Do you want to know the mantra to a 4000 words research?


Writing one Extended Essay on a topic of choice is a mandatory requirement for students opting Diploma Program. The extended essay, precisely, is a self-guided research paper of around 4000 words. A student may choose a topic of his/her own interest from or related to one of the six opted subjects for the diploma.

Candidate writing an extended essay on a topic should formulate the research question carefully because IB expects him/her to engage in a personal exploration of the problem and has to portray/convey the idea of research and final findings through finely knitted, clear and concise writing skills. Altogether, the sense of logical argument and analysis must prevail throughout the essay. Extended essays measure the analytical and comprehensive skills of a student towards research.

The student has to present his analysis and finding to his supervisor through three mandatory reflection sessions. However, the extended essay after submission is externally assessed by an examiner appointed by the IB. A student is awarded grade/band ranging from excellent to mediocre to the elementary level.

How to write a correct E.E with our IB Extended Essay Tutors in Mathematics

Basics for writing almost all essays are quite same, Being an IB Maths Tutor, I am taking Mathematics essay as an example

►Choose the topic that is concise and has focus. Objectivity should read out clearly on the topic. The broad or general topic is not good.  Choose the topic you are comfortable i.e. you like the most. A supervisor should know the mathematics involved in the fruitful outcome.

►The topic may be from areas of engineering, science, social science, and statistics with mathematics at its base. The extended essay should grow on the topic and reach the mentioned conclusion. Quality and measurable conclusion are what is desired.

►A student is expected to extend the knowledge base required writing the essay a little beyond what comprises the mathematics curriculum of Diploma course.  In fact, an extended essay is an opportunity for a candidate to present his ability in learning and practising mathematics.

►The extended essay should present correct arguments and reasoning. The methodology included must be elaborated. The language should be technical, have continuity and must grip the reader until the conclusion.

►Relevant graphs, tables, diagrams are to be incorporated in a text at proper places to help explain the topic and should break the continuity.

Some tips by IB Extended Essay Tutors

An extended essay demands student time, patience, continuity to evolve properly. A student, therefore, must I have crystal clear idea of the topic and should start reading and writing about essay at a proper time. Delayed start or laziness takes you nowhere. Mind these words.

Topic Suggestions by IB Extended Essay Tutors

Now I would talk specifically about some topics on which you can base your extended Essay or even Internal Assessment.

 Social Network Analysis: It is the study the Relations. The relation has many properties and how it has links to social life is part of social network analysis. There you would come with problems like

1. Community detection/ overlapping communities etc.

2. Finding a key player in-network, Ego nodes, Centrality.

3. Outliers, Marketing, Referral/Recommendation.

Graph Theory: It is the study of networks and has many exciting applications and uses. Some topic of interest for EE can be

1. Euler, Hamiltonian Graph, Travelling Sales problem.

2. Trees, Spanning trees, Minimal Spanning tree.

3. Shortest Path Algorithm, Floyd Warshall’s, etc.

4. Graph Colouring, Matching, Chromatic Number, and Polynomial.

5. Decomposition of Graphs

Differential Calculus and Integral Calculus

1. Rates, Maxima and Minima, Curvature, Working in the polar coordinate system.

2. Taylor series and errors

3. Quadrature and Rectification.

4. Area, Volume, and Surface of Revolution.

Algebra/ Linear Algebra

1. Groups, Subgroups, Coding, and Decoding Theory

2. Boolean Algebra.

3. Matrices, Decomposition of Matrices, Data Compression Ideas.

Discrete Mathematics

1. Relation, Functions, Closures of Relation and Application, Equivalence relation, and partial ordered relation and its applications.

2. Logic and Circuit Design.

3. Deductive and Inductive reasoning

4. Recurrence relation, Generating function and applications

5. Counting Problems, Pigeon Hole Principle, etc.

Numerical Methods

1. Finding roots (Bisection, Newton Raphson, Muller, etc.)

2. Solving System of Linear equation, non-linear equation.

3. Interpolation and Approximation, Least Square method, Lagrange’s interpolation, piecewise interpolation, splines.

4. Solving System of Linear equations (Jacobian and Siedel )

5. Solving Differential Equation using numerical methods such as Euler, Picard, Taylor Series Method, Runge-Kutta Method, etc.


1. Locus, envelopes, evolute.

2. Distance measuring in the different coordinate system. 

3. Tangent, Normal, Binormal.

4. 3D parallel geometry problems.


1. Measures of Central tendency and applications.

2. Deviations and variance.

3. Regression and Correlation.

4. Quality Testing, using Sampling theory.

5. Problems related to Poisson Distribution and Normal Distribution.

6. Questions associated with Chi-square test, T- distribution.

7. Monte Carlo Simulation, Bayes Classifiers.

Vector Calculus

 It has two parts Differential and Integral vector calculus. The topic introduces the concepts of 

1. Vector field, Velocity Acceleration

2. Line Integral, Work done.

3. Gradient, directional derivatives, Divergence, Curl.

4. Conservative and non-conservative vector fields.

5. Concept of Flux, Circulation, etc.


1. Fourier Series and applications

2. Monty Hall Problem.

3. Cryptography Techniques

4. Modular Mathematics and its uses.

5. Mathematics Behind barcodes

6. Approximation of functions

7. Models in Economics

8. Non- Linear Dynamics and different models, Chaos, Fractals.

9. Romeo-Juliet Problem, Hostel Partner problem.

10. Number Theory and Cryptography

11. Complex numbers and variables.

The topic of your choice can also include problems that have appeared in International Mathematical Olympiad. The website has very many interesting issues related to Algebra, Geometry, and Combinatorics. Even the solutions are given on the site. But you need to think and work on an independent solution of your own. Any creative problem of your own can also be considered but should include a solid mathematical background.

Structure of the Extended Essay

The essay has six sections or elements

►Title page

It includes title, research question, and word count. The word count should not increase in 4000. Word count crossing the limit is considered negative.

►Content page

The content page provides information regarding ordering and page numbering of sections and subsections in the essay.

► Introduction

The introduction part explains the topic of research in short and the methodology exploited towards the focused conclusion.

►The body of the Essay

This is where extensive study with arguments, analysis, calculation, and evaluation is presented. It advised breaking this element into sections and subsections to clearly explain the idea. Graphs, diagram, and tables are included in the body of the essay. This part must also include the output and conclusion in full explanation.


Conclusion part must in the concise presentation of how you started and then highlight the main outcomes. It must like a sweet juice out of the pulp.

►Bibliography and references


This part contains auxiliary information required to explain the topic or bring completeness of thought to the essay.


The advice is to prepare in bits. This means that build the EE in stages, i.e., develop draft one then two and so on. Please write, either on-page or on the computer, do not have the thing in the air it would not materialize. The writing work is the measure of your ability to write EE.

The title must be clear and focused and should inform the reader about the content. The title need not be in question mode but should indicate the aim of Essay.

Who Can be helpful?

EE is meaningful only when its content has some originality and not predictable. This means that you think in-depth on a topic and must have something of your own to say. The EE cannot be bookish. If you want originality, then the thorough study of matter is essential. Therefore collect study material related to the topic. How to do it? The answer is, browse critical words related to your topic. Internet would provide a lot of content. Download research paper but only belonging to useful journals. Listen to video lectures related to the topic of EE.

 GOOGLE SCHOLAR and PLOS (Public library of Sciences) are generally of great help. Video lectures include an example which gives a good understanding of the topic. Listening to standards has a tickling effect on the brain and so produces new thoughts. This would bring originality in the work. If these things are not working visit university or good colleges near you and reach to professors, they can help you a great deal.

Idea of Presentations

Always include an example to explain concepts. Models present the understanding ability of the author, but the models must be relevant. Do not fill fancy words in the Essay; the moderators and evaluators are smarter than you. Data Presentation through the table is necessary. Illustration, wherever required, should be purposefully and necessarily be included. Quotes by scientists of famous personality can be included; they add to the presentation of EE a lot.

Conclusion Part

The conclusion part is although the last but essential section. It should sum up what has been done and then present bright concise reflections on findings. If the author writes a week conclusion, it severely affects the evaluation of EE. Do understand that conclusion demands the writing ability of the author, and mere filling words would not help.


Remember to note down the references or context from where the reading material is taken or adopted. It happens many a time that you would not be able to recall from where you had studied, and it creates a problem in presenting bibliography. Also, references are essential during viva voice. Think on the question asked by the evaluator, “ Which texts do you think are most important concerning the Essay and why? Such problem can throw anybody in the air if one has not prepared EE of even IA with full sincerity.

Word Count suggestion by IB Extended Essay Tutors

The word count of title page, content page and bibliography is such that IB does not include it in the total word count. Even equations, formulas, calculations, diagram legends, table heading don’t count. Appendix not part of the main idea and IB doesn’t count it too.

Before starting to write an extended essay, we advise students to see and refer some extended essays available on the net or some other repository at your disposal. The Internet is a good tool we should exploit and milk it. Writing an extended essay is hard work and hard work always repays with good grades. Remember an honest effort always has its value.

And we hope that this brief reading has served the purpose. Contact our IB Extended Essay Tutors for any type of help.

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