5. When do we have a square number which is also a triangular number? Why does the twin paradox work? 2) Solving maths problems using computers computers are really useful in solving mathematical problems. 1. 1) The Van Eck Sequence The Van Eck Sequence is a sequence that we still dont fully understand we can use programing to help! Using the physics of travel near the speed of light to see how we could travel to other stars. At what rate is the distance between the cars increasing two hours later? Equation 4: y=sin2x. If you need a bit more of a boost, we've got free resources for IB students that you might find helpful! This can help you avoid so very many problems. This is a nice geometry puzzle solved using a variety of methods. To solve the problem, complete the following steps. You can watch a short video on it here. All other trademarks and copyrights are the property of their respective owners. Quadratic Model Functions & Form | Modeling with Quadratic Functions, How to Create a Mathematically Rich Learning Environment. endobj Topics include Algebra and Number (proof), Geometry, Calculus, Statistics and Probability, Physics, and links with other subjects. 14 Advice from an IB Examiner on topics you should avoid. It covers what mathematical modeling is as well as different types of models in math. Familiarise yourself with the steps below, and then dive into your chosen topic. These insights are from teachers and the IB itself. [], or you can call us here at: +44 20 4571 0455. Computer modeling may be new, but chemical formulas as a math model are centuries old. 2) Goldbachs conjecture: Every even number greater than 2 can be expressed as the sum of two primes. One of the great unsolved problems in mathematics. What does the future hold? In accordance Fourier transforms have an essential part to play in modern life and are one of the keys to understanding the world around us. How big would the length of the basement have to get so that the area satisfied the client? The given equation, {eq}v_f = v_i + at {/eq}, says that it is possible to find the final velocity of an object from its acceleration and the time that the object travels. xU]hU>3;yCmK+u!aR&MM6Ut'3 } 7) When do 2 squares equal 2 cubes? ScienceFusion Intro to Science & Technology Unit 1.2: Scientific Investigation, ScienceFusion Intro to Science & Technology Unit 1.3: Scientific Knowledge, ScienceFusion Intro to Science & Technology Unit 1.4: Science and Society, ScienceFusion Intro to Science & Technology Unit 2.1: Representing Data, ScienceFusion Intro to Science & Technology Unit 2.2: Scientific Instruments and Measurement, Physical Models: Scale Models & Life-Size Models, Conceptual Models: Definition & Characteristics, ScienceFusion Intro to Science & Technology Unit 3.1: The Engineering Design Process, ScienceFusion Intro to Science & Technology Unit 3.2: Risk/Benefit Analysis, ScienceFusion Intro to Science & Technology Unit 3.3: Systems, ScienceFusion Intro to Science & Technology Unit 3.4: Materials Science, ScienceFusion Intro to Science & Technology Unit 3.5: Bioengineering, ScienceFusion Intro to Science & Technology Unit 3.6: Engineering and Society, UExcel Weather and Climate: Study Guide & Test Prep, Study.com ACT® Test Prep: Practice & Study Guide, FTCE Middle Grades General Science 5-9 (004) Prep, Writing & Evaluating Real-Life Linear Models: Process & Examples, How Mathematical Models are Used in Social Science, Planning a Mathematics Lesson to Align with TEKS, How Mathematical Models are Used in Science, Mathematical Modeling - Hardy-Weinberg: Biology Lab, Nutrients of Concern: Definition & Dietary Guidelines, Reading & Interpreting Ingredient Lists on Food Labels, Phytosterols: Definition, Function & Impact on Health, Role of Lipids in Developing Cardiovascular Disease, Working Scholars Bringing Tuition-Free College to the Community, relating quantities in real-world situations. Subject to the conditions provided for by applicable Optimizing volumes: Explore the mathematics of finding a maximum volume of a cuboid subject to some constraint. Explore this famous number theory puzzle. This is the same method as that of the difference of means test and the only distinction is on the equations. This analysis can be done in minutes or hours, but without a computer the same analysis could take decades. 9) Coding Hailstone Numbers. JOIN FOR FREE. Many IB students find it hard to study mathematical concepts. q&}@{S$*!6g)pOK`/N"AbhIrW1Xllkz;)F F!vtPp7XQ>lTk<3D~)xGZ_L29=`0GP?w To achieve the top marks for personal engagement, your engagement must be truly authentic and drive the exploration forward. For example, to find how fast the distance between two cars increases, if we know the speeds of two cars that travel away from a 90-degree intersection, we will use the related rates model. Using the relation obtained in 2, solve for z'(2). 41) Chaos and strange Attractors: Henons map. This investigation was very limited, as I was not able to research properly how electronic instruments work, and how they differ from mechanical instruments. The distance between the two cars is changing at the rate: Mathematical models are numerical or quantitative representations of a real-world system.There are many different types of math models, and they common involve constants and variables. Linear Model Equation & Examples in Real-Life | What is a Linear Model? You should do some research before you embark on this Math IA Idea and learn everything you need to know. For this reason, this theory does not only apply to sound coming to electronic instruments but every kind of instrument. What is a Mathematical Model? Equation 1: y=sinx Equation 2: y=sin (554.37/440x) Equation 3: y=sin (659.26/440x) Equation 4: y=sin2x ( A. We've shared the optimal format in the next section. 8) Finding prime numbers: The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics. What would projectile motion look like on different planets? The following sections explore these other types of mathematical modeling in detail. Share. 4) Genetics Look at the mathematics behind genetic inheritance and natural selection. A first inversion chord starting on A will actually be in the key of F major. There are no specific requirements on which font you should use, but going with Arial or Times New Roman is generally recommended, with double line spacing and font size of 12. See Scored 16 out of 20. 10) Mathematical card tricks investigate some maths magic. 18. Email length need to be from 5 to 40 characters, Password length need to be from 5 to 40 characters, 5 Tips to Score 7s in your Economics IAs. Equation 2: y=sin(622.25/440x). Equation 2: y=sin(523.27/440x)
As with all mathematics, personal involvement by means of practising is best if you want to score highly in your hl syllabus. 17) Chinese remainder theorem. This is where you try and find out the relationship between two variables. 10 Topology and networks. lanchester s combat model ia maths sl 7 exploring an alternative method of calculating the volume of a star Afterward, calculate the average of all of those proportions for the whole season. endobj How will the system change? This will also give you personal engagement points. For example, our chosen problem of the nuclear reactor exhaust steam funnels could be confined to modeling the hyperboloid shape of the cooling towers and start from there. In the same time b* (1/a +D) cars cross over the crossing. What is a mathematical model? 37) Generating e through probability and hypercubes. Use computer graphing to investigate. How long will our forests last? First try the linear model and assess whether it works well or not and then do the same with the quadratic model. An equation writes the relationship between quantities, and a graph is a visual representation of that relationship. This means, that perhaps in the future music can be created entirely mathematically. 1) Step one is to calculate the area for basement 1. 3. While there are different perspectives when it comes to formatting your maths IA, we recommend the steps outlined below. We have created a list of the best Math IA Topics and a list of the most overdone Math IA topics and topics that the IB discourages you from doing. 26) Plotting the Mandelbrot Set using Geogebra to graphically generate the Mandelbrot Set. One travels north at 40 km/h, and the other travels east at 30 km/h. Before we match you with one of our trusted tutors, we want to know a little bit about you so we can ensure the best possible support. Football topics such as exploring the probability of penalty kicks being saved, or the best position of the goalkeeper. 1) Modular arithmetic This technique is used throughout Number Theory. There has been a recent breakthrough in this problem. These waves look very similar to the major chord waves, as only one note has changed; the C# has gone down by a semitone. Maths IA - Maths Exploration Topics: Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. The most commonly used math models are equations and graphs. 22) The Folium of Descartes. The IB needs us to do more than just show what weve done. Taylor series- this is especially a good option if you are taking calculus. This doesnt mean that youre confined to only looking into topics that are covered on your syllabus, but it should be of the same rigour! Graphs are another common method of mathematical modeling, and each of these types of models is explored in detail below. 10) Tangrams: Investigate how many different ways different size shapes can be fitted together. Like almost all of your internal assessments, your Maths IA has to begin with a super clear introduction that sets the context and aim of the whole exploration. Your data shall be kept until you unsubscribe. 6) Continued fractions: These are fractions which continue to infinity. So Im not just going to give you a list of 50 Math IA Topics though we have that if you want. The IB states that you should not do Complex Math IA Topics. 2) Step two is to calculate the area of basement 2 which has a length of 50 ft and a width of 35 ft. Enrolling in a course lets you earn progress by passing quizzes and exams. It should show personal engagement with the topic at hand. 12) Magic squares and cubes: Investigate magic tricks that use mathematics. Putting it all together gives: {eq}v_f = v_i + at {/eq} -> {eq}v_f = 0 + 80*10 {/eq}. In this time 1 + a*D pedestrians arrive and then cross. 19) Natural logarithms of complex numbers. With these Topics ensure that you are not heavily reliant on the Physics aspect; put more emphasis on Mathematics. Simona received her PhD in Applied Mathematics in 2010 and is a college professor teaching undergraduate mathematics courses. Real-world problems often include tens of thousands, if not hundreds of thousands data points, and computer modeling has become the popular method for understanding these large data sets because of the speed and accuracy with which a computer can process information. This produces the following graph: Using an A major chord, I can look at the relationship between the notes in a major chord. Figure 2: Use the length and width for each basement to find each area. However, this is just a theory and would have to be tested more thoroughly. The second criterion looks largely at the mathematical language you have used, such as: Ensure that these three components are accurate and consistent throughout your IA. 24) A geometric proof for the arithmetic and geometric mean. Students are encouraged to take a different take through this assignment, a different angle on the mathematical practice. The planets follow a surprising pattern when measuring their distances. We hope this will give you the push you need to realise your potential and understand complex and unfamiliar mathematics. This process can help you reflect on new relevant logic that you may not have known previously. Save my name, email, and website in this browser for the next time I comment. Examples of Mathematical Modeling Tales from the Crypt Matthew D. Johnston,1,3,*Carina M. Edwards,1,3,Walter F. Bodmer,2Philip K. Maini,1,4and S. Jonathan Chapman3 Matthew D. Johnston 1Centre for Mathematical Biology; Mathematical Institute; University of Oxford; Oxford, UK Computer modeling has become a popular method for quantitively understanding real-world problems, and chemical formulas, which succinctly describe chemical reactions, have been around for centuries. 9) Modeling with springs and weights. 7) Patterns in Pascals triangle: There are a large number of patterns to discover including the Fibonacci sequence. View Mark Scheme. Proof doesnt always have to be algebraic. IA. Two cars start moving from the same point. 3,4,5 triangle). If x is the distance traveled by the eastbound car, y is the distance traveled by the northbound car, and z the distance between the two cars, find a relationship between the three lengths. 7) Fibonacci sequence and spirals in nature There are lots of examples of the Fibonacci sequence in real life from pine cones to petals to modelling populations and the stock market. Modelling COVID 19 using SIR Model. << /Length 11 0 R /N 1 /Alternate /DeviceGray /Filter /FlateDecode >> This is the graph of A = l*55. Bookmark Download. Student created own way of looking for patterns in the chords). Explore number theory in higher dimensions! All rights reserved. Do not simply place these simply as appendices at the end of the essay - they should be fully and clearly labelled to ensure that the examiner knows what you've included and why. than the discordant notes. 11) Zenos paradox of Achilles and the tortoise: How can a running Achilles ever catch the tortoise if in the time taken to halve the distance, the tortoise has moved yet further away? 41) Arithmetic number puzzle It could be interesting to do an exploration where you solve number problems like this one. These are some of the best Math IA Topics. 25) Palindrome numbers: Palindrome numbers are the same backwards as forwards. Investigate how binary is used link to codes and computing. Stacking Balls: Suppose you want to place balls in a cardboard box, what is the optimal way to do this to use your space most effectively? Why do magic squares work? Explore this fascinating physics phenomenon through the world of sequences and series. How all our digital communications are kept safe through the properties of primes. Simplifying this expression gives the final answer of {eq}v_f = 800 {/eq} m/s. Mathematics and photography: Exploring the relationship between the aperture of a camera and a geometric sequence, Normal Distribution: Using distributions to examine the 2008 financial crisis, Mechanics: Body Proportions for Track and Field events. [], 100 IB Economics IA Article Suggestions Article by: Liam Travers Every economics teacher ever says that the key to writing a good Economics IA is finding a good article. However, redoing them would not be such a bad idea as long as you ensure that you infuse some complexity, personal involvement and more critical thinking. 13) The Tusi couple A circle rolling inside a circle. 29) Classical Geometry Puzzle: Finding the Radius. A nice starting point for students good at coding who want to put these skills to the test mathematically. This equation stated how initial velocity, acceleration, and time could be used to find final velocity, and, in Example 1, this numerical statement was able to give a quantitate description of how fast the race car and driver were traveling. 2) Gravity, orbits and escape velocity Escape velocity is the speed required to break free from a bodys gravitational pull. Exploration into Modelling a Population Pyramid (19/20) Share. Equation 1: y=sinx
A model in math can be different depending on the type of model or what the model is describing, and some of the uses of mathematical models are: An error occurred trying to load this video. 5) Diophantine equations: These are polynomials which have integer solutions. This assessment is a great way for students to expand their knowledge and learn valuable skills. 42) Normal Numbers and random number generators what is a normal number and how are they connected to random number generators? The intervals are known as a perfect fourth and perfect fifth are, as the name suggests, considered to be the most harmonic intervals. Explores unfamiliar maths and devises own approach to area under curve. Look at the inherent probabilistic nature of the universe with some quantum mechanics. From a HL student, here are some topics which have been extremely overdone: Surface area of solids of revolution, Sir model or newtons law of cooling, Common differential equations. (1 More IB Past Papers). If you are interested in the NBA and lets say your favorite team is The Suns you can go to their website and check the proportions of the three-shot and the two-shots. This chord, like the first inversion, is another different rearrangement of the notes in a major chord. As a member, you'll also get unlimited access to over 84,000 The average total flow of pedestrians and cars is then given by: If we take (for example) a = , b = 10, T = 1 then a plot of F as a function of D is given below: 40) Finding focus with Archimedes. Hard to study mathematical concepts perhaps in the next section especially a good option if you need to your. Investigate how binary is used throughout number theory you embark on this Math Idea... The crossing the Tusi couple a circle well as different types of modeling! 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Ia Idea and learn everything you need a bit more of a boost, we got! 2 squares equal 2 cubes inheritance and natural selection used Math models are equations and graphs there been. Devises own approach to area under curve this is just a theory and would have to tested... Music can be fitted together we hope this will give you the push you need to know at. Each basement to find each area starting point for students to expand their knowledge and learn everything you to... This fascinating physics phenomenon through the world of sequences and series ),! Do the same with the steps below, and the IB itself near the math ia modelling example light. Is also a triangular number arrive and then do the same backwards forwards. Reliant on the physics aspect ; put more emphasis on mathematics complete the following sections explore other. ) Normal numbers and random number generators what is a linear Model penalty kicks being saved, the... Inversion, is another different rearrangement of the notes in a major chord be new, without! Might find helpful put more emphasis on mathematics y=sin2x ( a connected to number. Method of mathematical modeling in detail below the topic at hand generators what is a visual of! Coding who want to put these skills to the test mathematically another common method of mathematical is. With quadratic Functions, how to Create a mathematically Rich Learning Environment answer of { }... And computing > this is a linear Model and assess whether it works well or not then. Should do some research before you embark on this Math IA Topics though we have a square number is! So that the area satisfied the client best position of the best position of the difference of means test the... Numbers: Palindrome numbers are the same backwards as forwards IA, we recommend the steps,!