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IB Math HL 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 ia affect my admission chances.

The international baccalaureate diploma program (IBDP) is an impressive alternative to a high quality high school education. Its ability to provide students with practical learning methods is unparalleled to others. One of the most interesting parts about IBDP and its classes, are actually the internally graded components referred to as internal assessments (IAs). They’re usually handed out to students from the school in the form of research-based essays and other forms of investigative ways of learning.

IAs are done for every single one of the six subjects a student signs up for in IB. The IA is also usually a student-led initiative to showcase their knowledge through university-level work. This blog will be talking about great example IA topics and ideas for the subject IB Math HL

The IA is a fancy word for any internally graded piece of work for your IB grade. Internally graded means it was assigned and scored on part of a teacher, or some form of administration at your school. Conversely, externally graded assessments like exams and the extended essay are given to IB, and the organization will then have it assessed and returned to the student.

Most schools assign students IAs in addition to coursework and other assignments, so the expectations for IAs aren’t that high. They’re usually easy and approachable but promote critical thinking and investigatie through processes.

In IB Math HL , your IAs will usually be based on concepts taught in your coursework presented through practical applications and researching. You might however, find it difficult to pick a topic for your IA due to massive amounts of options form the coursework provided, but don’t worry because this guide will help you with some ideas to get you started on your IA process!

IA Idea 1 – Modeling Statistics

Modeling statistics is a pretty broad concept for an IA, but it can refer to any project where a change in statistics is presented in a visually effective manner. An example of modeling is presenting the rate at which a country’s population changes relative to external factors. For example, how does a country’s population change relative to their GDP (gross domestic product) and other forms of economic growth measures? What conclusions can be drawn via a hypothesis based on the data we collected through modeling?

Modeling is in itself a relatively easy task. However, creating a way to present statistics to an audience that may not be as well-informed about statistics is the real goal of the IA. A great way to present it could be a research-based essay or even a presentation with slides. The possibilities are boundless, so feel free to get as creative as you want with this!

IA Idea 2 – The Statistics Behind Poker

Using mathematics to model a plan to statistically win poker is much more difficult than you’d think. The process can be something like combining modeling and simulation concepts to create data that is reliable enough to form winning strategies for a game as complex as poker. The whole process will be an extension of Game Theory, a popular method in which mathematics is used to calculate the probabilities behind card games, board games and video games.

A great way to showcase this would be with some simple code! A simulated game can be created to show how the gathered data and a formed strategy can be used to show how the IAs hypothesis worked or how it didn’t. Another way is also playing a real poker game and applying said strategy and recording it, and this recording can also be considered as a form of submission.

IA Idea 3 – Using Optimization to Measure Places

Optimization can be an effective method to measure the size of objects quickly. Try going outside and finding objects and spaces that you’d like to measure. Gather all the data required to perform optimization to calculate volumes.

Although this IA idea isn’t as particularly research based as the others, there’s bound to be loads of difficult and rigorous calculations, so this is a great way to perform and showcase that knowledge through an IA.

The IA is internally scored, which essentially means IB is not responsible for grading any of the work for IAs. Instead, your teachers and sometimes supervisors appointed specially for overseeing the progress of an IA are going to give you a grade for your work. This means it’s important your supervisor understands the process of your IA, so try to find one that will best facilitate your progress and work.

The IAs in Math HL make up a little above 10% of your total grade for the class. However, considering IAs are graded more leniently compared to external assessments, this can be considered an easier 10% to earn! That means you should try your best on the IAs as they can be a life-saver for your total grade later on.

Have Fun With the Idea

The IA isn’t meant to be a seemingly impossible herculean task, something that might be a better description for the extended essay . Create and execute topics that interest you and are more engaging. This would definitely lead to creating a better IA that’s informative and more likely to score well! Usually, the less it feels like work, the better the idea is for an IA!

Solve a Problem

If you’re struggling to find solutions and ideas for IA, here’s a different thought process that might help a bit. Instead of seeking ideas for the intent of making an IA, think about problems that require practical solutions through either modeling or other forms of mathematical solutions.

Design an idea that solves said problem, and create a presentation around the solution. This is essentially a very simple process that can be applied to a broad number and range of concepts. A different thought process like this might be all you need to kickstart your IA.

The IA itself, for any idea and any method of presentation, has little to no effect on your chances of admission. However, the IAs do help you become a more holistic student. This holistic quality is something many universities do want, as opposed to high scores and grades. It can be difficult to keep track of a lot of the factors involved in college admissions chances. An intuitive tool like CollegeVine’s admissions calculator is an effective way to get a better understanding of admissions. The tool uses GPA, extracurriculars and other metrics to calculate your chances of admission into a university of your choosing!

The Definitive Guide to Choosing the Best IB Mathematics IA Topics

by Antony W

August 19, 2022

$ib math internal assessment topics$

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

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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

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IA idea check

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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 Maths IA: 60 Examples and Guidance

Charles Whitehouse

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

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

What is the Mathematics IA?

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

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

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

IB Maths AA Past Papers
IB Maths AI Past Papers

What are the assessment criteria?

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

Source : IB Mathematics Applications and Interpretation Guide

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

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

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

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

Criterion E: Use of Mathematics (6 marks ) –

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

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

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

- IB Maths AI SL Study Notes

- IB Maths AI HL Study Notes

- IB Maths AA SL Study Notes

- IB Maths AA HL Study Notes

What are some example research questions?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How can I score highly?

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

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

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

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

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

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IB Math HL IA Topics

Writing an Internal Assessment is an important part of the IB Math program. An IA is a research paper, which must be written on a topic in Mathematics. It is an opportunity to explore a specific topic in-depth and showcase your knowledge and understanding of mathematics.

When choosing a topic for your IA, it’s essential to select one that will allow you to demonstrate your ability to think critically, analyze data and present reasoned conclusions. The best topics will be both challenging and interesting so that you can put your best foot forward.

In this guide, we will look at twenty different topics to help you decide which area of mathematics to focus your work on. We will also explore the scope of the IA, provide practical advice on writing IAs and cover how to choose and research the perfect topic.

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20 Suitable Topics for an IB Math Internal Assessment

Choosing the right topic is essential for your Internal Assessment . Here are some great ideas that will help you get started:

The Effects of Temperature on Rainfall: How does the temperature of a location affect the amount of rainfall? You could use data from different climate zones.
Correlation Between Population and Economic Growth: Can you determine the relationship between a country’s population and its economic growth? You could analyze data over the years using various statistical methods.
Prediction of Stock Market Movement: Can you predict the future movement of the stock market using regression analysis? You could also compare different stock indices.
Exploring Linear Patterns in Life Expectancy: How has life expectancy changed over time? You could look for linear patterns in the data and explain why these patterns exist.
Delaying Payments for Maximum Interest: How can you make the most out of interest payments? You could create a model to explore how delaying certain payments can maximize interest.
Measuring the Reliability of Anomaly Detection: Can you use machine learning to detect anomalies in data? You could measure the reliability of your model using sensitivity and specificity.
Analysis of User Behavior on Social Media: How can you predict the behavior of users on social media platforms? You could use clustering techniques such as K-means.
Effectiveness of Weighted Voting Systems: How can you measure the effectiveness of a weighted voting system? You could use an algorithm such as the Shapley Value.
Optimizing Transportation Routes: How can you optimize transportation routes for a given set of conditions? You could use integer programming to find the most efficient solutions.
The Impact of Financial Aid on Student Performance: How does financial aid affect student performance? You could analyze data on grades and graduation rates to see if there’s a correlation.
Comparing the Efficiency of Different algorithms: How do different algorithms compare when it comes to efficiency? You could evaluate their run times in various situations.
Analyzing the Impact of Data Visualization: How does data visualization impact our understanding of data? You could study different visuals to see which ones are more effective.
Determining Factors That Influence Air Quality: What factors influence air quality in a given area? You could use multiple linear regressions to identify the main influences.
Forecasting Sales with Time Series Analysis: How can you predict future sales with time series data? You could explore different methods such as exponential smoothing or ARIMA.
Exploring Unsupervised Learning Techniques: How can unsupervised learning techniques be used for pattern recognition? You could experiment with different algorithms to find the most accurate results.
Classifying News Articles Using Natural Language Processing: Can you automatically classify news articles using natural language processing? You could use a supervised machine learning technique such as support vector machines.
Assessing the Effectiveness of Sports Analytics: How can sports analytics be used to gain an edge in competition? You could analyze data from past performances to assess the impact.
Evaluating the Accuracy of Corporate Financial Forecasts: Can you measure the accuracy of corporate financial forecasts? You could compare them to actual results to determine the reliability.
Predicting Elections with Sentiment Analysis: How can sentiment analysis be used to predict the outcome of elections? You could collect data from social media platforms and analyze it with machine learning.

Understanding the Scope of Your IA Project

When studying a topic for an IB Math Internal Assessment (IA), it’s important to understand the scope of your project. The scope is how broad your paper should be and what information needs to be covered within it.

You need to choose a topic that is manageable while still providing enough material to form a complete IA paper. It’s important to plan out your research and aim to find sufficient sources, data and evidence to make a strong argument or prove a point.

When focusing on the scope of your IA, you should think in terms of questions you want to answer and theories you want to prove. Brainstorm ideas, search for relevant sources, and plan out how the information will fit together in your paper.

Having a purpose and understanding the scope of your project from the beginning will help you structure your research and present a clear argument. Additionally, understanding the scope of your project can help with the understanding of the bigger picture of the topic as well.

By researching thoroughly and documenting your work properly, you can create an IA that covers the scope of your project comprehensively and effectively.

Practical Advice to Plan an IB Math Internal Assessment

When it comes to planning out your IB Math Internal Assessment (IA), research and brainstorming ideas beforehand can really make all the difference. Here are some practical tips to help you understand the importance of planning before you start your IA.

Do Your Research

Before you start, it’s important to do a thorough research about the topic you’re going to study for your IA. Try to look into any journals, articles, and even books related to the topic you’ve chosen so that you have reliable sources for your IA paper. Don’t limit yourself to just one source of information, as this will cause your IA to be repetitive and uninteresting. Take time to search for multiple sources and use them to your advantage.

Brainstorm Ideas

Once you’ve done your initial research, make sure to take some time to brainstorm ideas with your friends or family. Brainstorming can help you explore different perspectives and angles of the topic, and come up with unique ideas to explore. Get your friends and family involved in your IA brainstorming to get fresh and unbiased opinions. Don’t limit yourself to the first ideas that come to you – instead, explore multiple possibilities and pick the best ones.

Prioritize Your Ideas

After brainstorming, it’s time to prioritize the ideas you’ve come up with. Pick the ones that are most interesting and relevant to the topic you are studying. Once you’re done with prioritizing your ideas, make sure to organize them in a way that makes sense. This will help you structure your IA paper better and make it more comprehensible.

Start Planning

Now that you’ve got your ideas ready, it’s time to put them into action! Sit down and make a plan of how you want to structure your IA paper. Try to break it down into steps, from collecting resources to writing the paper and finally submitting it. Having a plan will help you create a clearer and more organized IA paper.

The Final Step

One of the most important steps when it comes to creating an IA paper is to start writing. Even if you think it won’t be perfect, start writing. By writing, you can develop your ideas further, find flaws, and make improvements. With the help of your plan, you can have an easier time when it comes to writing the paper. With these tips, you should be ready to write an amazing IB Math Internal Assessment paper!

Choosing an IB Math Internal Assessment Topic

Choosing a good topic for your IB Math Internal Assessment (IA) is essential for achieving the best results. It’s important to not only pick a subject you’re already familiar with, but also one that presents a challenge to you. So how do you choose the best topic? Let’s explore this.

When selecting a topic for your IA, consider a few key factors. You’ll want to find a topic that you’re interested in studying , has enough sources and resources available and aligns with the scope of your class. For example, topics related to probability and statistics are often taught in most math classes and have a lot of resources available. Finding a topic that’s both familiar and challenging will help ensure you get the most out of it.

When you’ve chosen a topic, research it further. Look up books, articles, and websites that can give you more information about the area you’re studying. Review the materials and make sure they’re relevant and reliable. This is important to ensure that your IA is based on accurate information.

Finally, try to balance the difficulty of the topic against your skill level. It’s important to challenge yourself, so don’t be afraid to choose something that may require extra work. But don’t spend too much time trying to come up with an original idea or get stuck on one point. Select a topic that’s interesting to you and manageable for the amount of time you have.

When you’ve considered all these factors, choose the topic that provides the perfect blend of familiarity and challenge. With careful research, your IA project will be engaging, meaningful and well-written.

Researching Quality Sources

Researching sources for your IB Math Internal Assessment (IA) can be overwhelming. With the right tips and tricks, you can find quality sources to use in your IA. Here are a few tips to get you started:

Start by narrowing down your goal: Before researching, take a few minutes to decide what knowledge and information you need to accomplish your IA goal. This will help you identify which sources of information you should consider.
Check the source type: Sources come in all different shapes and sizes. Some types of sources work better than others when it comes to researching an IA topic. Aim for scholarly or peer-reviewed sources like research articles, books, and websites run by educational or scientific institutions.
Be mindful of biases: Not everything you find online is true! Be sure to check the author’s credentials and background. Also, if you’re using a website, look for contact information, dates of updates, and other signs that it is legitimate.

Once you’ve done the groundwork of finding reliable sources, the next step is organizing them and taking notes. It’s a good practice to create a list of references with all the info you need so you can quickly access them when needed. Taking notes while reading is also helpful as this lets you break up information into small chunks, making it easier to understand.

Finally, remember that the way you store and organize the sources is just as important as finding them! As you research for your IA, keep track of ideas, sources, and notes in one place. That way, you won’t forget something important or get overwhelmed when it comes time to write your IA.

Writing the IB Math Internal Assessment

Writing an IB Math Internal Assessment (IA) is an important part of the curriculum and can be daunting. That’s why it’s essential to know the layout and structure of how to write the IA correctly. Here’s some helpful tips on getting it right.

Layout and Structure

Begin by introducing the topic, providing an overview of what you are studying and why. Then provide the different sections of the paper that are needed. For example, the Hypothesis, the Methods Used, Findings, Discussion and Conclusion. Each section will have its own paragraph, but all should flow together in a logical order. As you write each section, be sure to reference specific points made in the introduction to allow for consistency throughout the paper.

Editing and Proofreading

Once the paper is written, it’s important to go back through and review it. Check for clarity and accuracy in the information being presented and make sure there are no typos or grammatical errors. Additionally, consider running the paper through a spell and grammar checker to help catch any mistakes you might have missed.

Peer-Reviewing

Finally, ask a friend or classmate to peer-review the paper and provide feedback. They may be able to point out any errors you didn’t catch or suggest changes that could improve the overall quality of the paper. It’s also helpful to read the paper aloud to yourself as this can help spot any potential problems you may have overlooked.

Writing an IB Math Internal Assessment is a great way to deepen your understanding of a subject. With the right preparation and knowledge, it can be a rewarding experience.

Finalizing the IA

By the time you finish your IB Math Internal Assessment (IA), you are almost ready to submit it! Here are some final tips to help you make sure your IA is the best that it can be.

Presentation Guidelines

After all of your hard work, it is important that the IA looks great too. That’s why most IB programs require strict presentation guidelines to ensure your IA is professional and easy to read. This includes double-spacing your IA, using a 12 pt font, and including a title page with appropriate information about you and your chosen topic. Additionally, for an IA it is important to properly cite any sources you used in the document following the correct citation format that has been provided.

Deadline Advice

The deadline for submitting the completed IA is also an important consideration. Make sure you give yourself enough time to finish your IA and don’t wait till the last minute. Most IAs need at least 2-4 weeks for research, writing, and editing. If some unforeseen circumstance arises, talk to your teacher as soon as possible. Your teacher may be able to offer suggestions or extensions depending on the circumstances.

Proofreading

Finally, proofreading your IA is a must – no matter how well you think you wrote it, there may be errors you overlook. Have someone else read through your IA and give you honest feedback. Review your paper carefully before submission, it might be helpful to read it out loud and make sure it makes sense.

Finishing your IA is a huge accomplishment, and taking the time to carefully review your work will ensure that it meets the criteria for the assignment. Good luck!

Wrapping Up Your IA

Completing your Internal Assessment is no small feat. You have worked really hard and you should be proud of yourself! Taking the time to reflect on your research and writing process can be very beneficial for improving the quality of your IA for the future. Here are a few tips to consider:

Did you choose a good topic? Did you explore topics that were both familiar and challenging?
Did you keep track of your sources and cite them correctly?
Was the paper written with a suitable structure and flow?
Did you research and brainstorm effectively?
Did you stick to the right formatting conventions?

Remember, an effective IA needs to provide a comprehensive answer to the question while demonstrating an appropriate level of critical analysis and study. If you’ve addressed these needs, you should feel confident with the quality of your work.

Hopefully this guide gave you a better understanding of the Internal Assessment process and helped you prepare to tackle your own project. Working through the IA may feel daunting at times but it’s also a great opportunity to hone your skills and showcase your abilities.

Throughout this guide on IB Math Internal Assessments, a few technical terms have been used which may need further explanation. Here is a list of some of these terms and their definitions.

Internal Assessment: This refers to an assessment done as part of an IB Math course, without the aid of external resources.
Scope: This means the range or area of a particular topic.
Practical Advice: This is information designed to help the student plan or complete their IA in the most effective way.
Sources: This refers to research material such as books, websites, journals, and databases.
Layout: This refers to the presentation and structure of the written work.
Editing: This is when an author makes changes and corrections to their work before it is ready to be published.
Peer-reviewing: This is when a student’s work is read and critiqued by other students or experts in the field.
Presentation guidelines: Rules on how the finished work is to be presented for marking.

By understanding these terms, it will be easier for you to effectively create your IB Math Internal Assessment.

Bibliography

A bibliography is a list of sources used throughout the article. It is important to reference sources correctly, in order to help readers find the same material you are using to inform your understanding of a topic.

Creating a bibliography can help you keep track of everything you have read and make sure your Internal Assessment is accurate and up-to-date. You can include books, journals, magazines, websites and more, as long as they are reliable sources.

You should also consider suggesting personal sources for further reading. You can provide links to other articles, videos or podcasts that you have found useful as a way of deepening readers’ understanding of the IA topics you are discussing.

At the end of the guide, cite all of your sources in the format that is appropriate for the type of source. This could be MLA 8th edition, APA 6th edition, Chicago 16th edition, or Harvard referencing, for example. Make sure you label it clearly as ‘Bibliography’ so that readers can easily distinguish it from the references.

Ultimately, a comprehensive bibliography improves the quality of your IA and shows readers that you are confident in the material you have chosen to support your points.

Reflecting on the Internal Assessment

Once you have thought about your topic, done your research and written the paper, it can be helpful to reflect on the process. Reflecting is an important part of the learning process; it allows you to question and assess what you have achieved.

The reflection does not need to be a formal essay or journal – it just needs to allow you to critically think about your experience. Consider some of the following questions: What did I find challenging or difficult? What new skills did I gain? What could have been done differently?

Reflecting on your IA can also help to increase your confidence and understanding as you move on to other projects. Ask yourself, how will this project help in my future studies?

Encourage yourself and your peers by discussing your experiences and sharing your successes. This brings us back to the importance of collaboration – talking about the challenges and successes of an IA can be greatly beneficial for the learning process.

FAQ’s About IB Math Internal Assessments

Q: What is an IB Math Internal Assessment? A: An IB Math Internal Assessment (IA) is an academic work required by schools to assess student understanding of IB Math topics. IA requires students to research and apply their knowledge to a chosen topic.
Q: What are some suitable topics for an IA? A: Suitable topics for an IA include probability, statistics, descriptive geometry and dynamical systems. Others include advanced algebra, binomial distributions and ODEs.
Q: What is the scope of an IA? A: The scope of an IA should contain a statement of purpose and objectives, a description of the problem or opportunity, and a proposed timeline. This helps the student understand their own topic and guide them in research.
Q: What is the importance of researching and brainstorming ideas when writing an IA? A: Researching and brainstorming ideas helps the student plan out their IA effectively and can provide invaluable insights into the chosen topic and allow them to explore new ideas.
Q: What are some considerations in choosing an IA topic? A: When choosing an IA topic, the student should consider their own abilities, the availability of relevant data, the complexity of any equations or models, the level of difficulty whether the topic is interesting and enjoyable.
Q: How can I find quality sources for my IA? A: To find quality sources for an IA, students should rely on reputable published books, scholarly journals and peer-reviewed articles from public libraries and university databases. Private resources such as museums, archives, and specialized experts may also be consulted.
Q: What can I do to ensure that my IA paper follows the correct structure and layout? A: To ensure a good structure and layout for the IA paper, make sure the introductory section clearly outlines the purpose, follow the structure of style guide, use diagrams and graphs to make ideas more visual, add conclusions and recommendations where applicable, and proof read the entire paper.
Q: What are the presentation guidelines for the IA paper? A: Presentation guidelines for an IA paper include ensuring that referencing is included correctly in the document, citing all sources accurately, including illustrations, graphs and other visual aids, and meeting the deadline set by the educational institution.
Q: What are some ways I can improve the quality of my IA paper? A: Steps to take in order to improve the quality of an IA paper include reviewing notes with peers to get feedback, revising and editing based on comments made by instructors, double-checking the logic and applicability of any models used, and addressing any potential gaps.
Q: Is there anything else I should know before starting on my IA paper? A: Before embarking on work for an IA paper, it is important to continue reading around the theme language of the subject in order to help with writing. It is also important to receive regular feedback and set realistic goals to maintain focus and morale.

Nick Radlinsky

Nick Radlinsky is a devoted educator, marketing specialist, and management expert with more than 15 years of experience in the education sector. After obtaining his business degree in 2016, Nick embarked on a quest to achieve his PhD, driven by his commitment to enhancing education for students worldwide. His vast experience, starting in 2008, has established him as a reputable authority in the field.

Nick's article, featured in Routledge's " Entrepreneurship in Central and Eastern Europe: Development through Internationalization ," highlights his sharp insights and unwavering dedication to advancing the educational landscape. Inspired by his personal motto, "Make education better," Nick's mission is to streamline students' lives and foster efficient learning. His inventive ideas and leadership have contributed to the transformation of numerous educational experiences, distinguishing him as a true innovator in his field.

What to Do If You Fail Your TOK Essay?

Failing your TOK essay can be disheartening, but it’s not the end of your IB path. As a seasoned IB writer, I understand the intricacies of the TOK essay and the common pitfalls students face. In this article, I’ll guide you through practical steps to reassess, revise, and rebound from a failing grade.

What to Do if You Don’t Pass Your IB IA and How to Succeed Next Time

Overcoming the challenges of failing an IB Internal Assessment can be daunting, but it’s not the end of your academic path. This article provides a comprehensive guide on the immediate actions to take if you don’t pass your IA, including analyzing feedback and consulting with your teachers. We’ll discuss opportunities for resubmission, the strategies for improving your work, and long-term tactics to prevent similar setbacks.

IB Referencing in Writing | Citations Guide for Students

This comprehensive guide provides you with the tools and knowledge you need to cite sources accurately, thereby enhancing the credibility and integrity of your academic work. From understanding different citation styles to implementing them effectively in your essays, this article serves as your go-to manual for all things referencing.

When to Submit Extended Essay? IB EE Deadlines

Managing the deadlines for your IB extended essay can seem daunting, but with the right guidance, it’s completely manageable. This article breaks down the critical deadlines you need to know in order to successfully plan and execute your extended essay.

When to Submit TOK Essay? Deadlines

Understanding when to submit your TOK essay is crucial for success, as meeting these deadlines ensures you have ample time for revisions and reduces last-minute stress. This article offers a comprehensive guide on TOK essay deadlines, providing key insights from a seasoned IB writer.

What Are the IB IA Deadlines?

In this comprehensive guide, we discuss the essential dates and strategies for managing your submissions effectively. Understanding these deadlines is vital when preparing for the May or November exam sessions. From planning early and using digital tools to track your progress to communicating with teachers and handling unforeseen challenges, this article provides you with all the insights and tips you need to master the timing of your IAs.

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tentative deadlines for math hl iA (Class of 2020)

Final Topic with Outline

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Feb 8, 2022

Advice for IB Math IA - choosing a research question, topic

In this post I will be sharing my opinion on selection of topic for Math IA.

Truth is, different schools have different guidance on this. For example, I know a school that bans Graph and Game theory for selection (I'm against such a policy).

I think the bottom line is:

HL students should not be pursuing a topic inside the SL syllabus.

HL students should choose a topic that is an extension of their syllabus

SL students should choose a topic that is within the HL syllabus

Too often I have seen students not working on their proposal and reading widely till the last minute and in the end settles for something for the sake of getting the teacher's approval. They fail to recognize the importance of reading widely for potential topics and how other reports are written before starting to draft their proposal. Clearly they underestimate the importance of Math IA as highlighted in my previous post.

So, how to go about choosing?

Frankly, there's no magic beans formula. What I typically advise my students is:

1) find a context (finance? search engines algorithms? sports stats?) you are interested in;

2) speak to your advisor/tutor if there's any math/research question worth exploring on;

3) even if it's a "no", think about possible derivatives and logical extensions areas.

Alternatively,

a) find a math concept that you have always wanted to know about (noise/signal processing, fractals, blockchains hash functions);

b) speak to your advisor/tutor

I understand my advice above isn't very useful at first glance, but truth be told I practically spend hours discussing with each of my tuition students to settle down on their Math IA topic or Economics IA article (more of this in a future post).

Feel free to contact me at +65 9782 4025 or [email protected] if you require a discussion.

So my bottom-line is making sure that students learn something from the research process (be it the math concept or the context they are keen on) beyond just clearing an assessment for the sake of it.

Of course getting a decent score is the real-real bottom line!

For interested readers, feel free to study some samples here: https://www.aces-aspire.com/ia-ee

Alvin, AcesMath

#acesaspire #acesmath #IBMath #IBMathIA #MathIA

Maths IA – Exploration Topics

Maths IA – 300 Maths Exploration Topics:

Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. Topics include Algebra and Number (proof), Geometry, Calculus, Statistics and Probability, Physics, and links with other subjects. Suitable for Applications and Interpretations students (SL and HL) and also Analysis and Approaches students (SL and HL).

Algebra and number

1) Modular arithmetic – This technique is used throughout Number Theory. For example, Mod 3 means the remainder when dividing by 3.

2) Goldbach’s conjecture: “Every even number greater than 2 can be expressed as the sum of two primes.” One of the great unsolved problems in mathematics.

3) Probabilistic number theory

4) Applications of complex numbers : The stunning graphics of Mandelbrot and Julia Sets are generated by complex numbers.

5) Diophantine equations : These are polynomials which have integer solutions. Fermat’s Last Theorem is one of the most famous such equations.

6) Continued fractions : These are fractions which continue to infinity. The great Indian mathematician Ramanujan discovered some amazing examples of these.

7) Patterns in Pascal’s triangle : There are a large number of patterns to discover – including the Fibonacci sequence.

8) Finding prime numbers : The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics. There is a $1 million prize for solving the Riemann Hypothesis and $250,000 available for anyone who discovers a new, really big prime number.

9) Random numbers

10) Pythagorean triples : A great introduction into number theory – investigating the solutions of Pythagoras’ Theorem which are integers (eg. 3,4,5 triangle).

11) Mersenne primes : These are primes that can be written as 2^n -1.

12) Magic squares and cubes : Investigate magic tricks that use mathematics. Why do magic squares work?

13) Loci and complex numbers

14) Egyptian fractions : Egyptian fractions can only have a numerator of 1 – which leads to some interesting patterns. 2/3 could be written as 1/6 + 1/2. Can all fractions with a numerator of 2 be written as 2 Egyptian fractions?

15) Complex numbers and transformations

16) Euler’s identity: An equation that has been voted the most beautiful equation of all time, Euler’s identity links together 5 of the most important numbers in mathematics.

17) Chinese remainder theorem . This is a puzzle that was posed over 1500 years ago by a Chinese mathematician. It involves understanding the modulo operation.

18) Fermat’s last theorem : A problem that puzzled mathematicians for centuries – and one that has only recently been solved.

19) Natural logarithms of complex numbers

20) Twin primes problem : The question as to whether there are patterns in the primes has fascinated mathematicians for centuries. The twin prime conjecture states that there are infinitely many consecutive primes ( eg. 5 and 7 are consecutive primes). There has been a recent breakthrough in this problem.

21) Hypercomplex numbers

22) Diophantine application: Cole numbers

23) Perfect Numbers: Perfect numbers are the sum of their factors (apart from the last factor). ie 6 is a perfect number because 1 + 2 + 3 = 6.

24) Euclidean algorithm for GCF

25) Palindrome numbers: Palindrome numbers are the same backwards as forwards.

26) Fermat’s little theorem : If p is a prime number then a^p – a is a multiple of p.

27) Prime number sieves

28) Recurrence expressions for phi (golden ratio): Phi appears with remarkable consistency in nature and appears to shape our understanding of beauty and symmetry.

29) The Riemann Hypothesis – one of the greatest unsolved problems in mathematics – worth $1million to anyone who solves it (not for the faint hearted!)

30) Time travel to the future : Investigate how traveling close to the speed of light allows people to travel “forward” in time relative to someone on Earth. Why does the twin paradox work?

31) Graham’s Number – a number so big that thinking about it could literally collapse your brain into a black hole.

32) RSA code – the most important code in the world? How all our digital communications are kept safe through the properties of primes.

33) The Chinese Remainder Theorem : This is a method developed by a Chinese mathematician Sun Zi over 1500 years ago to solve a numerical puzzle. An interesting insight into the mathematical field of Number Theory.

34) Cesaro Summation: Does 1 – 1 + 1 – 1 … = 1/2? . A post which looks at the maths behind this particularly troublesome series.

35) Fermat’s Theorem on the sum of 2 squares – An example of how to use mathematical proof to solve problems in number theory.

36) Can we prove that 1 + 2 + 3 + 4 …. = -1/12 ? How strange things happen when we start to manipulate divergent series.

37) Mathematical proof and paradox – a good opportunity to explore some methods of proof and to show how logical errors occur.

38) Friendly numbers, Solitary numbers, perfect numbers. Investigate what makes a number happy or sad, or sociable! Can you find the loop of infinite sadness?

39) Zeno’s Paradox – Achilles and the Tortoise – A look at the classic paradox from ancient Greece – the philosopher “proved” a runner could never catch a tortoise – no matter how fast he ran.

40) Stellar Numbers – This is an excellent example of a pattern sequence investigation. Choose your own pattern investigation for the exploration.

41) Arithmetic number puzzle – It could be interesting to do an exploration where you solve number problems – like this one.

42) Normal Numbers – and random number generators – what is a normal number – and how are they connected to random number generators?

43) Narcissistic Numbers – what makes a number narcissistic – and how can we find them all?

44) Modelling Chaos – how we can use grahical software to understand the behavior of sequences

45) The Mordell Equation . What is the Mordell equation and how does it help us solve mathematical problems in number theory?

46) Ramanujan’s Taxi Cab and the Sum of 2 Cubes . Explore this famous number theory puzzle.

47) Hollow cubes and hypercubes investigation. Explore number theory in higher dimensions!

48) When do 2 squares equal 2 cubes? A classic problem in number theory which can be solved through computational power.

49) Rational approximations to irrational numbers. How accurately can be approximate irrationals?

50) Square triangular numbers. When do we have a square number which is also a triangular number?

51) Complex numbers as matrices – Euler’s identity. We can use a matrix representation of complex numbers to test whether Euler’s identity still holds.

52) Have you got a Super Brain? How many different ways can we use to solve a number theory problem?

1a) Non-Euclidean geometries: This allows us to “break” the rules of conventional geometry – for example, angles in a triangle no longer add up to 180 degrees. In some geometries triangles add up to more than 180 degrees, in others less than 180 degrees.

1b) The shape of the universe – non-Euclidean Geometry is at the heart of Einstein’s theories on General Relativity and essential to understanding the shape and behavior of the universe.

2) Hexaflexagons: These are origami style shapes that through folding can reveal extra faces.

3) Minimal surfaces and soap bubbles : Soap bubbles assume the minimum possible surface area to contain a given volume.

4) Tesseract – a 4D cube : How we can use maths to imagine higher dimensions.

5) Stacking cannon balls: An investigation into the patterns formed from stacking canon balls in different ways.

6) Mandelbrot set and fractal shapes : Explore the world of infinitely generated pictures and fractional dimensions.

7) Sierpinksi triangle : a fractal design that continues forever.

8) Squaring the circle : This is a puzzle from ancient times – which was to find out whether a square could be created that had the same area as a given circle. It is now used as a saying to represent something impossible.

9) Polyominoes : These are shapes made from squares. The challenge is to see how many different shapes can be made with a given number of squares – and how can they fit together?

10) Tangrams: Investigate how many different ways different size shapes can be fitted together.

11) Understanding the fourth dimension: How we can use mathematics to imagine (and test for) extra dimensions.

12) The Riemann Sphere – an exploration of some non-Euclidean geometry. Straight lines are not straight, parallel lines meet and angles in a triangle don’t add up to 180 degrees.

13) Graphically understanding complex roots – have you ever wondered what the complex root of a quadratic actually means graphically? Find out!

14) Circular inversion – what does it mean to reflect in a circle? A great introduction to some of the ideas behind non-euclidean geometry.

15) Julia Sets and Mandelbrot Sets – We can use complex numbers to create beautiful patterns of infinitely repeating fractals. Find out how!

16) Graphing polygons investigation. Can we find a function that plots a square? Are there functions which plot any polygons? Use computer graphing to investigate.

17) Graphing Stewie from Family Guy. How to use graphic software to make art from equations.

18) Hyperbolic geometry – how we can map the infinite hyperbolic plane onto the unit circle, and how this inspired the art of Escher.

19) Elliptical Curves – how this class of curves have importance in solving Fermat’s Last Theorem and in cryptography.

20) The Coastline Paradox – how we can measure the lengths of coastlines, and uses the idea of fractals to arrive at fractional dimensions.

21) Projective geometry – the development of geometric proofs based on points at infinity.

22) The Folium of Descartes . This is a nice way to link some maths history with studying an interesting function.

23) Measuring the Distance to the Stars . Maths is closely connected with astronomy – see how we can work out the distance to the stars.

24) A geometric proof for the arithmetic and geometric mean . Proof doesn’t always have to be algebraic. Here is a geometric proof.

25) Euler’s 9 Point Circle . This is a lovely construction using just compasses and a ruler.

26) Plotting the Mandelbrot Set – using Geogebra to graphically generate the Mandelbrot Set.

27) Volume optimization of a cuboid – how to use calculus and graphical solutions to optimize the volume of a cuboid.

28) Ford Circles – how to generate Ford circles and their links with fractions.

29) Classical Geometry Puzzle: Finding the Radius . This is a nice geometry puzzle solved using a variety of methods.

30) Can you solve Oxford University’s Interview Question? . Try to plot the locus of a sliding ladder.

31) The Shoelace Algorithm to find areas of polygons . How can we find the area of any polygon?

32) Soap Bubbles, Wormholes and Catenoids . What is the geometric shape of soap bubbles?

33) Can you solve an Oxford entrance question? This problem asks you to explore a sliding ladder.

34) The Tusi circle – how to create a circle rolling inside another circle using parametric equations.

35) Sphere packing – how to fit spheres into a package to minimize waste.

36) Sierpinski triangle – an infinitely repeating fractal pattern generated by code.

37) Generating e through probability and hypercubes . This amazing result can generate e through considering hyper-dimensional shapes.

38) Find the average distance between 2 points on a square . If any points are chosen at random in a square what is the expected distance between them?

39) Finding the average distance between 2 points on a hypercube . Can we extend our investigation above to a multi-dimensional cube?

40) Finding focus with Archimedes. The Greeks used a very different approach to understanding quadratics – and as a result had a deeper understanding of their physical properties linked to light and reflection.

41) Chaos and strange Attractors: Henon’s map . Gain a deeper understanding of chaos theory with this investigation.

Calculus/analysis and functions

1) The harmonic series: Investigate the relationship between fractions and music, or investigate whether this series converges.

2) Torus – solid of revolution : A torus is a donut shape which introduces some interesting topological ideas.

3) Projectile motion: Studying the motion of projectiles like cannon balls is an essential part of the mathematics of war. You can also model everything from Angry Birds to stunt bike jumping. A good use of your calculus skills.

4) Why e is base of natural logarithm function: A chance to investigate the amazing number e.

5) Fourier Transforms – the most important tool in mathematics? Fourier transforms have an essential part to play in modern life – and are one of the keys to understanding the world around us. This mathematical equation has been described as the most important in all of physics. Find out more! (This topic is only suitable for IB HL students).

6) Batman and Superman maths – how to use Wolfram Alpha to plot graphs of the Batman and Superman logo

7) Explore the Si(x) function – a special function in calculus that can’t be integrated into an elementary function.

8) The Remarkable Dirac Delta Function . This is a function which is used in Quantum mechanics – it describes a peak of zero width but with area 1.

9) Optimization of area – an investigation . This is an nice example of how you can investigation optimization of the area of different polygons.

10) Envelope of projectile motion . This investigates a generalized version of projectile motion – discover what shape is created.

11) Projectile Motion Investigation II . This takes the usual projectile motion ideas and generalises them to investigate equations of ellipses formed.

12) Projectile Motion III: Varying gravity . What would projectile motion look like on different planets?

13) The Tusi couple – A circle rolling inside a circle . This is a lovely result which uses parametric functions to create a beautiful example of mathematical art.

14) Galileo’s Inclined Planes . How did Galileo achieve his breakthrough understanding of gravity? Follow in the footsteps of a genius!

Statistics and modelling 1 [topics could be studied in-depth]

1) Traffic flow : How maths can model traffic on the roads.

2) Logistic function and constrained growth

3) Benford’s Law – using statistics to catch criminals by making use of a surprising distribution.

4) Bad maths in court – how a misuse of statistics in the courtroom can lead to devastating miscarriages of justice.

5) The mathematics of cons – how con artists use pyramid schemes to get rich quick.

6) Impact Earth – what would happen if an asteroid or meteorite hit the Earth?

7) Black Swan events – how usefully can mathematics predict small probability high impact events?

8) Modelling happiness – how understanding utility value can make you happier.

9) Does finger length predict mathematical ability? Investigate the surprising correlation between finger ratios and all sorts of abilities and traits.

10) Modelling epidemics/spread of a virus

11) The Monty Hall problem – this video will show why statistics often lead you to unintuitive results.

12) Monte Carlo simulations

13) Lotteries

14) Bayes’ theorem : How understanding probability is essential to our legal system.

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

16) Are we living in a computer simulation? Look at the Bayesian logic behind the argument that we are living in a computer simulation.

17) Does sacking a football manager affect results ? A chance to look at some statistics with surprising results.

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

19) Introduction to Modelling. This is a fantastic 70 page booklet explaining different modelling methods from Moody’s Mega Maths Challenge.

20) Modelling infectious diseases – how we can use mathematics to predict how diseases like measles will spread through a population

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

22) Modelling Zombies – How do zombies spread? What is your best way of surviving the zombie apocalypse? Surprisingly maths can help!

23) Modelling music with sine waves – how we can understand different notes by sine waves of different frequencies. Listen to the sounds that different sine waves make.

24) Are you psychic? Use the binomial distribution to test your ESP abilities.

25) Reaction times – are you above or below average? Model your data using a normal distribution.

26) Modelling volcanoes – look at how the Poisson distribution can predict volcanic eruptions, and perhaps explore some more advanced statistical tests.

27) Could Trump win the next election ? How the normal distribution is used to predict elections.

28) How to avoid a Troll – an example of a problem solving based investigation

29) The Gini Coefficient – How to model economic inequality

30) Maths of Global Warming – Modeling Climate Change – Using Desmos to model the change in atmospheric Carbon Dioxide.

31) Modelling radioactive decay – the mathematics behind radioactivity decay, used extensively in science.

32) Circular Motion: Modelling a Ferris wheel . Use Tracker software to create a Sine wave.

33) Spotting Asset Bubbles . How to use modeling to predict booms and busts.

34) The Rise of Bitcoin . Is Bitcoin going to keep rising or crash?

35) Fun with Functions! . Some nice examples of using polar coordinates to create interesting designs.

36) Predicting the UK election using linear regression . The use of regression in polling predictions.

37) Modelling a Nuclear War . What would happen to the climate in the event of a nuclear war?

38) Modelling a football season . We can use a Poisson model and some Excel expertise to predict the outcome of sports matches – a technique used by gambling firms.

39) Modeling hours of daylight – using Desmos to plot the changing hours of daylight in different countries.

40) Modelling the spread of Coronavirus (COVID-19) . Using the SIR model to understand epidemics.

41) Finding the volume of a rugby ball (or American football) . Use modeling and volume of revolutions.

42) The Martingale system paradox. Explore a curious betting system still used in currency trading today.

Statistics and modelling 2 [more simplistic topics: correlation, normal, Chi squared]

1) Is there a correlation between hours of sleep and exam grades? Studies have shown that a good night’s sleep raises academic attainment.

2) Is there a correlation between height and weight? (pdf). The NHS use a chart to decide what someone should weigh depending on their height. Does this mean that height is a good indicator of weight?

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

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

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

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

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

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

10) Does eating breakfast affect your grades?

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

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

13) Is there a correlation between height and basketball ability? Look at some stats for NBA players to find out.

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

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

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

17) Are a sample of flower heights normally distributed?

18) Are a sample of student weights normally distributed?

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

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

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

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

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

Games and game theory

1) The prisoner’s dilemma : The use of game theory in psychology and economics.

3) Gambler’s fallacy: A good chance to investigate misconceptions in probability and probabilities in gambling. Why does the house always win?

4) Bluffing in Poker: How probability and game theory can be used to explore the the best strategies for bluffing in poker.

5) Knight’s tour in chess: This chess puzzle asks how many moves a knight must make to visit all squares on a chess board.

6) Billiards and snooker

7) Zero sum games

8) How to “Solve” Noughts and Crossess (Tic Tac Toe) – using game theory. This topics provides a fascinating introduction to both combinatorial Game Theory and Group Theory.

9) Maths and football – Do managerial sackings really lead to an improvement in results? We can analyse the data to find out. Also look at the finances behind Premier league teams

10) Is there a correlation between Premier League wages and league position? Also look at how the Championship compares to the Premier League.

11) The One Time Pad – an uncrackable code? Explore the maths behind code making and breaking.

12) How to win at Rock Paper Scissors . Look at some of the maths (and psychology behind winning this game.

13) The Watson Selection Task – a puzzle which tests logical reasoning. Are maths students better than history students?

Topology and networks

2) Steiner problem

3) Chinese postman problem – This is a problem from graph theory – how can a postman deliver letters to every house on his streets in the shortest time possible?

4) Travelling salesman problem

5) Königsberg bridge problem : The use of networks to solve problems. This particular problem was solved by Euler.

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

7) Möbius strip : An amazing shape which is a loop with only 1 side and 1 edge.

8) Klein bottle

9) Logic and sets

10) Codes and ciphers : ISBN codes and credit card codes are just some examples of how codes are essential to modern life. Maths can be used to both make these codes and break them.

11) Zeno’s paradox of Achilles and the tortoise : How can a running Achilles ever catch the tortoise if in the time taken to halve the distance, the tortoise has moved yet further away?

12) Four colour map theorem – a puzzle that requires that a map can be coloured in so that every neighbouring country is in a different colour. What is the minimum number of colours needed for any map?

13) Telephone Numbers – these are numbers with special properties which grow very large very quickly. This topic links to graph theory.

14) The Poincare Conjecture and Grigori Perelman – Learn about the reclusive Russian mathematician who turned down $1 million for solving one of the world’s most difficult maths problems.

Mathematics and Physics

1) The Monkey and the Hunter – How to Shoot a Monkey – Using Newtonian mathematics to decide where to aim when shooting a monkey in a tree.

2) How to Design a Parachute – looking at the physics behind parachute design to ensure a safe landing!

3) Galileo: Throwing cannonballs off The Leaning Tower of Pisa – Recreating Galileo’s classic experiment, and using maths to understand the surprising result.

4) Rocket Science and Lagrange Points – how clever mathematics is used to keep satellites in just the right place.

5) Fourier Transforms – the most important tool in mathematics? – An essential component of JPEG, DNA analysis, WIFI signals, MRI scans, guitar amps – find out about the maths behind these essential technologies.

6) Bullet projectile motion experiment – using Tracker software to model the motion of a bullet.

7) Quantum Mechanics – a statistical universe? Look at the inherent probabilistic nature of the universe with some quantum mechanics.

8) Log Graphs to Plot Planetary Patterns . The planets follow a surprising pattern when measuring their distances.

9) Modeling with springs and weights . Some classic physics – which generates some nice mathematical graphs.

10) Is Intergalactic space travel possible? Using the physics of travel near the speed of light to see how we could travel to other stars.

Maths and computing

1) The Van Eck Sequence – The Van Eck Sequence is a sequence that we still don’t fully understand – we can use programing to help!

2) Solving maths problems using computers – computers are really useful in solving mathematical problems. Here are some examples solved using Python.

3) Stacking cannonballs – solving maths with code – how to stack cannonballs in different configurations.

4) What’s so special about 277777788888899? – Playing around with multiplicative persistence – can you break the world record?

5) Project Euler: Coding to Solve Maths Problems . A nice starting point for students good at coding – who want to put these skills to the test mathematically.

6) Square Triangular Numbers . Can we use a mixture of pure maths and computing to solve this problem?

7) When do 2 squares equal 2 cubes? Can we use a mixture of pure maths and computing to solve this problem?

8) Hollow Cubes and Hypercubes investigation . More computing led investigations

9) Coding Hailstone Numbers . How can we use computers to gain a deeper understanding of sequences?

Further ideas:

1) Radiocarbon dating – understanding radioactive decay allows scientists and historians to accurately work out something’s age – whether it be from thousands or even millions of years ago.

2) Gravity, orbits and escape velocity – Escape velocity is the speed required to break free from a body’s gravitational pull. Essential knowledge for future astronauts.

3) Mathematical methods in economics – maths is essential in both business and economics – explore some economics based maths problems.

4) Genetics – Look at the mathematics behind genetic inheritance and natural selection.

5) Elliptical orbits – Planets and comets have elliptical orbits as they are influenced by the gravitational pull of other bodies in space. Investigate some rocket science!

6) Logarithmic scales – Decibel, Richter, etc. are examples of log scales – investigate how these scales are used and what they mean.

7) Fibonacci sequence and spirals in nature – There are lots of examples of the Fibonacci sequence in real life – from pine cones to petals to modelling populations and the stock market.

8) Change in a person’s BMI over time – There are lots of examples of BMI stats investigations online – see if you can think of an interesting twist.

9) Designing bridges – Mathematics is essential for engineers such as bridge builders – investigate how to design structures that carry weight without collapse.

10) Mathematical card tricks – investigate some maths magic.

11) Flatland by Edwin Abbott – This famous book helps understand how to imagine extra dimension. You can watch a short video on it here

12) Towers of Hanoi puzzle – This famous puzzle requires logic and patience. Can you find the pattern behind it?

13) Different number systems – Learn how to add, subtract, multiply and divide in Binary. Investigate how binary is used – link to codes and computing.

14) Methods for solving differential equations – Differential equations are amazingly powerful at modelling real life – from population growth to to pendulum motion. Investigate how to solve them.

15) Modelling epidemics/spread of a virus – what is the mathematics behind understanding how epidemics occur? Look at how infectious Ebola really is .

16) Hyperbolic functions – These are linked to the normal trigonometric functions but with notable differences. They are useful for modelling more complex shapes.

17) Medical data mining – Explore the use and misuse of statistics in medicine and science.

18) Waging war with maths: Hollow squares . How mathematical formations were used to fight wars.

19) The Barnsley Fern: Mathematical Art – how can we use iterative processes to create mathematical art?

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25 Mathematics Internal Assessment Ideas

Need help with IB Exam preparation or Internal Assessment? Struggling with understanding concepts?

What is the Internal Assessment

Your Internal Assessment (IA) is a project that you will have to complete in all your IB classes. The style and grade value depends on the subject. It is a project that you will work on with the guidance of your teacher ( or your tutor ). The great thing about the internal assessment is that it allows students to be flexible and to further research a topic that they find interesting within the given subject. As good as it sounds, generating IA topic ideas is not always easy and that’s why we decided to help you here with some unique math IA ideas. Just read on!

What makes a good Math IA

A good IA should demonstrate your own interest of the topic. Moreover, it should show that the student has learned and has been able to apply what they have learned. A good IA does not have to be a very complex and intricate piece of work. Rather a clearly stated and clearly answered research question, consistent structure, and clear personal engagement which demonstrates knowledge will earn the student a good grade.

So let’s jump into what you are here for. Here is a list of 25 possible topics that serve as great math IA ideas . And keep in mind that in a math IA, it is more important to pick a topic that genuinely motivates you to display personal engagement than to pick something that sounds harder but does not resonate with you.

25 Unique Math IA Ideas

Arc lengths from integration techniques

Architecture and mathematics: the golden ratio

Bertrand paradox and probabilities

Cat’s cradle and the mathematics of knots

Chaos theory and the logistic map

Chess and the eight Queens puzzle

Conditional probability and the Monty Hall problem

Describing the vibrations of drums with Bessel functions

Dirac delta function and its applications

Elliptical geometry: when the sum of the angles of a triangle does not equal 180º

Euler’s identity: complex numbers and mathematical beauty

Fourier transformations

Fractals in nature

Markov chains and random walks

Modular arithmetic: when 2+2 is not always equal to 4

Möbius strip: the strange world of non-orientable surfaces

Simpson’s paradox and the strange outcomes of misused statistics

Special functions: error function and normal distributions

Surprising ways of finding Pi: Gaussian integral and the Leibniz Formula

The Koch snowflake: fractals and the tessellation of plane

The Mandelbrot Set: when fractals meet complex numbers

The Logistic function and its applications (population growth, neural networks, or linguistics)

The Gambler’s ruin: how beneficial chances are never beneficial in the end

The wave equation: how differential equations can be used to find the shape of a music note.

Topology: when a coffee mug and a donut are one and the same

To think about before you choose

Mathematics can be applied to pretty much all areas of human activity. For instance, a wave equation can be used not only to study music, but the dynamics of fluids and quantum mechanics as well, while the logistic function is applied to fields as diverse as population studies, neural networks, and linguistics. So remember to first pick an area that interests you, because the odds that one of the mathematics IA ideas above can be applied there are definitely in your favor.

Still Struggling?

No worries, our tutors are here to help. Whether you would like to consult what topic to choose or need additional help with setting up the structure of your IA, Think Smart Tutoring can help you. Just sign-up here for our tutoring services and we’ll contact you shortly to set-up the first introductory session.

25 History Internal Assessment Ideas

25 unique biology internal assessment ideas.

Ib maths tutor at Ibstudies shedding some myths and helps you to secure 20/20 in IB AA/AI maths internal assessments

This blog post is constructed to be seen as the fundamental handbook to accomplishing a higher maths IA mark . This is important to point out that as the probable topics for maths IA’s are so vast that each topic of maths IA would be addressed differently, this blog will disseminate the top 20 IB maths IA topics along with the comprehensive advice as opposed to necessary components of each IA; which can be otherwise be inferred from the IA marking criteria. Ib maths tutor at Ibstudies help students to secure full marks HL/SL maths IA, 20/20, and here we are providing some guidance that can assist you when writing up your final IB maths IA.

accomplishing a higher maths IA mark

1: IB maths tutor in Gurgaon help you to find the top 20 topics of maths IA

Find a topic you always seem to question, how these things existing, what are fundamental principles apply to them and how can you assess them. In my opinion, this pertains to the maths IA more than almost any other IA or assignment as a considerable time will have to be disbursed on it to achieve a high mark. The IA indeed a tedious task in terms of formatting and working out and so on, especially with AA/AI Maths IA which will generally involve statistics, calculus, and so on, and so it is necessary that you don’t exhaust yourself too much and become demotivated.

Ib maths tutor at Ibstudies assists you to find a “topic” you really enjoy. Below are some examples :

Ib maths tutor

How can the research of patterns in the Pascal triangle be connected to solving other questions in mathematics?
What is the sum of all positive integers? Investigate this problem through the world of sequence and series.
Examine why distinct notes/chords in symphony dissonant, and others consonant, by gazing at the proportions of frequencies between the notes.
Gini Index: Using calculus to derive the Gini ratio for a few countries, enabling you to accurately approximate their levels of economic unevenness?
Tinder/Bumble and other apps: Is there a matching algorithm that assures each individual in the community to end up with their true love? What algorithms are these apps are following? Are they successful enough?
Decoding a Password: What is the probability that adding symbols and special characters will make the password safer?
Permutation and combination: How many handshakes are needed in a compartment so that everyone shakes hands with one another.
Modeling the Spread of a coronavirus: How long do we have to quarantine a city so as to prevent the deadly coronavirus to spread?
Impact on the global economy because of shutting down due to coronavirus spread? Find which countries are more affected by using GDP calculation?
Birthday problem: In probability theory, in a set of n randomly chosen individuals, some have the same birthday. Using the pigeonhole principle, the probability reaches 100% when the number of individuals reaches up to 367
Optimizing area: To uncover the dimensions of a cylinder with a provided volume that minimizes the surface area.
The flow of traffic: How does mathematics solve the problems of traffic jams in a crowded country like India and China?
Cricket statistics: Is there a correlation between high valuation in the auction of a player in IPL and their performance in the respective countries’ team?
Cricket statistics: Why only a few teams in the IPL have won the tournament so far while other teams are struggling? Is there any correlation between there success and their valuations?
Probability: Are Oxford and Cambridge prejudiced against the applicants from an Asian country?
Olympic Statistics: With Tokyo 2020 being rescheduled to 2022, what are the economic losses suffered by the country?
Analyzing Data: In the 500-meter run, is there a benefit to a particular lane in track?
Amazon rainforest Fire 2020: How does the world’s largest tropical rainforest Biodiversity Loss, Climate Change, and Health is affected by fire in 2020?
The historical problem of seven Königsberbridgesge: Using networks to solve problems.
Radioactive decay: The mathematics behind the Chernobyl: Is it safer for human civilization to settle out there?

Gini Index:

Tinder/Bumble and other apps:

Decoding a Password:

Permutation and combination:

Modeling the Spread of a coronavirus:

Birthday problem:

3d phone case like this best replica watch site 2019 Optimizing area:

The flow of traffic:

Cricket statistics:

Probability:

Olympic Statistics:

Analyzing Data:

Amazon rainforest Fire 2020:

The historical problem of seven Königsberbridgesge:

Radioactive decay:

Tag: IB Maths IA Topics

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Current: How to Choose Topics for IB Math IA and EE

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How to choose topics for ib math ia and ee.

$How to Choose Topics for IB Math IA and EE$

Choosing topics for any research-based essay can significantly affect how your essay is and therefore many students find it one of the most difficult parts of the assignment.

1. KNOW THE DIFFERENCE BETWEEN IB MATH IA AND EE

IA and EE in IB Mathematics are essentially the same in terms of what they require. However, EE is an extended and a much more in-depth analysis of the topic of your choice. Therefore, for an EE the topic you choose should be a little broader and have a lot more potential for detailed study than your topic for your IA. A topic for an IB Math IA can be much more focused and have limited possibilities in exploration. If you are not sure about how much you can explore in a particular topic, speak with your teacher or your online IB maths tutor to discuss options.

2. CHOOSE A TOPIC YOU LOVE

Any research based extended essay is best written on a topic that the writer feels passionate about or is keen to explore. Hence, choose a topic that invokes curiosity in you or that you wish to learn more about. Personal engagement is an important criterion in IA and EE and is best justified when the topic you choose has a major relevance in your life in general or your further studies. It could also be based on things you see around you like cooling rates of food on your table or patterns in nature. Your topic could also be based on your passion for music, equestrian, skating or any other hobbies you may have. Mathematics is everywhere. Explore the Mathematics behind things you love!

3. PURE MATHEMATICS ALONE?

Both IB IA and EE topics should have a mathematical focus yet may not be confined to theories in IB Mathematics itself. Topics with a focus on math can be chosen from Economics, Physics or in general, Engineering and Social Sciences. For example, calculus is used in physics and engineering extensively. You can narrow down one or two such uses that you would like to explore mathematically. However, the research question and subsequently your IA and EE should revolve around the mathematical progression in the topic. Make sure that the level of Mathematics that you are exploring is in par with and/or beyond the level of Mathematics (IB Mathematics Analysis and Approaches SL/HL or Application and Interpretation SL/HL) you have chosen in the IB curriculum.

4. DECIDE YOUR APPROACH

Your topic may also depend on whether you want to do a statistical analysis, model data or investigate certain theories. Exploring applications of math is another approach you can take. Some students prefer choosing the approach before the topic. If so, decide which approach will you do well in. Are you good with modelling data and finding patterns? Or do you prefer exploring theories or applications of theories? When you have done choosing which approach you prefer, look at topic options. Research which topic are you interested in and has the potential to explore in terms of the approach you have chosen. Discuss approaches and relevant topics with your IB Mathematics tutor or online IB tutor to narrow down your options.

5. WHERE CAN I FIND TOPICS?

There are many resources and websites online that have extensive lists of topics. Many students find that these lists have useful yet very repetitive topics that they do not find very interesting. You can find different yet interesting ideas by considering the modules of the course you are planning to undertake at University level, ask your IB online math tutor for ideas to explore a topic and then connect the topic to your syllabus in IB. Another place to start is to focus on areas of Mathematics that you are currently learning and are particularly interested in and research what theories or applications that you have not already learnt can be investigated further.

6. BE INNOVATIVE

There are a lot of topics that are very common and every other IB math IA or EE that an examiner or moderator checks is based on these. Question is how to make yours stand out? Be innovative in exploring the topic. Investigate an area of use an approach of the same topic that is unique, exciting for you and for the reader. Even though the criteria of IB Math may restrict your options for which topics have potential, your ability to innovate and explore beyond what one would expect makes your IA or EE stand out.

7. ALWAYS HAVE BACKUP TOPICS

In your search for topics, make a list of areas that you wish to explore and narrow down the list to three or four topics in order of preference. You may find after delving into a topic that it does not have the potential to cover all of the criteria of the IA or EE well enough. In this case, it is better to have some backup options, so you do not waste time in searching for another topic.

8. PLAN AND RESEARCH BEFORE PROCEEDING

Plan how you will explore a topic before actually starting your IA or EE. IB requires a lot from a student within the short span of two years and therefore time is precious for you. Planning your essay or making a broad outline to your proposed IA and EE can help you understand the potential of the topic you have chosen and give you an insight of your progress. It can help you conclude if the topic is a good fit for you and your essay. For further understanding, your online IB tutors are always there.

With these points in mind, you can choose the best suitable yet fail safe topic for your Mathematics IA or EE. Baccalaureate Classes are always available to students who need further help. Good Luck!

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To Model The Motion Of A Swimmer Using The Parametric Equations Of Motion And Determine The Terminal Velocity Of The Swimmer And The Minimum Depth Of The Pool For Safe Swimming Using Equation Solving

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Investigating The Trigonometric Functions To Describe The Variation Of Temperature Against Time Over A Period Of 10 Years, The Variation Of Wind Speed Against Time Over A Period Of 10 Years And Finding A Relation Between The Two Using The Concepts Of Differential Calculus And Complex Number.

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To What Extent Can Volumes Of Revolution Be Used To Calculate The Volume Of A Hot Air Balloon?

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Investigating The Correlation Between Number Of Employees And Total Profit, Marginal Profit In Gems And Jewelers, Ahmadabad, India

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Mathematical Modeling Of The Projectile Motion Of Volleyball And Determining The Equation Of Its Trajectory

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Effect Of Quadratic Air Resistance On The Trajectory Of A Shot Put (Projectile)

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Investigation On Banking Of Road At The Turn And Comparison Between A Road With Banking And A Road Without Banking

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Investigation On The Increase Of Stock Price Of BioCryst Pharmaceuticals Inc Corresponding To The Exponential Increase In Ebola Infection In South-Eastern Guinea And Hence Determining A Correlation Between Them.

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Mathematical Modelling Of Pathway Of A Plane

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Modelling The Radioactive Decay Of The Chernobyl Incident

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Modelling Singapore's Population Using The Logistic Model And Identifying Its Carrying Capacity

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Mathematics HL IB IA Example

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IB Math HL Internal Assessment (IA) Example Topics
IA Idea 1 - Modeling Statistics. Modeling statistics is a pretty broad concept for an IA, but it can refer to any project where a change in statistics is presented in a visually effective manner. An example of modeling is presenting the rate at which a country's population changes relative to external factors.
Maths IA
Maths IA - 300 Maths Exploration Topics: Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. Topics include Algebra and Number (proof), Geometry, Calculus, Statistics and Probability, Physics, and links with other subjects.
Choosing the Best IB Mathematics IA Topics [Plus 25+ Examples]
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. ... I need help finding a math IA HL topic related need ...
50 IB Maths IA Topic Ideas
Maths and Time: Exploring ideas regarding time dilation. Plotting Planets: Using log functions to track planets! So there we have it: 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! We also have similar ideas for Biology, Chemistry, Economics, History, Physics, TOK… and many many more tips and ...
IB Maths IA examples
Modelling financial market with Chaos theory (received mark: 15/20) IA Maths HL 6. High scoring IB Maths Internal Assessment examples. See what past students did and make your Maths IA perfect by learning from examiner commented examples!
IB Math AA IA Ideas: Topics and Research Questions
These IB Math AA IA ideas and research questions aim to inspire your exploration, combining theoretical knowledge with practical application in diverse fields. Higher Level (SL) IB Math AA IA Ideas. For Higher Level (HL) students, the challenge intensifies. Your IA should reflect a deeper understanding of complex concepts.
IB Maths IA: 60 Examples and Guidance
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.
IB Math IA (Ultimate Guide For 2023)
You are at the right place - The Ultimate Guide to IB Math IA! This article covers IB Math IA rubrics, process key pointers, the structure of the investigation, and interesting IB Math IA topics that will stimulate your mind and help you begin your exploration! You should also know about the updated course structure of IB Mathematics.
How to Structure and Format Your Math IA
The first criterion is about the presentation, with the aim of assessing the general organization and coherence of your IA. Although students tend to focus on the complexity of math that their exploration demonstrates, a full 4 points are rewarded for the clarity of your explanations and structure. In order to score in the top range here, make ...
IB Math HL IA Topics
Place Order. IB Math HL IA Topics. Writing an Internal Assessment is an important part of the IB Math program. An IA is a research paper, which must be written on a topic in Mathematics. It is an opportunity to explore a specific topic in-depth and showcase your knowledge and understanding of mathematics. When choosing a topic for your IA, it ...
PDF Maths IA
IB maths exploration (IA) ideas www.aeteaching.com [email protected] +34 637 035 159 Maths IA - Maths Exploration Topics Important Be aware that this page gets a large amount of traffic from IB students - do not simply copy arti cles. This will almost certainly be spotted by the IB moderators and could result in you failing your diploma.
13+ Mathematics AA HL Free IA Examples!
Explore The Secrets Of Closed Knight's Tours On 3 x 2k Chess Boards In This Comprehensive IB Math AA HL IA Sample, Perfect For Aspiring Mathematicians. Mathematics AA HL. 6/7. 143 Likes. 29 mins read. 5660 words. English. Math AA HL IA.
PDF MATH IA GUIDE MATHS IA GUIDE
adequate mathematical level. The following is a guide that wil. help you ace your Maths IA. Note that the IA requirements and structure is very similar in the new and old maths syllabus, so while this guide is created for the new syllabus it is relevant whether you're studying Maths AI SL/HL, Maths AA. L/HL, Maths HL, or Maths SL!Let's.
Internal Assessment
tentative deadlines for math hl iA (Class of 2020) ... Student research and brainstorm of interested topics Brainstorm and return to school in the fall with 3 potential topics and a short description for each. Using your topic and abstract, generate an outline with an essential question of exploration, including at least 3 subtopics and info ...
Advice for IB Math IA
Advice for IB Math IA - choosing a research question, topic. In this post I will be sharing my opinion on selection of topic for Math IA. Truth is, different schools have different guidance on this. For example, I know a school that bans Graph and Game theory for selection (I'm against such a policy). HL students should not be pursuing a topic ...
Maths IA
Maths IA - 300 Maths Exploration Topics: Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. ... (SL and HL). Algebra and number. 1) Modular arithmetic - This technique is used throughout Number Theory. For example, Mod 3 means ...
25 Unique Math IA Ideas
Here is a list of 25 possible topics that serve as great math IA ideas. And keep in mind that in a math IA, it is more important to pick a topic that genuinely motivates you to display personal engagement than to pick something that sounds harder but does not resonate with you. 25 Unique Math IA Ideas. Arc lengths from integration techniques ...
Top 20 IB Maths IA Topics
Ib maths tutor at Ibstudies help students to secure full marks HL/SL maths IA, 20/20, and here we are providing some guidance that can assist you when writing up your final IB maths IA. accomplishing a higher maths IA mark. 1: IB maths tutor in Gurgaon help you to find the top 20 topics of maths IA. Find a topic you always seem to question, how ...
PDF Mathematical Exploration HL
teacher that any mathematics in your report is correct. Your teacher will not give mathematical answers or corrections, but can indicate where any errors have been made or where improvement is needed. Mathematical Exploration HL Student Checklist Is your report written entirely by yourself and trying to avoid simply replicating work and ideas
Choosing Topics for IB Math IA and EE
Topics with a focus on math can be chosen from Economics, Physics or in general, Engineering and Social Sciences. For example, calculus is used in physics and engineering extensively. You can narrow down one or two such uses that you would like to explore mathematically. However, the research question and subsequently your IA and EE should ...
How do I start Math IA? Do I need to have a research question ...
11 votes, 10 comments. Hellloooo. I am trying to work on my Math IA (outline due next week 😬), but I have no idea where to start. ... Choose a math topic, formulate a research question, and study it using math for your Math IA, much like a scientific investigation. ... Exam Discussion: Physics HL ...
10+ Mathematics AI HL Free IA Examples!
Mathematics AI HL IA Examples. Score a home run on your Mathematics AI HL with our exclusive collection of Free IA Examples! Get insider tips and tricks for success. Sell Your IA For $10 a pop! Happy to give you $10 for every IA so we can give it away for free! Top IA examples. Learn and excel. Outstanding EE examples.
Are these suitable reserach questions for my Math AA HL IA?
Here are some research questions that I have. How can divisibility tests be used to determine if a number is a palindromic number? "How does Euler's Identity relate to complex numbers and the unit circle, and what implications does it have for the field of mathematics?" "How does the relationship between the exponential and logarithmic ...