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IB Maths IA examples

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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.

The International Baccalaureate (IB) made several changes to the curriculum and assessment methods, particularly in Mathematics. As of 2024, the IB has updated the syllabi for Mathematics Analysis and Approaches (AA) and Mathematics Applications and Interpretation (AI). The IAs now include a greater emphasis on real-world applications and data analysis.

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. A top-rated Singapore IB tutor recommended that the exploration should be 10 to 15 pages long and students will spend 8 to 12 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

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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”. Use of Mathematics has been updated to emphasize the importance of not only correctness but also the innovative application of mathematical concepts.

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.

61. What are Interdisciplinary Approaches in Mathematics IA?

With the increasing focus on interdisciplinary learning, students are encouraged to link their Mathematics IA with subjects such as economics, environmental science, and computer science. This approach not only enriches the mathematical exploration but also allows students to showcase their ability to connect concepts across different fields.

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.

An IB tutor in Hong Kong said:

"One important aspect that students ignore is that they 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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Mathematics AA SL IA Examples

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IB IA/Essay Examples From May 2019

Published Aug 17, 2020 by Ritij Jain

A screenshot from my mathematical exploration IA.

My IAs/Essays from IB May 2019 examination session – Mathematics HL IA, Economics HL IA, and TOK Essay. These were assessed in the May 2019 examination session.

Maths HL IA Mathematical-Exploration.pdf Final Grade: 17/20 – 7

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TOK Essay TOK-Essay.pdf Final Grade: 6/10 – B

© Ritij Jain. Copying in whole or parts of any of the work in these files will count as plagiarism and may result in disqualification from the IB. For more info, read academic integrity policy from the IBO.

For more IB examples, search ib publishing + subject name.

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The Definitive Guide to Choosing the Best IB Mathematics IA Topics

45  Comments

by  Antony W

August 19, 2022

Imagine you were fascinated by the shape of nuclear reactor chimneys, called Natural Draft Cooling Towers. What an odd shape, you think (a hyperboloid, if you’re wondering). But how would you find out why they are so shaped? As it turns out, mathematics is a beautiful, fascinating language you can use to describe something like that. And when you explore such a personally fascinating subject within certain regulations of the IB, you will be writing your mathematics internal assessment.

As you can deduce, the IB math internal assessment is all about exploring mathematically a subject of personal interest. How well you do that and present your process determines how many marks out of the total 20 you will receive. However, most students live in mortal fear or both the IB math exam and the internal assessment.

If you are one such student, fear not. This detailed guide will teach you how you need to approach the math assessment by choosing the right topics, as well as how to make a top-grade essay. You can also get further IB guides in full detail here on our blog.

The team at Help for Assessments is also ready to give more than just passive “how to” assistance. Let us take the IB internal assessment nightmare away from you and write the essay for you. Our highly skilled and experienced team assures you of top-notch work, original and flawless in research and quality. All these at the best rates, so don’t hesitate to give us your order. We will even give you 25% off your first order to get you started.

Do you still want to push on? This article will give you all you need to choose suitable topics for your maths IA, explore what the test is about, and finish with some fresh sample idea topics for the math IA.

Struggling to pick your Math IA or AA topic? 

What the IB Maths Internal Assessment Topics All About

The mathematics internal assessment is about exploring the math behind a topic of interest, then presenting the whole thing in the form of a short thorough report. Ideally, the topic should be completely original and serve to prove that you have a firm grasp of mathematical concepts, principals, and knowledge.

According to the IA mathematics rubric, the IBO is looking for the following in a good essay:

• Communication : Communication measures how well you organize and explain your exploration. It must be logically developed and coherent. The essay generally should have three parts: an introduction, the rationale or explanation, and a conclusion.
• Mathematical presentation:  You need to use appropriate mathematical languages, with the right formulae, diagrams, tables, charts, models, and other figures as needed.
• Personal engagement:  This is a measure of the level to which the student interacts with the subject matter on a personal level. It is more than being original or authentic with the idea - it has to stem from some experience in your life or one you have direct links with.
• Reflection:  This criterion assesses how the student reviews and analyzes the problem and its solution in the exploration.
• Use of mathematics:  This is self-explanatory - how well does the student use the concepts, knowledge, and skills gained in their respective mathematical level so far?

Thus, the maths IA is about displaying your ability to apply abstract concepts and knowledge in math to a real-world situation and communicating clearly to your audience. In this case, the audience is your instructor/professor, and writing a good IA essay starts from picking the right topic.

Not sure whether to order Math IA or AA? Click below to see our latest samples! 

What Makes a Good Math IA Topic

A good topic for the IB mathematics internal assessment is one that allows you to fulfill all the above requirements. It will help you explore an area of interest deeply and exhaustively, while at the same time providing an avenue for you to put your acquired mathematical skills into good use.

If you are to be successful in these goals, your essay should have certain important qualities. These are the same qualities your topic should have:

• Simple and clear language: The rule of thumb is that everyone in your age group (your classmates) must be able to understand your essay. Thus, your topic needs to be simple. A complex subject will be hard for you to write, tough to break down into manageable bites, and ultimately cost you valuable marks.
• Concise and well-focused: The essay will be 6-12 pages in length, so you need to have a topic that can be exhaustively examined in that range. As is said in other IB assessments, the topic should be specific but not too narrow that it restrains or limits you. For example, our chosen problem of the nuclear reactor exhaust steam funnels could be confined to modeling the hyperboloid shape of the cooling towers and start from there.
• Interesting : The chosen topic needs to be exciting enough to elicit not only your interest but that of your audience. It needs to be one that is naturally intriguing to warrant a 12-page study into its underlying mathematical principles.
• Fresh : By fresh, we mean a relatively unexplored topic. Too many students do game theory, but that topic has been gone through by thousands of students in decades of consecutive years. Don't do that - go for something fresh, or seek to add an extra twist to something that already exists.
• Has clear connections with one or more mathematical fields: Your chosen topic should be based on a given mathematical area, or rely on a few of them. Drawing connections between different areas, e.g. Calculus and geometry will impress your instructor. However, always keep it within your attained academic level.

With the goal in mind, it's time to look into the process that precedes choosing a perfect math IA topic.

How to Choose a Mathematics IA Topic

Most math gurus insist that math is not just an abstract subject. It has real and effective links to the real world, and that is what the whole point of the internal assessment is.

To choose the topic, start with the real-life experiences to help you pinpoint an area of math you want to explore.

The following steps will help you:

• Brainstorm:  The first hurdle is to find a general area of interest, which ideally should be related or founded on your interests. For example, if you love medicine and want to study it in the future, you can start with a certain field that fascinates you. Future lawyers, businessmen, engineers, and IT enthusiasts can all find something intriguing to pursue.
• Narrow down: With the first few ideas, the next step is to find a topic that has a lot of mathematical potential. You will find that reading lots of journals, watching videos, and talking with friends gives you lots of seed ideas for this stage.
• Evaluate: Evaluate each of the ideas you have on the strength of the qualities above. Is it relevant? Simple enough for your level? Exciting? Will it be useful to you in your career or your life?
• General research: General research into the mathematics involved in your chosen topic will help you determine what you need to learn and determine how feasible your topic is. The point here is to find out if the topic is right for you, and whether you can find the right material to base your exploration on.
• Come up with a working research question: Every IA needs to have a research question to streamline the exploration and provide direction to the essay. As with the topic, the research question needs to be specific but just wide enough to give you enough material to fill the said 6-12 pages.

Or the other hand, perhaps this topic would be better suited to the Physics IA? It’s up to you!

Do you need help with your Math IA or AA? 

30+ Math IA Topics for SL and HL Levels

We’ve been writing IB Math IA assignments for over 5 years. From a professional academic writing assistance point of view, the number one challenge that many IB learners have is topic selection.

On the surface, Math IA is about investigating concepts within a topic of interest and presenting your findings in a 2,200-word report.

In practice, coming up with an original topic, which you can investigate to prove that you have a strong grip of mathematical concepts and principles can be somewhat challenging.

In this section, we put together a list of 20+ IB Math IA topic for SL and HL to help you understand what good topic looks like based on the selection criteria that we’ve shared in this guide.

• How accurate are mathematical predictions for events with a low likelihood but huge impact?
• Considering the risks involved in making decisions based on incomplete or conflicting information might make us more cautious.
• How do normal numbers fare when compared to random number generators?
• Create a virtual version of the disaster at Chernobyl and its subsequent effects on Japan.
• Do the numbers that make up a Pythagorean triple follow any kind of regularity?
• Does a high degree of association exist between BMI and GDP per capita?
• What kinds of character combinations are best for online safety in light of brute force attacks?
• To what extent does Bayesian probability work in a real-life setting and is it possible to add complexity to it?
• How do those involved in pyramid schemes or other forms of fast-paced fraud use mathematics to amass huge fortunes so quickly?
• Determine the climber's fall severity by measuring the distance from the final point of connection.
• Is it feasible to forecast the outcome of athletic events using a Poisson model and some familiarity with Excel?
• How long would it take someone to try to guess someone else’s password? What's the deal with adding symbols and digits to a password?
• How can we identify individual tones using sine waves of different frequencies?
• Is there a way to utilize arithmetic to predict how contagious diseases like measles will move across a population?
• Do large transfer window expenditures result in a higher victory percentage a sports season?
• With what method of voting can the most people be certain that their preferred candidate will win the election?
• A study of the geometric sequence's connection to the camera's aperture
• How well do you think integration would work to determine the gini coefficient for a sample of nations, allowing you to make reliable comparisons of the economic inequality between them?
• Find out if there's a correlation between music and fractions, or see if this series converges.
• If a fatal flu virus were to sweep the globe, how long do you think it would take humanity to perish?
• Examine the ratios of frequencies between notes to see why some do not sound good together while others do.
• What kinds of numbers have the most bearing on a basketball team's success?
• A look at how uncertainty about the future might make people more risk-averse and how asymmetric information plays a role in this phenomenon.
• The ideal amount of force and launch angle for a javelin or shot put world record throw.
• The gravitational attraction of other things in space causes the orbits of planets and comets to be elliptical. Look into the field of space exploration!
• Study the numbers behind the processes of heredity and natural selection.
• How can we utilize computers to learn more about sequences?
• Is it possible to employ computational methods in addition to pure mathematics to find an answer?
• Applying the mechanics of fast-moving spacecraft to the problem of interstellar travel
• Applying quantum mechanics, we may examine the universe's innate probabilistic character.
• If it takes the tortoise twice as long to cover the same distance as a runner, then there's no way the runner can catch up to it no matter how fast he runs.
• Using tools from probability and game theory, researchers investigate the most effective bluffing techniques for poker.
• Does the time it takes a kid to arrive to school depend on how far they live from the school?
• Check out the Guardian Stats to see if the top teams in the league are also the ones that commit the most fouls.

Tips to Help You Write the Best Math IA Assignment

The following tips can help you write a more comprehensive IB Math IA assignment:

1. Choose a Topic You’re Interested In

Since you will be working on your Math IA for a few months, it would be preferable if you choose a topic that genuinely interests you, rather than one that is simply required.

2. Use a Simple Language

Ensure that language is exact, clear, and succinct. Write your IA in a way that anybody of your age can read and understand.

Choosing a complicated topic may result in a disorganized and difficult-to-understand IA, so try to avoid doing so. Also, avoid writing lengthy accounts of your own experiences. This is the requirement for "Communication" on the math IA.

3. Use Appropriate Terms

Use appropriate mathematical notation and symbols throughout your IA report.

To properly format all mathematical symbols, use MathType or a comparable program for mathematical expressions. Doing so will enhance clarity and will get you easy points for "Mathematical Presentation"

IB also requires you to reflect on your findings in the report as part of your IA. Comment (thoughtfully), but avoid paraphrasing the results.

Describe some of the insights you've acquired from the IA mathematical conclusion. The greater the depth of your contemplation, the more points you will receive for the "Reflection" criterion.

Do You Need Help With Your IB Math Internal Assessment?

The mathematics internal assessment requires an astute mind to complete, and choosing the topic is the least of your worries. Many students are scared stiff on its account, but you don’t have to be. Help for Assessment is here to help you pass the internal assessment in maths, and not just because of this guide. The team here is made up of top IB experts who will do the internal assessment for you upon request. All you have to do is leave us your order here , and we guarantee you top grades and 100% original, impeccably researched, and fully proofed work. Of course, confidentiality is guaranteed, no matter where you come from. 

About the author 

Antony W is a professional writer and coach at Help for Assessment. He spends countless hours every day researching and writing great content filled with expert advice on how to write engaging essays, research papers, and assignments.

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I need help finding a math ia topic related to cars as its my interest but i am very confused and need some guidance

Hello Muhannad.

Thanks for reaching out. We’re happy to help. One of our representatives will get back to you via e-mail shortly. Thank you.

I need help in deciding a viable topic for my math is. I am very interested in cryptocurrency, the stock market, cricket, exercise, video games. Anything, but guidance would be highly appreciated.

Thanks for reaching out. We’re happy to help. One of our representatives will get back to you via your email for further assistance

Hi there, can you provide some help regarding math IA topics? I am a bit interested in the billiards topic and the math behind billiards, is the mathematics in billiards hard? or else I would like to use your help to choose a topic that has easy maths as I am an application student standard level, thank you for your coordination.

Hi, I stuck in choosing the best topic inline with the 3D shapes, for my exploration . Would you please assist me?

I am not really sure where to start for this IA. I am interested in the piano and music, however there have been past IAs on that. I don't know what else to think of.

I need help finding a math ia topic related to medicine and business

hi i need to find a topic and a research question that I am interested in. i have a few ideas but it is hard to narrow it down

Hey, I'm in need of some help finding an IA topic related to cars and I'm not sure where to start or what to do

Hi, I am Dina I need help in deciding my IA topic. I'm more concerned with the medical field and pharmacokinetics of medicines.

Hi, I would like to engage Mr. Anthony W for IB IA topic for Math AA HL for my son. Appreciate if you can get in touch wtih me at the earliest.

Hi, I need help in finding a topic about my math IA, I'm interested in the statistics and probabilities of winning a sneaker raffle. But I don't know how to do the maths of it.

Good day, I am currently struggling to come up with a math IA. I would like to do my exploration around medicine or something relating to careers. I currently have a few ideas about what I want to do, but I am in need of some assistance.

I need help finding a math IA HL topic related need some guidance.Please help me

I need help finding a math analysis and approach IA HL topic related need some guidance. Please help me

I need help in Maths IA for HL maths. How to go about to seek help?

I need a math IA topic that is related to statistics and could include something that is easy to find data for. I was thinking traffic flow, yet I don't know where to get the data from.

Hey, I have an research question for maths, but I not sure how to start it. Will someone be able to help me out?

I need to find my IA topic based on an example of how mathematics apply to real life

Hi! I need some assistance in finding an IA topic and the math. I am thinking of how essential immigrant workers are to the community and how without them especially during the pandemic, affects the food industry. I am not sure what kind of math I would have to be doing. Can you please help me?

Please help me choose an IA topic !!

Kindly read this guide carefully again. It should help you choose an IA topic for your next assignment.

i clearly don't know what to choose for my IA I don't really have some favorite stuff but I play basketball by myself not within a team or I thought if I can do an IA about coffee because I drink a lot of different types of coffee but in the same time I want a great IA that interests the person that is gonna read it

i need a ia topic and writing it

I need help finding a math ia topic related to keyboards or computers related. I was wondering if you can reach back to me immediately and we can talk about it? Thank you

Hello, I want to write a maths IA about Scouts because I was a scout and I am interested in scouts. I am finding it difficult to relate to maths and to find a research question. Do you have any suggestions for me?

hello! im currently struggling on finding my math IA topics and the due date is already getting near. can you please help me and give some guidance?

hi i need help choosing a math ia topic, anything easy and simple will be good please and thank you

i need help in find a IA for math AI HL I'm interested in exercise, dance, business, food

IA idea check

I need help in finding my internal assessment topic, which will be on modeling

I AM FINDING DIFFICUTLY IN SEARCHING IA HL MATH TOPIC. PLZ.HELP

Hello, I want help in math aa IA. I am interested in cooking so please tell me something related to it.

Hello, I am not sure what to choose as a topic for my math IA. I am a standard level student and math is not my strength so something where knowledge of simple maths is enough would be perfect. I am very interested in medicine so something in this area would suit my interest but I don't exactly know how to combine it with maths. Also, maybe math behind billiards but I don't know if this is too complicated for me.

I want to do a AA math IA in Statistics or logarithms but I don't know what topics to do or where to start.

Hey, I need help in finding a maths IA topic. I am interested in cars, technology, and cricket. Could you please help me

Hi I need help with finding a math IA topic. I'm interested in something along the lines of differentiation or volume of revolution. I'm also really interested on the knitting idea mentioned above but could not see how IB math would relate to that. Can you help me out? Thanks.

hey i need help for my math ia

i need help picking a maths IA topic related to zeno's paradox and infinite geometric sequences, I need an example that differs Achilles and the Tortoise. Otherwise a topic in medicine would also be really interesting.

We’ve updated the guide to include example topics to help you get started.

Hello Everyone,

We've updated this guide with 30+ topic ideas in Math IA for SL and HL levels for inspiration. We hope this guide continues to be helpful.

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IB Math SL Internal Assessment (IA) Example Topics

What’s covered:, what is the ib internal assessment (ia), ib math ia examples and ideas, how is the ib math ia scored, how does the ib math ia affect my admissions chances.

The International Baccalaureate Diploma Program , or IBDP for short, is the most common alternative to an upper-level highschool education to an AP class. It is not only challenging, but also highly recognized for college admissions around the world, making its rigor and academic difficulty worthwhile. 

One of the best parts about the IBDP is that the program takes a holistic approach to schooling, as opposed to a system solely based on examinations. An important component of this is the internal assessment (IA). An IA is any component of IB that is internally graded (i.e not graded by IB). Usually the biggest one of these is a research-based essay, often called an investigation at most schools, that will allow students to take concepts learned in their 6 classes, and write a university-level paper to showcase their extents to learn above the required amount. In this blog, we will be talking about the IA for IB Math SL, one of IB’s most popular courses. 

The IA is more simple than it sounds. Any piece of work that is internally graded at your school, be it oral, a presentation, or any form for media, is considered an IA. An externally graded assessment such as the official examinations at the end of the two-year program, is an external assessment. Understanding this difference is important to better prepare for your numerous IAs. 

Most schools will require students to submit research papers for an IA on top of presentations and other mediums, with this research paper constituting a bulk of the IA portion of the total grade. This research paper is often intended to be investigative in nature, allowing the student to question a concept and use this curiosity to show higher-level thinking.

In the case of IB Math SL , most students will take concepts taught in class and find practical ways to use these concepts in real life. This allows students to prove understanding of a concept and its uses. 

You might be struggling with getting started on your IB Math IA, but don’t worry because this is very common. Most students struggle to come up with original ideas that are interesting and enjoyable to do. Hopefully the following ideas can provide some inspiration for your IAs. 

IA Idea 1 – Birthday Paradox 

The idea tackles the paradoxical concept of how probability dictates that those in a room full of people are very likely to share a birthday.

This idea uses concepts from probability and data coursework in Math SL. While solving the paradox would be nothing new, perhaps taking the information and applying it into other mathematical concepts, or testing the data with a sample population of people would be an interesting direction to take. Presentation of the data is as important too – powerpoints are the go to method, so try something new! Maybe you could develop a simple application to showcase the paradox in the form of a game. The possibilities are endless, and just goes to show how creative you can be with the IA.

IA Idea 2 – Modeling Statistics

Modeling IAs can generally refer to any project where a certain change in statistics is being presented in a visual manner. One example is modeling the radioactive decay of chernobyl, and determining if conditions are suitable for living. Another example can be modeling the population of a country and determining the time left until the area is deemed overpopulated. 

Modeling is in itself an easy task but trying to make the information digestible and interesting is the hard part.

IA Idea 3 – Analyzing the Math of Monopoly

A fun IA idea could be analyzing the probability and statistics behind the game Monopoly! Is there a certain strategy to win or is the game luck-based? Try collecting data on how the game behaves based on numerous trials, conveniently collected through playing the game with friends! Maybe you find that the game isn’t so based on luck, and probability shows a consistent and reliable tactic to win? This concept can be done with almost any board game, making the application of the idea boundless!

This IA idea brings the fun into Mathematics SL, and would be as fun to write a report on!

The IA is internally scored, meaning the IB isn’t responsible for any grade associated with your IA assignments. Your teachers however, are heavily associated with the process of creating your IAs for all your classes. They are the ones responsible for your IA grades, so it’s always best to refer to your teacher and request any sort of rubric that you could work with! 

Each class will require a different method of grading IAs. For example, a practical science like Chemistry HL would need a more investigative approach in an IA through the scientific method as compared to an IA in Spanish SL. This means you must face each IA with a different mindset!

The IAs in Math SL make a little more than 10% of the total grade, which is a sizable chunk! You should aim to take advantage of this, because the IAs are definitely scored more leniently than the examinations and other external assessments. This 10% can be the difference between a 6 and 7 in the final grade of the class!

Don’t Overdo It

While the IAs are important, they are not intended to be as massive of a research project as the extended essay (EE), the most important piece of research work you’ll be doing as an IB student. If you find that an IA takes up time from working on your EE, you should change the IA topic to make it easier. The EE is worth much more than the IA, to the point where failing the EE immediately disqualifies a student from gaining the diploma!

Save a Great Idea

If you notice your IA idea is too difficult for the scope of an IA, then maybe it could make a great EE idea. Perhaps with more fleshing out, you could create a great EE topic, which would be beneficial in making it easier to get the diploma!

Make it Interesting

The IAs are a great opportunity to be more fun and creative compared to other projects that require more serious tones and formats. Create media and forms of presentations that are enjoyable and fun! 

The IAs have no direct effects on your chances of admissions, but they do help you become a more holistic student, a quality that schools find attractive. Amongst holistic mindsets, there are numerous other factors admissions officers seek out when accepting students into their schools. To get a better understanding of your shots into a university, try CollegeVine’s admission calculator ! This intuitive tool accounts for many factors, from GPA to extracurriculars, and tells you your shots of getting into your dream school!

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Your Ultimate IB Math IA (Internal Assessment) Guide

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The article titled “Understanding the IB Math IA” provides valuable insights and guidance for students undertaking the International Baccalaureate (IB) Math Internal Assessment (IA). With a focus on choosing the right IA topic, structuring the IA effectively, collecting and analyzing data, writing a strong report, avoiding common mistakes, seeking feedback and peer review, presenting the IA, and celebrating success, this article offers comprehensive advice to ensure success in completing one’s IA. Written in an academic style that is objective and impersonal, this resource caters to an audience seeking safety by providing clear instructions and strategies for navigating through the IB Math IA process. By following these guidelines outlined in the article, students can enhance their understanding of how to approach their IB Math IA with confidence and achieve excellent results.

Before we start, IB-Pros offers resources and tutors willing to enhance the quality and effectiveness of your IA project.

Key Takeaways

• The IB Math IA requires applying mathematical concepts to real-world scenarios.
• Choosing the right IA topic is a key aspect and factors to consider include relevance, feasibility, and personal interest.
• Collecting reliable and relevant data is crucial for the credibility and validity of findings.
• Using appropriate mathematical models and tools, such as regression analysis and statistical software, helps analyze data accurately.

Table of Contents

Understanding the IB Math IA

The IB Math IA is a comprehensive and rigorous assessment that requires students to apply mathematical concepts and principles to real-world scenarios in order to demonstrate their understanding of the subject. It serves as an opportunity for students to showcase their analytical skills and problem-solving abilities, as well as their ability to communicate mathematical ideas effectively. The IA consists of several components, including a introduction, exploration, analysis, conclusion, and reflection. Students are expected to clearly define the problem they are investigating and develop a coherent argument supported by mathematical evidence.

One key aspect of the IA is the choice of topic. Selecting the right IA topic is crucial as it determines the direction and scope of the investigation. Students should opt for topics that align with their interests and strengths while considering feasibility within a given timeframe. It is important to choose a topic that offers opportunities for applying various mathematical concepts and techniques.

The next section will delve into strategies for selecting an appropriate IA topic without compromising on its relevance or complexity.

Choosing the Right IA Topic

When selecting an IA topic for the IB Math course, it is crucial to carefully consider various factors such as relevance, feasibility, and personal interest. Relevance refers to the topic’s connection to real-world situations or other subjects within the mathematics curriculum. Choosing a relevant IA topic allows students to apply their mathematical knowledge in practical scenarios and develop a deeper understanding of its applications. Feasibility involves ensuring that the chosen topic can be investigated within the given time frame and resources available. It is important to select a topic that can be explored using appropriate mathematical techniques and data sources. Additionally, personal interest plays a significant role in determining the success of an IA project. Selecting a topic that genuinely interests the student will make the research process more enjoyable and motivate them to delve deeper into their investigation.

By considering these factors, students can choose an appropriate IA topic that aligns with their skills, interests, and goals. This thoughtful selection process sets a solid foundation for structuring their IA and producing a high-quality piece of work.

In the subsequent section about ‘structuring your ia,’ students will learn how to organize their chosen IA topic effectively while adhering to specific guidelines provided by the IB Math course.

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Structuring Your IA

To effectively structure the IA, students should carefully organize their chosen topic while following specific guidelines provided by the IB Math course. Structuring the IA involves several key steps:

• Introduction: Begin by clearly stating the research question and its significance. Provide background information to give context to the topic.
• Methodology: Outline the methods used for data collection and analysis. This includes specifying variables, explaining equations or models utilized, and discussing any assumptions made.
• Results: Present the findings of the study in a clear and organized manner. Use graphs, charts, or tables to illustrate trends or patterns observed in the data.
• Conclusion: Summarize the main findings and discuss their implications. Address any limitations or areas for further research.

By following these steps, students can ensure that their IA is well-structured and coherent. It allows readers to easily follow the logical progression of ideas and understand the purpose of each section. In the subsequent section about ‘tips for effective data collection and analysis,’ students will learn how to gather reliable data and analyze it accurately without compromising safety precautions.

Tips for Effective Data Collection and Analysis

This discussion will focus on the importance of collecting reliable and relevant data, as well as using appropriate mathematical models and tools in order to ensure accurate analysis. Collecting reliable and relevant data is crucial for obtaining meaningful results that can be applied to real-world situations. Using appropriate mathematical models and tools helps to organize and analyze the collected data effectively, while interpreting and analyzing the data accurately allows for valid conclusions to be drawn.

Collecting reliable and relevant data

Collecting reliable and relevant data is crucial in conducting a comprehensive academic investigation to ensure the credibility and validity of the findings. It is important to use language appropriate for an audience that desires safety, as this helps establish trust and confidence in the research process. One way to enhance the engagement of readers is by incorporating a table that presents information clearly and concisely. For instance, a table comparing different sources of data collection methods can be used to highlight their advantages and disadvantages. This not only makes the writing more interesting but also provides readers with a quick reference point for evaluating different approaches. Transitioning into the subsequent section about ‘using appropriate mathematical models and tools,’ it is essential to consider how these models can effectively analyze the collected data to draw meaningful conclusions.

Using appropriate mathematical models and tools

After collecting reliable and relevant data, the next step in an IB Math IA is to use appropriate mathematical models and tools. This involves selecting the most suitable models and techniques to analyze and interpret the collected data accurately. One of the commonly used mathematical tools is regression analysis, which helps identify relationships between variables and make predictions based on the data. Another useful tool is statistical software, such as Excel or Python, which allows for efficient calculations and visualizations. By employing these tools, students can delve deeper into their data sets, uncover hidden patterns or trends, and draw meaningful conclusions. In doing so, they can better understand the significance of their findings and present a comprehensive analysis in their IA report.

Transition: Moving on to interpreting and analyzing your data accurately…

Interpreting and analyzing your data accurately

To ensure an accurate interpretation and analysis of the data, students must carefully consider the relationships between variables and utilize statistical software tools like regression analysis or Excel to uncover hidden patterns or trends. This step is crucial in providing a comprehensive understanding of the data and avoiding any misinterpretations that may lead to erroneous conclusions. By examining the data using appropriate mathematical models and tools, students can identify significant correlations, outliers, or other important features that may impact their analysis. Moreover, by employing objective and impersonal language when presenting their findings, they can effectively communicate their results to an audience that prioritizes safety. With a thorough examination of the data completed, the next section will focus on writing a strong IA report that accurately portrays these findings without bias or personal opinion.

Writing a Strong IA Report

A comprehensive and well-structured IA report contains a clear and logical flow of ideas, enabling the reader to easily follow the reasoning behind the mathematical investigation. To achieve this, it is important to adopt an academic writing style that is objective and impersonal, eliminating personal pronouns. This style of writing creates a sense of professionalism and allows the focus to remain on the mathematical concepts being presented.

When writing an IA report, it is crucial to use language appropriate for an audience that desires safety. Avoiding jargon or technical terms without proper explanation can create confusion and hinder understanding. Instead, strive for clarity by using precise mathematical language while providing clear explanations and examples.

Furthermore, incorporating mathematical concepts and notations into the report strengthens its overall quality. By clearly defining terms, using appropriate symbols, and explaining equations thoroughly, readers can grasp the underlying mathematics more effectively. This ensures that your investigation is accurately communicated and understood.

Incorporating these elements will help you write a strong IA report that effectively presents your ideas in a clear manner. Transitioning into the subsequent section about incorporating mathematical concepts can be done seamlessly by emphasizing the importance of precise definitions and symbols in conveying mathematical ideas accurately.

Incorporating Mathematical Concepts and Notations

This paragraph will discuss the importance of demonstrating a deep understanding of mathematical concepts and using appropriate notations and symbols in calculations. Demonstrating a deep understanding of mathematical concepts is crucial in writing an IA report as it shows the examiner that you have a strong grasp of the subject matter. Additionally, using appropriate notations and symbols in your calculations helps to convey your ideas clearly and effectively. By adhering to these rules, you can ensure that your IA report is written in an academic style that is objective and impersonal.

Demonstrating a deep understanding of mathematical concepts

Achieving a profound comprehension of mathematical concepts is crucial in order to demonstrate a comprehensive understanding of the subject matter. To evoke emotion in the audience, it is important to recognize that gaining such deep knowledge can be both challenging and rewarding. It requires perseverance and dedication, but the sense of accomplishment when mastering complex mathematical ideas can be immensely satisfying. Additionally, developing a strong foundation in mathematical concepts instills confidence and empowers individuals to solve real-world problems with precision and accuracy. This knowledge serves as a safety net, enabling us to make informed decisions based on logical reasoning rather than guesswork or assumptions. By understanding the intricacies of mathematical concepts, we can navigate through calculations effectively and efficiently, using appropriate notations and symbols to convey our findings accurately. Transitioning into the next section about ‘using appropriate notations and symbols in your calculations’, it is essential to consider how these tools enhance clarity and facilitate communication within the realm of mathematics.

Using appropriate notations and symbols in your calculations

To effectively communicate mathematical calculations, it is imperative to employ appropriate notations and symbols that promote clarity and precision. Mathematical notations serve as a universal language in the field, allowing mathematicians to convey complex concepts concisely. Using standardized symbols ensures consistency and facilitates understanding among researchers, educators, and students alike. In addition to promoting accuracy, proper use of notation enhances the professional presentation of mathematical work. It demonstrates a rigorous approach and attention to detail, which are essential qualities in the discipline. Moreover, accurate notation helps prevent errors and misinterpretations that may arise from ambiguous or inconsistent representations. By utilizing appropriate symbols and notations in their calculations, mathematicians ensure effective communication within the field and contribute to the advancement of mathematical knowledge.

Transitioning into examples of successful IA topics…

Examples of Successful IA Topics

Examples of successful IA topics in the field of mathematics can showcase the range and diversity of investigations undertaken by students, offering inspiration and ideas for future projects. One such topic could be exploring the relationship between music and mathematics, analyzing how mathematical concepts are applied in musical compositions. Another interesting IA topic could involve investigating the patterns and properties of prime numbers, delving into their distribution and potential applications in cryptography. Additionally, a student might choose to explore the mathematics behind origami, examining how geometric principles are utilized to create intricate paper structures. Other possibilities include studying fractals and chaos theory, analyzing their mathematical properties and exploring their real-world applications. These examples highlight the vast array of intriguing IA topics that students can choose from when undertaking a math investigation.

In order to excel in these investigations, students may seek resources for IB Math IA help. These resources can provide guidance on choosing a suitable topic, conducting research effectively, using appropriate mathematical notations and symbols, and organizing data accurately. By utilizing these resources effectively, students can enhance their understanding of mathematical concepts while developing essential research skills required for success in their IA project.

Resources for IB Math IA Help

Utilizing available resources can greatly enhance students’ understanding of mathematical concepts and help develop essential research skills required for success in their IB Math IA project. When embarking on the IA journey, students may find themselves seeking additional support and guidance to navigate through the complexities of their chosen topic. Fortunately, there are numerous resources available that can provide valuable assistance.

One such resource is online forums and discussion boards dedicated to IB Math IA. These platforms allow students to connect with others who are also working on their IA projects, providing a space for exchanging ideas, asking questions, and receiving feedback from peers. Additionally, websites such as Khan Academy offer comprehensive video tutorials covering various mathematical topics relevant to the IA.

In addition to online resources, textbooks specifically designed for the IB Mathematics curriculum can be extremely helpful. These textbooks often include worked examples, practice problems, and explanations of key concepts that align with the requirements of the IA.

By taking advantage of these resources, students can deepen their understanding of mathematical concepts and gain insights into effective research methodologies. With a solid foundation in place, they will be better equipped to avoid common mistakes in their IA project while confidently exploring their chosen topic further.

Avoiding Common Mistakes in the IA

A thorough understanding of the IA requirements is crucial in order to avoid common mistakes and ensure a successful project. When working on an IB Math IA, it is important to be aware of potential pitfalls and take steps to avoid them. Here are some common mistakes that students should strive to avoid:

• Lack of clarity: Clearly defining the research question and objectives from the beginning will help maintain focus throughout the project.
• Insufficient data analysis: Properly analyzing and interpreting data is essential for drawing meaningful conclusions. Students should ensure they use appropriate statistical methods and provide clear explanations for their findings.
• Inadequate mathematical rigor: The IA should demonstrate a strong application of mathematical concepts, so it is important to show logical reasoning, accurate calculations, and precise notation.

By being mindful of these potential pitfalls, students can create a solid foundation for their IA. Additionally, seeking feedback from peers or teachers can provide valuable insights and help identify any areas that may need improvement. Taking advantage of opportunities for peer review can enhance the quality of the project by allowing for constructive criticism and suggestions for improvement. This step allows students to refine their work further before final submission.

Getting Feedback and Peer Review

To ensure accuracy and validity in your IB Math IA, it is crucial to seek feedback and engage in a peer review process. This step allows you to gain valuable insights from others who can provide constructive criticism and identify any errors or weaknesses in your work. By obtaining feedback, you have the opportunity to refine your IA and strengthen its overall quality.

When seeking feedback, it is important to approach individuals who possess knowledge and expertise in mathematics or a related field. They can offer guidance on areas that may require improvement or clarification. Peer review is particularly helpful as it allows for multiple perspectives, enhancing the credibility of your research.

Engaging in this process demonstrates a commitment to producing high-quality work while adhering to academic standards. It also promotes an environment of collaboration and continuous learning, which is essential for personal growth.

In the subsequent section about tips for presenting your IA, you will learn how to effectively communicate your findings and showcase the depth of your research.

Tips for Presenting Your IA

One effective way to enhance the presentation of your IB Math IA is by utilizing clear and concise language, allowing your audience to easily understand and appreciate the depth of your research. By using language that is simple yet precise, you can effectively communicate complex mathematical concepts without overwhelming or confusing your audience. This will create a safer environment for them, as they won’t feel intimidated or discouraged from engaging with your work.

To achieve this objective, consider the following tips:

• Simplify technical terms: Avoid jargon or overly complicated terminology. Instead, use everyday language to explain mathematical concepts in a relatable manner.
• Use visuals: Incorporate graphs, charts, and diagrams to visually represent data and illustrate key points. Visual aids can help simplify complex ideas and make them more accessible.
• Provide explanations: Clearly explain any equations or formulas used in your IA so that even those who may not have an extensive background in mathematics can follow along.

By adopting these strategies, you can ensure that your IA presentation is engaging and accessible to all audiences. With clear language and visual aids at hand, you can confidently celebrate the success of your research in the subsequent section about ‘celebrating your success’.

Celebrating Your Success

Achieving a sense of accomplishment in your IB Math IA can be done by reflecting on the successful completion of your research and analysis, highlighting the significance of your findings within the broader context of mathematical exploration. Celebrating your success in this endeavor is crucial to acknowledge the hard work, dedication, and intellectual growth that went into producing a meaningful piece of mathematical investigation.

When presenting your IA, it is important to emphasize the importance of adhering to safety guidelines. By following ethical practices and ensuring that all data collection methods are conducted responsibly, you demonstrate a commitment to maintaining both personal and academic integrity. Discussing any potential risks involved in carrying out the research also helps create an environment that prioritizes safety.

Furthermore, celebrating success means acknowledging not only individual achievements but also recognizing the collective effort put forth by teachers, peers, and educational institutions. It is essential to express gratitude for their support throughout this process.

Celebrating your success in completing your IB Math IA involves reflection on personal accomplishments while considering the wider implications within the field of mathematics. Demonstrating a commitment to safety ensures ethical practices are followed throughout the research journey. Recognizing those who have contributed to your achievement fosters an atmosphere of gratitude and appreciation for collaborative efforts.

Frequently Asked Questions

How many pages should my ib math ia report be.

The length of an IB Math IA report varies, but it is generally recommended to be around 6-12 pages. However, it ultimately depends on the depth and complexity of the topic being researched and discussed.

Is it necessary to include real-life applications of mathematical concepts in my IA?

Including real-life applications of mathematical concepts in an IB Math IA is not necessary, but it can enhance the relevance and practicality of the research. It allows for a deeper understanding and application of mathematical theories in real-world scenarios.

What are some common mistakes that students make in their IA and how can I avoid them?

Common mistakes in IA include not clearly defining the research question, inadequate data analysis, lack of mathematical rigor, and insufficient referencing. To avoid them, students should carefully plan and structure their IA, use appropriate mathematical techniques, analyze data accurately, and cite sources correctly.

Are there any specific formatting or citation guidelines that I should follow in my IA report?

Specific formatting and citation guidelines should be followed in an IA report. These guidelines ensure accuracy, consistency, and proper attribution of sources. Adhering to them demonstrates professionalism and enhances the credibility of the research findings.

How can I effectively incorporate graphs and visual representations of data in my IA?

Effectively incorporating graphs and visual representations of data in an IA involves providing clear labels, appropriate scales, and accurate data representation. This enhances understanding and communication of the information to the desired audience.

In conclusion, the IB Math IA is a crucial component of the International Baccalaureate program. It requires careful planning and execution to choose the right topic, structure the IA effectively, collect and analyze data, write a strong report, and avoid common mistakes. Seeking feedback and peer review can enhance the quality of the IA. Finally, presenting the IA confidently and celebrating one’s success are important steps in completing this academic endeavor successfully.

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