maths coursework ideas

50 IB Maths IA Topic Ideas

IB Maths is a struggle for most people going through their diploma. To make matters worse, on top of just doing the dreaded maths exam, we’re also expected to write a Maths IA exploration into a topic of our choice! Where do you even begin such a task? How do you even choose a topic? To make things easier, we have plenty of free Maths resources! Firstly though, we’ve compiled 50 common Maths IA topics that may spark some creative juices and set you on your way to conquering one of the hardest assignments of the diploma!

Once you have chosen your topic, you may want to check out our other posts on how to structure and format your Maths IA or how to write your IA .

NOTE: These topics are purely meant as inspiration and are not to be chosen blindly. Even though many of these topics led to high scores for some of our graduates in the past, it is important that you listen to the advice of your subject teacher before choosing any topic!

• Pascal’s triangle : Discovering patterns within this famous array of numbers
• Pythagorean triples : Can you find patterns in what numbers form a pythagorean triple?
• Monty Hall problem : How does Bayesian probability work in this real-life example, and can you add a layer of complexity to it?
• The Chinese Remainder Theorem : An insight into the mathematics of number theory
• Sum of all positive integers is -1/12? Explore this fascinating physics phenomenon through the world of sequences and series
• Birthday paradox : Why is it that in a room of people probability dictates that people are very likely to share a birthday? 
• Harmonic series : Explore why certain notes/chords in music sound dissonant, and others consonant, by looking at the ratios of frequencies between the notes.
• Optimizing areas : Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon?
• Optimizing volumes : Explore the mathematics of finding a maximum volume of a cuboid subject to some constraint
• Flow of traffic : How does mathematics feed into our traffic jams that we endure every morning?
• Football statistics : Does spending a lot of cash during the transfer window translate to more points the following year? Or is there a better predictor of a team’s success like wages, historic performance, or player valuation?
• Football statistics #2 : How does a manager sacking affect results? 
• Gini coefficient : Can you use integration to derive the gini coefficient for a few countries, allowing you to accurately compare their levels of economic inequality?
• Linear regressions : Run linear regressions using OLS to predict and estimate the effect of one variable on another.
• The Prisoner’s Dilemma : Use game theory in order to deduce the optimal strategy in this famous situation
• Tic Tac Toe : What is the optimal strategy in this legendary game? Will my probability of winning drastically increase by some move that I can make?
• Monopoly : Is there a strategy that dominates all others? Which properties should I be most excited to land on?
• Rock Paper Scissors : If I played and won with rock already, should I make sure to change what I play this time? Or is it better to switch? 
• The Toast problem : If there is a room of some number of people, how many toasts are necessary for everyone to have toasted with everyone?
• Cracking a Password : How long would it take to be able to correctly guess a password? How much safer does a password get by adding symbols or numbers?
• Stacking Balls : Suppose you want to place balls in a cardboard box, what is the optimal way to do this to use your space most effectively?
• The Wobbly Table : Many tables are wobbly because of uneven ground, but is there a way to orient the tables to make sure they are always stable?
• The Stable Marriage Problem : Is there a matching algorithm that ensures each person in society ends up with their one true love? What is the next best alternative if this is not viable?
• Mathematical Card Tricks : Look at the probabilities at play in the famous 3 card monte scam. 
• Modelling the Spread of a Virus : How long would it take for us all to be wiped out if a deadly influenza spreads throughout the population?
• The Tragedy of the Common s : Our population of fish is dwindling, but how much do we need to reduce our production by in order to ensure the fish can replenish faster than we kill?
• The Risk of Insurance : An investigation into asymmetric information and how being unsure about the future state of the world may lead us to be risk-averse
• Gabriel’s Horn : This figure has an infinite surface area but a finite volume, can you p rove this?
• Modelling the Shape of an Egg : Although it may sound easy, finding the surface area or volume of this common shape requires some in-depth mathematical investigation
• Voting Systems : What voting system ensures that the largest amount of people get the official that they would prefer? With 2 candidates this is logical, but what if they have more than 2?
• Probability : Are Oxford and Cambridge biased against state-school applicants?
• Statistics : With Tokyo 2020 around the corner, how aboutmodelling change in record performances for a particular discipline?
• Analysing Data : In the 200 meter dash, is there an advantage to a particular lane in track? 
• Coverage : Calculation of rate of deforestation, and afforestation. How long will our forests last?
• Friendly numbers, Solitary numbers, perfect numbers : Investigate what changes the condition of numbers
• Force : Calculating the intensity of a climber’s fall based upon their distance above where they last clamped in
• Königsberg bridge problem : Using networks to solve problems. 
• Handshake problem : How many handshakes are required so that everyone shakes hands with all the other people in the room? 
• The mathematics of deceit : How con artists use pyramid schemes to get rich quick!
• Modelling radioactive decay : The maths of Chernobyl – when will it be safe to live there?
• Mathematics and photography : Exploring the relationship between the aperture of a camera and a geometric sequence
• Normal Distribution : Using distributions to examine the 2008 financial crisis
• Mechanics : Body Proportions for Track and Field events
• Modelling : How does a cup of Tea cool?
• Relationships : Do BMI ratings and country wealth share a significant relationship?
• Modelling : Can we mathematically model musical chords and concepts like dissonance?
• Evaluating limits : Exploring L’Hôpital’s rule
• Chinese postman problem : How do we calculate shortest possible routes?
• Maths and Time : Exploring ideas regarding time dilation
• Plotting Planets : Using log functions to track planets!

So there we have it: 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework ! We also have similar ideas for Biology , Chemistry , Economics , History , Physics , TOK … and many many more tips and tricks on securing those top marks on our free resources page – just click the ‘Maths resources’ button!

Still feeling confused, or want some personalised help? We offer online private tuition from experienced IB graduates who got top marks in their Maths IA. 

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IB Maths IA examples

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Not sure what to search for? You can always look through our example Internal Assessments below for inspiration.

All Maths IA Examples

Filter exemplars, modelling india’s population, what trajectory should the spaceship use to minimise the total amount of radiation obtained when travelling to the point exactly opposite of the star, want to get full marks for your ia allow us to review it for you 🎯, fourier transform in neuroscience: an application to electric signal analysis, investigating the correlation between height and shooting ability in basketball., how does the volume of water inside a bottle determine the frequency of the sound emitted by the bottle as more water is filled, fast track your coursework with mark schemes moderated by ib examiners. upgrade now 🚀, what is the mathematical formula for the key of c major, employing optimization to minimize amount of packaging material, exploration into modelling a population pyramid (19/20), extension of the moving ladder problem, modelling covid 19 using sir model, a model of earth’s orbit, modelling the surface area of a ceramic pot, investigation of the relationship between leg length and lateral jumping distance, an investigation into predicting the outcome of the 2020 new zealand election, how can we develop an accurate model to describe radioactive decay, comparing the rates of change of in temperature for three water bottles, the determination of pi constant using geometry, calculus, and technology, how does club face loft affect how far the ball carries in golf, how to calculate the surface area and volume of a bottle through modelling, mathematical modelling of doraemon, how can math demonstrate how people can play music by ear without ever reading sheet music, how air pressure affects a soccer ball, exploring an alternative method of calculating the volume of a star, lanchester’s combat model, investigating the interaction between sinusoidal sound waves and resultant superposition in assembling harmonious guitar chords, optimizing blood vessel branching, tower of hanoi, the role of mathematics in cryptography, modeling a chicken egg, the mathematics behind singapore's student loans (19/20), analysing the cost of filling and crown's structure for humans., small neural networks for simple binary classification., an investigation on authorship, modeling the curve of a dolphin kick of a swimmer, what is the relationship between gdp per capita and co2 emissions per capita, logarithmic transformations of graphs and its importance in real life, plotting log graphs of planetary patterns, bayes’ thorem and the probability of inaccurate diagnosis in 40-89 year-old individuals in relation to the excess healthcare burden of osteoporosis in the united kingdom, modelling financial market with chaos theory (received mark: 15/20).

IB Maths IA: 60 Examples and Guidance

Charles Whitehouse

The International Baccalaureate Diploma Programme offers a variety of assessments for students, including Internal Assessments (IAs), which are pieces of coursework marked by students’ teachers. The Mathematics Internal Assessment follows the same assessment criteria across Mathematics Analysis and Approaches (AA) and Mathematics Application and Interpretation (AI). It forms 20% of a student’s Mathematics grade.

In this article, we will cover everything you need to know about the IB Mathematics IA, including the structure, assessment criteria, and some tips for success.

What is the Mathematics IA?

The Maths IA is an individual exploration of an area of mathematics, based on the student’s own work with guidance from their teacher. Mathematical communication is an important part of the IA, which should be demonstrated through both effective written communication and use of formulae, diagrams, tables, and graphs. The exploration should be 12 to 20 pages long and students will spend 10 to 15 hours on the work.

Even A-Level Maths tutors and A-Level Further Maths tutors have found the concept of an IA-like component in IB Maths to be both challenging and rewarding, enriching the learning experience.

To learn more about the IB Maths Internal Assessment, you can have a look at the IB Maths AA resources as well as the IB Maths AI resources :

• IB Maths AA Past Papers
• IB Maths AI Past Papers

What are the assessment criteria?

Like most IB IAs, the IB Maths IA is marked on a group of 5 criteria which add up to 20 marks. Online Maths tutors recommend to look through these carefully before and during your investigation, to ensure that you are hitting the criteria to maximise your mark.

Source : IB Mathematics Applications and Interpretation Guide

Criterion A: Communication (4 marks) – This refers to the organisation and coherence of your work, and the clarity of your explanations. The investigation should be coherent, well-organized, and concise.

Criterion B: Mathematical Presentation (4 marks) – This refers to how well you use mathematical language, including notation, symbols and terminology. Your notation should be accurate, sophisticated, and consistent. Define your key terms and present your data in a varied but proper way (including labelling those graphs).

Criterion C: Personal Engagement (3 marks) – There should be evidence of outstanding personal engagement in the IA. This is primarily demonstrated through showing unique thinking, not just repeating analysis found in textbooks. This can be evidenced through analysing independently or creatively, presenting mathematical ideas in their own way, exploring the topic from different perspectives, making and testing predictions.

Criterion D: Reflection (3 marks) – This refers to how you evaluate both your sources and the strengths and weaknesses of any methodology you use. There should be “substantial evidence of critical reflection”. This could be demonstrated by considering what another stage of investigation could be, discussing implications of results, discussing strengths and weaknesses of approaches, and considering different perspectives.

Criterion E: Use of Mathematics (6 marks ) –

Note that only 6 marks are available for the actual use of mathematics! The focus of the investigation is on explaining well and analysing with genuine, personal curiosity. The level of mathematics expected also depends on the level the subject is studied at: Standard Level students’ maths is expected to be “correct”, while Higher Level students’ maths is expected to be “precise” and demonstrate “sophistication and rigour”.

Examiners are primarily looking for thorough understanding, which also requires clear communication of the principles behind the mathematics used - not just coming to the right answer.

Have a look at our comprehensive set resources for IB Maths developed by expert IB teachers and examiners!

- IB Maths AI SL Study Notes

- IB Maths AI HL Study Notes

- IB Maths AA SL Study Notes

- IB Maths AA HL Study Notes

What are some example research questions?

Students should choose a research area that they are interested in and have a comprehensive understanding of. Often, student may choose to consult with an expert IB Maths tutor to help them decide a good question. It should have a link to something of personal interest, as indicated by Criterion C. Popular topics include Calculus, Algebra and Number (proof), Geometry, Statistics, and Probability, or Physics. Some students make links between Math and other subjects – a good way to combine knowledge from your other IB courses!

Here are examples with details of potential research questions that could inspire your Mathematics IA:

1 - Investigating the properties of fractals and their relationship to chaos theory.

Use computer software or mathematical equations to generate and analyze fractals. Explore the patterns and properties of the fractals, such as self-similarity and complexity. Investigate how changes in the initial conditions or parameters affect the resulting fractals. Analyze the relationship between fractals and chaos theory, and how fractals can be used to model chaotic systems. Present findings through visual representations and data analysis.

2 - Analyzing the behavior of recursive sequences and their applications in computer science and cryptography.

Use mathematical formulas to generate recursive sequences and analyze their behavior. This could involve plotting the sequences and observing patterns, finding closed-form expressions for the sequences, and exploring their applications in computer science and cryptography. For example, recursive sequences can be used in algorithms for sorting and searching data, and in encryption methods such as the Fibonacci cipher. The results of the analysis could be presented in a research paper or presentation.

3 - Exploring the properties of different types of differential equations and their applications in physics and engineering.

Conduct research on the different types of differential equations and their applications in physics and engineering. This could involve studying examples of differential equations used in fields such as fluid dynamics, electromagnetism, and quantum mechanics. The properties of each type of differential equation could be analyzed, such as their order, linearity, and homogeneity. The applications of each type of differential equation could also be explored, such as how they are used to model physical systems and solve engineering problems. The findings could be presented in a report or presentation.

4 - Investigating the properties of chaotic dynamical systems and their applications in physics and biology.

Use computer simulations to model chaotic dynamical systems and explore their behavior. This could involve studying the Lorenz attractor, the logistic map, or other well-known examples of chaotic systems. The simulations could be used to investigate the sensitivity of the systems to initial conditions, the presence of strange attractors, and other key features of chaotic dynamics. The results could then be applied to real-world systems in physics and biology, such as weather patterns, population dynamics, or chemical reactions.

5 - Designing an optimized route for a delivery service to minimize travel time and fuel costs.

Use a computer program or algorithm to analyze data on the locations of delivery destinations and the most efficient routes to reach them. The program would need to take into account factors such as traffic patterns, road conditions, and the size and weight of the packages being delivered. The output would be a map or list of optimized delivery routes that minimize travel time and fuel costs. This could be used to improve the efficiency and profitability of the delivery service.

6 - Developing a model to predict the spread of infectious diseases in a population.

Collect data on the population size, infection rate, and transmission rate of the disease in question. Use this data to create a mathematical model that simulates the spread of the disease over time. The model should take into account factors such as population density, age distribution, and vaccination rates. The accuracy of the model can be tested by comparing its predictions to real-world data on the spread of the disease. The model can be used to explore different scenarios, such as the impact of different vaccination strategies or the effectiveness of quarantine measures.

7 - Investigating the relationship between different geometric shapes and their properties.

Conduct a series of experiments in which different geometric shapes are tested for various properties such as volume, surface area, and weight. The data collected could then be analyzed to determine if there is a relationship between the shape of an object and its properties. This could involve creating 3D models of the shapes using computer software, or physically measuring the shapes using laboratory equipment. The results could be presented in a graph or chart to illustrate any trends or patterns that emerge.

8 - Analyzing the behavior of projectile motion and its applications in physics.

Conduct experiments in which a projectile is launched at different angles and velocities, and its trajectory is tracked using high-speed cameras or other measurement devices. The data collected can be used to analyze the motion of the projectile and determine its velocity, acceleration, and other physical properties. This information can then be applied to real-world scenarios, such as designing rockets or calculating the trajectory of a ball in sports. Additionally, the behavior of projectile motion can be studied in different environments, such as in the presence of air resistance or in a vacuum, to better understand its applications in physics.

9 - Developing a model to predict the path of a planet based on gravitational forces.

Collect data on the mass, position, and velocity of the planet at a given time. Use the law of gravitation to calculate the gravitational forces acting on the planet from other celestial bodies in the system. Use this information to predict the path of the planet over time, taking into account any changes in velocity or direction caused by gravitational forces. The accuracy of the model could be tested by comparing its predictions to observations of the planet's actual path.

10 - Investigating the properties of conic sections and their applications in geometry and physics.

Use mathematical equations to explore the properties of conic sections such as circles, ellipses, parabolas, and hyperbolas. Investigate their applications in geometry, such as in the construction of satellite dishes and reflectors, and in physics, such as in the orbits of planets and comets. Develop models and simulations to demonstrate these applications and their impact on real-world scenarios.

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11 - Modeling the spread of a virus through a population and analyzing the effectiveness of different intervention strategies.

Develop a mathematical model that simulates the spread of the virus through a population. The model would need to take into account factors such as the infectiousness of the virus, the rate of transmission between individuals, and the effectiveness of different intervention strategies such as social distancing or vaccination. The model could then be used to analyze the effectiveness of different intervention strategies and predict the potential impact of future outbreaks. The output of the model would be a set of data and visualizations that show the predicted spread of the virus and the effectiveness of different intervention strategies.

12 - Modeling the spread of a rumor or disease through a network and analyzing the impact of network topology.

Develop a mathematical model that simulates the spread of the rumor or disease through a network. The model should take into account factors such as the probability of transmission between individuals, the rate of recovery or decay of the rumor or disease, and the structure of the network. The impact of network topology could be analyzed by comparing the spread of the rumor or disease in different types of networks, such as random, scale-free, or small-world networks. The results of the simulation could be visualized using graphs or heat maps to show the spread of the rumor or disease over time.

13 - Developing a model to predict the growth of a population over time.

Collect data on the current population size and growth rate of the population over a period of time. Use this data to develop a mathematical model that predicts the population growth rate over time. The model could be tested by comparing its predictions to actual population growth data from previous years. The model could also be used to predict future population growth and to identify factors that may affect the population's growth rate.

14 - Investigating the properties of exponential functions and their applications in finance and economics.

Develop a mathematical model for an exponential function, including its domain and range, growth/decay rate, and asymptotes. Use this model to analyze real-world scenarios in finance and economics, such as compound interest, population growth, or stock market trends. Graph the function and interpret the results in terms of the original problem.

15 - Developing a model to predict the outcomes of a sporting event based on historical data and team statistics.

Collect historical data on the two teams playing in the sporting event, including their win-loss records, player statistics, and any relevant trends or patterns. Use this data to develop a statistical model that predicts the outcome of the game based on these factors. The model can then be tested and refined using additional data and feedback from experts in the field. The final output would be a prediction of the outcome of the game, along with a measure of the model's accuracy and any potential limitations or uncertainties.

16 - Analyzing the behavior of different types of sequences and their convergence or divergence.

Use mathematical models and computer simulations to analyze the behavior of different types of sequences. This would involve testing various sequences for convergence or divergence, and comparing their behavior under different conditions. The results of these simulations could be used to develop new mathematical theories and algorithms for analyzing sequences, and could have applications in fields such as computer science, physics, and engineering.

17 -Investigating the properties of different types of angles and their relationship to geometry and trigonometry.

Conduct a study of different types of angles, including acute, obtuse, right, and straight angles. Explore their properties, such as their degree measurements, relationships to other angles, and their use in geometry and trigonometry. This could involve creating visual aids, such as diagrams or graphs, to illustrate the concepts being studied. The results of the study could be presented in a report or presentation format, highlighting the key findings and insights gained from the investigation.

18 - Developing a model to predict the outcomes of a game based on probability theory.

Collect data on the outcomes of previous games, including the teams playing, the score, and any relevant factors such as weather conditions or injuries. Use this data to calculate the probability of each team winning based on various factors. Develop a model that takes into account these probabilities and predicts the outcome of future games. The model would need to be tested and refined using additional data and statistical analysis. The final output would be a reliable model for predicting the outcomes of games based on probability theory.

19 - Analyzing the behavior of different types of inequalities and their applications in algebra and calculus.

Create a graph to visually represent the behavior of different types of inequalities, such as linear, quadratic, and exponential inequalities. Use examples to demonstrate how these inequalities can be applied in algebra and calculus, such as finding the maximum or minimum value of a function subject to certain constraints. Additionally, provide real-world applications of these concepts, such as optimizing production processes or predicting population growth.

20 - Investigating the properties of different types of graphs and their applications in computer science and social science.

Conduct a literature review to identify the different types of graphs and their applications in computer science and social science. Develop a set of criteria for evaluating the effectiveness of different types of graphs in conveying information and insights. Use these criteria to analyze and compare several examples of graphs from each field. Based on the analysis, identify the most effective types of graphs for different types of data and research questions in each field. Develop guidelines for selecting and creating effective graphs in computer science and social science research.

21 - Analyzing the behavior of different types of matrices and their applications in linear algebra and quantum mechanics.

Conduct experiments to test the behavior of different types of matrices in linear algebra and quantum mechanics. For example, in linear algebra, the inverse of a matrix can be calculated and used to solve systems of linear equations. In quantum mechanics, matrices are used to represent quantum states and operators. The behavior of these matrices can be analyzed by performing matrix operations and observing the resulting changes in the system. The applications of these matrices in various fields can also be explored and analyzed.

22 - Developing a model to predict the outcomes of a business investment based on market trends and financial data.

Collect and analyze market trends and financial data relevant to the business investment. This could include factors such as industry growth rates, consumer demand, and financial statements of similar companies. Using this data, develop a predictive model that takes into account various variables and their potential impact on the investment. The model could be tested and refined using historical data and adjusted as new information becomes available. The output would be a prediction of the potential outcomes of the investment based on the model's calculations.

23 - Modeling the spread of a forest fire and analyzing the effectiveness of different containment strategies.

Develop a computer model of the forest fire spread using data on wind direction, temperature, humidity, and fuel load. The model could be calibrated using historical data on past forest fires to ensure its accuracy. Different containment strategies could then be simulated in the model, such as creating fire breaks or using water or fire retardant chemicals to slow the spread of the fire. The effectiveness of each strategy could be evaluated by comparing the simulated fire spread with and without the strategy in place.

24 - Analyzing the behavior of different types of optimization problems and their applications in engineering and computer science.

Conduct a literature review to identify different types of optimization problems and their applications in engineering and computer science. Develop a framework for analyzing the behavior of these problems, taking into account factors such as the size of the problem, the complexity of the solution space, and the type of optimization algorithm used. Apply this framework to a set of case studies, comparing the performance of different optimization algorithms and identifying best practices for solving different types of optimization problems.

25 - Investigating the properties of different types of geometric transformations and their applications in computer graphics and animation.

Conduct a literature review to gather information on the properties of different geometric transformations and their applications in computer graphics and animation. This could include translations, rotations, scaling, and shearing. Develop a set of test cases to demonstrate the use of these transformations in creating different types of graphics and animations. The results of these tests could be used to compare the effectiveness of different types of transformations for different applications. Additionally, the limitations and challenges associated with each transformation could be identified and discussed.

26 - Developing a model to predict the outcomes of an election based on polling data.

Collect polling data from a representative sample of the population and analyze it using statistical methods such as regression analysis or machine learning algorithms. The model would need to be trained on historical election data to ensure its accuracy. The output of the model would be a prediction of the likely outcome of the election based on the polling data and the historical trends. The model could also be used to identify key factors that are driving voter behavior and to test different scenarios, such as changes in voter turnout or shifts in public opinion.

27 - Analyzing the behavior of different types of integrals and their applications in calculus and physics.

Conduct a series of experiments to analyze the behavior of different types of integrals, such as definite and indefinite integrals, and their applications in calculus and physics. For example, one experiment could involve calculating the area under a curve using both definite and indefinite integrals and comparing the results. Another experiment could involve analyzing the motion of an object using calculus and determining its velocity and acceleration at different points in time. The results of these experiments could be used to develop a deeper understanding of the behavior of integrals and their applications in various fields.

28 - Studying the properties of different types of probability distributions and their applications in statistics and finance.

Conduct a literature review to gather information on different types of probability distributions and their applications in statistics and finance. Develop a theoretical framework to analyze the properties of these distributions and their relevance in different contexts. Use statistical software to simulate data and test the theoretical framework. Analyze the results and draw conclusions about the usefulness of different probability distributions in various applications.

29 - Developing a model to predict the outcomes of a marketing campaign based on consumer data.

Collect consumer data such as demographics, purchasing habits, and social media activity. Use this data to identify patterns and trends that can be used to develop a predictive model. The model would need to be trained using historical data on marketing campaigns and their outcomes. Once the model is trained, it can be used to predict the outcomes of future marketing campaigns based on the input data. The accuracy of the model can be tested by comparing its predictions to the actual outcomes of the campaigns.

30 - Investigating the properties of different types of symmetry and their relationship to geometry and physics.

Conduct a study of different types of symmetry, such as bilateral, radial, and rotational symmetry. This could involve creating models or diagrams of different symmetrical shapes and analyzing their properties, such as the number of axes of symmetry and the angles of rotation. The relationship between symmetry and geometry could be explored by examining how different symmetrical shapes can be used to create geometric patterns. The relationship between symmetry and physics could be investigated by exploring how symmetrical structures are used in physics, such as in the design of crystals or the study of particle physics.

31 - Modeling the spread of a rumor or news story through a population and analyzing its impact.

Develop a mathematical model that simulates the spread of the rumor or news story through a population. This model could take into account factors such as the initial number of people who hear the rumor, the rate at which they share it with others, and the likelihood that each person will believe and share the rumor. The impact of the rumor could be analyzed by looking at factors such as changes in people's behavior or attitudes, or the spread of related rumors or misinformation. The model could be refined and tested using data from real-world examples of rumor or news story propagation.

32 - Analyzing the behavior of different types of exponential growth and decay functions and their applications in science and engineering.

Use mathematical models to analyze the behavior of exponential growth and decay functions. This could involve studying the equations that describe these functions, graphing them to visualize their behavior, and analyzing how they are used in various fields such as biology, economics, and physics. Applications could include modeling population growth, decay of radioactive materials, and the spread of diseases. The results of this analysis could be used to inform decision-making in these fields and to develop more accurate models for predicting future trends.

33 - Modeling the spread of a pandemic through a population and analyzing the effectiveness of different intervention strategies.

Develop a mathematical model that simulates the spread of the pandemic through a population, taking into account factors such as the transmission rate, incubation period, and recovery rate. The model could be used to predict the number of cases over time and the effectiveness of different intervention strategies, such as social distancing, mask-wearing, and vaccination. The model would need to be validated using real-world data and adjusted as new information becomes available. The results of the analysis could be used to inform public health policies and interventions to control the spread of the pandemic.

34 - Analyzing the behavior of different types of functions and their applications in science and engineering.

Conduct a study of different types of functions, such as linear, quadratic, exponential, and logarithmic functions, and their applications in science and engineering. This could involve analyzing real-world data sets and modeling them using different types of functions to determine which function best fits the data. The study could also explore the use of functions in fields such as physics, chemistry, and economics, and how they are used to make predictions and solve problems. The results of the study could be presented in a report or presentation, highlighting the importance of understanding the behavior of different types of functions in various fields.

35 - Analyzing the behavior of different types of numerical methods for solving differential equations and their applications in science and engineering.

Conduct a series of simulations using different numerical methods for solving differential equations, such as Euler's method, Runge-Kutta methods, and finite difference methods. The simulations could involve modeling physical phenomena such as fluid flow, heat transfer, or chemical reactions. The accuracy and efficiency of each method could be compared by analyzing the error and computational time for each simulation. The results could be applied to optimize numerical methods for solving differential equations in various scientific and engineering applications.

36 - Developing a model to predict the outcomes of a medical treatment based on patient data and medical history.

Collect patient data and medical history, including demographic information, medical conditions, medications, and treatment outcomes. Use statistical analysis and machine learning algorithms to develop a predictive model that can accurately predict the outcomes of a medical treatment based on patient data and medical history. The model would need to be validated using a separate set of patient data to ensure its accuracy and reliability. The model could then be used to inform medical decision-making and improve patient outcomes.

37 - Analyzing the behavior of different types of linear regression models and their applications in analyzing trends in public opinion polls.

Collect data from public opinion polls on a particular topic of interest, such as political preferences or social attitudes. Use different types of linear regression models, such as simple linear regression, multiple linear regression, and logistic regression, to analyze the data and identify trends and patterns. Compare the performance of the different models and determine which one is most appropriate for the specific data set and research question. The results of the analysis could be used to make predictions or inform policy decisions.

38 - Developing a model to predict the growth of a startup company based on market trends and financial data.

Collect market trend data and financial data for a range of startup companies. Use statistical analysis to identify patterns and correlations between the data. Develop a predictive model based on these patterns and correlations, taking into account factors such as industry trends, competition, funding, and management. The model could be tested and refined using data from existing startups, and could be used to make predictions about the growth potential of new startups based on their characteristics and market conditions.

39 - Studying the properties of different types of statistical distributions and their applications in analyzing public health data.

Analyze public health data using different statistical distributions such as normal, Poisson, and binomial distributions. This would involve understanding the properties and characteristics of each distribution and selecting the appropriate one based on the nature of the data being analyzed. The data could then be plotted and analyzed using statistical software to identify trends and patterns, and to draw conclusions about the health outcomes being studied. The results could be presented in the form of graphs, tables, and statistical summaries.

40 - Investigating the properties of different types of series and their convergence or divergence.

Conduct a series of tests on different types of series, such as geometric, arithmetic, and harmonic series. Use mathematical formulas and calculations to determine their convergence or divergence. Graphs and charts could be used to visually represent the data and make comparisons between the different types of series. The results of the tests could be analyzed to draw conclusions about the properties of each type of series and their behavior under different conditions.

41 - Analyzing the behavior of different types of functions and their limits.

Graph the different types of functions and analyze their behavior as the input values approach certain limits. This could involve finding the asymptotes, determining if the function is continuous or discontinuous at certain points, and identifying any points of inflection. The results could be presented in a report or presentation, highlighting the similarities and differences between the different types of functions and their limits.

42 - Investigating the properties of different types of sets and their relationships in set theory.

Conduct a comparative analysis of different types of sets, such as finite and infinite sets, empty sets, and subsets. Investigate their properties, such as cardinality, intersection, union, and complement. Use diagrams and examples to illustrate the relationships between the different types of sets. This analysis could be used to develop a deeper understanding of set theory and its applications in various fields.

43 - Exploring the properties of different types of number systems, such as real, complex, or p-adic numbers.

Conduct a literature review of the properties of different number systems and compile a list of key characteristics and equations. Then, design a series of mathematical problems that test these properties for each type of number system. These problems could include solving equations, graphing functions, and analyzing patterns. The results of these problems could be used to compare and contrast the properties of each number system.

44 - Developing a model to predict the behavior of a physical system using calculus of variations.

Collect data on the physical system being studied, such as its initial state and any external factors that may affect its behavior. Use the calculus of variations to develop a mathematical model that predicts the system's behavior over time. The model can then be tested against real-world observations to determine its accuracy and refine the model as needed. The final output would be a reliable model that accurately predicts the behavior of the physical system.

45 - Investigating the properties of different types of topological spaces and their relationships in topology.

Conduct a study of the different types of topological spaces, including Euclidean spaces, metric spaces, and topological manifolds. Analyze their properties, such as compactness, connectedness, and continuity, and explore how they are related to each other. This could involve creating visual representations of the spaces, such as diagrams or models, and using mathematical tools to analyze their properties. The results of the study could be used to better understand the fundamental principles of topology and their applications in various fields.

46 - Analyzing the behavior of different types of integrals, such as line integrals or surface integrals, and their applications in physics and engineering.

Conduct a literature review on the different types of integrals and their applications in physics and engineering. This could include researching the use of line integrals in calculating work done by a force field or the use of surface integrals in calculating flux through a surface. Based on the findings, develop a research question or hypothesis related to the behavior of a specific type of integral and its application in a particular field. Design and conduct an experiment or simulation to test the hypothesis and analyze the results to draw conclusions about the behavior of the integral and its practical applications.

47 - Developing a model to predict the behavior of a chemical reaction using chemical kinetics.

Collect data on the initial concentrations of reactants, temperature, and other relevant factors for the chemical reaction being studied. Use this data to develop a mathematical model that predicts the behavior of the reaction over time. The model could be tested by comparing its predictions to actual experimental data collected during the reaction. Adjustments could be made to the model as needed to improve its accuracy. The final model could be used to predict the behavior of the reaction under different conditions or to optimize reaction conditions for maximum efficiency.

48 - Investigating the properties of different types of algebraic structures, such as groups, rings, or fields.

Conduct a thorough literature review to gather information on the properties of different algebraic structures. Develop a clear research question or hypothesis to guide the investigation. Choose a specific algebraic structure to focus on and collect data by performing calculations and analyzing examples. Compare and contrast the properties of the chosen algebraic structure with other types of algebraic structures to draw conclusions about their similarities and differences. Present findings in a clear and organized manner, using appropriate mathematical language and notation.

49 - Analyzing the behavior of different types of functions, such as trigonometric, logarithmic, or hyperbolic functions, and their applications in science and engineering.

Conduct a study of the behavior of different types of functions, such as trigonometric, logarithmic, or hyperbolic functions, and their applications in science and engineering. This study could involve analyzing real-world data sets and identifying which type of function best fits the data. The study could also involve creating models using different types of functions to predict future outcomes or behavior. The results of this study could be used to inform decision-making in fields such as engineering, finance, or physics.

50 - Developing a model to predict the behavior of a financial market using mathematical finance.

Collect data on the financial market, such as stock prices, interest rates, and economic indicators. Use mathematical models, such as stochastic calculus and differential equations, to analyze the data and develop a predictive model. The model could be tested and refined using historical data and validated using real-time data. The output would be a model that can be used to predict the behavior of the financial market and inform investment decisions.

51 - Investigating the properties of different types of complex systems and their behavior, such as network dynamics, agent-based models, or game theory.

Develop a simulation model for each type of complex system being investigated. The model would need to incorporate the relevant variables and interactions between agents or components of the system. The behavior of the system could then be observed and analyzed under different conditions or scenarios. This would allow for a better understanding of the properties and dynamics of each type of complex system and how they may behave in real-world situations.

52 - Analyzing the behavior of different types of partial differential equations and their applications in physics and engineering.

Conduct a literature review to identify different types of partial differential equations and their applications in physics and engineering. Develop mathematical models to simulate the behavior of these equations and analyze their solutions using numerical methods. The results of the analysis could be used to gain insights into the behavior of physical systems and to develop new technologies or improve existing ones. Examples of applications could include fluid dynamics, heat transfer, and electromagnetic fields.

53 - Developing a model to predict the behavior of a fluid using fluid dynamics.

Use computational fluid dynamics software to create a model of the fluid system being studied. The software would simulate the behavior of the fluid under different conditions, such as changes in flow rate or temperature. The model could be validated by comparing its predictions to experimental data. Once validated, the model could be used to predict the behavior of the fluid under different conditions, such as changes in the geometry of the system or the addition of different chemicals. These predictions could be used to optimize the design and operation of the fluid system.

54 - Investigating the properties of different types of geometric objects, such as manifolds or curves, and their applications in geometry and physics.

Conduct a literature review to gather information on the properties of different geometric objects and their applications in geometry and physics. This could involve researching existing theories and models, as well as conducting experiments or simulations to test these theories. The findings could then be analyzed and synthesized to draw conclusions about the properties of different geometric objects and their potential applications in various fields. This could also involve developing new theories or models based on the findings.

55 - Analyzing the behavior of different types of stochastic processes, such as random walks or Markov chains, and their applications in probability theory and statistics.

Conduct simulations of different stochastic processes using software such as R or Python. Analyze the behavior of the simulations and compare them to theoretical predictions. Use the results to draw conclusions about the properties of the different stochastic processes and their applications in probability theory and statistics. Additionally, explore real-world examples of stochastic processes, such as stock prices or weather patterns, and analyze their behavior using the concepts learned from the simulations.

56 - Developing a model to predict the behavior of a biological system using mathematical biology, such as population dynamics, epidemiology, or ecology.

Collect data on the biological system being studied, such as population size, birth and death rates, and environmental factors. Use this data to develop a mathematical model that can predict the behavior of the system over time. The model can be tested and refined using additional data and compared to real-world observations to ensure its accuracy. This model could be used to make predictions about the future behavior of the system, such as the spread of a disease or the impact of environmental changes on a population.

57 - Investigating the properties of different types of wave phenomena, such as sound waves or electromagnetic waves, and their applications in physics and engineering.

Conduct experiments to study the properties of different types of wave phenomena, such as frequency, wavelength, amplitude, and speed. These experiments could involve using instruments such as oscilloscopes, microphones, and antennas to measure and analyze the waves. Applications of these wave phenomena could include designing communication systems, medical imaging technologies, and musical instruments. The results of these experiments could be presented in a report or presentation, highlighting the key findings and their significance in physics and engineering.

58 - Analyzing the behavior of different types of optimization problems in dynamic environments, such as optimal control or dynamic programming.

Conduct simulations of different optimization algorithms in dynamic environments, using various scenarios and parameters to test their performance. The results could be analyzed to determine which algorithms are most effective in different types of dynamic environments and under what conditions. This information could be used to develop more efficient and effective optimization strategies for real-world applications.

59 - Developing a model to predict the behavior of a social network using social network analysis, such as centrality measures, community detection, or opinion dynamics.

Collect data on the social network, such as the number of connections between individuals, the frequency and content of interactions, and any changes in the network over time. Use social network analysis techniques to identify patterns and trends in the data, such as the most influential individuals, the formation of subgroups or communities, and the spread of opinions or behaviors. Develop a model based on these findings that can predict future behavior or changes in the network. The model could be tested and refined using additional data or by comparing its predictions to real-world outcomes.

60 - Investigating the properties of different types of algebraic curves and surfaces, such as elliptic curves or algebraic varieties, and their applications in algebraic geometry.

Conduct a literature review to gather information on the properties of different types of algebraic curves and surfaces. Use mathematical software to generate and analyze examples of these curves and surfaces. Explore their applications in algebraic geometry, such as in cryptography or coding theory. Present findings in a research paper or presentation.

How can I score highly?

Scoring highly in the mathematics internal assessment in the IB requires a combination of a thorough understanding of mathematical concepts and techniques, effective problem-solving skills, and clear and effective communication.

To achieve a high score, students should start by choosing a topic that interests them and that they can explore in depth. They should also take the time to plan and organize their report, making sure to include a clear introduction, a thorough development, and a thoughtful conclusion. The introduction in particular should demonstrate students’ genuine personal engagement with the topics.

Students should pay attention to the formal presentation and mathematical communication, making sure to use proper mathematical notation, correct grammar and spelling, and appropriate use of headings and subheadings.

Finally, students should make sure to engage with the problem and reflect on their own learning, and also make connections between different mathematical concepts and techniques. If they feel difficulty in these, then taking the help of an IB tutor can prove to be quite beneficial.

By following these steps, students can increase their chances of scoring highly on their mathematics internal assessment and contribute positively to their overall grade in the IB Mathematics course.

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Written by: Charles Whitehouse

Charles scored 45/45 on the International Baccalaureate and has six years' experience tutoring IB and IGCSE students and advising them with their university applications. He studied a double integrated Masters at Magdalen College Oxford and has worked as a research scientist and strategy consultant.

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37 IB SL Math IA Topic Ideas that Actually Work!

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• Writing Metier

If you are here because you are stuck with an idea for your IB Mathematics Standard Level (SL) essay topic, you have come to the right place. We understand that the IB Math is the toughest subject (no kidding, we feel you) and therefore, we are here to aid you as much as we can. In this read, we are sharing a list of good Math IA topics for your ease.

Order originally written ⏩ Math IA ⏪

Before we proceed with the topic ideas, let’s fill you in with some basic pointers on the IB SL Math essay. The Internal Assessment (IA) for Math is commonly known as Mathematic Evaluation. This is a written assignment in which students are required to investigate a specific area of math subject. Students are encouraged to take a different take through this assignment, a different angle on the mathematical practice.

One of the mistakes that students commonly make is that they take this IB assignment very lightly. The IB Mathematics internal assessment makes up 20% of the entire grade . Rest assured, it definitely does not need to be taken lightly. And, of course, it is a lengthy assignment; consists of 6 to 12 pages that focus on demonstrating a student’s knowledge on a comprehensive assessment, requiring them to draw conclusion and arguments through formulae, graphs and more.

Why Do You Need to Choose an IB SL Math IA Topic of Interest?

Be it IB SL Maths IA topics or any other assessment or extended essay topic, whenever the topic is of your choice, it shows in the final outcome of the essay. Studying the concepts of Math is one thing, but interlinking the concepts with theory, abstract and evaluating a long report is an entirely different ball game.

When you are looking for topics and research questions, you need to go for one where you think you can put your mathematical knowledge and skills into good use. The topic should be the one which makes you excited. For instance, if you are into basketball, as a mathematician, you can always correlate the two varied but interlinked subjects. How? Well, that’s for you to decide.

Remember to Stick to the Criteria of the IB Internal Assessment

The common mistake students usually make is that they go out of the syllabus and go for complicated mathematical concepts. This is not only a bad idea but also leads to one wasting a lot of valuable time.

-Check another article on the best IB Chemistry IA topics and Economics IA ideas or ESS IA Topics for SL and HL level students-

How to steer away from this problem? Simple: stick to the syllabus. This is the ideal way for one to showcase their knowledge as well. Just be sure that your Mathematical IA addresses five concerns:

• Use of mathematics
• Reflection of mathematics
• Personal engagement
• Mathematical presentation
• Communication

Following this pattern will allow you to form a clear structure of your assessment as well.

Now, Let’s Look Into the Different Math IA Ideas

In this article, we have compiled a list of 22 topics you can choose for the International Baccalaureate standard-level Math Internal Assessment . You can, of course, select other topics and research questions of your personal interest that meet your requirements.

1. Month Hall problem

Looking into Bayesian probability work as a real-life example and add some sort of complexity to this Maths IA topic.

2. Pythagorean triples

See the Pythagorean triple and analyze the number patterns.

3. Pascal’s triangle

The infamous IB maths assessment is to discover patterns in the array of numbers.

4. Cracking a password

If you were to guess a password, how long will it take for one to do that? Furthermore, how safe does the password get when you add numbers and symbols to it?

5. The toast problem

If you are standing in a room full of people, how many toasts would you need to see that everyone has a toast?

6. Rock, paper and scissors

While playing the game, I got rock, and I won. Is it important that I make changes in the next round? Or should I choose rock again?

7. The Risk of Insurance

Investigating asymmetric information to see how sure we are of the future, concerning the various risk-averse situations.

8. The Tragedy of the Commons

The population of fish, for example, is reducing. As such, we how do we need to reduce the consumption and production to retain fishes?

9. Modeling Virus and its Spread

In case of a virus, how long will it take for the entire population to be wiped if there’s a deadly virus all over the world?

10. Normal Distribution

You can use the distributions to study a financial crisis.

11. Mathematics and photography

Explore the relationship shared between the geometric sequence and a camera’s aperture.

12. Cryptocurrency

You can also have a look at this short video where you will find some other topic options. It will take only a minute of your time.

13. Valuation of stock price

Using various mathematical techniques like Linear, Exponential, Quadratic, and Logistic Regression for valuation of the stock price of Facebook Inc / Microsoft.

14. Modeling, average rise in temperature

Mathematical Modeling for Melting of Glaciers and evaluate its relationship with an average rise in global temperature.

15. Carbon dioxide emissions

Evaluating relationship between change in Carbon dioxide (CO,) Emissions and the % Decline in forest-covered Area for the period between 1992 and 2016

16. GDP, population

Evaluating the effect of Gross Domestic Product (GDP) per capita on the severe food insecurity in the population of 90 countries in the year 2018 using linear and non-linear regression?

17. Unemployment, Pearson’s correlation coefficient

Evaluating the relationship between unemployment and prison population using linear regression and Person’s correlation techniques.

18. Probability distribution

Evaluating various mathematical models including SIR and probability distribution for coronavirus epidemic

19. Human development index

Evaluating relationship between Human Development Index (HDI) values and rankings on the mortalities for patients suffering from brain and heart-related diseases.

20. Integrals

Modeling a function for cooling hot chocolate cup using integrals

21. Board games

An exploration on increasing the efficiency and chance of winning in the board game monopoly

22. Hen Eggs

Modeling the volume, and surface area of a Hen Egg using Geogebra and integrals

Need more examples of Math IA topics?

And for those of you who have been waiting for an update, I’m adding more options to make it a total of 37 examples of Math IA topics that follow IB Math SL IA format and general rubric and criteria.

23. Solar System Orbits

Using Kepler’s laws and elliptical geometry to model the orbits of planets in our solar system. Analyze the accuracy of these models compared to actual planetary positions.

24. Network Optimization

Study the optimization of networks through various algorithms like the shortest path algorithm or minimum spanning tree, and apply them in real-life scenarios such as traffic flow or logistics.

25. Sports Analytics

Use statistical methods to analyze sports data. For example, evaluate a soccer player’s performance by analyzing goals, assists, passes, and other metrics.

26. Game Theory and Economic Behavior

Understand the mathematical models behind decision-making in economics. Analyze different strategies in hypothetical economic scenarios and predict outcomes based on different choices.

27. Fourier Series in Music

Analyze the mathematical representation of musical sounds using Fourier series. Examine how different instruments produce unique waveforms and how these can be broken down into sine and cosine functions.

28. Population Growth Models

Examine different mathematical models for population growth such as exponential growth, logistic growth, and their applications in predicting population trends.

29. Math in Art and Architecture

Explore the presence of mathematical concepts such as symmetry, geometry, and fractals in art and architecture. Analyze the use of the Golden Ratio and other mathematical principles in famous architectural structures.

30. Optimal Strategies in Games

Study game theory to understand optimal strategies in games like chess, poker, or tic-tac-toe. Analyze how different strategies affect the outcome and how players can optimize their choices.

31. Predicting Weather Patterns

Use statistical methods and historical data to create mathematical models for predicting weather patterns. Analyze the accuracy and limitations of these models.

32. Mathematics of Voting Systems

Explore the mathematics behind different voting systems like First-Past-The-Post, Proportional Representation, and Ranked Choice. Evaluate how each system affects election results.

33. Traffic Flow Analysis

Use mathematical modeling to analyze and optimize traffic flow through a network of roads. Study the impact of traffic lights, road layout, and traffic density on overall traffic flow.

34. Chaos Theory and the Butterfly Effect

Explore how small changes in initial conditions can lead to drastically different outcomes in complex systems. Analyze real-life examples and mathematical models to understand the concept of chaos theory.

35. Fractals and Natural Patterns

Investigate the occurrence of fractals in nature such as fern leaves, snowflakes, and coastlines. Explore mathematical models that replicate these natural patterns.

36. Price Optimization

Use mathematical models to determine the best pricing strategy for a product or service to maximize profit while considering factors such as demand elasticity, production cost, and competition.

37. Graph Theory in Social Networks

Analyze the structure of social networks using graph theory. Explore how information spreads, how communities are formed, and how influential nodes can be identified within the network.

By choosing any of these best Maths AI topics, students can delve into intriguing mathematical concepts and their applications in the real world for their International Baccalaureate standard-level Math Internal Assessment, solving math problems while working on their Maths IAs.

For those of you who are searching for differences between IB Math AA and AI , or looking for other IA topics for Math studies, make sure to read our article about IB Math AA ideas .

Start writing your Maths SL IA

Hope this article helps you in choosing the SL mathematics assessment topic following the IA marking criteria . Should you need custom topic ideas for your IB Internal Assessment as per your instructions, please contact our support team or our Math assignment writers .

Yes, topic selection is extremely important. If you are to choose a topic yourself, remember to use simple and clear language and stick to the topic and research question that meets your interest criteria. Like you always do with good math topics for IB EE , you should focus on what you like first. This is where you better start and finally get a good mark.

Get help with your IB Math IA 🆘

Furthermore, If you need assistance in writing an IB Internal assessment, extended essay , or looking for help from theory of knowledge ( TOK essay ) writers , you are always free to contact Writing Metier .

Free topic suggestions

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Vasyl Kafidoff is a co-founder and CEO at WritingMetier. He is interested in education and how modern technology makes it more accessible. He wants to bring awareness about new learning possibilities as an educational specialist. When Vasy is not working, he’s found behind a drum kit.

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Tes Maths: Projects, investigations and enrichment tasks

Tes resources team.

Take a trip off-plan and get creative with your maths lessons with projects, investigation ideas and enrichment tasks

As the final half-term of the school year approaches, there may be time to do something slightly different in your maths lessons. Perhaps an investigation to apply the knowledge and skills students have acquired over the year, a project to allow them to work creatively as a team to produce something special, or an enrichment activity to show students just how interesting maths can be. Whatever you have in mind, explore this selection of resources from the Tes community for some inspiration.

Investigations

Investigations offer an opportunity for students to pull together the skills and knowledge they have learned over the course of the year and to apply them in a different context.

Maths Investigations

Binomial Distribution Investigation

Assorted Investigations

3D enlargement investigation

Angles in polygons investigation

Much like investigations, projects prompt pupils to use and apply their knowledge, often with the option to work as part of a team in a fun context.

Build the School Project

Functional Mathematics: Design a Bedroom

DATA PROJECT

Make A Million - Maths Housing Design Project

KS3 Finance/Investment/Business Maths Project

The end of the year is the perfect time to stop worrying about whether something is on the GCSE/IGCSE or A-level syllabus and to challenge students with some interesting mathematics.

Theme Park - Enrichment Activities

Creativity in Maths

Emergency maths cover lesson? Enrichment materials

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Extended Tasks for GCSE Mathematics

This series, which formed a support package for GCSE coursework in mathematics, was developed as part of a joint project by the Shell Centre for Mathematical Education and the Midland Examining Group. The project followed the announcement in January 1984, by Sir Keith Joseph, the then Secretary of State for Education and Science to introduce a new common 16+ examination in England, Wales and Northern Ireland. This new examination, the General Certificate of Secondary Education (GCSE) included coursework which formed part of the school-based assessed element. Teachers were being asked to adopt a different role from that which they had previously, and in most cases successfully, used. There were to be new methods of assessment, carried out in the classroom, and a greater emphasis on practical and investigative work. These materials discuss the changing roles of teachers and students and offer ideas, suggestions and examples of investigations carried out by students along with extensisve teacher's notes and guidance. This resource comprises: *The Teacher's Guide *IMPACT - a departmental development programme *Eight books of investigations classified into four categories *Pure investigations, Statistics, Practical Geometry and Applications. Each of the eight books offer a lead task which is fully supported by detailed teacher's notes, a student's introduction to the problem, a case study, examples of students' work which demonstrate achievement at a variety of levels, together with six alternative tasks of a similar nature. The alternative tasks simply comprise the student's introduction to the problem and some brief teacher's notes. It was intended that these alternative tasks should be used in a similar manner to the lead task and hence only the lead task has been fully supported with more detailed teacher's notes and examples of students' work. The books conclude with comments from an examining board moderator.

• Mathematics
• Open-ended task
• Teacher guidance
• Include Physical Resources

Practical Geometry

These two books from the Shell Centre are part of the Extended Tasks for GCSE Mathematics support material produced for students as they pursued practical geometry tasks within any mathematics scheme. The practical geometry tasks were intended to stimulate students'...

Applications

These two books from the Shell Centre focus on applications. The tasks are intended to stimulate students' interest in, and understanding of, the world in which they live. As they pursue these tasks students will be involved in selecting materials and mathematics to use...

Pure Investigations

These two books from the Shell centre focus on the pure investigations. The pure investigation tasks are, perhaps, rather different from the other two main types of extended task, those of a practical nature and those of an applied nature, in the sense that they allow...

Extended Tasks for GCSE Mathematics: Teacher's Guide and Impact

The teacher’s guide from the Shell Centre which accompanies the series of modules to support school-based assessment is the main guide to the materials. It makes some suggestions as to how the materials might best be used. It was not intended that this guide should be...

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Mr Barton Maths Podcast

Long-form conversations about teaching and learning with craig barton, tes top 10 resource collection: maths projects.

The following collection of resources have been assembled by the  TES Maths Panel . They can be downloaded for free by registering on the TES website.

“Why are we doing this, Sir?”, “When are we ever going to use this in our lives?” – Two pretty standard questions that I for one have been asked many times as a teacher. Functional projects are a way to avoid ever being asked this again! It gives teachers a chance to bring lots of different areas of maths together and apply them to a real life situation.

Here are some project ideas for you to use to either bring a unit of work together, or just to have a bit of fun at the end of term.

Pick up and run project

These three resources feature a variety of project ideas with lots of detail. The tasks may need amending to suit the particular needs of your group but if you are just looking for some inspiration, this is a great place to start. There are three levels to choose from; Gold, which is suitable for 16-19 year olds; Silver which is aimed at the 14-16 age group, and Bronze for younger students, typically aged 11-14.

Darts project

Making a drawing of a dart board requires a lot more maths than you’d think, or should I say, what the students think. Your students are going to be practising lots of different mathematical skills without even realising it.

Star project

Like the author says, this project will produce fantastic display work and the students are going to have fun completing it. This might appear to be quite a low ability task at first, but one possible extension could be to introduce algebra to investigate the number of lines drawn inside the circle, for varying sizes of sector.

Code breaker project

This resource has a cross-curricular link with history. Explore the history of code breaking and its uses during the Second World War, but don’t forget about all the maths that goes with it. There are a variety of tasks all based around the concept of cracking codes – very engaging for students.

Build a school project

This project involves students building a model of their own school. They have to go outside and gather all the necessary measurements, construct nets for the different buildings and ultimately construct a miniature version of their very own school. A great way to engage any enthusiastic architects.

Lunar theme park

You won’t have any problems getting them on side with this task. Students get to design their own theme park, choosing which rides they would like to put in there and ultimately have to calculate the running costs of their park. From the cost of building the rides, to maintaining the toilets, and even throwing in a bit of advertising to boost the number of visitors, this sounds like a lot of fun.

Rocket project

I’ve seen this task completed many times by science teachers, but why should they be the ones that get to have all the fun? There is plenty of maths to be explored here and you’ll struggle to find a student who doesn’t want to build a rocket and fire it up into the sky.

Project office

There are many resources out there on TES Connect that involve designing a particular room, whether it is a classroom, bedroom or student common room. The maths that accompanies each project is very similar but I chose this resource on designing your own office space because of the visual stimulation that the author has included in the presentation. An initial ‘hook’ is needed for some students when being introduced to a new project and this resource has it.

Average student

What would the average student look like? What would their likes and dislikes be? Students can take this task in whatever direction they wish, whether they decide to look at the physical attributes of the ‘average’ student or focus more on the personality. This comes with a slight warning regarding the ’personal-questions/sensitive-students-combo’ but apart from that, it sounds like it will be a very interesting task indeed.

Plan a holiday

This project has an obvious cross-curricular link with geography and seems like it will be a huge amount of fun to complete. I doubt you will come across a student questioning when they are going to ever need this in their lives, unless they are planning on never going on holiday. Students have the option of staying in cheap, hostel like accommodation or choosing to go for the more upmarket 5-star resorts.

Phil Eden,  TES Maths panel

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75+ A-Level Computer Science NEA Ideas (and why they’re good)

In A-Level by Think Student Editor March 9, 2019 6 Comments

Computer Science at A-Level is sometimes misunderstood as being a subject where all you do is sit in front of a screen, coding away in Python, trying to build the next Google. While a lot of your time is spent staring at a computer screen, it’s not just about coding.

There is a theory side to Computer Science which plays a big role in determining what grade you get at the end of your two years. Your NEA will take a lot of analysis, planning and trial and error which many students do not expect. That’s why below I’ve provided a long list (in no particular order) of project ideas so at least one step is taken out of the equation. You can combine some of these ideas and create a Frankenstein-type project or maybe just take one and make it your own.

Remember, refer to the mark scheme to ensure you hit as many A-Level Computer Science skills as possible. It’s always worth taking a look at your relevant specification to see which skills you want to showcase, you can find specifications for OCR and AQA here. Without further ado, let’s get to it.

1. Maze Generation Software

There are many different algorithms that you could implement when programming a maze generator (like a lot). So, if you want a list on the different algorithms you could possibly implement, check out this article.

2. Rubik’s Cube Solver

This is probably the hardest project idea on this entire list – in terms of the actual implementation. Creating AI that can actually learn how to solve the Rubik’s cube is very, very difficult.

The good news however, is that I don’t think examiners will expect you to create AI that learns how to solve the Rubik’s cube entirely by itself. Therefore, if you do choose this idea, I highly recommend that you program your AI around one of the many pre-existing algorithms that have been created to solve Rubik’s cubes.

In my opinion, this is the best algorithm for you to base your AI around.

3. Bird Migration Pattern Predictor

If you actually pull this one off, I would eat my foot if you didn’t get top marks (an A*).

For this project, you will need to analyse how birds have migrated across the globe in the past. Then you will need to try and find correlations between migration patterns and geographic weather conditions. From this data, your program could predict future migration patterns depending on different climate changes.

I think a great start for this idea is to read into what web-scraping is and how to do it.

4. Nuclear Power Plant Meltdown Simulation

While programming this project, you would have simulate real world conditions. After you have created this Earth-like environment, you can model the effects that a nuclear power plant meltdown would have on said environment.

You could even add cities to see the affects that radiation would have on them too.

5. Supermarket Stock Management System

Supermarket’s not only need to manage stock, but also staff – both of which, they have lots of. This means that there is most definitely an opportunity for you to make a complex system that could aide a supermarket.

If you do choose this, make sure you read up on how a supermarket actually operates, so the system is suitable. There’s a great document here that should tell you all you need to know about managing a supermarket (and a lot more).

6. Restaurant Point Of Sale (POS) System

A point of sale system is very different to a stock management system (as you would find in a supermarket). The difference is that a point of sale system is used (guess what) at the “point of sale”, meaning staff will use the system at restaurant tables when taking food orders.

Therefore, you must make sure your POS system has an extremely friendly user interface, as customers don’t like waiting around!

7. Chess Playing AI

I don’t think I need to tell you that this is going to be challenging… Therefore, if done right, this could lead to a well earned A* for your NEA.

There are so many resources to help you develop this particular project idea online. So, whenever you get stuck, you will never be far away from help.

8. Image Recognition AI

I reckon this is probably equally as difficult as the Rubik’s cube one – AKA very, very hard.

This idea should be screaming at you: “machine learning and neural networks”. If it’s not, there might be something wrong with you…

Neural Networks + Machine Learning = High Marks

There are loads of free online resources that will help you a ton. However, I highly recommend that you get this book off Amazon.co.uk , it is the best book on getting started with neural networks that I have ever read – just going to have to trust me on this one.

9. Evolution Simulator

This project has the potential to be seriously complicated, however, you could also make it quite simple. It all depends on what’s evolving.

If you are going to simulate how animated stick figures get better at running over many generations, your program is going to be very complex. However, if you are going to simulate how a single-muscled slug can get better traveling between points as quickly as possible then it could be quite simple.

If you’re even considering this project, then you should definitely check out this YouTube playlist (it’s strangely satisfying watching his imaginary creatures evolve).

10. Voice Recognition AI

This project is (obviously) very similar to the image recognition project that was aforementioned. Therefore, this project too, should be screaming “machine learning and neural networks” at you.

I’ve never really programmed a voice recognition AI before, therefore, I can’t really recommend any specific books for you to get (as I can’t be certain of their quality). However, I have done a quick google search and within 5 minutes I can tell that there is shed loads of information on this topic, so on that front – don’t worry.

11. Sales Order Processing System (SOP)

An SOP system should, as the name suggests, manage sales. This means it should control the majority of communications between the warehouse, sales team and the client.

Below are things that a typical SOP system could do:

• Store Order History
• Generate Invoices
• Generate Reports
• Generate Delivery Notes
• Send Reminder Emails

You are tied down a bit with this project, as you do have to make sure a factory could actually use this software. However, there are still many different avenue’s for you take with the types of functionality you decide to implement.

12. Poker Game

For you to do this project, you would have to be fairly confident with networking. This game would allow multiple devices to join a “table” and start playing poker with each other.

Depending on how complex you want your program to be, you could add so many extra features. I think a great extra feature for this project would be to calculate the odds of someone winning per hand. Furthermore, you could also add a computer poker player (where you could definitely implement some AI).

13. DJ Software (Can Mix Music)

This one is definitely a fun project for those of you who have an affection for music. This project would clearly require you to learn a shed load about manipulating audio files, however, if you can pull it off I think you could really make a project that is A* worthy.

You could also build a control system which could implement the software. This might cost a bit of money, but once again, it’s going to make you like you really know what you’re doing.

14. Interactive Circuit Builder

If you want to know what I’m on about, get the free trial of Logicly or just go on YouTube and look at a video of someone else using Logicly.

Assuming you have done that, you will know what I mean by an “interactive circuit builder”. I would say that the most important aspect of this project would have to be the UI. Without a good user interface, the software would not be fit for purpose and you would definitely lose marks.

15. Quiz App

You could either make an offline quiz app or you make a much more complex client-server quiz style app. There is definitely much more opportunity to get an A* with the latter of those options.

If you decide to do a client-server model, I think a real time quiz app would work great – something (even remotely) similar to Kahoot would really stand out.

16. Software for Calculating The Big O of an Algorithm

Examiners will absolutely love this one, but why?

Because in doing this project, you would be making a computer science theory topic actually come to life. Therefore, if you do this project, you are showing to the examiner that you can get a concept off paper and actually make use of it in a real situation.

Besides that, this project is amazingly complex and will certainly provide you with plenty of opportunity’s for you to incorporate A* level concepts into your program.

If you have forgotten what Big O is, don’t worry (you should worry a bit actually) and just go give this a read.

17. Tracking And Monitoring Global Shipping Routes

This project is going to require you to get comfortable with web-scraping and API’s. You will need to be able to gather information about the global whereabouts of cargo ships frequently.

Once you have mastered the back-end tracking, you will need to think of a nice way to present the data. Maybe you could use certain programming libraries to make route representations on a global map?

18. Implementation of Machine Learning To Maximize Profits At An Airport

This could be my favorite project idea on here.

The lengths that airport companies go to when designing the layout of a particular airport is crazy. Everything is where it is for a reason: the route you take to board a plane, where you wait to board and the even where the security is. If you want more information about how airports maximize profits, check this out.

If you choose this project, I think you should do a simulation where people are represented by a particular sprite, shape or whatever you choose, and then they you follow them through the airport. After each day you could track the profits that the airport made.

Now this is where machine learning comes in… you could implement an algorithm that changes the layout of the airport each day and see if profits increase or decrease. Then the program would learn accordingly.

19. 3D First Person Shooter Game

Although many people choose to program a 2D game for their NEA, I think that programming a 3D game is just… better. Programming in 3D makes it so much easier for you to implement A* level programming techniques.

20. Implementation of AI To Model The Effects of Global Warming

Global warming is becoming an ever increasing issue in today’s world – so this project certainly checks the box “assists with a real world problem”.

Anyway, designing a program (using AI) that can attempt to predict what the effects of climate change are going to be on the planet is a great idea. It’s complicated enough, time-consuming enough and definitely “real worldy” enough.

A great place to start with this project is to check out the currently predicted effects of climate change, which you can find here.

21. Encrypted Instant Messaging App

An instant messaging app is one thing, but an encrypted instant messaging app is a whole different thing. This project is great because it just ticks so many boxes. You will be covering encryption and client-server networking in the same project!

Before you start this project, make sure you take out the different types of encryption methods (you can find some here).

22. E-Commerce Web App

Almost every single large company out there now has an online e-commerce website. Therefore, there is going to be plenty of helpful resources out there for you to learn from.

This project will also require some encryption as you will be dealing with payment methods such as debit and credit cards, which are VERY much confidential information.

23. Fitness Monitoring App

Programming a fitness app will allow you to actually interact with the hardware that is on the phone. For example, you could have a fitness app that tracks footsteps, in which case you would need to directly communicate with the phones pedometer.

24. Virtual Flashcard App

This can be a great project, if done right.

You’re going to have to get very good at databases if you do this project as a virtual flashcard app would require crap loads of them. A great example of a virtual flashcard app is Quizlet (I’m sure you have head of it already).

A simple virtual flashcard app should allow a user to:

• Create Folders For Different Subjects
• Create Flashcards Sets For Particular Modules
• Revise Flashcard Sets Effectively.

25. Public Transport Timetable App

Now, I don’t mean just display a PDF image of a pre-existing bus timetable and say “finished!”…

This app should be able to perform web-scraping on live bus and train timetables and display the information is a user friendly way.

Your program could even take two postal codes and calculate the quickest way to get there using a mixture of public transport and walking. It could also return the current price for that specific journey. An example of how this can be implemented is on the Stagecoaches “Plan A Journey” page.

26. Social Networking Platform

You all know what a social networking platform is. I don’t think I need to explain this one to you…

27. Physics Projectile Modelling Tool

If you are a fan of mechanics, this is your project. One of the many reasons this project is so good is because when programming it, you are forced to simulate a real world environment – in the sense that you program in gravity, terrain, air resistance etc.

Furthermore, if you were so inclined, you could very easily transform this project into a game, where you try to hit particular objects using a projectile. Angry birds is a great example of what I mean.

28. Nuclear Power Plant Management System

There’s more to managing a nuclear power plant than you think. Therefore, a nuclear power plant management system can either be super simple or extremely complex depending on what you choose to implement into the system.

I highly recommend you check out this link , it tells you all about the parts of a nuclear power station and you will get a feel for what your system will be managing very quickly.

29. Weather Forecasting Software

There are many paths you could take with this particular project, so it’s really down to what you decide. However, the fundamental core of this project is that you need to at least make an attempt at predicting what the weather will be like tomorrow, the day after or perhaps even a week from now.

You could implement some kind of machine learning algorithm that could compare what your weather prediction was and what the weather actually turned out to be like. From here, the algorithm could adjust the factors that went into making the prediction accordingly.

30. Air Traffic Controller AI

Air traffic controllers are essential to ensure that planes aren’t going to collide when coming in or going out of an airport. However, humans tend to make mistakes – fairly regularly. Maybe an AI would always get it right?

For this project, you would have to create a model of an airport and simulate planes coming in and leaving. Your, AI would ensure that no planes crash… hopefully.

31. Interpreter For Chosen Programming Language

Interpreters convert high level language code into machine code that can be directly processed by the CPU. Furthermore, interpreters normally translate code per line, not all at once.

Although this programming project is challenging, you might struggle to incorporate some of the A* level programming concepts in your code. All I’m saying is that make sure you keep an eye on the marking criteria and don’t forget why you’re doing this project – to get the grades!

32. Internet Speed Tester

There’s more that goes into getting an accurate assessment of your internet bandwidth than you think. Therefore, making an internet speed test is definitely complex enough.

For this project, you will need to add feature to bulk it up. You could maybe try different methods of testing internet speed then compare how accurate each of them are.

33. Secure FTP Server

FTP stands for File Transfer Protocol. So this project would basically be making software that allows devices to easily transfer files between each other. I know I’ve said this a lot, but, once again, this project is going to be as complex as you make it.

If you choose this project, make sure you don’t just use an FTP library that does everything for you! Try and do as much as possible by yourself.

34. Software To Find The Best Online Deals

For this project, you’re going to need to “scrape” all of the current prices for a particular product off their respective websites. That’s the hard part. Next, you will have to present all of your various comparisons to the user in an easy-to-understand way (and give a conclusion containing where they can find the cheapest price).

A great example of this type of software is the website Trivago.

35. AI Chat Bot

This project would entail you creating a program that can talk to humans as if it was a human too. If there was such thing as a perfect AI chat bot, you shouldn’t be able to distinguish it from a human.

When programming this, you are going to need to be able to program in some sort of artificial intelligence that can learn from previous conversations it had with real people.

Two examples of chat bots that I have seen before are CleverBot,   Eviee, and more recently ChatGPT.

36. Search Engine

Examples of search engines are: Google, Bing and Yahoo. There role is to receive a query from a user and index webpages in accordance with how relevant they are to the particular query. So if you googled “what is a pineapple?”, the idea is that a webpage containing information about pineapples would come up first before information about bananas.

There are many factors to consider when ranking webpages. Possible ranking factors for your SE could be:

• Keyword Frequency
• Image ALT Tags
• How Users Have Interacted With Page Previously.

37. AI Spam Filter

If you’ve ever been directly (or even indirectly) involved in front-end website development or survey development, you will know how big of a problem spam is. Spam messages can take many forms and with each passing year, it is getting more and more difficult to decypher what messages are genuine and which are spam.

This means that for your A-Level Computer Science NEA project, an idea could be to build a spam filter that could be run on an email server, implementing AI and Machine Learning. There is huge potential with this project idea and it is certainly not an easy one to develop!

38. Music Suggestion Tool

We’ve all used and heard of the famous YouTube recommendation service… Every time you go on YouTube, they have an algorithm running that recommends videos based on what they think you’ll like. Why not make your own version but just for music?

You could even tailor the recommendations to what mood the person is in by analysing music videos for particular themes e.g. sad, happy or exiting. If you did decide to go down this route with your NEA project, there is huge potential with this idea for machine learning implantation which would be designed around user feedback (user specifies whether or not the recommendation was good).

There is a great video on how the YouTube recommendation algorithm works here.

39. Graph Plotting Software

If you’re currently studying A-Level Maths or A-Level Further Maths, you will know the importance of graph plotting software is very high. So, there’s demand, why not provide the supply in the form of an NEA computer science project?

Your project could receive a polynomial expression as an input, and output (plot) a visual graphic of that graph… There are many examples of these types of software out there, one that you should check out is GeoGebra .

40. Foreign Language Teacher

This project idea could be made extremely basic, or extremely advanced. However, the fundamental building blocks of this project idea will always be the same; it will assist users in learning a foreign language. I don’t think I need to say too much about this idea, but I would recommend you checkout examples of this type of software such as Babbel or Duolingo.

41. Sat Nav

This NEA project could potentially consist of both web-scrapping and Dijkstra’s algorithm. That is a seriously nice combination!

What is not immediately obvious about this project idea is how much graphical work there is to it – there’s a lot. All I’m saying is that if you do decide to choose a project idea similar to this one, be sure that your graphical skills are very strong!

The most obvious example of software similar to what’s mentioned above is Google Maps, go check it out , if you’re interested.

42. Make Your Own IDE

Now this might seem intimidating at first but hear me out. There’s lots of resources out there to help you out on this project and it allows you to be as creative as you want since you’re the designer. You should be able to run, debug and compile the code.

You can use this video and this article to get you off to a good starting point.

43. 2D Platformer Game

This A-Level NEA project allows you to be as creative and go into as much detail as you want. You could include enemies, randomly generated levels, level editors where the player could make their own levels, multiplayer capabilities etc. One of the more challenging things you could do is include the ability to save your position and access it later.

This project will really get your creative juices flowing as, even if someone has the same idea as you, your games could come out wildly different. You can find many game making tutorials, particularly in Python. You may have heard of the popular library pygame which most games in Python are based on. You can click here to find a tutorial on the basics of pygame.

44. 3D Platformer Game

This will certainly push you into the top marks as it requires a deeper understanding of how to render vector graphics and some maths. Remember, the examiners aren’t worried about how good the game looks, they want to know about the complexity of your code and the skills you showcase within it. Some of the most popular libraries include OpenGL (in C/C++) and Panda 3D (Python).

One of the advantages of doing a 3D game is that the game itself doesn’t actually need to be very complicated. If all goes well, the complexity should come from the 3D rendering, meaning your game could be relatively simple.

45. Revision Aid

This idea is very popular amongst students as they likely already use one, or are taking this opportunity to build their own. This can be anywhere from a flashcards application to a quiz or a game where you have to dodge the wrong answers. See Quizlet or Anki for inspiration.

As with the platformer, the scalability of this project is up to you and how complex you want to make it. Maybe you want to have a competition element where users get a score for how many questions they get right. This project will require a knowledge of databases (e.g. SQL) so if that’s something you’re not good with then there’s still a few more to go.

46. Circuit Simulator

This project is heavily centred around a good-looking GUI, so you will need to have an immense amount of self-control to ensure you don’t throw away hours and hours into a part of the code that barely gets you any marks.

The idea is based around an interactive, online version of a circuit builder, allowing users to connect resistors, lamps and other electrical things I don’t know the names of using wires. You may want to make use of TKinter , a python library, to help with your GUI.

47. Live Chat Forum/Room

This one is pretty self-explanatory but requires a deep knowledge of networking and client-server communications. There are many tutorials you can find online on how to create chat software which is where your creativity will need to come in.

You could think about allowing users to send pictures, create their own group chats, send videos etc. You could even create an AI moderator which censors inappropriate language or detects inappropriate pictures and takes them down.

48. Robotics

This seems quite vague but what I mean is using code to control and communicate with a robot that serves a certain purpose. For example, you could code a robot vacuum to detect walls or the size of the room, where dirt is etc. You can do this through image recognition which by itself is very complex and high level, securing you those marks.

The biggest thing with this is that it requires you to have access to the required hardware so you can check if it works correctly. With the robot vacuum idea, you’re going to need to have a robot vacuum on hand.

49. Business Rota Application

Some of you might have part-time jobs, in which case you will have a better idea of what this is. In order to make sure too many people aren’t working the same shift at once, businesses often have a rota which keeps track of who goes where and at what time.

You could create a database with a simple GUI which considers new employees and their shifts and orders them accordingly. This ensures shifts aren’t clashing or overlapping. You could make this as customisable as you want to where it could apply to any business who have any number of employees working at one time or several related times.

You may need to get into contact with a real business and analyse their current system. That way, you can find anything wrong with it and improve upon it. It also means you have a bit less work to do because you aren’t starting from scratch.

50. Recreate a Classic / Retro Game

This takes away the element of coming up with brand new game logic. Instead, you have the rules laid out for you and you just have to follow them. However, there is a definite danger of copying and pasting premade code as the game already exists. Try to add your own twist to the game.

For example, you could remake Pacman but instead of having the ghosts controlled by AI, you could have them be controlled by other users. Not only is this complex, but it also ensures your code isn’t identical to the original game. There’s a whole library dedicated to retro game making in Python which you can find here .

51. Weather Forecaster

As boring as it sounds, it has the potential to get you into that high grade band. It may require some web-scraping and you might want to build your own site to display this info. You could show the predictions for the weather on this site and you could allow the user to enter their email to be sent alerts or notifications if extreme weather is to occur.

52. GPS App

Here’s your chance to implement all those path-finding algorithms your teacher might have been telling you about (I’m looking at you Dijkstra ). You can implement this in different ways, whether it’s the “Google Maps” approach where the user defines a destination or the “Find My iPhone” approach where the destination is unknown by the user until the app is activated. Maybe they want to put a GPS on their kid’s device or their own device.

53. Meteor Trajectory Simulator

If you like space or physics, this one is for you. You can really go wild with this in terms of the GUI and the back-end code. It will need a lot of complex mathematical formulae in order to function correctly, but it will be worth it when you get that top A-Level grade. That’s why having at least some interest in mathematics will benefit you in this project. You’ll be working with a lot of numbers whether that’s calculating velocity or determining the angle of a meteor.

54. 2D Shooter

This is similar to the platformer except the focus will be on the shooting aspect. You could use AI to control the enemies and maybe include different levels of guns that do different damage. You could even do a boss battle. Refer to NEA idea two to find a pygame tutorial which should give you a good base on making the game.

55. Street Fighter Remake

If you’ve ever played or heard of street fighter, you know what you need to know. However, for the three people at the back who have never heard of it, it’s a 2D fighter game. You can customise this however you want and include power ups, boss fights etc. You may need to look at the code of several other similar games to combine them and make your own.

56. Finding the Shortest Route on the London Underground

This project will allow you to use the path finding algorithms and maybe a website. You can calculate the shortest distance between two stations and calculate the time taken to get there. You will probably need to do some research on JavaScript in order to get the backend of your website working. I’ll link a website tutorial here to get you started.

57. Workshop / Club Booking Timetable

Similar to the rota system, this project will ensure that two people are not booked at the same time on the same day. This will require a knowledge on relational databases, namely SQL which, at this point in your A Level, you should know a bit about. If not, there’s a quick project you can do to get yourself familiar with queries, primary keys, foreign keys etc.

58. Visualising the Spread of a Disease

You could web-scrape here and show on a map of the world and the associated deaths from a certain disease. In other words, you could for example show hot spots for the disease in reds or oranges and leave the others as white. Web scraping is a relatively easy thing to learn and can be extremely powerful, even outside of your A-Level. Here’s a quick tutorial to get you started. The complexity will come from how you present the data you’ve scraped.

59. Plane Seat Booking System

This will be like the workshop booking system in that you need databases to store the customer’s information. You would ensure that one seat is not offered to two people at once. You could even keep track of the details of loyal customers and offer them first class tickets or other deals.

60. Stock Management System

This would be a database which stores the amount of stock a business has. You could produce sales reports for the most popular items or see which items are low in stock. There are many combinations of ways you could output this information (e.g. a report, website, email). Just ensure it is more complex than placing the output in the terminal.

61. Traffic Light Controller

This project entails coding an AI to ensure that cars don’t collide. You could possibly set it up where, if there’s an ambulance, you give it all green lights. You might even want to use image recognition based on a satellite image of a city and gather the locations of the traffic lights on that image. That would really push your grade up as, instead of using a built in library, you can “teach” your AI what traffic lights look like. Find a video tutorial on machine learning in Python here .

62. Coupon Collector

If you’ve ever heard of “Honey”, you’ll know the gist of this project. You will have to scrape the internet for coupons for a certain website specified by the user. The code could automatically test these coupons and output the cheapest one. See number 17 for a website scraping tutorial.

63. Facial Recognition Software

This project seems complex but that’s a good thing if you want the highest grade. This has a variety of purposes as many of you are likely familiar with the face recognition on many phones. Read this article o n how the basics of how to do it in Python and find out more.

Make sure you aren’t just relying on built in libraries to handle the complex algorithms because all those marks will disappear. You have to write the code yourself and typing “import facialRecognition” doesn’t count, as sad as that is.

64. Chess Over Two Computers

Here you can include networking and client-server communication (both of which are references in the A-Level Computer Science specification). There is a possibility to include AI which detects automatically if there is a check or checkmate. This would require you to keep track of the ending positions of each piece and know what constitutes as a check for example. Most turn-based games rely on a sort of algorithm which you can find out more about here .

65. Sudoku Solver

This requires intense programming and AI but will totally be worth it by the end. You could give the user the opportunity to try and solve it themselves at first then, afterwards, give them the answer. You could also set a time limit, you could have a scoreboard, there’s lots of things you could do with it. Also, you may want to have the unsolved puzzle be randomly generated which adds a whole new layer of complexity. Computerphile has a great video on this exact subject in Python.

66. Social Media Specifically for Students in the Same College or University

A social media idea has already been suggested but you may want to make one specifically for your college. The students could input their timetables and the code could suggest other students with the same timetable. That way, they can meet during their mutual break time. You could also include group chats for specific subjects at your college.

67. Fantasy Football Team

Web scraping is going to be a major concept in this project unless you want to hard code in every footballer on every team. You could set up a network where fantasy teams can “play” against each other and winners get more points. The user can customise their own team and earn points. You can then display it in a website or another GUI like TKinter.

68. Planet Orbit Simulator

This one goes out to the physics and maths students again. Allow the user to change the size, direction and colour (why not?) of planets and calculate the trajectory of their new orbit. This would entail many mathematical calculations so, if you like this sort of thing, this is for you. It also gives you the chance to use and render 3D graphics in order to visualise the planets for the user.

Take a look at the game Kerbal Space Program for an advanced implementation of this idea!

69. Pathfinding Comparer

Here, you would test and visualise the efficiency of certain pathfinders in different situations. For example, the user could place certain obstacles between two points and then employ the Dijkstra and A star path finders. You can find what I mean in a tutorial here . There are many, many, many pathfinders you can compare so you can really pick whichever ones you would like. I won’t list them all here, but you can find a some of them through this link .

70. Finding Shortest Path on a College / University Campus

With this project, you would need to create a graph with each node corresponding to the buildings or departments on the map. This would make more sense if you choose a college or university that has a big campus that spans over a large geographical area. It may end up being very useful for those students who have 5 minutes to speed walk all the way across their campus. The heuristic or weight of each edge could be determined by many things (e.g. whether you have to cross a road, if you have to go through a certain building with stairs etc).

71. Solitaire

This popular card game might be simple to code but to add that layer of complexity, you can include the option for an AI to complete the game for the user. It needs to be able to recognise if the game is completable though.

72. Password Manager

Think “LastPass” or “DashLane”. You securely store and encrypt your user’s passwords and, if you wanted to, you could include a password suggestion element where the application offers a potential strong password to the user. This takes away the need for the user to memorise their passwords and think of a way to make it stronger. You can find an example here and extra info here .

73. Simple Board Game

You might want to come up with your own board game or copy another anywhere from Scrabble to Monopoly. This will take a lot of time and consideration into how you would like it to work. You may want to set up a tutorial or make it multiplayer against other humans (this might be your chance to include AI)

74. Cash register

A cash register would be great as you can base it off pre-existing cash registers in terms of the functionality. It offers a web version of a cash register that would be used by small businesses. This means you could contact small businesses in your area and cater to their needs. It may track sales, inventory and checkout credit cards. The options for what you want the cash register to do are completely up to you and your client’s needs.

This kind of goes under the retro games column however, there is the potential for AI to be implemented. You could program the AI to play the most efficient move and get the most points. The best way to go about this is to code the game by itself first the add the AI afterwards. You can even apply a competitive element by having a score system via relational database or multiplayer functionality.

76. Pacman Recreation

You can use AI to control the ghosts and, to really push yourself, you can add difficulty levels to these ghosts. Maybe the longer/more a user plays, the harder the ghosts get. You can increase their difficulty by making them faster or making them “smarter”. This would require path-finders to find the shortest path from the ghost to the player.

The Importance of Mark Schemes and Specifications

The mark schemes and specifications for A-Level Computer Science will be your best friends throughout your whole coursework experience. Though they can sometimes be vague, you should be working closely with them to ensure your project hits all the points you need so you can collect those marks. Good luck!

• AQA Computer Science Mark Scheme
• OCR Computer Science Mark Scheme

nice project

the exemplar is motion control and thats bares hard

bruh what do i put as stakeholders for the rubiks ai

Your idea is brilliant and many puzzle solvers are going to really benefit from your programme, and for that reason, I’m out.

Hi i was just wondering how i could make the (“visualizing the spread of a disease”) program to show a large amount of skill as I worry that there wont be enough coding involved to showcase a lot of skill.

IB Maths Resources from Intermathematics

IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides

Maths Studies and Applications IA Exploration Topics

This is the British International School Phuket’s IB maths exploration page. This list is primarily for IB Maths Applications SL students (exam in 2021 onwards).  If you are doing IB Maths Analysis (exam in 2021 onwards) then go to  this page  instead.  Scroll down for the full list of possible topics and ideas!

Essential resources for IB students:

1) Revision Village

Revision Village has been put together to help IB students with topic revision both for during the course and for the end of Year 12 school exams and Year 13 final exams.  I would strongly recommend students use this as a resource during the course (not just for final revision in Y13!) There are specific resources for HL and SL students for both Analysis and Applications.

There is a comprehensive  Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and then provides a large bank of graded questions.  What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial.  Really useful!

The Practice Exams section takes you to a large number of ready made quizzes, exams and predicted papers.   These all have worked solutions and allow you to focus on specific topics or start general revision.  This also has some excellent challenging questions for those students aiming for 6s and 7s.

Each course also has a dedicated video tutorial section which provides 5-15 minute tutorial videos on every single syllabus part – handily sorted into topic categories.

2) Exploration Guides  and Paper 3 Resources

I’ve put together four comprehensive pdf guides to help students prepare for their exploration coursework and Paper 3 investigations. The exploration guides talk through the marking criteria, common student mistakes, excellent ideas for explorations, technology advice, modeling methods and a variety of statistical techniques with detailed explanations. I’ve also made 17 full investigation questions which are also excellent starting points for explorations.  The Exploration Guides can be downloaded here  and the Paper 3 Questions can be downloaded here .

Make sure you read the Maths Studies guidance from the IB prior to starting your IA maths exploration – this linked site gives the full list of assessment criteria you will be judged against and also gives 9 full examples of investigations students have done.

Given the assessment criteria it’s probably easiest to conduct a data analysis investigation, though you can choose to explore other parts of the syllabus instead.  To get good marks make sure you carefully follow the marking criteria points given by the IB and try and personalise your investigation as much as possible.  Be innovative, choose something you are interested in and enjoy it!

Primary or Secondary data? 

The main benefit of primary data is that you can really personalise your investigation.  It allows you scope to investigate something that perhaps no-one else has ever done.  It also allows you the ability to generate data that you might not be able to find online.  The main drawback is that collecting good quality data in sufficient quantity to analyze can be time consuming.    You should aim for an absolute minimum of 50 pieces of data – and ideally 60-100 to give yourself a good amount of data to look at.

The benefits of secondary data are that you can gain access to good quality raw data on topics that you wouldn’t be able to collect data on personally – and it’s also much quicker to get the data.  Potential drawbacks are not being able to find the raw data that fits what you  want to investigate – or sometimes having too much data to wade through.

Secondary data sources:

1) The Census at School website is a fantastic source of secondary data to use.  If you go to the random data generator you can download up to 200 questionnaire results from school children around the world on a number of topics (each year’s questionnaire has up to 20 different questions).

2) If you’re interested in sports statistics then the Olympic Database is a great resource.  It contains an enormous amount of data on winning times and distances in all events in all Olympics.  Follow links at the top of the page to similar databases on basketball, golf, baseball and American football.

3) If you prefer football you can also find a lot of football stats on the Who Scored website.  This gives you data on things like individual players’ shots per game, pass completion rate etc.

4) The World Bank has a huge data bank – which you can search by country or by specific topic.  You can compare life-expectancy rates, GDP, access to secondary education, spending on military, social inequality, how many cars per 1000 people and much much more.

5) Gapminder is another great resource for comparing development indicators – you can plot 2 variables on a graph (for example urbanisation against unemployment, or murder rates against urbanisation) and then run them over a number of years. You can also download Excel speadsheets of the associated data.

6) Wolfram Alpha is one of the most powerful maths and statistics tools available – it has a staggering amount of information that you can use.  If you go to the examples link above, then you can choose from data on everything from astronomy, the human body, geography, food nutrition, sports, socioeconomics, education and shopping.

7) Plotly is a great visual graphic site – you can create visually interesting infographics and analyse data from hundreds of other sources.

8) TSM – the Technology for Secondary  Mathematics is something of an internet dinosaur – but has a great deal of downloadable data files on everything from belly-button ratios to lottery number analysis and baby weights.

9) Google Public Data  – an enormous source for public data, which is displayed graphically and can be searched.

10) Nationmaster  – another huge site with pretty much any statistic and data comparing countries.  Currently they have 19 million data points – so you’re likely to find something useful!

11) Google word usage analysis – a great tool which allows you to track the usage of words over the centuries.

Example Maths Studies IA Investigations:

Some of these ideas taken from the excellent Oxford IB Maths Studies textbook.

Correlations:

1) Is there a correlation between hours of sleep and exam grades?

Studies have shown that a good night’s sleep raises academic attainment. 2) Is there a correlation between height and weight? The NHS use a chart to decide what someone should weigh depending on their height. Does this mean that height is a good indicator of weight?

3) Is there a correlation between arm span and foot height? This is also a potential opportunity to discuss the Golden Ratio in nature.

4) Is there a correlation between the digit ratio and maths ability? Studies show there is a correlation between digit ratio and everything from academic ability, aggression and even sexuality.

5) Is there a correlation between smoking and lung capacity?

6) Is there a correlation between GDP and life expectancy? Run the Gapminder graph to show the changing relationship between GDP and life expectancy over the past few decades.

7) Is there a correlation between numbers of yellow cards a game and league position? Use the Guardian Stats data to find out if teams which commit the most fouls also do the best in the league.

8) Is there a correlation between Olympic 100m sprint times and Olympic 15000m times? Use the Olympic database to find out if the 1500m times have go faster in the same way the 100m times have got quicker over the past few decades.

9) Is there a correlation between sacking a football manager and improved results? A recent study suggests that sacking a manager has no benefit and the perceived improvement in results is just regression to the mean .

10) Is there a correlation between time taken getting to school and the distance a student lives from school?

11) Does eating breakfast affect your grades?

12) Is there a correlation between stock prices of different companies? Use Google Finance to collect data on company share prices.

13) Does teenage drinking affect grades? A recent study suggests that higher alcohol consumption amongst teenagers leads to greater social stress and poorer grades.

14) Is there a correlation between unemployment rates and crime? If there are less work opportunities, do more people turn to crime?

15) Is there a correlation between female participation in politics and wider access to further education?

16) Is there a correlation between blood alcohol laws and traffic accidents ?

17) Is there a correlation between height and basketball ability?

18) Is there a correlation between stress and blood pressure ?

19) Is there a correlation between Premier League wages and league positions ?

Normal distributions:

1) Are a sample of student heights normally distributed? We know that adult population heights are normally distributed – what about student heights?

2) Are a sample of flower heights normally distributed?

3) Are a sample of student weights normally distributed?

4) Are a sample of student reaction times normally distributed? Conduct this BBC reaction time test to find out.

5) Are a sample of student digit ratios normally distributed?

6) Are the IB maths test scores normally distributed? IB test scores are designed to fit a bell curve. Investigate how the scores from different IB subjects compare.

7) Are the weights of “1kg” bags of sugar normally distributed?

Other statistical investigations

1) Does gender affect hours playing sport? A UK study showed that primary school girls play much less sport than boys.

2) Investigation into the distribution of word lengths in different languages . The English language has an average word length of 5.1 words.  How does that compare with other languages?

3) Do bilingual students have a greater memory recall than non-bilingual students? Studies have shown that bilingual students have better “working memory” – does this include memory recall?

4) Investigation about the distribution of sweets in packets of Smarties.  A chance to buy lots of sweets!  Also you could link this with some optimisation investigation.

5) 22) Using Chi Squared to crack codes – Chi squared can be used to crack Vigenere codes which for hundreds of years were thought to be unbreakable. Unleash your inner spy!

6) Which times tables do students find most difficult to learn? – Are some calculations like 7×8 harder than others?  Why?

Modelling using calculus

1) How can you optimise the area of a farmer’s field for a given length of fence? A chance to use some real life maths to find out the fence sides that maximise area.

2) Optimisation in product packaging.   Product design needs optimisation techniques to find out the best packaging dimensions.

Probability and statistics

1) The probability behind poker games

2) Finding expected values for games of chance in a casino .

3) Birthday paradox: The birthday paradox shows how intuitive ideas on probability can often be wrong.  How many people need to be in a room for it to be at least 50% likely that two people will share the same birthday? Find out!

4)  Which times tables do students find most difficult? A good example of how to conduct a statistical investigation in mathematics.

5) Handshake problem With n people in a room, how many handshakes are required so that everyone shakes hands with everyone else?

Other ideas

If you want to do an investigation with a bit more mathematical content then have a look at this page for over 300 ideas for Maths SL and HL students.

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6 thoughts on “ maths studies and applications ia exploration topics ”.

Which ia’s are considered the most effective or interesting?

Reblogged this on thoughtsreflectionsandpersonalmodifications and commented: I guess I need this…stupid IA

Very useful!!

Very beneficial thank you !

Stoppage times in National Football League (NFL) games

the “How can you optimise the area of a farmer’s field for a given length of fence?” link won´t open

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