optimising an ingredient ratio for maximum baking volume with minimum mass loss | A=3 | C=9 | P=1,7,11 | M=2,3,6,7,13 | S=1
909 | Baking & food models | Oven temperature and its effect on core temperature, baking time, and final height | A=3 | C=9 | P=1,7,11 | M=2,3,4,6,7,13 | S=1
910 | Baking & food models | Oven temperature and browning: colour analysis of the surface during baking | A=3 | C=9 | P=1,7,11 | M=2,3,4,6,7,13 | S=1
911 | Baking & food models | Constant or stepwise oven temperature: comparing volume and moisture loss | A=3 | C=9 | P=1,7,11 | M=2,3,4,6,7,13 | S=1
912 | Baking & food models | Position in the oven and its effect on temperature distribution and baking outcome | A=3 | C=9 | P=1,7,11 | M=2,3,4,6,7,13 | S=1
913 | Baking & food models | Preheating time and its effect on baking time, energy demand, and product size | A=3 | C=9 | P=1,7,11 | M=2,3,4,6,7,13 | S=1
914 | Baking & food models | Fan oven or conventional heat: comparing baking time, surface, and energy use | A=3 | C=9 | P=1,7,11 | M=2,3,4,6,7,13 | S=1
915 | Ice & heat transfer | Surface-area-to-volume ratio and melting time of ice cubes | A=3 | C=9 | P=1,7,11 | M=1,2,3,4,6,7,13 | S=0
916 | Ice & heat transfer | Ambient temperature and the changing melting rate of an ice cube | A=3 | C=9 | P=1,7,11 | M=1,2,3,4,6,7,13 | S=0
917 | Ice & heat transfer | Salt concentration and its effect on the melting point and melting time of ice | A=3 | C=9 | P=1,7,11 | M=1,2,3,4,6,7,13 | S=0
918 | Ice & heat transfer | Spread of food colouring as a coloured ice cube melts | A=3 | C=9 | P=1,7,11 | M=1,2,3,4,6,7,13 | S=0
919 | Ice & heat transfer | Cube, sphere, or cylinder: comparing shapes with equal ice mass | A=3 | C=9 | P=1,7,11 | M=1,2,3,4,6,7,13 | S=0
920 | Ice & heat transfer | Air movement and its effect on ice-melting time | A=3 | C=9 | P=1,7,11 | M=1,2,3,4,6,7,13 | S=0
921 | Ice & heat transfer | Support material and its effect on heat flow and melting time | A=3 | C=9 | P=1,7,11 | M=1,2,3,4,6,7,13 | S=0
922 | Ice & heat transfer | Initial ice temperature and its effect on total thawing time | A=3 | C=9 | P=1,7,11 | M=1,2,3,4,6,7,13 | S=0
923 | Vehicle mathematics | Power-to-weight ratio and 0–100 km/h acceleration in a vehicle comparison | A=3 | C=9 | P=9,11,12 | M=13 | S=0
924 | Vehicle mathematics | Drag coefficient C_d and acceleration at higher speeds | A=3 | C=9 | P=9,11,12 | M=13 | S=0
925 | Vehicle mathematics | Relationship between drag coefficient, frontal area, and fuel consumption | A=3 | C=9 | P=9,11,12 | M=13 | S=0
926 | Vehicle mathematics | Torque curve and theoretical acceleration in different gears | A=3 | C=9 | P=9,11,12 | M=13 | S=0
927 | Vehicle mathematics | Vehicle mass and its effect on acceleration and braking-distance models | A=3 | C=9 | P=9,11,12 | M=13 | S=0
928 | Vehicle mathematics | Stated fuel consumption, engine power, and measured acceleration in a model comparison | A=3 | C=9 | P=9,11,12 | M=13 | S=0
929 | Vehicle mathematics | Optimal cruising speed from aerodynamic drag, rolling resistance, and energy consumption | A=3 | C=9 | P=9,11,12 | M=13 | S=0
930 | Electric & magnetic fields | Magnet shape and the spatial distribution of measured magnetic-field strength | A=3 | C=9 | P=1,2,11,12 | M=1,5,13,20 | S=1
931 | Electric & magnetic fields | Distance law for the field strength of a bar magnet | A=3 | C=9 | P=1,2,11,12 | M=1,5,13,20 | S=1
932 | Electric & magnetic fields | Number of coil turns and current as determinants of a solenoid's magnetic field | A=3 | C=9 | P=1,2,11,12 | M=1,5,13,20 | S=1
933 | Electric & magnetic fields | Shielding effect of different materials on a magnetic field | A=3 | C=9 | P=1,2,11,12 | M=1,5,13,20 | S=1
934 | Electric & magnetic fields | Safety distance and field strength below or beside high-voltage power lines | A=3 | C=9 | P=1,2,11,12 | M=1,5,13,20 | S=1
935 | Electric & magnetic fields | Electromagnetic field strength of household appliances as a function of distance | A=3 | C=9 | P=1,2,11,12 | M=1,5,13,20 | S=1
936 | Electric & magnetic fields | Superposition of the magnetic fields of two magnets in different arrangements | A=3 | C=9 | P=1,2,11,12 | M=1,5,13,20 | S=1
937 | Experimental physics | Determining gravitational acceleration with a simple pendulum at different lengths | A=3 | C=9 | P=1,7,11 | M=1,6,7,13 | S=1
938 | Experimental physics | Determining gravitational acceleration through video analysis of free fall | A=3 | C=9 | P=1,7,11 | M=1,6,7,13 | S=1
939 | Experimental physics | Indirect measurement of gravitational acceleration on an inclined plane | A=3 | C=9 | P=1,7,11 | M=1,6,7,13 | S=1
940 | Experimental physics | A smartphone accelerometer in a lift as a model of apparent weight | A=3 | C=9 | P=1,7,11 | M=1,6,7,13 | S=1
941 | Experimental physics | Stability of repeated gravitational-acceleration measurements across time of day and experimental setup | A=3 | C=9 | P=1,7,11 | M=1,6,7,13 | S=1
942 | Solar energy & thermal effects | Solar-cell voltage as an indirect measure of solar activity and irradiance over a day | A=3 | C=9 | P=1,7,11 | M=3,4,5,10,13 | S=1
943 | Solar energy & thermal effects | Solar-cell current as a function of angle of incidence and solar elevation | A=3 | C=9 | P=1,7,11 | M=3,4,5,10,13 | S=1
944 | Solar energy & thermal effects | Module temperature and its effect on voltage, current, and electrical power | A=3 | C=9 | P=1,7,11 | M=3,4,5,10,13 | S=1
945 | Solar energy & thermal effects | Cloud cover and short-interval fluctuations in solar power | A=3 | C=9 | P=1,7,11 | M=3,4,5,10,13 | S=1
946 | Solar energy & thermal effects | Heat absorption by light and dark surfaces as an indirect measure of solar effects | A=3 | C=9 | P=1,7,11 | M=3,4,5,10,13 | S=1
947 | Solar energy & thermal effects | Daily solar-energy yield as the integral of a measured power curve | A=3 | C=9 | P=1,7,11 | M=3,4,5,10,13 | S=1
948 | Thermal expansion | Linear expansion of a metal rod as a function of temperature | A=3 | C=9 | P=1,7,11 | M=1,3,5,13,20 | S=1
949 | Thermal expansion | Comparing the thermal-expansion coefficients of aluminium, steel, and copper | A=3 | C=9 | P=1,7,11 | M=1,3,5,13,20 | S=1
950 | Thermal expansion | Current, heating, and change in length of a metal wire | A=3 | C=9 | P=1,7,11 | M=1,3,5,13,20 | S=1
951 | Thermal expansion | Expansion during heating and contraction during cooling: investigating hysteresis | A=3 | C=9 | P=1,7,11 | M=1,3,5,13,20 | S=1
952 | Thermal expansion | Curvature of a bimetallic strip as a function of temperature | A=3 | C=9 | P=1,7,11 | M=1,3,5,13,20 | S=1
953 | Thermal expansion | Model of a bridge expansion joint for seasonal temperature changes | A=3 | C=9 | P=1,7,11 | M=1,3,5,13,20 | S=1
954 | Mathematical constants & experiments | Buffon's needle experiment: effect of needle length and line spacing on the approximation of π | A=3 | C=9 | P=1,7,10,12 | M=1,6,7,13 | S=0
955 | Mathematical constants & experiments | Monte Carlo approximation of π using random points in a square | A=3 | C=9 | P=1,7,10,12 | M=1,6,7,13 | S=0
956 | Mathematical constants & experiments | Circumference and diameter of real objects: experimental verification of π with error analysis | A=3 | C=9 | P=1,7,10,12 | M=1,6,7,13 | S=0
957 | Mathematical constants & experiments | Determining π from pendulum periods with known pendulum length and gravitational acceleration | A=3 | C=9 | P=1,7,10,12 | M=1,6,7,13 | S=0
958 | Mathematical constants & experiments | Wheel rotations and distance travelled as an experimental approximation of π | A=3 | C=9 | P=1,7,10,12 | M=1,6,7,13 | S=0
959 | Mathematical constants & experiments | Compound interest with ever shorter compounding intervals as an approximation to e | A=3 | C=9 | P=1,7,10,11 | M=3,5,6,13 | S=1
960 | Mathematical constants & experiments | Numerical investigation of the sequence (1 + 1/n)^n as evidence for e | A=3 | C=9 | P=1,7,10,11 | M=3,5,6,13 | S=1
961 | Mathematical constants & experiments | Estimating e by fitting exponential growth and cooling models | A=3 | C=9 | P=1,7,10,11 | M=3,5,6,13 | S=1
962 | Mathematical constants & experiments | Products of uniformly distributed random numbers and the expected number of factors before falling below a threshold | A=3 | C=9 | P=1,7,10,11 | M=3,5,6,13 | S=1
963 | Mathematical constants & experiments | Capacitor discharge and the time constant as an experimental route to e | A=3 | C=9 | P=1,7,10,11 | M=3,5,6,13 | S=1
964 | Mathematical constants & experiments | Leaf arrangements in a plant and their closeness to the golden angle | A=3 | C=9 | P=1,2,8,10 | M=1,7,13 | S=0
965 | Mathematical constants & experiments | Proportions of everyday products compared with the golden ratio | A=3 | C=9 | P=1,2,8,10 | M=1,7,13 | S=0
966 | Mathematical constants & experiments | Image composition and the golden ratio in self-taken photographs | A=3 | C=9 | P=1,2,8,10 | M=1,7,13 | S=0
967 | Mathematical constants & experiments | Proportions of the hand and finger segments compared with the golden ratio | A=3 | C=9 | P=1,2,8,10 | M=1,7,13 | S=0
968 | Mathematical constants & experiments | Convergence of successive Fibonacci ratios to the golden ratio | A=3 | C=9 | P=1,2,8,10 | M=1,7,13 | S=0
969 | Raspberry Pi & human–computer interaction | Reaction time to different colours using a Raspberry Pi and touchscreen | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
970 | Raspberry Pi & human–computer interaction | Auditory or visual stimuli: comparing reaction time with a Raspberry Pi | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
971 | Raspberry Pi & human–computer interaction | Learning curve in repeated touchscreen tasks | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
972 | Raspberry Pi & human–computer interaction | Display time and number of recalled characters in a digital short-term memory test | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
973 | Raspberry Pi & human–computer interaction | Fitts's law: target size, distance, and tapping time on a touchscreen | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
974 | Raspberry Pi & human–computer interaction | Virtual keyboard size and the relationship between typing speed and error rate | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
975 | Raspberry Pi & human–computer interaction | Adaptive quiz: response time, difficulty, and accuracy on a Raspberry Pi | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
976 | Raspberry Pi & human–computer interaction | Time of day, test duration, and change in reaction speed | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
977 | Temperature modelling & vehicle safety | Interior temperature of an empty parked car as a function of outside temperature and time | A=3 | C=9 | P=1,6,7,11,12 | M=3,4,10,12,13 | S=1
978 | Temperature modelling & vehicle safety | Dashboard and seat colour as determinants of surface temperature in an empty car | A=3 | C=9 | P=1,6,7,11,12 | M=3,4,10,12,13 | S=1
979 | Temperature modelling & vehicle safety | Effectiveness of different sunshades in reducing the heating of an empty vehicle | A=3 | C=9 | P=1,6,7,11,12 | M=3,4,10,12,13 | S=1
980 | Temperature modelling & vehicle safety | Window gap and air exchange: effect on the heating of an empty parked car | A=3 | C=9 | P=1,6,7,11,12 | M=3,4,10,12,13 | S=1
981 | Temperature modelling & vehicle safety | Prediction model and warning threshold for dangerous interior temperatures in a car | A=3 | C=9 | P=1,6,7,11,12 | M=3,4,10,12,13 | S=1
982 | Football economics & sports statistics | Player salaries at a football club and league points achieved | A=3 | C=9 | P=3,8,9,11,12 | M=13 | S=0
983 | Football economics & sports statistics | Transfer spending and final league position | A=3 | C=9 | P=3,8,9,11,12 | M=13 | S=0
984 | Football economics & sports statistics | Squad market value and probability of advancing in a tournament | A=3 | C=9 | P=3,8,9,11,12 | M=13 | S=0
985 | Football economics & sports statistics | Attendance and sporting success of a club over a season | A=3 | C=9 | P=3,8,9,11,12 | M=13 | S=0
986 | Football economics & sports statistics | Ticket price, stadium occupancy, and home-match revenue | A=3 | C=9 | P=3,8,9,11,12 | M=13 | S=0
987 | Football economics & sports statistics | Possession and win probability across different leagues | A=3 | C=9 | P=3,8,9,11,12 | M=13 | S=0
988 | Football economics & sports statistics | Expected goals and actual goals: model performance over a season | A=3 | C=9 | P=3,8,9,11,12 | M=13 | S=0
989 | Football economics & sports statistics | Manager changes and change in average points per match | A=3 | C=9 | P=3,8,9,11,12 | M=13 | S=0
990 | Football economics & sports statistics | Travel distance and the strength of home advantage | A=3 | C=9 | P=3,8,9,11,12 | M=13 | S=0
991 | Football economics & sports statistics | Investment in youth development and later market value of the first-team squad | A=3 | C=9 | P=3,8,9,11,12 | M=13 | S=0
992 | Business mathematics | Number of employees and revenue across industries | A=3 | C=9 | P=9,11,12 | M=13 | S=0
993 | Business mathematics | Number of employees and company profit | A=3 | C=9 | P=9,11,12 | M=13 | S=0
994 | Business mathematics | Revenue per employee as a function of company size | A=3 | C=9 | P=9,11,12 | M=13 | S=0
995 | Business mathematics | Workforce growth and subsequent revenue development | A=3 | C=9 | P=9,11,12 | M=13 | S=0
996 | Business mathematics | Employee turnover and operating profit margin | A=3 | C=9 | P=9,11,12 | M=13 | S=0
997 | Innovation & patent statistics | Number of patent applications and company profit | A=3 | C=9 | P=9,11,12 | M=13 | S=0
998 | Innovation & patent statistics | Citation-weighted patents and a company's market value | A=3 | C=9 | P=9,11,12 | M=13 | S=0
999 | Innovation & patent statistics | Research and development expenditure, patent count, and revenue growth | A=3 | C=9 | P=9,11,12 | M=13 | S=0
1000 | Innovation & patent statistics | Time lag between a patent application and a measurable change in profit | A=3 | C=9 | P=9,11,12 | M=13 | S=0
1001 | Innovation & patent statistics | Technological diversity of a patent portfolio and profitability | A=3 | C=9 | P=9,11,12 | M=13 | S=0
1002 | Financial markets & media | Number of daily company announcements and stock return | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1003 | Financial markets & media | News sentiment and short-term price change | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1004 | Financial markets & media | Publication time of a news item and subsequent price volatility | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1005 | Financial markets & media | AI-related company announcements and abnormal stock returns | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1006 | Financial markets & media | Media attention and trading volume of a stock | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1007 | Financial markets & media | Correction of false information and duration of the subsequent price recovery | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1008 | Artificial intelligence & data analysis | Accuracy of AI answers as a function of the difficulty of mathematical questions | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1009 | Artificial intelligence & data analysis | RAG versus no RAG: effect of external sources on the accuracy of AI answers | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1010 | Artificial intelligence & data analysis | Prompt length and accuracy of an AI answer | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1011 | Artificial intelligence & data analysis | Language-model temperature and variation in repeated answers | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1012 | Artificial intelligence & data analysis | Hallucination rate of an AI across different knowledge domains | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1013 | Artificial intelligence & data analysis | Model size, usage cost, and answer quality in comparison | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1014 | Artificial intelligence & data analysis | Consistency of an AI when the same question is asked repeatedly | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1015 | Artificial intelligence & data analysis | Confusion matrix of an AI image classifier under changing lighting conditions | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1016 | Artificial intelligence & data analysis | AI forecast versus a simple baseline model: comparing error metrics | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1017 | Artificial intelligence & data analysis | Measuring possible bias in AI answers using controlled prompt variants | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1018 | Artificial intelligence & data analysis | AI response latency as a function of input and output length | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1019 | Artificial intelligence & data analysis | Synthetic versus real training data: effect on classification performance | A=3 | C=9 | P=7,9,11,12 | M=13 | S=0
1020 | Learning research with AI | Learning gain between pre-test and post-test with AI-supported tutoring | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
1021 | Learning research with AI | AI-supported review intervals compared with a fixed study plan | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
1022 | Learning research with AI | Number and depth of AI hints as determinants of independently solved tasks | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
1023 | Learning research with AI | Task-completion time and learning success with AI support compared with a textbook | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
1024 | Learning research with AI | Knowledge retention after seven days with and without AI feedback | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
1025 | Learning research with AI | Adaptive task difficulty using Raspberry Pi, touchscreen, and AI evaluation | A=3 | C=9 | P=1,4,7,11,12 | M=13,14,19 | S=3
1026 | Smartphone data & technology | Effect of screen brightness on the battery life of a smartphone | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1027 | Smartphone data & technology | Wi-Fi, 4G, or 5G: effect of network type on battery life | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1028 | Smartphone data & technology | Charging power and the smartphone charging-time curve from 0 to 100 per cent | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1029 | Smartphone data & technology | Charge cycles and measurable decline in battery capacity | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1030 | Smartphone data & technology | Smartphone price and actual useful life of different models | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1031 | Smartphone data & technology | Smartphone sales as a function of price and feature set | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1032 | Smartphone data & technology | Daily smartphone use and sleep duration in an anonymised survey | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1033 | Smartphone data & technology | Distribution of usage time across app categories | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1034 | Smartphone data & technology | Screen time, processor load, and battery temperature | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1035 | Smartphone data & technology | Smartphone GPS accuracy in urban areas, woodland, and open terrain | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1036 | Smartphone data & technology | Camera resolution, file size, and smartphone processing time | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0
1037 | Smartphone data & technology | Device age and launch time of selected apps | A=3 | C=9 | P=1,5,7,11,12 | M=5,6,7,8,13,14 | S=0

Editorial note: The codes are planning guidance, not an official IB approval. Course fit depends on the current subject guide, assessment session, scope and mathematical depth.