ib mathematics extended essay examples

IB Maths EE examples

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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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• How to write?

How to Write a Math Extended Essay? A Comprehensive Guide

Luke MacQuoid

• September 28, 2023

Table of Contents

Ah, the Math extended essay! It’s an excellent opportunity for students in the IB program to showcase their knack for numbers. From my experience, crafting an impactful essay requires mathematical talent and a solid understanding of what makes a paper genuinely resonate.

Throughout this article, you’ll find gems on selecting Math extended essay topics , how to structure your essay, and even some common pitfalls to avoid. So, let’s jump right in, shall we?

What is a Math Extended Essay?

You may be pondering, “What is a Math extended essay?” According to the IB criteria, this piece is a 4,000-word research document that prompts students to research a mathematical topic of interest thoroughly. It’s not just an ordinary research paper; think of it as your gateway to mastering a subject you’re genuinely passionate about. Trust me, from my experience, it’s a pivotal component of your academic growth.

Let’s clarify further. Math extended essay isn’t just a routine school assignment you might complete on a typical day. Instead, it’s a comprehensive exploration of a distinct topic within Mathematics. But remember, it’s not all about numbers or equations. It’s about showcasing your ability to reason, analyze, and communicate your findings in writing.

Here are all the critical elements of a top-notch Math extended essay :

• Clear Thesis . A strong paper begins with a defined proposition or statement set for investigation.
• Thorough Research . Look into reputable sources, journals, and academic papers. Absorb as much relevant information as possible.
• Logical Flow . Your essay should transition smoothly from one topic to the next, ensuring readers can follow your train of thought easily.
• In-depth Analysis . Beyond stating facts, analyze them critically and draw your conclusions.
• Personal Touch . Reflect on your genuine interest and connection with the topic.
• Effective Expression . Aim for clarity in your writing, ensuring readers can quickly grasp your points.
• Ethical Standards . Properly cite all your sources and avoid any form of plagiarism.
• Reflection . Share insights on your learning process, the challenges faced, and the strategies you employed to address them.

So, you might wonder, “Why take on such a demanding task?” Here’s the thing: based on what I’ve learned and observed, the Math extended essay plays a significant role in the IB program. It’s essential for obtaining your IB diploma and can significantly enhance your college application. More importantly, it’s an opportunity to challenge yourself academically, fostering intellectual growth.

Committing to this task and seeing it through will be a significant academic accomplishment. Best of luck!

Getting Started with Your Math Extended Essay

The inception of any great essay starts with topic selection and understanding the guidelines, naturally.

Topic Selection

Choosing the right topic is the first milestone. Think about the Mathematical areas that captivate your interest. Whether it’s the logic of algebra, the complexity of calculus, or any other field, there’s a vast Mathematical universe to explore. While broad subjects might seem tempting, concentrating on specific IB Math extended essay topics is often more effective. Your issue should be clear-cut and straightforward and uphold strong academic integrity in line with IB standards.

Understanding Guidelines

After settling on a topic, it’s essential to acquaint yourself with the IB’s precise expectations . From my experience, grasping these guidelines is foundational to the essay’s success:

• The IB has detailed guidelines regarding the structure and layout of extended essays. Ensure you’re well-versed in font choice, spacing, and the like.
• While the IB often leans towards MLA or APA citation styles, be sure to check the style preferred by your institution. Accurate citations aren’t just about avoiding plagiarism; they lend authenticity to your work.
• IB evaluates your extended essay based on distinct criteria, such as clarity, depth of knowledge, presentation, and personal connection to the topic. Familiarizing yourself with these parameters can guide your research and writing trajectory.
• The extended essay process in the IB program includes consultations with a designated supervisor. These sessions are golden opportunities to glean insights and refine your approach.

In essence, the proper groundwork ensures a smoother path ahead. With a compelling topic and a robust grasp of the IB guidelines, you’re primed to craft a stellar Math extended essay. Embrace the process and aim for excellence!

Math Extended Essay: Research and Planning

Research is the backbone of your essay! Adequate preparation is necessary for a subject as complex and layered as Math.

Behind every successful essay is a bedrock of meticulous research and detailed planning. Given the intricate nature of Mathematics, gathering your tools and strategies is paramount before plunging into the writing phase. First, seek out robust platforms that offer a plethora of verified information :

• Online Databases . Websites like JSTOR , Google Scholar , and MathSciNet host a rich collection of articles, papers, and journals dedicated to Mathematics.
• Academic Journals . Publications such as the “American Journal of Mathematics” or the “European Journal of Mathematics” provide peer-reviewed papers on many topics.
• University Libraries . Many universities offer access to their digital libraries, which can be goldmines for in-depth research.
• Professors and Mentors . Never underestimate the power of a conversation. Sometimes, discussing your topic with experts can lead to new insights and perspectives.

Remember, the depth and breadth of your research directly influence the strength of your arguments. Always verify the authenticity of your sources; a well-researched essay stands tall among its peers.

Timeline for Writing Math Extended Essay

Managing time is a lifesaver in the whirlwind of IB coursework, deadlines, and extracurriculars. Crafting a detailed timeline ensures you stay on track and prevents last-minute scrambles.

• Exploration . Dedicate the initial phase to exploring potential topics, understanding guidelines, and preliminary reading.
• Intensive Research . This phase involves deep diving into your chosen topic, gathering data, and organizing your findings.
• Drafting . Begin with an initial draft. Lay down your arguments, flesh out your thoughts, and structure your content.
• Review and Refinement . Revisit your draft, make necessary revisions, and incorporate feedback from peers or mentors.
• Finalization . Proofread, ensure adherence to guidelines, and prepare for submission.

Breaking down your process into manageable chunks alleviates stress and enhances the quality of your work.

Need help with your IB extended essay?

From research and analysis to structuring and editing, our skilled mentors will be by your side, helping you craft an exceptional extended essay that not only meets the wordcount and stringent IB criteria but also reflects your passion for selected IB group .

To wrap it up, remember that while the task might seem daunting, meticulous research and detailed planning are your allies. Harness them wisely; your Math extended essay will meet and exceed expectations. Happy researching!

Structuring Your Math Extended Essay

Organization is key, folks! How you structure your essay could make or break your grade.

Introduction

Your introduction should present the issue you’re investigating, why it matters, and how you plan to tackle it. This part is the roadmap of your essay; it sets the tone for the reader.

In this section, present your research, arguments, and findings. Dabble in some theory, show your equations or models, and remember to analyze their relevance. As you go, remember to build a logical flow. Use transition words to guide your reader through your discussion.

It is where you tie all your findings together. A well-crafted conclusion leaves a lasting impression, briefly highlighting your significant discoveries and their implications.

Math Extended Essay: Common Mistakes to Avoid

When creating an essay of the caliber expected for the IB program, the devil is often in the details. Many students have sailed through the bulk of their paper writing only to stumble near the finish line due to seemingly minor oversights. Awareness of these pitfalls is essential, especially in an undertaking as significant as the Math extended essay.

A common trap that students often fall into is vagueness. One might use ambiguous phrases or general statements to sound sophisticated or cover a wide range of ideas. Instead of making broad claims, focus on your main idea and flesh it out with detail and precision. 

Another critical area that cannot be overemphasized is plagiarism. While it’s tempting to borrow a perfectly phrased sentence or a well-structured argument, doing so without proper attribution is academically dishonest and can jeopardize your entire essay. When in doubt, always give credit where credit is due.

Another often overlooked aspect is the flow and structure of the essay. Transitioning smoothly from one point to the next, ensuring that each segment of your paper leads seamlessly into the next, can make a difference in your work’s overall quality and readability.

Review and Revision in Math Extended Essay

One of the most powerful tools in this phase is peer review. While you’ve been deeply engrossed in your essay and every argument, equation, and citation, there’s immense value in having another set of eyes scan your work. It doesn’t necessarily mean someone who’s an expert in your topic but can provide a fresh perspective. They can identify areas that might be unclear to a new reader.

Following peer review, there’s the intricate task of editing and proofreading. While these terms are often used interchangeably, they serve distinct purposes. Editing is all about refining the content. Proofreading, on the other hand, is about the nitty-gritty. It ensures that your grammar is spot-on and that there are no misplaced punctuations.

In all of this, reflection is a vital element often overlooked. Taking a step back, setting your essay aside for a day or two, and returning to it with renewed vigor is immensely beneficial. With a fresh mindset, you might find new angles to consider or realize there are redundant points that can be removed.

To Sum It Up

Writing a Math extended essay can be challenging but also incredibly rewarding. So, according to general IB criteria and years of personal experience, the time and effort you invest in this project will be well worth it. Good luck, young scholars!

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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Extended Essay (First Exams 2018): Examples of Extended Essays

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Samples from the IBO

The IBO publishes two volumes of  50 Excellent Extended Essays , covering all Diploma Programme groups -- and all scored a top A grade.

Click on the link below to access PDFs of the essays. 

50 Excellent Extended Essays

All 50 essays are also available in electronic form in the QD Library on the iPads.  Look for the display at the circulation desk. The essays are found in the iBooks app. The iPads are available for check out at the circulation for periods of 30 minutes at one time.

Recently, the IBO has produced another list of exemplars with marks. Click on the link below to access this:

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IB Math EE – Math Extended Essay Guide

• Home . 

The IB Math Extended Essay is a challenging yet rewarding academic endeavor that allows students to explore and delve deeper into various mathematical concepts and techniques. This article aims to provide valuable insights and guidance on how to successfully navigate through the process of writing an IB Math Extended Essay.

With a focus on conducting effective research, applying mathematical concepts, developing a coherent argument, and managing time and organization, this article offers practical tips to help students overcome challenges and roadblocks they may encounter along the way.

Furthermore, this article emphasizes the importance of showcasing personal engagement in the essay by demonstrating genuine curiosity and passion for the chosen topic. By doing so, students can celebrate their accomplishment in producing a well-written piece that reflects their dedication and understanding of mathematics.

Whether you are just beginning your journey or already immersed in your IB Math Extended Essay, this informative guide will equip you with essential tools to excel in your academic pursuit while ensuring safety within an objective academic writing style.

Key Takeaways

• IB Math Extended Essay is a challenging academic endeavor that allows students to explore mathematical concepts and techniques.
• The essay requires effective research, application of mathematical concepts, coherent argument, and time management.
• Personal engagement and passion are important for a successful extended essay.
• Effective research strategies include consulting scholarly articles, books, and reputable online resources, and following clear plans and systematic methodologies.

Table of Contents

Understanding the IB Math Extended Essay

The IB Math Extended Essay is a research project that requires students to investigate a mathematical topic of their choice in depth, demonstrating their understanding and application of mathematical principles. It serves as an opportunity for students to engage in independent research and explore the subject matter beyond the scope of the standard math curriculum. The essay allows students to delve into complex mathematical concepts, develop logical arguments, and present their findings in a structured manner.

To ensure safety within this academic pursuit, it is crucial for students to adhere to ethical guidelines when conducting their research. This includes citing all sources accurately and giving credit where it is due. Additionally, students should prioritize data integrity by using reliable sources and verifying information before incorporating it into their essays.

In order to conduct effective research for the IB Math Extended Essay, students must employ various strategies such as consulting scholarly articles, books, and reputable online resources. They should also consider seeking guidance from experts or professionals who can provide valuable insights on their chosen topic. By utilizing these resources effectively, students can enhance the quality of their research and ultimately produce a comprehensive essay that contributes meaningfully to the field of mathematics.

Transitioning into the next section on conducting effective research without explicitly stating “step,” it is essential for students to approach their investigation with a clear plan and systematic methodology.

Conducting Effective Research

To effectively conduct research for an IB Math extended essay, it is essential to approach the task with an objective and impersonal mindset. This ensures that the research is conducted in a systematic and unbiased manner, allowing for reliable and valid results. Here are four helpful tips to consider when conducting research for your IB Math extended essay:

• Define your research question clearly: Start by identifying a specific problem or topic within the field of mathematics that you want to explore. Clearly define your research question to provide focus and direction throughout the process.
• Gather relevant sources: Conduct a thorough literature review to identify existing theories, models, and studies related to your research question. This will help you build a solid foundation of knowledge and understand previous findings in order to contribute something new to the field.
• Collect and analyze data: Depending on your chosen topic, collect data using appropriate methods such as surveys, experiments, or simulations. Ensure that your data collection process is rigorous and follows ethical guidelines.
• Draw meaningful conclusions: Analyze your data using appropriate mathematical techniques and interpret the results objectively. Draw meaningful conclusions that address your research question’s objectives while considering any limitations or uncertainties present in the study.

By following these steps, you can conduct effective research for your IB Math extended essay that contributes valuable insights into the field of mathematics. Moving forward into applying mathematical concepts and techniques…

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Applying Mathematical Concepts and Techniques

Applying mathematical concepts and techniques involves seamlessly integrating complex equations, formulas, and algorithms into practical real-world scenarios, unlocking the potential for innovative solutions and transformative insights. By harnessing the power of mathematics, researchers can analyze data, model systems, and make predictions with precision and accuracy. Mathematical tools provide a structured framework to explore relationships between variables, identify patterns, and test hypotheses.

To illustrate the significance of applying mathematical concepts in research, let us consider a 2-column table:

Mathematical ConceptPractical ApplicationProbability theoryAssessing risks in safety engineeringOptimizationOptimizing resource allocation in disaster managementStatistical analysisAnalyzing crime patterns for effective law enforcement

This table demonstrates how mathematical concepts can be applied to enhance safety measures. Probability theory enables engineers to assess risks associated with different design choices. Optimization techniques help allocate limited resources efficiently during emergencies. Statistical analysis allows law enforcement agencies to identify crime hotspots for targeted interventions.

By incorporating mathematical concepts and techniques into research methodologies, researchers can derive meaningful insights that contribute to safe and reliable solutions. In the subsequent section about ‘writing a strong introduction,’ we will explore how an effective opening sets the stage for further investigation without being overly prescriptive or formulaic.

Writing a Strong Introduction

Engaging the reader and providing context is crucial in writing a strong introduction for an essay. By presenting relevant background information or posing thought-provoking questions, the writer can capture the reader’s attention and create a sense of relevance to the topic. Additionally, formulating a clear thesis statement in the introductory paragraph helps establish the main argument of the essay and provides a roadmap for what will be discussed. Lastly, outlining the structure and scope of the essay allows readers to understand how different sections will be organized and what specific aspects will be explored, ensuring clarity and coherence throughout the paper.

Engaging the reader and providing context

In order to fully immerse the reader into the world of mathematics, it is crucial to provide a rich contextual backdrop that allows for a clearer understanding and appreciation of the subject matter. Mathematics can often seem abstract and disconnected from everyday life, leading some individuals to view it as intimidating or irrelevant. By engaging the reader through relatable examples and real-world applications, we can create a safe and approachable environment for learning. Exploring how mathematical concepts are applied in various fields such as engineering, finance, or computer science not only helps students see the practicality of mathematics but also fosters an interest in further exploration. Moreover, providing historical context can highlight the development and significance of different branches within mathematics. This sets the stage for formulating a clear thesis statement that builds upon this foundation of knowledge.

Formulating a clear thesis statement

To effectively convey the main focus of a mathematical exploration, it is crucial to craft a concise and clear thesis statement that serves as a guiding framework for the subsequent analysis. A well-formulated thesis statement not only states the main argument or hypothesis but also provides a roadmap for the reader to follow throughout the essay. In an academic style of writing, it is important to maintain objectivity and impersonality, eliminating personal pronouns to create a sense of professionalism and neutrality. By presenting the thesis statement in an objective manner, the writer can engage with an audience that desires safety and assurance in their understanding of complex mathematical concepts. With a solid thesis statement in place, the subsequent section will outline the structure and scope of the essay seamlessly, ensuring clarity and coherence in presenting mathematical ideas.

Outlining the structure and scope of the essay

In the previous subtopic, we discussed the importance of formulating a clear thesis statement for an IB Math Extended Essay. Now, let’s move on to outlining the structure and scope of the essay. This step is crucial as it helps provide a roadmap for the reader to navigate through your work. By clearly outlining the structure and scope, you ensure that all relevant aspects are covered while maintaining coherence and logical flow.

To achieve this, consider incorporating an unordered 3 item bullet list in markdown format:

• Begin with an introduction that introduces the topic and provides context.
• Divide your essay into sections or chapters based on different aspects or arguments.
• Conclude with a summary of key findings and a reflection on their significance.

By following these guidelines, you can create a well-structured essay that effectively communicates your ideas. Transitioning into the next section about developing a coherent argument, it is essential to build upon this foundation by presenting compelling evidence and reasoning to support your thesis statement.

Developing a Coherent Argument

Developing a coherent argument requires the use of logical reasoning and well-structured evidence. When constructing an argument, it is essential to present facts and information in a clear and organized manner. This involves avoiding personal biases and emotions, as well as eliminating personal pronouns to maintain objectivity.

To ensure a strong argument, it is crucial to rely on credible sources and data that support the claims being made. Using evidence from reputable academic journals or textbooks helps establish credibility and adds weight to the argument being presented. Additionally, incorporating logical reasoning allows for connections to be made between different pieces of evidence, further strengthening the overall coherence of the argument.

When writing for an audience that desires safety, it is important to use language that is appropriate and sensitive. Avoiding inflammatory or offensive language ensures that readers feel respected and engaged with the content. By presenting arguments in a respectful manner, readers are more likely to consider different perspectives without feeling attacked or threatened.

Developing a coherent argument requires logical reasoning backed by well-structured evidence. By employing these strategies, writers can effectively communicate their ideas while maintaining objectivity. In the subsequent section about using clear and concise language, we will explore how this aspect contributes to the overall coherence of an essay’s argumentation process.

Using Clear and Concise Language

Using precise and concise language enhances the clarity and impact of an argument, captivating readers and facilitating their understanding. When writing academically, it is important to eliminate personal pronouns and adopt an objective and impersonal tone. This approach allows the focus to remain on the content rather than the writer’s subjective perspective. By using clear and concise language, writers can effectively convey complex ideas without overwhelming or confusing their audience.

In an academic setting, it is crucial to cater to an audience that values safety in their reading material. Using language appropriate for this type of audience ensures that readers feel secure in engaging with the content. It also helps build trust between the writer and the reader, as clear communication fosters a sense of reliability.

Transitioning into the subsequent section about formatting and citations, it is essential to maintain precision throughout all aspects of academic writing. Formatting guidelines ensure consistency in presenting information while citations acknowledge sources used in support of arguments. These elements contribute to establishing credibility within academia by demonstrating a thorough understanding of scholarly norms.

By adhering to these rules of using clear and concise language, as well as following proper formatting guidelines and including accurate citations, writers can effectively communicate their ideas while maintaining professionalism within academic discourse.

Formatting and Citations

This paragraph will discuss the importance of following the IB guidelines for formatting and citation style, using proper citations and references, and creating a bibliography or works cited page. Following the IB guidelines is crucial to ensure consistency and professionalism in academic writing. Proper citations and references are essential to give credit to the original authors and avoid plagiarism. Creating a bibliography or works cited page helps readers locate and verify the sources used in research.

Following the IB guidelines for formatting and citation style

To adhere to the IB guidelines for formatting and citation style, it is essential to employ an academic writing style that maintains objectivity and avoids personal pronouns, thus conveying a sense of professionalism and scholarly rigor to the intended readership. One effective way to enhance the readability of academic writing is through the use of tables. Tables provide a clear and organized format for presenting data or information in a concise manner. They allow readers to quickly grasp key points and make comparisons between different elements. In this context, a 2 column by 4 row table can be utilized, providing a visually appealing layout that facilitates understanding. By incorporating tables into academic writing, authors can effectively communicate complex ideas while maintaining clarity and coherence.

Moving forward, it is important to also consider the importance of using proper citations and references in order to acknowledge the sources of information used in academic writing without plagiarizing.

Using proper citations and references

A crucial aspect of scholarly writing involves the integration of accurate citations and references, which serve to acknowledge the sources of information employed in academic discourse while maintaining integrity and avoiding plagiarism. By providing proper citations, researchers ensure that their work is transparent and reliable, allowing readers to verify claims and build upon established knowledge. Additionally, citations demonstrate respect for intellectual property rights and ethical research practices. In an academic setting where safety is a priority, precise referencing becomes even more important as it enables readers to access relevant sources and evaluate the reliability of information provided. Moving forward into the next section about creating a bibliography or works cited page, attention to citation details will continue to play a pivotal role in upholding academic standards and fostering a culture of accountability in research endeavors.

Creating a bibliography or works cited page

The creation of a bibliography or works cited page is an essential step in scholarly writing, as it provides a comprehensive list of all the sources referenced in an academic work, enabling readers to access and evaluate the reliability of the information presented. By including a bibliography, authors demonstrate transparency and accountability by acknowledging the contributions of other scholars and researchers. This not only strengthens their own arguments but also allows readers to verify the credibility of the sources used. A well-constructed bibliography typically includes information such as author names, publication dates, titles, and any relevant page numbers. It is important to adhere to specific citation styles, such as APA or MLA, to ensure consistency and accuracy throughout the document. With a complete bibliography in place, authors can confidently move on to seeking feedback and revisions for their work.

Seeking Feedback and Revisions

Revising and seeking feedback on the IB Math EE is an essential step in ensuring a well-rounded and academically rigorous research project. The process of seeking feedback allows for constructive criticism, which can help identify areas for improvement and strengthen the overall quality of the Extended Essay. Here are three key reasons why seeking feedback and revisions are crucial:

• Enhancing clarity: Feedback from teachers, peers, or subject experts can provide valuable insights into areas that may be unclear or confusing. This allows the researcher to refine their arguments and ensure that their ideas are effectively communicated.
• Identifying errors: Through feedback, researchers can identify any mistakes or inaccuracies in their work. This could include mathematical errors, incorrect data analysis techniques, or flawed reasoning. Addressing these issues helps maintain the integrity and accuracy of the research.
• Strengthening analysis: Seeking feedback enables researchers to evaluate whether their analysis is comprehensive and thorough enough to support their claims. It encourages critical thinking by challenging assumptions and highlighting potential gaps in reasoning.

By actively seeking feedback and making necessary revisions based on this input, researchers can produce a more polished and robust IB Math EE. Transitioning into the subsequent section on time management and organization, careful planning is also crucial for successfully completing this project within given timelines.

Time Management and Organization

Efficient time management and effective organization are crucial in successfully completing the IB Math EE within designated timelines. The process of researching, analyzing data, and writing a comprehensive extended essay requires careful planning and allocation of time. By creating a detailed schedule that outlines specific tasks and deadlines, students can ensure that they stay on track throughout the research and writing process.

To effectively manage their time, students should prioritize their tasks based on urgency and importance. Breaking down the project into smaller, manageable chunks allows for a more systematic approach to research and writing. Setting realistic goals for each stage of the EE helps to prevent procrastination and ensures progress is made consistently.

Furthermore, maintaining an organized workspace is paramount to staying focused and minimizing distractions. Keeping research materials, notes, and drafts neatly organized not only saves time but also aids in efficiently retrieving information when needed.

By adhering to these principles of time management and organization, students can confidently navigate through the various stages of their IB Math EE while meeting deadlines. In the upcoming section about dealing with challenges and roadblocks, we will explore strategies for overcoming obstacles that may arise during this demanding process.

Dealing with Challenges and Roadblocks

This paragraph introduces a discussion on dealing with challenges and roadblocks in the context of writing an IB Math EE. It highlights three key points: overcoming writer’s block and lack of motivation, managing stress and pressure, and seeking help and support when needed. These issues are important to address in order to maintain productivity and achieve success in the research process.

Overcoming writer’s block and lack of motivation

Overcoming writer’s block and lack of motivation can be a significant challenge when working on an IB Math Extended Essay. To help navigate these obstacles, it is important to implement strategies that promote productivity and maintain focus. Here are five effective approaches:

• Break the task into smaller, manageable parts.
• Establish a routine that includes dedicated work sessions.
• Seek support from teachers, peers, or online communities.
• Engage in activities that promote relaxation and reduce stress.
• Set realistic goals and celebrate achievements along the way.

Implementing these strategies can create a sense of structure and purpose, which can help overcome writer’s block and lack of motivation. By incorporating these practices into your writing process, you can increase productivity while maintaining a healthy balance. Transitioning into managing stress and pressure requires acknowledging the importance of self-care and adopting coping mechanisms to ensure overall well-being.

Managing stress and pressure

Having discussed strategies to overcome writer’s block and lack of motivation, it is crucial to address the issue of managing stress and pressure in order to maintain a healthy state of mind during the IB Math Extended Essay (EE) process. The demanding nature of this task can often lead students to feel overwhelmed and stressed, affecting their ability to perform well. It is important for students to develop effective stress management techniques such as time management, relaxation exercises, and seeking support from friends and family. Additionally, engaging in physical activities or hobbies can provide a much-needed break from academic pressures. By learning how to manage stress effectively, students can maintain focus and productivity throughout their EE journey. However, there may be instances when additional help and support are required. Thus, it becomes imperative to understand the significance of seeking assistance when needed while navigating through this challenging task without compromising mental well-being.

Seeking help and support when needed

To ensure a successful completion of the IB Math Extended Essay, it is important for students to recognize the value of seeking assistance and support when facing challenges or difficulties. When students seek help, they are not admitting weakness but rather acknowledging that everyone encounters obstacles at some point. Seeking assistance from teachers, peers, or online resources can provide valuable insights and guidance to overcome any hurdles encountered during the research process. Additionally, reaching out for support can alleviate stress and pressure, promoting a healthier mindset and overall well-being. By actively seeking help when needed, students demonstrate maturity and a commitment to their academic growth. This willingness to seek assistance sets them up for success in showcasing their personal engagement with their chosen topic in the subsequent section.

Showcasing Your Personal Engagement

Demonstrating personal engagement is crucial in an IB Math Extended Essay as it showcases the depth of the student’s involvement and passion for the chosen topic. By showcasing personal engagement, students highlight their commitment to exploring complex mathematical concepts and applying them to real-world scenarios. This level of involvement not only allows students to develop a deeper understanding of their chosen topic but also demonstrates their ability to think critically and independently.

To showcase personal engagement effectively, students should clearly articulate their motivation for selecting the particular research question or topic. They should provide a comprehensive overview of their thought process, including any challenges they encountered along the way and how they overcame them. Moreover, students should demonstrate a genuine interest in investigating alternative viewpoints or methodologies related to their research question.

In addition, students can exhibit personal engagement by actively seeking out feedback from teachers, peers, and other experts in the field. This shows a willingness to learn from others’ perspectives and incorporate constructive criticism into their work.

By demonstrating personal engagement throughout the essay, students not only establish themselves as credible researchers but also contribute valuable insights to the field of mathematics. Celebrating this accomplishment requires reflecting on one’s growth throughout the research process while acknowledging that there is always room for further exploration and improvement.

Celebrating Your Accomplishment

Recognizing the hard work and dedication involved in completing an IB Math EE is essential. The process of researching, analyzing data, and writing the essay requires a significant amount of time and effort. Embracing the learning experience gained from undertaking such a substantial project can lead to personal growth and development as a student.

Sharing your knowledge and insights with others in the IB community is not only an act of celebration but also a way to contribute to the collective learning experience. By disseminating your findings, you can inspire others to explore similar topics or provide valuable guidance for those who may be embarking on their own EE journey. Ultimately, celebrating your accomplishment goes beyond personal satisfaction; it becomes an opportunity to engage with others in meaningful discussions and foster intellectual curiosity within the IB community.

Recognizing the hard work and dedication involved

The arduous journey of an IB Math Extended Essay involves hours spent poring over complex mathematical concepts and tirelessly analyzing data sets. To recognize the hard work and dedication involved in completing this task, it is important to acknowledge the following:

• Intellectual rigor: The IB Math Extended Essay requires students to engage in critical thinking, problem-solving, and independent research. It demands a high level of intellectual rigor and analytical skills.
• Time commitment: Students invest a significant amount of time in conducting experiments, collecting data, and writing their essay. This commitment demonstrates their perseverance and determination to excel academically.
• Attention to detail: Success in the IB Math Extended Essay requires meticulous attention to detail. Students must ensure accuracy in calculations, interpretation of results, and adherence to formatting guidelines.

By recognizing the challenging nature of the IB Math Extended Essay process, we can better appreciate the accomplishments achieved by students. Embracing this learning experience allows for further growth and development in mathematical understanding.

Embracing the learning experience

Embracing the learning experience of completing an IB Math Extended Essay involves immersing oneself in intricate mathematical concepts and adopting a mindset of curiosity and continual growth. It requires a willingness to explore complex problems, analyze data, and formulate logical arguments. Throughout the process, students are encouraged to develop a deep understanding of mathematical principles and apply them in real-world contexts. This kind of engagement fosters intellectual rigor and critical thinking skills, preparing students for future academic pursuits. Additionally, embracing the learning experience allows individuals to appreciate the beauty and elegance of mathematics as they uncover connections between different areas of study. By actively seeking out new knowledge and challenging themselves, students can gain confidence in their abilities while nurturing a passion for mathematics. Ultimately, this mindset sets the stage for sharing one’s knowledge and insights with others in the IB community, fostering collaboration and mutual growth within this supportive network.

Sharing your knowledge and insights with others in the IB community

Sharing knowledge and insights with others in the IB community can foster a collaborative learning environment that encourages mutual growth and intellectual development. By sharing our expertise, we contribute to the collective understanding of complex concepts and enhance the quality of education within the IB program. One way to facilitate this exchange is through online forums and discussion platforms, where students can seek guidance from their peers or mentors. Engaging in respectful and inclusive conversations allows for diverse perspectives to be heard, fostering an atmosphere of safety and inclusivity. Additionally, active participation in group study sessions or study groups promotes effective communication skills, critical thinking, and problem-solving abilities. Through this process of sharing knowledge, individuals not only reinforce their own understanding but also contribute to the academic success of others within the IB community.

Frequently Asked Questions

Can you provide a step-by-step guide on how to choose a research question for my ib math extended essay.

Choosing a research question for the IB Math Extended Essay involves considering personal interests, access to data, and relevance to mathematics. It is important to formulate a clear and focused question that can be answered using mathematical methods and analysis techniques.

What are some common mistakes to avoid when conducting research for an IB Math Extended Essay?

Common mistakes to avoid when conducting research for an IB Math extended essay include: insufficient planning, lack of clarity in the research question, inadequate data collection methods, ignoring relevant sources, and neglecting to analyze and interpret the results accurately.

Is it necessary to use advanced mathematical concepts and techniques in my IB Math Extended Essay, or can I stick to basic concepts?

Advanced mathematical concepts and techniques are not necessary for an IB Math extended essay. While basic concepts can be sufficient, it is important to demonstrate a thorough understanding and application of those concepts in a rigorous and logical manner.

How can I effectively incorporate real-life examples and applications of mathematics in my IB Math Extended Essay?

To effectively incorporate real-life examples and applications of mathematics in the IB Math Extended Essay, one should choose relevant and relatable topics, gather accurate data, analyze it using appropriate mathematical techniques, and draw conclusions that reflect a practical understanding of the subject matter.

Are there any specific formatting guidelines or citation styles that I should follow when writing my IB Math Extended Essay?

Yes, there are specific formatting guidelines and citation styles that should be followed when writing an IB Math Extended Essay. These guidelines ensure clarity, consistency, and academic integrity in the essay.

The IB Math Extended Essay is a challenging but rewarding task that requires effective research, application of mathematical concepts and techniques, strong introduction, coherent argument development, time management and organization skills. It is important to be prepared for challenges and roadblocks along the way while showcasing personal engagement in the essay. By following these guidelines, students can successfully complete their IB Math EE and celebrate their accomplishment.

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