math extended essay research questions

Mathematics Extended Essay Topics for IB

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• Writing Metier

Ever felt the exhilaration that comes with cracking a complex math problem? That’s the sheer beauty of mathematics – it’s a world where numbers dance, patterns emerge, and solutions await the keen observer. Felt that? Hah?

Now, imagine channeling that same enthusiasm and zest into your Math Extended essay. It might sound like a challenge, but isn’t that what we thrive on? With the right Math EE topic, you can showcase your mathematical prowess and leave an indelible mark on your IB evaluators following the general criteria. 

To help you with that, I’ve curated a list of Math extended essay ideas that span the spectrum from the accessible to the intricate. 

So, let’s begin.

IB Math extended essay ideas

These aren’t just topics; they’re gateways to exploration, understanding, and innovation. 

Ready to get started?

Easy-to-approach topics

For those looking for a gentler introduction to the Math Extended essay, below is a list of 10 engaging and manageable IB Math EE topic ideas, each with a research question and a brief description on how to approach it:

Patterns in Pascal’s Triangle

Research Question: 

How do patterns emerge in Pascal’s Triangle?

Description: 

Begin with the construction of Pascal’s Triangle, then delve into the exploration of its patterns, such as triangular numbers and the Fibonacci sequence.

Mathematics of Voting Systems

How do different voting systems weigh individual votes mathematically?

Introduce various voting systems, then analyze the mathematical principles behind each, discussing fairness and potential biases.

Geometry in Art

Research Question:  

How is geometry used to create visual appeal in art?

Explore various art pieces, highlighting the geometric principles employed, and discuss their impact on aesthetics.

The Math Behind Baking

How do ratios in baking recipes affect the final product?

Investigate the importance of maintaining specific ratios in baking recipes and experiment with variations to observe changes in outcomes.

Probability in Card Games

How does understanding probability enhance success in card games like Poker?

Delve into the rules of Poker and then analyze various hands and scenarios using probability principles.

Symmetry in Nature

How is symmetry exhibited in natural formations?

Explore the concept of symmetry mathematically and then identify and analyze its presence in various natural formations like leaves, flowers, and animals.

Mathematics of Music

How do mathematical patterns influence musical scales and rhythms?

Investigate the structure of musical scales, rhythms, and time signatures, highlighting the underlying mathematical patterns.

Simple Interest vs. Compound Interest

How do simple and compound interest methods impact savings over time?

Define both interest methods and then use mathematical modeling to compare their effects on savings over various periods.

The Golden Ratio in Architecture

How is the Golden Ratio applied in iconic architectural designs?

Introduce the concept of the Golden Ratio and then analyze its application in various famous architectural structures.

Mathematics of Juggling

How do mathematical patterns and sequences dictate juggling techniques?

Explore basic juggling techniques and patterns, analyzing the mathematical sequences that jugglers use to maintain rhythm and control.

Each of these topic ideas and RQs is approachable yet offers ample scope for exploration and analysis within the realm of mathematics.

Intermediate topics

For those seeking a bit more challenge without diving into the deep end, the topics below offer a balanced blend of complexity and accessibility.

Here’s a list of 10 average-difficulty IB Math Extended essay topics, each with a research question and a brief description of how to approach it:

Game Theory in Economics

How does game theory provide insights into competitive market behaviors?

Introduce game theory principles and use business world case studies to show strategic decision-making influenced by game theory.

Fractals and Nature

How do fractal patterns manifest in natural phenomena?

Description:  

Delve into the mathematical concept of fractals and explore their appearance in various natural settings, such as coastlines, mountains, and plants.

Mathematics of Population Growth Models

How do mathematical models accurately predict population growth in urban areas?

Introduce population growth models and use real urban area data to validate these models, discussing influencing factors.

Cryptography and Internet Security

How do modern cryptographic techniques ensure data security on the internet?

Explore the evolution of cryptography, focusing on modern techniques, and discuss their role in ensuring data security in online transactions.

Mathematical Modeling of Epidemics

How can mathematical models predict the spread of infectious diseases?

Introduce basic epidemiological models and analyze their effectiveness in predicting disease spread using real-world data.

Topology and Coffee Cups

How does topology explain the mathematical similarity between a coffee cup and a donut?

Dive into the basics of topology and use it to explain the often-cited comparison between coffee cups and donuts, emphasizing the concept of homeomorphism.

Chaos Theory and Weather Forecasting

How does chaos theory impact the accuracy of long-term weather forecasts?

Introduce chaos theory, then delve into its application in meteorology, discussing the challenges and limitations in predicting weather.

Mathematics Behind Neural Networks

How do mathematical algorithms drive the functioning of neural networks in artificial intelligence?

Explore the structure of neural networks and delve into the mathematical algorithms that enable their learning and functioning.

Optimization Problems in Logistics

How can mathematical optimization improve efficiency in supply chain logistics?

Investigate real-world logistics challenges and demonstrate how mathematical optimization techniques can offer solutions.

Number Theory in Modern Cryptography

How does advanced number theory underpin modern cryptographic techniques?

Delve into number theory concepts and their application in modern cryptographic methods, emphasizing their role in ensuring data security.

These topics and research questions offer a balanced blend of complexity and accessibility, making them suitable for students seeking a moderate challenge in their Math Extended essay.

Advanced topics (with potential for higher rewards)

For the brave hearts ready to dive deep, these topics are challenging but can yield impressive results when tackled effectively.

The list of 10 challenging IB Math Extended essay ideas, each with a research question and a brief description:

Navier–Stokes Existence and Smoothness

What are the mathematical implications of the unsolved Navier–Stokes existence and smoothness problem in fluid dynamics?

Delve deep into the Navier–Stokes equations, exploring their significance in fluid dynamics and the challenges surrounding their unsolved problems.

Riemann Hypothesis and Prime Numbers

How does the Riemann Hypothesis relate to the distribution of prime numbers?

Investigate the Riemann Hypothesis, its historical context, and its profound implications for the distribution of prime numbers.

Quantum Cryptography and Key Distribution

How does quantum cryptography enhance security in key distribution?

Explore the principles of quantum mechanics applied to cryptography, focusing on the advantages and challenges of quantum key distribution.

Elliptic Curves and Cryptography

How do elliptic curves underpin modern cryptographic techniques?

Dive into the mathematics of elliptic curves and their pivotal role in modern cryptographic algorithms.

Four Color Theorem and Graph Theory

How does the Four Color Theorem demonstrate the complexities of graph coloring?

Investigate the history and proof of the Four Color Theorem, discussing its implications and challenges in graph theory.

Complex Analysis in Quantum Mechanics

How does complex analysis influence the mathematical foundations of quantum mechanics?

Delve into the principles of complex analysis and explore their applications and significance in quantum mechanics.

Twin Prime Conjecture

What are the implications and challenges of the Twin Prime Conjecture in number theory?

Investigate the Twin Prime Conjecture, its history, and its significance in the realm of number theory.

Knot Theory and DNA Replication

How does knot theory provide insights into the process of DNA replication?

Explore the mathematical intricacies of knot theory and its applications in understanding the complexities of DNA replication.

Ergodic Theory and Thermodynamics

How does ergodic theory connect with the principles of statistical thermodynamics?

Dive deep into ergodic theory, exploring its foundational concepts and its connections to statistical thermodynamics.

Langlands Program and Number Theory

What is the Langlands Program, and how does it seek to unify different areas of mathematics?

Investigate the Langlands Program, its objectives, and its profound implications in unifying disparate areas of mathematics, particularly number theory.

These topics are undoubtedly challenging but can yield impressive results when tackled effectively. They offer a deep dive into complex mathematical concepts and theories, making them ideal for students aiming for the highest grades in their Math Extended essay.

Get extended essay help

Before continuing to the next block, I suggest our Math EE writing or editing services . Our company has been working with numerous IB students and helped them write custom IB extended essays.

Join a team of happy IB students who have followed the IB extended essay rubric and criteria and gained better results with Writing Metier and our Math assignments help !

Overused Math EE topics (proceed with caution)

While these topics are popular, they’ve been explored extensively. If you choose one, ensure you bring a fresh perspective:

• The Fibonacci Sequence in Nature.
• Pi and its Mysteries.
• The Monty Hall Problem.
• The Birthday Paradox.
• Exploring Pascal’s Triangle.
• The Mathematics of the Pyramids.
• The Tower of Hanoi Problem.
• Benford’s Law.
• The Four Color Theorem.
• The Mathematics of the Rubik’s Cube.

Keep in mind that selecting such a topic will require hard work to find a new custom angle of research and sometimes might not lead to higher grades .

In Conclusion

Alright, IB champs, that wraps up our curated selection of Math EE topics, each with its unique flavor and challenge. The topic is just the starting point. The real magic happens when you infuse it with your insights, analysis, and unique perspective. 

Mathematics isn’t just about numbers; it’s about stories and trips within the confines of equations and graphs. As you gear up to tackle your Extended essay, keep that passion alive, keep questioning, and most importantly, enjoy the process. 

Don’t forget to reserve extra space because it may take time to write an extended essay . And if you’re ever in doubt, remember that Writing Metier is here to guide you through every step of the process.

Free topic suggestions

Vasy kafidoff.

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

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Sat / act prep online guides and tips, the complete ib extended essay guide: examples, topics, and ideas.

International Baccalaureate (IB)

IB students around the globe fear writing the Extended Essay, but it doesn't have to be a source of stress! In this article, I'll get you excited about writing your Extended Essay and provide you with the resources you need to get an A on it.

If you're reading this article, I'm going to assume you're an IB student getting ready to write your Extended Essay. If you're looking at this as a potential future IB student, I recommend reading our introductory IB articles first, including our guide to what the IB program is and our full coverage of the IB curriculum .

IB Extended Essay: Why Should You Trust My Advice?

I myself am a recipient of an IB Diploma, and I happened to receive an A on my IB Extended Essay. Don't believe me? The proof is in the IBO pudding:

If you're confused by what this report means, EE is short for Extended Essay , and English A1 is the subject that my Extended Essay topic coordinated with. In layman's terms, my IB Diploma was graded in May 2010, I wrote my Extended Essay in the English A1 category, and I received an A grade on it.

What Is the Extended Essay in the IB Diploma Programme?

The IB Extended Essay, or EE , is a mini-thesis you write under the supervision of an IB advisor (an IB teacher at your school), which counts toward your IB Diploma (learn more about the major IB Diploma requirements in our guide) . I will explain exactly how the EE affects your Diploma later in this article.

For the Extended Essay, you will choose a research question as a topic, conduct the research independently, then write an essay on your findings . The essay itself is a long one—although there's a cap of 4,000 words, most successful essays get very close to this limit.

Keep in mind that the IB requires this essay to be a "formal piece of academic writing," meaning you'll have to do outside research and cite additional sources.

The IB Extended Essay must include the following:

• A title page
• Contents page
• Introduction
• Body of the essay
• References and bibliography

Additionally, your research topic must fall into one of the six approved DP categories , or IB subject groups, which are as follows:

• Group 1: Studies in Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts

Once you figure out your category and have identified a potential research topic, it's time to pick your advisor, who is normally an IB teacher at your school (though you can also find one online ). This person will help direct your research, and they'll conduct the reflection sessions you'll have to do as part of your Extended Essay.

As of 2018, the IB requires a "reflection process" as part of your EE supervision process. To fulfill this requirement, you have to meet at least three times with your supervisor in what the IB calls "reflection sessions." These meetings are not only mandatory but are also part of the formal assessment of the EE and your research methods.

According to the IB, the purpose of these meetings is to "provide an opportunity for students to reflect on their engagement with the research process." Basically, these meetings give your supervisor the opportunity to offer feedback, push you to think differently, and encourage you to evaluate your research process.

The final reflection session is called the viva voce, and it's a short 10- to 15-minute interview between you and your advisor. This happens at the very end of the EE process, and it's designed to help your advisor write their report, which factors into your EE grade.

Here are the topics covered in your viva voce :

• A check on plagiarism and malpractice
• Your reflection on your project's successes and difficulties
• Your reflection on what you've learned during the EE process

Your completed Extended Essay, along with your supervisor's report, will then be sent to the IB to be graded. We'll cover the assessment criteria in just a moment.

We'll help you learn how to have those "lightbulb" moments...even on test day!  

What Should You Write About in Your IB Extended Essay?

You can technically write about anything, so long as it falls within one of the approved categories listed above.

It's best to choose a topic that matches one of the IB courses , (such as Theatre, Film, Spanish, French, Math, Biology, etc.), which shouldn't be difficult because there are so many class subjects.

Here is a range of sample topics with the attached extended essay:

• Biology: The Effect of Age and Gender on the Photoreceptor Cells in the Human Retina
• Chemistry: How Does Reflux Time Affect the Yield and Purity of Ethyl Aminobenzoate (Benzocaine), and How Effective is Recrystallisation as a Purification Technique for This Compound?
• English: An Exploration of Jane Austen's Use of the Outdoors in Emma
• Geography: The Effect of Location on the Educational Attainment of Indigenous Secondary Students in Queensland, Australia
• Math: Alhazen's Billiard Problem
• Visual Arts: Can Luc Tuymans Be Classified as a Political Painter?

You can see from how varied the topics are that you have a lot of freedom when it comes to picking a topic . So how do you pick when the options are limitless?

How to Write a Stellar IB Extended Essay: 6 Essential Tips

Below are six key tips to keep in mind as you work on your Extended Essay for the IB DP. Follow these and you're sure to get an A!

#1: Write About Something You Enjoy

You can't expect to write a compelling essay if you're not a fan of the topic on which you're writing. For example, I just love British theatre and ended up writing my Extended Essay on a revolution in post-WWII British theatre. (Yes, I'm definitely a #TheatreNerd.)

I really encourage anyone who pursues an IB Diploma to take the Extended Essay seriously. I was fortunate enough to receive a full-tuition merit scholarship to USC's School of Dramatic Arts program. In my interview for the scholarship, I spoke passionately about my Extended Essay; thus, I genuinely think my Extended Essay helped me get my scholarship.

But how do you find a topic you're passionate about? Start by thinking about which classes you enjoy the most and why . Do you like math classes because you like to solve problems? Or do you enjoy English because you like to analyze literary texts?

Keep in mind that there's no right or wrong answer when it comes to choosing your Extended Essay topic. You're not more likely to get high marks because you're writing about science, just like you're not doomed to failure because you've chosen to tackle the social sciences. The quality of what you produce—not the field you choose to research within—will determine your grade.

Once you've figured out your category, you should brainstorm more specific topics by putting pen to paper . What was your favorite chapter you learned in that class? Was it astrophysics or mechanics? What did you like about that specific chapter? Is there something you want to learn more about? I recommend spending a few hours on this type of brainstorming.

One last note: if you're truly stumped on what to research, pick a topic that will help you in your future major or career . That way you can use your Extended Essay as a talking point in your college essays (and it will prepare you for your studies to come too!).

#2: Select a Topic That Is Neither Too Broad nor Too Narrow

There's a fine line between broad and narrow. You need to write about something specific, but not so specific that you can't write 4,000 words on it.

You can't write about WWII because that would be a book's worth of material. You also don't want to write about what type of soup prisoners of war received behind enemy lines, because you probably won’t be able to come up with 4,000 words of material about it. However, you could possibly write about how the conditions in German POW camps—and the rations provided—were directly affected by the Nazis' successes and failures on the front, including the use of captured factories and prison labor in Eastern Europe to increase production. WWII military history might be a little overdone, but you get my point.

If you're really stuck trying to pinpoint a not-too-broad-or-too-narrow topic, I suggest trying to brainstorm a topic that uses a comparison. Once you begin looking through the list of sample essays below, you'll notice that many use comparisons to formulate their main arguments.

I also used a comparison in my EE, contrasting Harold Pinter's Party Time with John Osborne's Look Back in Anger in order to show a transition in British theatre. Topics with comparisons of two to three plays, books, and so on tend to be the sweet spot. You can analyze each item and then compare them with one another after doing some in-depth analysis of each individually. The ways these items compare and contrast will end up forming the thesis of your essay!

When choosing a comparative topic, the key is that the comparison should be significant. I compared two plays to illustrate the transition in British theatre, but you could compare the ways different regional dialects affect people's job prospects or how different temperatures may or may not affect the mating patterns of lightning bugs. The point here is that comparisons not only help you limit your topic, but they also help you build your argument.

Comparisons are not the only way to get a grade-A EE, though. If after brainstorming, you pick a non-comparison-based topic and are still unsure whether your topic is too broad or narrow, spend about 30 minutes doing some basic research and see how much material is out there.

If there are more than 1,000 books, articles, or documentaries out there on that exact topic, it may be too broad. But if there are only two books that have any connection to your topic, it may be too narrow. If you're still unsure, ask your advisor—it's what they're there for! Speaking of advisors...

Don't get stuck with a narrow topic!

#3: Choose an Advisor Who Is Familiar With Your Topic

If you're not certain of who you would like to be your advisor, create a list of your top three choices. Next, write down the pros and cons of each possibility (I know this sounds tedious, but it really helps!).

For example, Mr. Green is my favorite teacher and we get along really well, but he teaches English. For my EE, I want to conduct an experiment that compares the efficiency of American electric cars with foreign electric cars.

I had Ms. White a year ago. She teaches physics and enjoyed having me in her class. Unlike Mr. Green, Ms. White could help me design my experiment.

Based on my topic and what I need from my advisor, Ms. White would be a better fit for me than would Mr. Green (even though I like him a lot).

The moral of my story is this: do not just ask your favorite teacher to be your advisor . They might be a hindrance to you if they teach another subject. For example, I would not recommend asking your biology teacher to guide you in writing an English literature-based EE.

There can, of course, be exceptions to this rule. If you have a teacher who's passionate and knowledgeable about your topic (as my English teacher was about my theatre topic), you could ask that instructor. Consider all your options before you do this. There was no theatre teacher at my high school, so I couldn't find a theatre-specific advisor, but I chose the next best thing.

Before you approach a teacher to serve as your advisor, check with your high school to see what requirements they have for this process. Some IB high schools require your IB Extended Essay advisor to sign an Agreement Form , for instance.

Make sure that you ask your IB coordinator whether there is any required paperwork to fill out. If your school needs a specific form signed, bring it with you when you ask your teacher to be your EE advisor.

#4: Pick an Advisor Who Will Push You to Be Your Best

Some teachers might just take on students because they have to and aren't very passionate about reading drafts, only giving you minimal feedback. Choose a teacher who will take the time to read several drafts of your essay and give you extensive notes. I would not have gotten my A without being pushed to make my Extended Essay draft better.

Ask a teacher that you have experience with through class or an extracurricular activity. Do not ask a teacher that you have absolutely no connection to. If a teacher already knows you, that means they already know your strengths and weaknesses, so they know what to look for, where you need to improve, and how to encourage your best work.

Also, don't forget that your supervisor's assessment is part of your overall EE score . If you're meeting with someone who pushes you to do better—and you actually take their advice—they'll have more impressive things to say about you than a supervisor who doesn't know you well and isn't heavily involved in your research process.

Be aware that the IB only allows advisors to make suggestions and give constructive criticism. Your teacher cannot actually help you write your EE. The IB recommends that the supervisor spends approximately two to three hours in total with the candidate discussing the EE.

#5: Make Sure Your Essay Has a Clear Structure and Flow

The IB likes structure. Your EE needs a clear introduction (which should be one to two double-spaced pages), research question/focus (i.e., what you're investigating), a body, and a conclusion (about one double-spaced page). An essay with unclear organization will be graded poorly.

The body of your EE should make up the bulk of the essay. It should be about eight to 18 pages long (again, depending on your topic). Your body can be split into multiple parts. For example, if you were doing a comparison, you might have one third of your body as Novel A Analysis, another third as Novel B Analysis, and the final third as your comparison of Novels A and B.

If you're conducting an experiment or analyzing data, such as in this EE , your EE body should have a clear structure that aligns with the scientific method ; you should state the research question, discuss your method, present the data, analyze the data, explain any uncertainties, and draw a conclusion and/or evaluate the success of the experiment.

#6: Start Writing Sooner Rather Than Later!

You will not be able to crank out a 4,000-word essay in just a week and get an A on it. You'll be reading many, many articles (and, depending on your topic, possibly books and plays as well!). As such, it's imperative that you start your research as soon as possible.

Each school has a slightly different deadline for the Extended Essay. Some schools want them as soon as November of your senior year; others will take them as late as February. Your school will tell you what your deadline is. If they haven't mentioned it by February of your junior year, ask your IB coordinator about it.

Some high schools will provide you with a timeline of when you need to come up with a topic, when you need to meet with your advisor, and when certain drafts are due. Not all schools do this. Ask your IB coordinator if you are unsure whether you are on a specific timeline.

Below is my recommended EE timeline. While it's earlier than most schools, it'll save you a ton of heartache (trust me, I remember how hard this process was!):

• January/February of Junior Year: Come up with your final research topic (or at least your top three options).
• February of Junior Year: Approach a teacher about being your EE advisor. If they decline, keep asking others until you find one. See my notes above on how to pick an EE advisor.
• April/May of Junior Year: Submit an outline of your EE and a bibliography of potential research sources (I recommend at least seven to 10) to your EE advisor. Meet with your EE advisor to discuss your outline.
• Summer Between Junior and Senior Year: Complete your first full draft over the summer between your junior and senior year. I know, I know—no one wants to work during the summer, but trust me—this will save you so much stress come fall when you are busy with college applications and other internal assessments for your IB classes. You will want to have this first full draft done because you will want to complete a couple of draft cycles as you likely won't be able to get everything you want to say into 4,000 articulate words on the first attempt. Try to get this first draft into the best possible shape so you don't have to work on too many revisions during the school year on top of your homework, college applications, and extracurriculars.
• August/September of Senior Year: Turn in your first draft of your EE to your advisor and receive feedback. Work on incorporating their feedback into your essay. If they have a lot of suggestions for improvement, ask if they will read one more draft before the final draft.
• September/October of Senior Year: Submit the second draft of your EE to your advisor (if necessary) and look at their feedback. Work on creating the best possible final draft.
• November-February of Senior Year: Schedule your viva voce. Submit two copies of your final draft to your school to be sent off to the IB. You likely will not get your grade until after you graduate.

Remember that in the middle of these milestones, you'll need to schedule two other reflection sessions with your advisor . (Your teachers will actually take notes on these sessions on a form like this one , which then gets submitted to the IB.)

I recommend doing them when you get feedback on your drafts, but these meetings will ultimately be up to your supervisor. Just don't forget to do them!

The early bird DOES get the worm!

How Is the IB Extended Essay Graded?

Extended Essays are graded by examiners appointed by the IB on a scale of 0 to 34 . You'll be graded on five criteria, each with its own set of points. You can learn more about how EE scoring works by reading the IB guide to extended essays .

• Criterion A: Focus and Method (6 points maximum)
• Criterion B: Knowledge and Understanding (6 points maximum)
• Criterion C: Critical Thinking (12 points maximum)
• Criterion D: Presentation (4 points maximum)
• Criterion E: Engagement (6 points maximum)

How well you do on each of these criteria will determine the final letter grade you get for your EE. You must earn at least a D to be eligible to receive your IB Diploma.

Although each criterion has a point value, the IB explicitly states that graders are not converting point totals into grades; instead, they're using qualitative grade descriptors to determine the final grade of your Extended Essay . Grade descriptors are on pages 102-103 of this document .

Here's a rough estimate of how these different point values translate to letter grades based on previous scoring methods for the EE. This is just an estimate —you should read and understand the grade descriptors so you know exactly what the scorers are looking for.

Here is the breakdown of EE scores (from the May 2021 bulletin):

How Does the Extended Essay Grade Affect Your IB Diploma?

The Extended Essay grade is combined with your TOK (Theory of Knowledge) grade to determine how many points you get toward your IB Diploma.

To learn about Theory of Knowledge or how many points you need to receive an IB Diploma, read our complete guide to the IB program and our guide to the IB Diploma requirements .

This diagram shows how the two scores are combined to determine how many points you receive for your IB diploma (3 being the most, 0 being the least). In order to get your IB Diploma, you have to earn 24 points across both categories (the TOK and EE). The highest score anyone can earn is 45 points.

Let's say you get an A on your EE and a B on TOK. You will get 3 points toward your Diploma. As of 2014, a student who scores an E on either the extended essay or TOK essay will not be eligible to receive an IB Diploma .

Prior to the class of 2010, a Diploma candidate could receive a failing grade in either the Extended Essay or Theory of Knowledge and still be awarded a Diploma, but this is no longer true.

Figuring out how you're assessed can be a little tricky. Luckily, the IB breaks everything down here in this document . (The assessment information begins on page 219.)

40+ Sample Extended Essays for the IB Diploma Programme

In case you want a little more guidance on how to get an A on your EE, here are over 40 excellent (grade A) sample extended essays for your reading pleasure. Essays are grouped by IB subject.

• Business Management 1
• Chemistry 1
• Chemistry 2
• Chemistry 3
• Chemistry 4
• Chemistry 5
• Chemistry 6
• Chemistry 7
• Computer Science 1
• Economics 1
• Design Technology 1
• Design Technology 2
• Environmental Systems and Societies 1
• Geography 1
• Geography 2
• Geography 3
• Geography 4
• Geography 5
• Geography 6
• Literature and Performance 1
• Mathematics 1
• Mathematics 2
• Mathematics 3
• Mathematics 4
• Mathematics 5
• Philosophy 1
• Philosophy 2
• Philosophy 3
• Philosophy 4
• Philosophy 5
• Psychology 1
• Psychology 2
• Psychology 3
• Psychology 4
• Psychology 5
• Social and Cultural Anthropology 1
• Social and Cultural Anthropology 2
• Social and Cultural Anthropology 3
• Sports, Exercise and Health Science 1
• Sports, Exercise and Health Science 2
• Visual Arts 1
• Visual Arts 2
• Visual Arts 3
• Visual Arts 4
• Visual Arts 5
• World Religion 1
• World Religion 2
• World Religion 3

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Extended Essay: Group 5: Mathematics

• General Timeline
• Group 1: English Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts
• Interdisciplinary essays
• Brainstorming
• Pre-Writing
• Research Techniques
• The Research Question
• Paraphrasing, Summarising and Quotations
• Writing an EE Introduction
• Writing the main body of your EE
• Writing your EE Conclusion
• Six sub-categories for WSEE
• IB Interdisciplinary EE Assessment Guide
• Sources: Finding, Organising and Evaluating Them
• Conducting Interviews and Surveys
• Citing and Referencing
• Check-in Sessions
• First Formal Reflection
• Second Formal Reflection
• Final Reflection (Viva Voce)
• Researcher's Reflection Space (RRS) Examples
• Information for Supervisors
• How is the EE Graded?
• EE Online Resources
• Stavanger Public Library
• Exemplar Essays
• Extended Essay Presentations
• ISS High School Academic Honesty Policy

Mathematics

An extended essay (EE) in mathematics is intended for students who are writing on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Essays in this group are divided into six categories:

• the applicability of mathematics to solve both real and abstract problems
• the beauty of mathematics—eg geometry or fractal theory
• the elegance of mathematics in the proving of theorems—eg number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds or thousands of years
• the effect of technology on mathematics:
• in forging links between different branches of mathematics,
• or in bringing about a new branch of mathematics, or causing a particular branch to flourish.

These are just some of the many different ways that mathematics can be enjoyable or useful, or, as in many cases, both.

For an Introduction in a Mathematics EE look HERE . 

Choice of topic

The EE may be written on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Students may choose mathematical topics from fields such as engineering, the sciences or the social sciences, as well as from mathematics itself.

Statistical analyses of experimental results taken from other subject areas are also acceptable, provided that they focus on the modeling process and discuss the limitations of the results; such essays should not include extensive non-mathematical detail.

A topic selected from the history of mathematics may also be appropriate, provided that a clear line of mathematical development is demonstrated. Concentration on the lives of, or personal rivalries between, mathematicians would be irrelevant and would not score highly on the assessment criteria.

It should be noted that the assessment criteria give credit for the nature of the investigation and for the extent that reasoned arguments are applied to an appropriate research question.

Students should avoid choosing a topic that gives rise to a trivial research question or one that is not sufficiently focused to allow appropriate treatment within the requirements of the EE.

Students will normally be expected either to extend their knowledge beyond that encountered in the Diploma Programme mathematics course they are studying or to apply techniques used in their mathematics course to modeling in an appropriately chosen topic.

However, it is very important to remember that it is an essay that is being written, not a research paper for a journal of advanced mathematics, and no result, however impressive, should be quoted without evidence of the student’s real understanding of it.

Example and Treatment of Topic

Examples of topics

These examples are just for guidance. Students must ensure their choice of topic is focused (left-hand column) rather than broad (right-hand column

Treatment of the topic

Whatever the title of the EE, students must apply good mathematical practice that is relevant to the

chosen topic, including:

• data analysed using appropriate techniques

• arguments correctly reasoned

• situations modeled using correct methodology

• problems clearly stated and techniques at the correct level of sophistication applied to their solution.

Research methods

Students must be advised that mathematical research is a long-term and open-ended exploration of a set of related mathematical problems that are based on personal observations. 

The answers to these problems connect to and build upon each other over time.

Students’ research should be guided by analysis of primary and secondary sources.

A primary source for research in mathematics involves:

• data-gathering

• visualization

• abstraction

• conjecturing

• proof.

A secondary source of research refers to a comprehensive review of scholarly work, including books, journal articles or essays in an edited collection.

A literature review for mathematics might not be as extensive as in other subjects, but students are expected to demonstrate their knowledge and understanding of the mathematics they are using in the context of the broader discipline, for example how the mathematics they are using has been applied before, or in a different area to the one they are investigating.

Writing the essay

Throughout the EE students should communicate mathematically:

• describing their way of thinking

• writing definitions and conjectures

• using symbols, theorems, graphs and diagrams

• justifying their conclusions.

There must be sufficient explanation and commentary throughout the essay to ensure that the reader does not lose sight of its purpose in a mass of mathematical symbols, formulae and analysis.

The unique disciplines of mathematics must be respected throughout. Relevant graphs and diagrams are often important and should be incorporated in the body of the essay, not relegated to an appendix.

However, lengthy printouts, tables of results and computer programs should not be allowed to interrupt the development of the essay, and should appear separately as footnotes or in an appendix. Proofs of key results may be included, but proofs of standard results should be either omitted or, if they illustrate an important point, included in an appendix.

Examples of topics, research questions and suggested approaches

Once students have identified their topic and written their research question, they can decide how to

research their answer. They may find it helpful to write a statement outlining their broad approach. These

examples are for guidance only.

An important note on “double-dipping”

Students must ensure that their EE does not duplicate other work they are submitting for the Diploma Programme. For example, students are not permitted to repeat any of the mathematics in their IA in their EE, or vice versa.

The mathematics EE and internal assessment

An EE in mathematics is not an extension of the internal assessment (IA) task. Students must ensure that they understand the differences between the two.

• The EE is a more substantial piece of work that requires formal research
• The IA is an exploration of an idea in mathematics.

It is not appropriate for a student to choose the same topic for an EE as the IA. There would be too much danger of duplication and it must therefore be discouraged.

• << Previous: Group 4: Sciences
• Next: Group 6: The Arts >>
• Last Updated: Apr 3, 2024 10:42 AM
• URL: https://isstavanger.libguides.com/c.php?g=695888

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12 Strong Topic Ideas For A Math Extended Essay

Writing a math extended essay can be quite a challenge unless you are using an IB extended essay writing service . You have many factors to consider such as following the right format, choosing the best approach for your study, and defending your thesis (if required). So choosing an engaging topic that pertains to today’s issues is a crucial first step when you are in the planning stages.

Obviously, mathematics are your primary interest or else you wouldn’t have this assignment, to begin with due to not being enrolled in a course that goes above and beyond Algebra 102 or Geometry 104. (Even if you’re forced to endure a statistics course, you would have some interest in mathematical data or at least possess an awareness of working with numbers in your chosen field.) So one bit of advice on selecting a topic for your extended essay topics is to combine your intrigue with math with a problem, scenario or specific career domain (e.g.: medical, technology, sociology, business, etc.) that will not only hold your attention but also relate to current trends or events.

So here some suggestions for fascinating math essay topics to get you started:

In the area of education, some possible themes are:

• Possible correlation between district-level standardized test scores or GPA’s and performance on the SAT
• Prevalence of stress and coping skills of secondary university-bound students (Think ratios and statistics)
• Effectiveness of literacy programs (school or community-wide) towards improving reading skills (You can probably narrow down to an age range or grade level(s))

For the medical field, the possibilities are endless. Consider these three suggestions:

• Possible direct correlation between usage of “antibacterial” products, like hand sanitizer for instance and the rise of the “Super Bug.”
• The odds of another pandemic, similar to the 1918 worldwide influenza outbreak, occurring
• The impact of advertising on childhood obesity (Again, think ratios, statistics, and probability)

In the realm of computer technology, you can look into any one of these subjects:

• Best formula and combinations for SEO
• The use of prime numbers and modular arithmetic to maintain privacy with RSA Public Key Cryptography
• Correlation between the use of electronic pay services (Skrill for example) and users’ professions.

Of course, there are a variety of areas to explore within the content of math itself and its applications. Some possibilities include the following:

• Study of alternatives to Euclidean geometry and their applications
• Close study of Sophie Germain’s Theorem
• Real life dilemmas that can be solved with strategies of complex number problem-solving

As you can see, there are many different subjects to explore when writing about mathematical concepts and how they relate to the real world. You can dive more into the content area of science and hypothesize the route(s) of a comet that could impact the earth. Concerning sociological and psychological studies, you can look into various statistical investigations of human behavior. Another rather amusing numerical investigation could involve a study of probability in gambling venues or about other types of gaming, like Fantasy Football. (Be careful with your finances, though.)

However, some tips to remember as you examine these topics is to choose the “sub-area” that interests you the most (unless it’s all about the math), as you will devote a lot of time to this project; make sure you have a clear and measurable hypothesis; and clarify any questions on format with your instructor. With these recommendations and a lot of calculating, you will compose the perfect paper.

Helpful Sources

Writing Tips

• Essay intro on math algorithms
• Paper about the chemistry of water

How to Choose an EE Topic (Mathematics)

The Extended Essay is undoubtedly one of the most feared components of the IB program. A 4,000 word research paper can, in fact, seem daunting to those who have only written 500-1000 word essays. Therefore, students should choose a topic that they can not only find sources for, but are also passionate about it.

Mathematics Extended Essays are rare — of the 87,519 Extended Essays submitted in the 2020 May Examination Session only 2,454 were done over Mathematics (2.8%) ( IB Statistical Bulletin 2020 ). Despite the rarity, I chose to write a Mathematics EE because maths is something that fascinates me. To many students, Mathematics EEs sound scary and barely consider writing one. There were many people that told me I was insane and that it was impossible. In the end, I put in the work to make it happen. 

I chose to write my paper on Game Theory and my research question was: “To what extent does Game Theory play a role in Modern Warfare?” 

I found this topic not unlike the way students writing History EEs find their own specific topics. Just as history has countless events in which one can write about, Mathematics is similar with its various branches. I chose a branch that interested me (Game Theory) and used it to solve a real-world problem (Modern Warfare). My economics teacher actually suggested this idea.  They said that, while Game Theory is primarily used in economics, it has numerous applications to maths when discussed alongside warfare. This qualified my essay as a Category 1 Mathematics Extended Essay, which is a paper that discusses “the applicability of mathematics to solve both real and abstract problems” (p. 96, IB Extended Essay Guide ). 

Writing the essay is where, I admit, it got challenging. During the process I had no peers to help me as only a few others had chosen a Mathematics EE, but none of their topics related to mine. Fortunately, my mentor was extremely helpful and I was able to find several books at my local university that were very useful.

Mathematics Extended Essays are bizarre in many ways as things such as word count, varied sentence structure, and high vocabulary do not matter. However, it should be noted that effective communication is key even if that’s done through mathematical expressions. Despite these challenges, I strongly believe that Mathematics EEs are doable, and more people would do them if there was not such a negative stigma about them. I encourage all future IB sessions to consider doing one as the feeling when you have finished is unlike any other. The pride and satisfaction I felt knowing that I took the path less travelled and still found success is something that I hope all future IB students will experience.

You may also like…

• Our Extended Essay series
• Tiffany’s tips for Mathematics HL

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Extended Essay Essentials

• Individuals and Societies
• Interdisciplinary
• Mathematics

Contact Your Librarian

Trish Pearson

she/her/hers

[email protected]

What's in this guide?

What's in this guide.

In this guide, you will find essential documents for writing the EE in 

Essential documents include Subject Specific Guidelines and Sample Essays.

Introduction to the EE in Mathematics

From Mathematics: An Introduction:

An extended essay (EE) in mathematics is intended for students who are writing on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Essays in this group are divided into six categories:

• the applicability of mathematics to solve both real and abstract problems
• the beauty of mathematics in the proving of theorems - e.g., number theory
• the history of mathematics; the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds, or thousands of years
• in forging links between different branches of mathematics,
• or in bringing about a new branch of mathematics, or causing a particular branch to flourish.

For a longer general overview of an arts-related EE, see Mathematics: An Introduction . This document contains information on:

• Topic Selection
• Examples of Topics
• Treatment of the Topic
• Research Methods
• A Framework for the EE in the Mathematics.

Mathematics EE

• Mathematics Subject Specific Guidelines  - A short guide on how to write the Mathematics EE
• Score Reports  - See what students did (and did not do) well in these short reports from the chief examiner.
• Sample Papers  - Read sample EE papers provided by IB and see how they scored
• Mathematics Subject Specific Guidelines
• 2021 Mathematics Score Report
• 2018 Mathematics Score Report
• << Previous: Languages
• Next: Sciences >>
• Last Updated: Mar 26, 2024 1:52 PM
• URL: https://uwcchina.libguides.com/extendedessayessentials

The IB Extended Essay: Topic ideas and research Questions

• Details of the EE
• Topic ideas and research Questions
• Subject Guides & documents you need
• Writing a research paper
• Check the list of available subjects  here
• Read the IB's criteria for your subject
• Read an exemplar essay in your subject
• Decide on a topic within this subject
• This means you will need to do some research!
• During the first meeting with your advisor, discuss the research you've done, your ideas, and the requirements for your subject.
• Your revised research question proposal is due May 16.

Adapted from O'Farrell, Finbar.  Approach your assessment the IB Way: Extended Essay.  pg. 13

Examples of marked EEs in all subjects

• From the IB website Have a look at the specific subject you plan on writing your EE for a marked example. You will be able to identify what you need to be successful.

Design Technology

• Guide on writing an EE in DT The pdf explains everything clearly and is full of ideas and topics to write about.

Question: Has the introduction of new materials improved the performance of modern racing bicycles?

  Question:  What are the most ethical and efficient methods--through current technologies--private organizations can use to make Mars habitable for Human life?

History or Geography

Question : In what ways did the Cold War impact American public education? Question:   To what extent have Maori non-violent struggles for their land been effective? Question: How could the UN intervention in the Rwandan genocide be justified?  Question :Is it politically possible for the US government to win the drugs war? (Politics)

Question:  How are the depictions of Marie Antoinette in politics and portraiture significant to the French revolution and the fall of the French Monarchy? 

Question:  To what extent was film able to further pro-Nazi sentiment in Germany during the early 1930s to mid 1940s?

Question:  To what extent were the Vietnam War and cultural shifts occurring in the 1960s and early 1970s vital factors in the development of the student activism on college campuses in the United States and abroad?

Question:  To what extent was Matthew Perry’s 1853 arrival in Edo Bay the leading motivator for Japan’s rapid modernization during the Meiji Restoration?

Question:  What made the Federal Theatre Project such a success when after only four years of operation it was disbanded by the House of un-American Activities Committee?

Question:  To what extent were Kepler’s scientific discoveries revolutionary and how did they impact the development of science in Europe in the 16th and 17th centuries?   

Question:  In what ways did the Hitler Youth organization impact the youth of Nazi Germany?

Question:  How did the works of classical Greek philosophers influence the domestic policy of Thomas Jefferson?  

Question:  How did the Bushido Code influence the meaning of tattoos in Asian culture?

Question:  In what way did the Catholic Church affect politics in the Kingdom of Spain during the Dark Ages?

Question:  What are the impacts of melting ice in the North and South Poles on the coastlines of the continental United States?

English EEs - ideas for Language and Literature

The EE Guide says the following on p 112 (EE Guide 2018, revised Jan 2017) - remember EACH subject has their own EE guides too.

   Quote The EE may relate to work students have already completed during the course, but they must also demonstrate relevant wider reading and individual study. It is the responsibility of the student to ensure that the topic of their EE does not overlap with any other work they are preparing for assessment in language A—for example, the written assignment in the literature course, or the written task in the language and literature course.   

Question:  How did Eugene Gladstone O'Neill express the themes of family relationship and sadness in his work Long Day's Journey Into Night?

Question:  How does the writing of Japanese horror artist and novelist Junji Ito contrast with the writing of American horror novelist Stephen King?

Question:  How do the final movies of the Harry Potter series compare to the final book? What has been changed or depicted differently in terms of characterization and storylines?

Sport Science

Question:  How does age affect the process of instant muscle reaction?

Economics or ITGS

Question:  What impact does public healthcare have on low income households in the United States compared to those in Canada?

Question:  To what extent has deforestation influenced Indonesia's economic and environmental growth?

Physics, Chemistry or Biology Ideas

Question:  How have climate change and forestry practices contributed to the spread of the mountain pine beetle in the Pacific Northwest in recent decades, and what does the outbreak show us about the ecological intricacies of climate change? 

Question:  What evidence is there to support the theory of life on Mars?

Question:  How does the DNA sequence of a transthyretin (TTR) gene affect whether Familial Amyloidotic Polyneuropathy (FAP), Familial Amyloidotic Cardiomyopathy (FAC) or Senile Systemic Amyloidosis (SSA) form?

Arts - Visual/Performing

Question : What female stereotypes did Brecht employ in his plays, and how can these be compared and contrasted in performance, based on an analysis of a selection of Brecht's plays? Question : Picasso: individual genius or cultural thief? 

Question:  How does Rachmaninoff apply thematic development in his composition, Rhapsody on a Theme of Paganini ?

Question:  How do the Peanuts comics, written by Charles Schultz, show visual language?

Question:  How did the casting of the leading lady in Cole Porter's Anything Goes affect each production on Broadway?

• << Previous: Details of the EE
• Next: Subject Guides & documents you need >>
• Last Updated: Apr 5, 2020 2:09 PM
• URL: https://disdubai.libguides.com/c.php?g=923128

Extended Essay: Step 5. Draft a Research Question

• Extended Essay- The Basics
• Step 1. Choose a Subject
• Step 2. Educate yourself!
• Using Brainstorming and Mind Maps
• Identify Keywords
• Do Background Reading
• Define Your Topic
• Conduct Research in a Specific Discipline
• Step 5. Draft a Research Question
• Step 6. Create a Timeline
• Find Articles
• Find Primary Sources
• Get Help from Experts
• Search Engines, Repositories, & Directories
• Databases and Websites by Subject Area
• Create an Annotated Bibliography
• Advice (and Warnings) from the IB
• Chicago Citation Syle
• MLA Works Cited & In-Text Citations
• Step 9. Set Deadlines for Yourself
• Step 10. Plan a structure for your essay
• Evaluate & Select: the CRAAP Test
• Conducting Secondary Research
• Conducting Primary Research
• Formal vs. Informal Writing
• Presentation Requirements
• Evaluating Your Work

RQ Resources

On this page you can find help with developing your preliminary research question.  See: 

Steps to Developing a Research Question

Sample research questions.

Practice Exercise:  Formulating Well-Focused Research Questions

IB Command Terms and Glossaries

• Research Question Formats for History Extended Essays

You've chosen a subject and topic that interests you, and carried out some preliminary reading.  What are the next steps ?

Evaluate the question.   Once you have posed possible research questions you should evaluate them.  This evaluation should be based on whether the question is clear , focused , and arguable .

• Clear  - Will the reader understand the nature of my research?  Will it direct the research being undertaken?
• Focused - Will the research question be specific enough to allow for exploration within the scope of the task (that is, the number of words and time available)?
• Arguable - Does the research question allow for analysis, evaluation and the development of a reasoned argument?

Consider research outcomes.   Once you have decided on a provisional research question you should start thinking about the direction your research might take.  You could do this by:

• suggesting possible outcomes of your research
• outlining the kind of argument you might make and how your research might support this
• considering options if the research available is not sufficient to support a sustained argument

The table below gives some examples showing the difference between unclear and unfocused research questions and those that are appropriately clear and focused, lending themselves to in-depth research.  

Practice exercise: Formulating well-focused research questions

Twelve-step plan for researching the extended essay - step 5.

5.  Formulate a preliminary research question.  Try to incorporate an IB command term in the research question if possible.

IB Command Terms & Glossaries

Command terms are the key terms and phrases used in examination questions for IB classes.  The lists below give the terms, and definitions, for specific IB subjects.

  These lists are glossaries of terms used in film and dance.

Students writing History Extended Essays can use these formats to help write research questions on their topics.

• << Previous: Conduct Research in a Specific Discipline
• Next: Step 6. Create a Timeline >>
• Last Updated: Feb 2, 2024 1:39 PM
• URL: https://libguides.westsoundacademy.org/ee

IB Math EE - Propel Your Mind To A 34/34

Unlock the secrets to acing your IB Math EE with a guaranteed 34/34 score! Propel your mind to success and make the most of your potential. 💯

Table of content

Extended essay & what is it❓, ib math ee vs math ia 🥊 , wth is an ib math extended essay 🌋, a brief about ib math ee 🩲, sexy pointers you can't-miss 🤤, 4 ways to find the right math ee topic ⭕, formulate your research question 🔎, planning your research & essay 📖, structuring your essay 🏗️, ib math ee reflection, what to do 🪞, ib math ee criteria 🧮, ib math ee examples 🛹.

It's time we address the elephant in the room.

IB Mathematics Extended Essay.

There, we said it.

If you've taken up IB Math EE, we're here to tell you that it isn't over, contrary to what you might have heard.

Researching, planning, and finally writing a good IB Math EE is no walk in the park, but rest assured that you'll feel different once you've gone through this valuable document.

Nail IB presents the only comprehensive guide you need to nail your IB Math EE.

Let's keep it accurate.

IB Math EE is a rigorous, independent, academic research essay that calls for,

• a keen interest in Mathematics,
• strong mathematical aptitude & reasoning,
• a focused and disciplined approach, and most importantly,
• essential tips, techniques, and quality guidance.

When one opts for IB Math EE, one should ensure a strong passion for Mathematics and a solid mathematical foundation. Not to mention being willing to devote their time and effort to this self-directed research.

Disclaimer -  If you have second thoughts, you should reconsider and re-evaluate your choice because it's no use aiming in the dark.

There needs to be more!

Invaluable tips and techniques are the last missing piece of the IB Math EE puzzle.

Given the panic and stigma around Math Extended Essay, what students need, is not some more panic; instead, expert guidance to keep them pumped to write their EE papers with skill, precision, and utmost zeal. And so, true to our word, we're here to help you.

Say it out loud for me - I got this!

Before diving any further, we are thrilled to share our premium IB Math resources. Check out the  IB Math AI SL  bundle and the  IB Math AI HL  bundle, including everything from comprehensive, up-to-date video lecture courses by Adam Nazha to curated IB Resource Libraries. All your IB DP Math queries are now answered!

While you're at it, check out our  IB Math AA SL  repository, where Patrick Jones (yep, you got that right, our very own  PatrickJMT  - the best Mathematics instructor in the world) will guide you with a brilliant video lecture course he has created to help you nail your concepts and exams alike! Happy learning!

Returning to our one-stop guide for all things IB Math EE, let us see what this article will cover.

• Extended Essay & What is it ❓
• IB Math EE Vs Math IA  🥊
• WTH Is An IB Math Extended Essay?  🌋
• A Brief About IB Math EE ?  🩲
• Sexy Pointers You Can't Miss  🤤
• 4 Ways To Find The Right Math EE topic  ⭕
• Formulate Your Research Question  🔎
• Planning Your Research and Essay  📖
• Structuring Your Essay  🏗️
• Writing Your Essay Writing Your Reflection  🪞
• IB Math EE Criteria  🧮
• IB Math EE Examples  🛹

First things first, let’s briefly discuss what an Extended Essay is.

As the IB defines it, the Extended Essay is a  4000-word in-depth  study, part of the IB Diploma Programme core mandatory for all students.

A  500-word  reflection component-inclusive of 3 reflections - is submitted with the academic writing.

This, of course, is done under the supervision of your IB advisor. The critical thing to note is that you can choose to write an Extended Essay on any subject offered by the IB in your session, though it is highly recommended you settle on a topic you are studying as a part of your IB curriculum.

The purpose of an Extended Essay is to motivate students to conduct formal research on a subject area of interest, independently work on the chosen research question and gain guidance from their respective IB mentors every step of the way.

The IB highlights the significance of the Extended Essay:

• Hands-on learning for undergraduate research
• An opportunity for students to research an area of interest relating to one of the 6 DP subjects opted for by the student.

The skills the Extended Essay aims to develop in students are:

• Coming up with a relevant Research Question
• Personally engaging with a topic of exploration
• A coherent communication of ideas
• Strong Argument building

For better understanding, go through  this document on Extended Essays   by the IB. It will make things more transparent.

Students often confuse their Internal Assessments with Extended Essays, which is a grave mistake. Gaining clarity on both these components of the IB DP core is essential. Let us understand the significant difference between the two.

• While Internal Assessments require students to investigate and explore an idea, Extended Essays are more formal. Students need to perform primary and secondary research on a research question they choose based on a diverse topic about the subject. Since EE is an independently researched essay, your mentor may only be able to give you some of the answers you wanted, unlike the IA.
• Students must write one Extended Essay on a subject of their choice for their IB Diploma Programme, but I must be prepared for all the topics.
• Internal Assessments are graded internally by the subject instructor and then moderated externally. Extended Essays are marked externally by examiners appointed by the IB. Your grade on your Extended Essay is combined with your Theory of Knowledge Essay/Exhibition score to assign you your overall score/points.

Word of caution:  Do not choose the same investigation topic/research question for your Internal Assessment and the Extended Essay.

For a much better breakdown of the EE document, you must go through our article on the  IB Extended Essay . It contains an IB EE checklist you must attend to and a detailed overview of the structure and planning of the EE.

Now that we’ve got our basics to, let’s get down to business. The fear around IB Math Extended Essay makes the most confident students hesitate and doubt their choices. But we aren’t here to scare you. The myth about the horrors of the IB Math EE isn’t all false; it’s a caution. Because unless you’re prepared with ammunition, strategy, and the will to put in the effort, there’s a slim chance you can survive the Math Extended Essay battle.

If you’ve opted for Math Extended Essay, we assume you have a strong passion for Mathematics. When the going gets tough while working on one’s Extended Essay-which, which is usually the case-your only hope at the end of the tunnel is your drive for the subject you’ve chosen. Being a rigorous subject for writing one’s Extended Essay, Mathematics can be incredibly demanding. So unless you want to play it risky, we suggest you reassess your liking for Mathematics. Once you know for sure, that’s when it begins. Lots of research. Since it is an independently written document, you want to be doing your homework well.

We will further break down the IB Math Extended Essay, from planning to execution, so that you can organize your thoughts and make appropriate decisions.

The Math Extended Essay is an in-depth research document covering any topic with a mathematical focus, i.e., not limited to the mathematics theory (shouldn’t be entirely descriptive). IB has divided Math Extended Essays into six categories:

• the applicability of mathematics to solve both real and abstract problems
• The beauty of mathematics examples includes geometry or fractal theory.
• the application of mathematics in the proving of theorems, for example, number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over some time, measured in tens, hundreds, or thousands of years
• the effect of technology on mathematics
• in creating links between different branches of mathematics,
• Or in bringing about a new branch of mathematics or causing a particular unit to flourish.

Your Math EE topic should be an extension of your IB Maths syllabus or the practical application of the knowledge you’ve gained in class.

Before moving on to the planning and structure of the Math Extended Essay, here are some pointers you absolutely cannot afford to miss:

• Attempting a Math EE requires a decent amount of hard work. While conducting preliminary research, ensure you land on a topic you can personally engage with and are familiar with. Going for a complicated subject, you can’t comprehend and interpret futile.
• The mathematical work you put in will have to meet a certain level of sophistication, so avoid going for a topic that gives rise to a trivial research question. Your research question shouldn’t be too generic or broad on similar lines. Ensure you can sufficiently narrow down your area of investigation.
• Another thing to remember is that the topic you finally choose should have a good research foundation and room for a novel contribution.
• Incorporate Primary and Secondary research wherever appropriate.
• Proper Referencing should be done for the essay.
• For Reflection, emphasize the Planning, Research, and Writing Processes.

Spitball ideas -  You begin here. Write down any interesting ideas you can come up with. This is your brainstorming session.

Do your Research -  You could not, would not want to meddle with this step, let alone skip it. Research. Read reports, articles, and documentation. Keep jotting important points down simultaneously. The study will and must go on throughout your search for the right math EE topic.

Approach professors/professionals/experts -  Contact concerned lecturers, professors, and industry professionals. They can provide you with invaluable insights. It would be best if you also discussed ideas with your mentor.

Point to Note -  Your goal should be to find a topic you understand and contribute to. It is always recommended to refer to your Math syllabus; something there inspires you to get the ball rolling!

Your essay will be structured as a document answering the Research Question you’re working on. It should be focused, clear and arguable. You will build your essay around your Research Question; hence pay close attention to it.

All you will include in your essay must be mentioned in your Research Question. This means the focused area you will be exploring and the methods you will use to achieve a plausible outcome.

Honing your Research Question is a continuous process. If it appears relatively easy or complex, please rephrase it. Good Research Questions may start with: “How can we model…”, “To what extent…” etc.

Collect Primary and Secondary data and incorporate it wherever appropriate.

Primary sources for Math research include 

• Data-gathering
• Visualization
• Abstraction
• Conjecturing

A few sources to gather Secondary data include Google Scholar, textbooks, databases such as JSTOR, etc. For your essay, know your aims and devise a step-by-step plan to answer your research question while maintaining a mathematical focus.

• Though you can approach your essay in whichever way you like, there should be a consistent logical structure.
• The work done in your essay should develop to answer your research question.
• Subheadings will provide your work with much-needed coherence and viability.
• Describe your way of thinking
• Write definitions and Conjectures.
• Use symbols, theorems, graphs, and diagrams
• Justify your conclusions.
• Visual aids such as graphs and diagrams should be included in the body, while tables and computer programs should be mentioned in the footnotes or the appendix.
• Data must be analyzed appropriately using relevant techniques, correctly reasoned arguments, and adequate methodology to achieve a result.
• Provide the necessary explanation and commentary for all your work.
• Throughout the writing, you may need to re-evaluate the method, approach, and structure to fit the word count adequately.

Once you’re finished writing, you will have to reassess everything from scratch- the equations, the theory, etc., to ensure the coherence of your essay.

• The three reflections should highlight how the process of writing your essay changed in due course of work and what you’ve learned from it.
• The Reflection should emphasize the planning, research, and writing process.
• You should discuss your choices, the re-evaluations you had to make, the limitations of your work, and how you overcame them, if at all.
• The three reflections are written at the beginning, mid, and towards the end of your essay and should have a word limit of approximately 150, 150, and 200, respectively.

Extended Essays are assessed externally by IB-appointed examiners and are marked on a scale of 0 to 34. The score obtained by a student corresponds to a particular band. The bands are:

A -  refers to work of an excellent standard (Level 6)

B -  refers to the creation of a good standard (Level 6)

C -  refers to work of a satisfactory standard (Level-12)

D -  refers to the product of a mediocre standard (Level 4)

E -  refers to the design of an elementary average (Level 6)

Anything below D will be considered a failing grade, and the student will not be awarded the IB diploma.  As we said, your EE is not a component you can mess up.

The Extended Essay Rubric includes the following Assessment Criteria:

Criterion A -   Focus and Method (Covers the topic, research question, and methodology)

Criterion B -  Knowledge and Understanding (Covers context, subject-specific terminology, and concepts)

Criterion C -  Critical Thinking (Covers research, analysis, discussion, and evaluation)

Criterion D -  Presentation (Covers structure, layout)

Criterion E -  Engagement (Covers reflection on planning and progress)

Now that we’ve discovered and learned about the process of writing a Math EE, here are a couple of ideas to give you an idea about how your Math EE questions should be framed:

Topic -  Archimedes’ calculation of areas

Research Question -  What is the legacy of Archimedes’ calculations of circular and parabolic areas in today’s integration methods?

Topic -  Approximation of irrational numbers by rational numbers

Research Question -  How well can π, e, √2, and other irrationals be approximated by rational numbers?

Topic -   The geometry of navigation

Research Question -  What was the role of mathematics and geometry in navigation when we relied on the stars? Does it still play a part now we have manufactured satellites?

You should also check out this  sample band, A Math EE, published by the IB . This will give you an honest insight into making a band-A essay. Also, go through  band B, C, and D extended essays  to understand the loopholes to avoid.

And that’s a wrap!

We hope this comprehensive IB Math EE guide answers your queries regarding the EE. We also suggest you go through  this IB Extended Essay guide  to clarify the Extended Essay component of your IB DP curriculum. You should also try Nail IB’s Extended Essay guide; check it out  here !

At Nail IB, we’re committed to delivering A-quality guidance so that your IB DP journey is smooth and successful. You can explore  our take-test  series here and access   premium guides  here.

Happy learning!

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IB Math EE: The Complete Guide for IB Students in 2023

by  Antony W

February 20, 2023

While it’s one of the most dreaded subjects in the IB program, the IB Math EE can be such an interesting area to explore if you love new challenges and can work with numbers.

In this guide, we’ll cover everything you need to know about IB Mathematics EE and even give you some tips to help you score top marks – if not a 34 in the IB program .

IB Math EE is a subject with its own level of difficulty. It requires in-depth research, prior planning, and writing a comprehensive extended essay in a way that aligns with the set guidelines.

If you read this guide carefully and implement the advice we give, we’re confident that you’ll score the grades that you desire for the assignment.

Before we get to anything else, it’s important that you have an interest in Math, a focused approach, and a mathematical aptitude and reasoning. Collectively, these characteristics will help you do well in the subject. 

What’s IB Math Extended Essay?

The Math Extended Essay is a comprehensive research paper on any topic with a mathematical emphasis, including but not limited to mathematics theory. The IB groups math Extended Essays into six categories:

• The applicability of mathematics to solve both real and abstract problems
• The beauty of mathematics, examples include: geometry or fractal theory
• The application of mathematics in the proving of theorems, for example, number theory
• The history of mathematics: the origin and subsequent development of a branch of mathematics over some time, measured in tens, hundreds, or thousands of years
• The effect of technology on mathematics
• In creating links between different branches of mathematics,
• Or in bringing about a new branch of mathematics or causing a particular branch to flourish.

What IB is trying to communicate is quite simple.

If anything, the Math Extended Essay can be either an extension of the Math syllabus or an application of the practical knowledge you gained in your classroom.

IB Math EE vs IB Math IA

One of the most common mistakes that IB students make is to assume that Math EE and Math IA mean the same thing.

So before we discuss the Math EE any further, let’ make sure you understand the difference between an EE and an IA.

Extended Essays are more rigorous and formal. They require you to conduct primary and secondary research on a research question that you pick based on the subject you have chosen to study.

Because the EE is a self-researched essay, unlike the IA, your mentor may not be able to provide you with all of the answers you require.

An Internal Assessment, on the other hand, requires you to explore and investigate an idea, but it’s less formal than an Extended Essay. 

For their IB Diploma Program, students must write one Extended Essay on a subject of their choice. However, they will have to write an IA for all their subjects.

The subject teacher grades internal assessments, which are subsequently moderated externally. Examiners appointed by the IB mark Extended Essays externally. Your overall score/points are determined by adding your Extended Essay grade to your Theory of Knowledge Essay/Exhibition grade.

Tips to Help You Get a 7 in IB Math

The following tips will help you to revise well for your IB Math AA or IB Math AI and place you in the position where you’re likely to score a 7:

1. Break a Big Topic into Smaller Topics

Break down a broad Math topic and categorize it into smaller themes before you begin your revision. It’s important to do this to figure out where new knowledge fits into the wider picture.

We understand that breaking down a subject into smaller topic is a little out of the ordinary for math revision because many students tend to leap right into practice almost immediately.

However, splitting a huge subject into smaller and easily manageable sections makes it easy for you to filter each inquiry type and fit the information into your pre-existing mental models.

So get a blank piece of paper, and create a bullet list of all the themes, sub-topics and question types you wish to practice.

2. Read, Analyze, and Understand the Subject Guideline

IB is quite detailed, and all of the questions tested in the examinations are in the guide's curriculum. Read the content, as doing so will direct your learning and show you every type of question you might encounter.

Make a list of all the questions that you’re likely to do in the upcoming examinations by going over each unit's sub-topics that IB could evaluate you, along with examples.

Because the approach provides a personalized checklist of questions the IB can ask, this strategy will lead you through the whole revision process.

Final Thoughts

In May 2021, IB made significant changes to its mathematics subject by dividing it into IB Math AA and IB Math AI . F

rom the time the changes took effect, IB students have the option to choose between the two subject segments depending on their strength and background in Math as well as their future goals.

While the changes give you some kind of flexibility, it does bring with it new challenges to tackle.

And if you don’t know how to get your head around the subject, it can be too complex to handle.

As people who’ve done Math AA and Math AI for as long as we can remember, we know there are those who love to work with numbers and those who label themselves as “not Math people”.

Regardless of where your stand is, the tips we’ve shared in this guide should help you do well in your Math EE.

Get IB Math Help

IB Math assignments can be quite challenging to handle, but you don’t always have to fret because we’re here to help.

Our IB writers have years of experience and knowledge in everything IB, so we can help you get your assignment in Math done within the shortest time possible.

Whether you need your paper in the next 7 days or you have a deadline shorter than that, Click Here to Place Order .

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.

IB Maths EE examples

Filter exemplars, to what extent prime counting function and the riemann zeta function are similar, and what is the importance of their similarities, how are elliptic curves used in cryptography to make information secure in today’s world, want to get full marks for your ee allow us to review it for you 🎯, how does elliptic curve cryptography ensure secure communication of information on the internet, to what extent is the naive bayes classifier effective in classifying iris plants data set, to what extent is the insight into the concepts of consonance and dissonance in music theory provided by the mathematical descriptions of the string motions within stringed instruments described by the fourier series, fast track your coursework with mark schemes moderated by ib examiners. upgrade now 🚀, how can laplace transformation be used to solve differential equations in undamped vibration and kirchhoff's laws of current and voltage, to what length does the lotka-volterra model help us understand the predator-prey relation in an ecosystem, how does the implementation of pell's equation in rsa cryptography affect its efficiency, and what is the security of the prime fake modulus variant against fermat's factorization and wiener's attack, dans quelle mesure, l’utilisation de pi (π) est-il devenu un facteur important dans la vie quotidienne et l’évolution du monde, how can matrix analysis of game theory be used to guide foreign policy in the ongoing us-iran nuclear tensions, how does the idea of transpositions from group theory apply itself to the solution of the futurama problem, how can the surface area of a violin's top plate be calculated, what is the height and number of towers in a suspension bridge between tuas and jurong island such that it will bear the heaviest possible load and have the lowest cost, how trigonomotry applied in astronomy, how do laplace transformations and complex exponential substitution enable the solution of a first order differential equation to obtain the sinusoidal current in a basic rl circuit, the analysis of approaches and extension of a combinatorial geometry problem, to what extent, statistically, are the causal effects of parenting programs on rural chinese toddlers’ cognition different between genders, to what extent is the mathematical proof of ‘ac ohm’s law’ applicable to ac circuits, to what extent do trigonometry, elliptical geometry and calculus aid forensic analysts in blood spatter analysis and the estimation of the time of death of a corpse, how does the fourier series is used as a musical signal for chord structure, what is modular arithmetic, and how can it be applied to solve problems in the field of number theory, to what extent do the motion of strings within stringed instruments described by fourier series give insight into consonance and dissonance in music theory, how can we use fourier series to analyse and produce an electrocardiogram signal, (35/36) hyperbolic flyby trajectories in orbital mechanicss, analyzing the distribution of cards in the "egg game”, what are some ways the riemann zeta function is connected to the prime numbers, that helps us investigate and better understand them, generating arbitrary uniform probability distributions, to what extent the areas of mathematics such as differ- ential geometry and calculus of variations can be used to generalize the brachis- tochrone problem at planes to curved surfaces embedded in three dimensions, probability factors that influence the game of roulette, we will investigate whether the supply and demand affect the performance of a stock in the us equity market, to what extent does the distance between the path that goes through the gold nucleus and one of the asymptotes of the α particle’s hyperbolic trajectory affect the trajectory of the α particle in rutherford's gold foil experiment, what is the most optimal point on football field to score a goal, how does abstract mathematics apply to physical phenomena in the process of the development of schrodinger’s equations, the rsa algorithm and its vulnerabilities, how can mathematics be used to work out the optimal distance from the try line to position the ball for a conversion kick in rugby union.

Extended Essay

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Mathematics Sample A

Mathematics sample b, mathematics sample c.

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Extended Essay Writers

Math Extended Essay Topics

Luke MacQuoid

A math extended essay (EE) is a research paper that is written by students who are enrolled in the International Baccalaureate (IB) program as a part of their Diploma. The Extended Essay is self-directed research that aims to provide students with the opportunity to explore a topic of their interest in depth, with a particular focus on the application of math concepts and skills. In order to pass the paper successfully, it is very important to choose the right topic for the Math Extended Essay Topics.

In an Group 5: Mathematics extended essay, students work independently under the guidance of a supervisor to plan and carry out a research project on a math-related topic . This research project should demonstrate the student’s ability to engage in independent research, apply critical thinking and problem-solving skills, and communicate their findings clearly and effectively.

The math extended essay has strict word count in length and should be written in a clear, concise, and formal style, it should also include an introduction, a body of discussion, a conclusion, and a bibliography.

The student is expected to demonstrate the ability to design and conduct a research project, use mathematical concepts and skills to analyze and interpret the data and discuss their findings in the context of relevant mathematical literature.

The math extended essay also allows students to explore a mathematical topic in a way that is not possible in the classroom, it also gives a chance to students to demonstrate their mathematical knowledge and skills and to develop a more global understanding of mathematics.

What’s the Purpose of IB Math Extended Essay?

The purpose of the IB math extended essay is to provide students with the opportunity to engage in independent research and to apply their mathematical knowledge and skills to a topic of their own choosing. The extended essay is designed to give students a chance to explore a topic in depth and to develop the following key skills:

Research skills : Students learn how to design and conduct a research project and how to collect, analyze, and interpret data.

Critical thinking skills : Students learn how to evaluate sources, make a clear and well-supported argument, and solve problems.

Communication skills : Students learn how to write a formal academic paper and how to present their findings and arguments clearly and effectively.

Time management skills:  Students learn how to plan their time effectively and manage their workload.

Subject-specific knowledge : Students get the opportunity to deepen their understanding of a particular area of mathematics and to explore the ways in which mathematical concepts and methods can be applied to solve problems.

The IB Math Extended Essay allows students to research and write about a specific mathematical topic that they find interesting. It also allows students to apply the knowledge and skills they have learned in the classroom to a real-world problem or scenario. 

Completing the extended essay is an important requirement for students to receive the International Baccalaureate Diploma, and it also provides students with the opportunity to develop important research and analytical skills which will be useful in the future, regardless of their chosen career path.

Need help with your IB Math extended essay?

You can also use our extended essay writers team’s services if you need assistance selecting a topic . Furthermore, we can also help you write your IB extended essay from scratch or edit your draft following the IB criteria.

IB Math Extended Essay Topics

An extended essay in mathematics provides students with an opportunity to explore an area of math that interests them in depth. Here are some potential topics for a math extended essay:

• Investigating the properties of a specific mathematical function and its applications.
• Examining the history of a particular mathematical concept or problem
• Investigating the relationship between different branches of mathematics, such as algebra and geometry.
• Investigating the properties and application of geometric shapes in different branches of mathematics.
• Applying mathematical modeling to a real-world problem, such as optimizing logistics or predicting weather patterns.
• Investigating the use of mathematical methods in computer science, such as complexity theory and algorithms.
• Exploring the application of number theory in cryptography and information security
• Investigating the role of statistics in decision-making and forecasting.
• Investigating the use of mathematical logic in Artificial Intelligence and machine learning
• Examining the applications of mathematical methods in the field of engineering and physics, such as fluid dynamics and mechanics.
• Investigating the properties of fractals and their applications in computer graphics and image processing.
• Exploring the concept of infinity and infinitesimals in calculus and their implications in other branches of mathematics.
• Investigating the application of graph theory in network analysis and computer science
• Examining the relationship between topology and other branches of mathematics such as algebra and analysis.
• Investigating the properties of mathematical knots and their applications in physics and biology.
• Exploring the application of game theory in economics and decision making
• Investigating the use of mathematical methods in the field of finance and financial modeling
• Examining the relationship between chaos theory and other areas of mathematics and science
• Investigating the use of mathematical methods in the field of cryptography, such as elliptic curve cryptography.
• Exploring the application of mathematical methods in the study of complexity in natural systems, such as studying the Mandelbrot set in the field of chaos theory.

Remember to check with your teacher or supervisor for guidelines or restrictions and pick a topic that you find interesting and engaging. Also, make sure you have a clear and testable research question as part of the planning and writing process.

Students can use these themes as a starting point for their research and then narrow down their focus to a specific problem or question related to the theme. For example, if a student is interested in investigating the properties of a specific mathematical function, they could begin by researching the history of the function, its key properties, and its applications. 

They could then narrow down their focus to a specific problem or question, such as “How does the shape of the graph of this function change as its parameters are varied?” or “What are the implications of this function’s properties for other areas of mathematics?”

Similarly, if a student is interested in exploring the concept of infinity in calculus, they could begin by researching the history of the concept and its implications in other branches of mathematics. They could then narrow down their focus to a specific question, such as “How does the concept of infinity affect the way we think about limits and continuity in calculus?”

Once a student has a specific problem or question in mind, they can begin to design and conduct their research. This will typically involve collecting data, analyzing it using mathematical methods, and interpreting their findings. They should also read and critically evaluate relevant literature on their topic and use it as a foundation to construct their own arguments.

It’s also important to mention that the research and writing process should be guided by the student’s supervisor and that the student should be able to clearly communicate the research question, methodology, findings, and conclusions in a formal academic paper.

Finally, the extended essay is an opportunity for students to demonstrate their ability to apply mathematical concepts and skills to a real-world problem and to communicate their findings in a clear and effective way, and this can be greatly beneficial for students who wish to pursue further studies or careers in fields related to mathematics and other sciences.

Some Tips to Help You Choose a Relevant Math EE Topic

Choosing a relevant and engaging topic for your math extended essay can be challenging, but by following these tips, you can make the process easier:

Start by identifying your interests: Think about the areas of math that you enjoy and find most interesting. These are likely to be the areas that you will find most engaging to research.

Consider the scope of the topic: Your topic should be narrow enough to be manageable within the 4,000-word limit of the extended essay but broad enough to allow for a thorough investigation.

Look for connections between different areas of mathematics: Often, the most interesting and relevant topics lie at the intersection of different areas of mathematics.

Talk to your supervisor: Your supervisor is a valuable resource and can provide guidance on choosing a relevant and manageable topic. They can also help you refine your research question and give you feedback on your ideas.

Make sure your topic is original: You want your extended essay to be unique and to make a meaningful contribution to the field. Avoid topics that have been extensively researched or that are too similar to other extended essays.

Think about the resources available: Consider whether the resources available to you (books, articles, data, etc.) are sufficient to allow you to conduct the research you want to do.

Consider the audience: Your Extended Essay is read by a group of examiners appointed by the International Baccalaureate, so consider the level of mathematical sophistication of your topic and the language used to communicate it.

Research to find a feasible topic: Once you have some ideas, research them to see if they are feasible, given the time, resources, and supervisor’s expertise you have.

In conclusion,  writing a math extended essay can be a challenging but rewarding experience. The key to success is to choose a relevant and engaging topic that aligns with your interests and allows you to showcase your understanding and skills in mathematics. By considering the tips provided, such as identifying your interests, talking to your supervisor, and making sure your topic is original, you will be able to choose a topic that is both manageable and meaningful. 

One way to ensure the success of their essay is to seek out professional assistance. Professional writers and editors can provide valuable feedback and guidance throughout the research and writing process, helping students to improve their understanding of the topic and to communicate their findings more effectively.

It could be a good idea to consider looking into reputable academic writing services where you can get help with your math extended essay and improve your chances of getting a good grade. They can also help ensure that the paper meets academic standards and requirement. However, always be sure to evaluate the source carefully and do your due diligence, as not all academic writing services are created equal.

Remember that the extended essay is an opportunity to conduct independent research and apply critical thinking and problem-solving skills to a topic of your own choosing. By following a systematic and well-structured approach, you will be able to successfully complete your math extended essay and demonstrate your knowledge and understanding of the subject.

Luke MacQuoid has extensive experience teaching English as a foreign language in Japan, having worked with students of all ages for over 12 years. Currently, he is teaching at the tertiary level. Luke holds a BA from the University of Sussex and an MA in TESOL from Lancaster University, both located in England. As well to his work as an IB Examiner and Master Tutor, Luke also enjoys sharing his experiences and insights with others through writing articles for various websites, including extendedessaywriters.com blog

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IB Mathematics Extended Essay: Decoding Dogs’ Barks with Fourier Analysis - Grade Received: B

Research Question: How can Fourier Analysis be used to differentiate between the motivational changes of a dog by examining the recordings of the dog’s barks? My aim in this essay is to find a mathematical correlation between Lucky’s barks and his motivational changes through Fourier Analysis.

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Research Questions: Class of 2020

Visual Arts: To what extent are the developments in American military aircraft nose designs from World War 2, Vietnam War and Gulf War more connected to individual crew preference than to the visual culture of America, 1940 - 1990?

English A: To what extent does William Shakespeare employ Elizabethan elements in Romeo and Juliet to build towards the eventual tragedy?

English A: To what extent did news media outlets, specifically CNN and Fox News, use different reporting methods to portray the candidates in the 2016 United States presidential election?

English A: How do aspects of real-life societies inform and shape A Clockwork Orange and The Handmaid’s Tale?

English A: How were African Americans portrayed in American sitcoms from 1980 to 2000?

English B: To what extent does 'The Fault in Our Stars' by John Green reflect 'The Hero's Journey'?

English B: To what extent does social media influence or have an effect on the english language usage?

English B: To what extent does the usage of AAVE affect an individual’s social status and mobility?

English B: To what extent does the development of the Super Bowl mirror specific aspects of American cultural, social, and economic trends?

Psychology: To what extent is the phenomenon of Karoshi, the overworking of office workers in Southeast Asia, interconnected with symptoms of depression?

Psychology: To What Extent is Cognitive Behavioral Therapy, as an addition to traditional pharmacotherapy necessary for the successful treatment of Schizophrenia?

Psychology: To what extent is Δ9-THC an effective antidepressant that can be used to treat patients with depression?

Chinese B: 论新时代网络语言对现代汉语有何种影响？

Chinese B: 中国嘻哈歌手如何运用歌词传播中华文化？How do Chinese Hip-hop Artists Promote Chinese Culture through Lyrics?

Economics: To what extent have increases in rental prices (2017-2018) shrunken the market for Korean restaurants in Chegongmiao, Shenzhen?

Economics: How does President Moon's minimum wage policy affect convenience store market in Seocho 1-dong, South Korea?

Business: To What Extent Does the WeChat Application in Tencent's Business Model Play a Role in its Success?

Business: To what extent has Samsung's acquisition of Harman Kardon helped in increasing revenue and access to new markets?

Research Questions: Class of 2019

World Studies (Biology & Economics): How does mountain gorilla (Gorilla beringei beringei) ecotourism support and strengthen local economies while ensuring the mountain gorillas’ health and survival?

English A, Category 3: How are skincare companies like: Neutrogena, Nivea, and Dove promoting white supremacy?

English B, Category 2B: To what extent do the changes in Cersei’s and Daenerys’s character development in the HBO series Game of Thrones show they are ultimately both motivated for and by power?

Visual Arts: To what extent did visual qualities in Coco Chanel’s Little Black Dress 1913, influence black dresses created by Chinese fashion designer Vivienne Tam and haute couture designer Yiqing Yin in regards to development in visual elements and societal acceptances in the 21st century?

Business Management: “To what extent was Apple Inc.’s acquisition of Beats Electronics, LLC an effective growth strategy?”

Math, Group 5: Investigating the Korean MERS outbreak using the SEIR model: How would hypothetical diseases be simulated if variables of the SEIR model were to be altered?

Business Management : To what extent has the benefits offered by Shekou International School helped them retain staff?

Economics: To what extent has the subsidy that was introduced in 2016 for hybrid electric vehicles led to a rise in demand for domestic car producers in Baden Württemberg?

Chemistry: How does the addition of salt (NaCl) which modifies the salinity affects the interfacial tension and stability of oil-in-water emulsion?

World Studies (History & Literature): What aspects of the anti-vaccination movement, and “The Crucible” relate to mass hysteria during the Salem Witch Trials?

Psychology: To What Extent Do Behavioural Addictions Fit The Criteria for ‘The Disease Model of Addiction’?

World Studies (Economics & Politics): To what extent has the political decision to host the 2016 Olympic Games in Rio de Janeiro affected Brazils’ economy and the financial welfare of its citizens?

Physics: To what extent does the volume of water affect the altitude gained by adding a constant pressure?

Psychology: To what extent are sociocultural and biological factors major causes of elderly people’s depressive behavior?

World Studies (History & Economics): To what extent did the LGBTQ community contribute to making attractive neighborhoods in the US and why are they pushed to leave them now?

Economics: To what extent is the cafe market in Shekou, Shenzhen, monopolistically competitive?

Economics: “Which is the most important factor that changes the real estate price rate in Magok-dong, Gangseo-gu, Seoul Korea?”

Business Management: To what extent has McDonald’s marketing strategies played a major role in becoming a prominent fast-food company in Korea?

World Studies (Physics & Geography): To What Extent is the Design of the Standard Houses that Gawak Kalinga Builds Able to Withstand the Seismic Hazards Present in Manila?

World Studies (Economics & Music): To what extent is electronic music’s economy expanding?

Visual Arts: To what extent did artistic influences and material sources impact the chair designs of Gerrit Thomas Rietveld Zig-Zag (1934), Verner Panton Panton S (1956), and Tom Dixon, Capellini, S Chair (1991)?

Business Management: To what extent has Apple Inc.’s prioritization of product innovation and advertising led to sales of iPhone X?

World Studies (Psychology & Geography): How do the combined effects of Socioeconomic Status and Diabetes increase prevalences of Alzheimer’s Disease in different regions within China (PRC)?

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Research question.

The research question is the cornerstone of the Extended Essay. The words 'research question' appear in Criteria A-C. What are the characteristics of a good research question? Compare the poor research questions with the good questions in the table below. What improvements have been made? Discuss these improvements with a classmate or colleague and make a list of the characteristics of a good research question, before revealing the word cloud below.

Characteristics of a good research question

Phrasing your research question

Which phrases and words often appear in good research questions? Here are some phrases to consider and some phrases to avoid when articulating your research question. Discuss how the useful phrases can help you demonstrate the characteristics of a good research question (see word cloud above). 

Some teachers advise against using the phrase 'to what extent', because it is so popular. It is popular, however, for good reason. It inserts an element of 'why' into a 'how' question, which helps make your essay more evaluative. Watch out for closed questions (which can be answered with a 'yes' or 'no', weasel words (such as 'some people say') or sweeping generalisations (such as 'true artists do not care about financial success.'

Over to you

Below are several mediocre research questions that could be improved. Read each mediocre question (a) and discuss how you would improve it, before revealing the improved version (b). The improved versions are only suggestions, as there are many ways to improve them.

1a: English A, Cat. 1: Mediocre question

1b: english a, cat. 1: improved question.

For what reasons and to what effects do Terry Pratchet and Markus Zusak employ characterization and narration in Mort and The Book Thief respectively?

Notice how this improved version is more focused on the stylistic features of the primary sources and 'why' ("for what reasons") the authors wrote these works. The phrase "to what effects" also allows the essays to be more evaluative than descriptive.

2a: English B, Cat. 2a: Mediocre question

How are American views on infidelity expressed through language?

2b: English B, Cat. 2a: Improved question

Category 2b:  How does the use of English by Tiger Woods and Bill Clinton in their confessional speeches reveal America’s attitudes toward marriage and infidelity in the 1990s?

Notice how this question has been moved from Category 2a to 2b and now refers to cultural artefacts, namely the speeches of two men. While the original question meets the 2a requirements, 2b essays are generally more focused because they require primary sources (cultural artefacts). Primary sources are a key ingredient in any Group 1,2 or 6 essay because Criterion C: Critical thinking refers to analysis and evaluation of primary sources. In the subject-specific guidance on Group 2 Extended Essays, the word 'analysis' appears, even though this word does not appear anywhere in the subject guide for Language Acquisition. Students are not allowed to write a Language B essay (Group 2) in a language that they are taking as a Language A (Group 1). The above-mentioned research question would also be very appropriate as an English A, Cat. 3 essay on 'language', which is IB-speak for 'non-literary text(s)'.

3a: History: Mediocre question

3a: history: improved question.

To what extent were foreign influences the main cause in the Khmer Rouge’s rise to power in Cambodia in 1975?

Notice how this question cuts out the Holocaust and focuses on foreign influences as the main cause of the Khemer Rouge's rise to power in 1975. Most History essays receive a 'C' (see Statistical Bulletin), because they tend to be too descriptive and not evaluative or argumentative. Good History essay try to identify a causal relationship and persuade the reader (examiner) of the significance of these causes.

4a: Biology: Mediocre question

4b: biology: improved question.

What is the optimal amount of ethylene and the optimal temperature for bananas that ripen in sea containers?

Ethylene makes fruit ripen faster. This process is affected by temperature. These variables are already known and tested. But why do they matter? Every day bananas are transported in sea containers around the world. For grocery stores and their customers, it is important that bananas are not too ripe or unripe upon arrival. What data are available from shipping companies? How can experiments with bananas, ethylene various temperatures and spaces generate useful data for shipping companies? The improved research question puts a much greater emphasis on the significance of the research. Generally speaking, students who conduct experiments do better than students who only analyse other researchers' data.

5a: Maths: Mediocre question

5a: maths: improved question.

How can the kinds of batting strageties described in the movie Money Ball be used to recruit players and create the optimal batting order?

Students are often told not to write their Extended Essay in Maths, because it is too difficult. Check out the Statistical Bulletin to see that many students do very well in Maths. Applied mathematics is popular for good reason. It addresses the relevance of maths to real-world problems. The 'mediocre' question could be too descriptive, exploring correlations between RBIs and wins in baseball. The 'improved' question does something with an already-proven batting strategy, which is explored in the movie Money Ball ). It shows its relevance to the recruitment of players and a team's batting order, which are important responsibilities of baseball managers and coaches.

6a: Visual arts: Mediocre question

Why is M.C. Escher an underappreciated artist in his country of origin, the Netherlands?

6b: Visual arts: Improved question

To what extent and for what reasons have the works of M.C. Escher been received differently in the United States and the Netherlands?

The 'mediocre' question has built-in assumptions that the artist is underappreciated in the Netherlands. The 'improved' question explores how his works have been received differently in two countries. This exploration will require a broad range of secondary sources that review Escher's works, possibly in both English and Dutch. Cross-cultural comparisons are relevant for those who are interested in the artist, the commercialisation of art and what makes art 'art'.

How do you know what you think you know? This is a guiding question for Theory of Knowledge (TOK), which also has relevance to your Extended Essay. Research questions should go beyond 'what is known' and explore 'how much can be known' about your topic.

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