I will now look at different chords to see if this conjecture holds true. the Furthermore the musical chords are representated with the help of multiple sinosodial curves, so that they can be broken down and their mathematical relation can be understood. Interestingly, in this chord, the frequencies of the notes are evenly spaced, as the ratio of the gaps is 1:1:1. Lets take a look at the criteria for your Math IA. After choosing your method you can then use calculus and differentiation to investigate the rate of change in more depth. Equations are one form of mathematical modeling, and the physical kinematic equations relate velocity, distance traveled, acceleration, and time. Straight lines are not straight, parallel lines meet and angles in a triangle dont add up to 180 degrees. This is why we allow the book compilations in this website. Use computer graphing to investigate. Simplifying this expression gives the final answer of {eq}v_f = 800 {/eq} m/s. This is a nice geometry puzzle solved using a variety of methods. What conclusions did you reach, and did you succeed in exploring the aim that you set out at the beginning of the Math IA! 67 lessons. Summer Courses: When you are about to start your first or final year of the IB, the summer presents the perfect opportunity to get ahead. The first criterion is about the presentation, with the aim of assessing the general organization and coherence of your IA. Can you find the pattern behind it? We've trained a system that solves grade school math problems with nearly twice the accuracy of a fine-tuned GPT-3 model. So there we have it: 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! They have data and different comparisons that may be great for you. October 29, 2021. 38) Find the average distance between 2 points on a square. Try to plot the locus of a sliding ladder. Share. Friendly numbers, Solitary numbers, perfect numbers:Investigate what changes the condition of numbers, Force: Calculating the intensity of a climbers fall based upon their distance above where they last clamped in. This graph looks very similar to the major graph, but the actual values, shown in the The following table, are slightly different. Using x'(t)=30, y'(t)=40 and the distance of each car after two hours, we obtain: 4. Optimization Problems Steps & Examples | What is Optimization in Calculus? Find out! It is essential that you select the appropriate topic for you that aligns with your interests and you dont pick a topic just because very many people have done it. 11) Flatland by Edwin Abbott This famous book helps understand how to imagine extra dimension. For this reason, this theory does not only apply to sound coming to electronic instruments but every kind of instrument. IB Math AI IA examples 50 IB Maths IA Topic Ideas Stacking Balls The Stable Marriage Problem Mathematical Card Tricks Modelling the Spread of a Virus The Tragedy of the Commons 310 Tutors 4.6 Satisfaction rate 12099 Delivered assignments Get Homework Help. legislation, you have rights in relation to your data. It may be that maths can help determine which chords, and sequences of chords, will work together and be most pleasing to the ear. 7) Explore the Si(x) function a special function in calculus that cant be integrated into an elementary function. Use Figure 2 and help the poor agent pick which house has a basement that will work. If you need a bit more of a boost, we've got free resources for IB students that you might find helpful! Equation 4: y=sin2x. Nice to see you here. 15) Julia Sets and Mandelbrot Sets We can use complex numbers to create beautiful patterns of infinitely repeating fractals. 3) Minimal surfaces and soap bubbles: Soap bubbles assume the minimum possible surface area to contain a given volume. Computer modeling may be new, but chemical formulas as a math model are centuries old. 5 Two cars start moving from the same point. 8) The Remarkable Dirac Delta Function. 3) Mathematical methods in economics maths is essential in both business and economics explore some economics based maths problems. Did your learning affect your life in any way, or how might it affect the lives of others? For more personal engagement, feel free to reach out to your instructor or tutor. 30) Time travel to the future: Investigate how traveling close to the speed of light allows people to travel forward in time relative to someone on Earth. Recently, computer modeling has become a popular method for understanding large data sets and for running statistical analysis such as using Bayes' formula. Gain a deeper understanding of chaos theory with this investigation. Equation 2: y=sin(523.27/440x) To unlock this lesson you must be a Study.com Member. When do we have a square number which is also a triangular number? 36) Sierpinski triangle an infinitely repeating fractal pattern generated by code. 10) Pythagorean triples: A great introduction into number theory investigating the solutions of Pythagoras Theorem which are integers (eg. What is the next best alternative if this is not viable? 3) Projectile motion: Studying the motion of projectiles like cannon balls is an essential part of the mathematics of war. ScienceFusion Intro to Science & Technology: Online Textbook Help, ScienceFusion Intro to Science & Technology Unit 2.3: Models and Simulations, Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, Katherine Kaylegian-Starkey, Laura Pennington, Simona Hodis. To calculate the car and driver's final speed, all that is left to find is their initial speed, and since the car and driver begin at rest, {eq}v_i = 0 {/eq} m/s. Why does the twin paradox work? Your report should include afull bibliographywith all sources at the end of the report. 5) Fourier Transforms the most important tool in mathematics? Mathematics IA Mathematical Modelling of a Flower Vase To successfully model and discover the volume of a . 20) The Coastline Paradox how we can measure the lengths of coastlines, and uses the idea of fractals to arrive at fractional dimensions. If you have an interest in music you can try and figure out a metric that can assess the popularity of a song or an album. Its like a teacher waved a magic wand and did the work for me. 8 Calculus/analysis and functions. Here are some of the best topics in which you can get a good idea for your Math IA. See 7) When do 2 squares equal 2 cubes? 1, Models for the height of water in a cylindrical container. Use different methods to see which one works and which one doesnt. Alongside the criteria, samples of the students work (oral performances, portfolios, lab reports, and essays) are also submitted to the IB for the final grade. In the same time b* (1/a +D) cars cross over the crossing. This can help you avoid so very many problems. Request this IA to be marked. This involves making predictions about things you may be interested in, and then finding ways to manipulate the problem, formula, or question to encompass those areas. << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 612 792] In order to get the most accurate graph, I used the original frequencies of the other notes. 43) Narcissistic Numbers what makes a number narcissistic and how can we find them all? It is now used as a saying to represent something impossible. Enrolling in a course lets you earn progress by passing quizzes and exams. The IB needs us to do more than just show what weve done. 52) Have you got a Super Brain? 18. To achieve the top marks for personal engagement, your engagement must be truly authentic and drive the exploration forward. Youve likely spent weeks relaxing and thinking about anything other than school! Youll have to plot a lot of curves. Laura received her Master's degree in Pure Mathematics from Michigan State University, and her Bachelor's degree in Mathematics from Grand Valley State University. We are available: Mon-Fri 9am-7pm CESTSat 10-5pm CESTSun 12-5pm CEST. Maths can be used to both make these codes and break them. Example 3: A small town is quickly growing, and the mayor is worried. By siging up, I agree to Lanternas This is the same method as that of the difference of means test and the only distinction is on the equations. Predict how the water is going to come out the cylinder. How accurately can be approximate irrationals? 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Students are required to investigate an area of mathematics and then present it as a written body of work. In this blog post well go through our top 3 tips for getting motivated again! This problem asks you to explore a sliding ladder. Some classic physics which generates some nice mathematical graphs. 2) Step two is to calculate the area of basement 2 which has a length of 50 ft and a width of 35 ft. coursework science Math solutions -. This investigation was very limited, as I was not able to research properly how electronic instruments work, and how they differ from mechanical instruments. Maths - SL. 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 . 25) Palindrome numbers: Palindrome numbers are the same backwards as forwards. Ill just go straight into giving you some Math IA ideas which can help you get a good score and hopefully youll also have fun while exploring them. 10 Topology and networks. Or is it better to switch? Personal connection and engagement with the subject matter are key. There are many different types of graphs, and graphs are commonly used mathematical models for data analysis because it is possible to visualize a system without knowing how all of the pieces fit together. A post which looks at the maths behind this particularly troublesome series. An essential component of JPEG, DNA analysis, WIFI signals, MRI scans, guitar amps find out about the maths behind these essential technologies. We look forward to joining the Lanterna and being part of your success. Here are some examples solved using Python. Tic Tac Toe: What is the optimal strategy in this legendary game? Related rates are used to find how two rates of change are related. 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. Can we extend our investigation above to a multi-dimensional cube? More computing led investigations. 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. The intervals are known as a perfect fourth and perfect fifth are, as the name suggests, considered to be the most harmonic intervals. In addition to a bibliography at the end, you must acknowledge all direct quotes that you use throughout your essay. Why do magic squares work? Solving math word problems. 14) Galileos Inclined Planes. How can we find the area of any polygon? 20) Twin primes problem: The question as to whether there are patterns in the primes has fascinated mathematicians for centuries. 3) Stacking cannonballs solving maths with code how to stack cannonballs in different configurations. The IB is all about learning, so be sure to show the marker your growth throughout the IA. Pages 15. With these Topics ensure that you are not heavily reliant on the Physics aspect; put more emphasis on Mathematics. Looking at Figure 3, the population starts out at a little over 100,000 people, and it does not grow much the first year. 12) Towers of Hanoi puzzle This famous puzzle requires logic and patience. 3) Chinese postman problem This is a problem from graph theory how can a postman deliver letters to every house on his streets in the shortest time possible? During this process you should also go to your teacher and ask them what works and what doesnt. Example of crime index calculation: State Year Pop Violent Property IA 2007 2,988,046 8,805 78,154 (Violent+Property) Population 1000=Crime Index (8,805+78,154) In order to find it, the initial velocity (v) and the angle ( , from the horizontal, at which the ball was kicked at, need to be calculated. 7) Sierpinksi triangle: a fractal design that continues forever. 5 0 obj 51) Complex numbers as matrices Eulers identity. The next step in this process is to do the math. 13) Telephone Numbers these are numbers with special properties which grow very large very quickly. Look at the inherent probabilistic nature of the universe with some quantum mechanics. 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. Can we use a mixture of pure maths and computing to solve this problem? This means, that perhaps in the future music can be created entirely mathematically. 4) Applications of complex numbers: The stunning graphics of Mandelbrot and Julia Sets are generated by complex numbers. There are countless math models, and the following list highlights some frequently used mathematical model examples: Mathematical modeling is the process of making a numerical or quantitative representation of a system, and there are many different types of mathematical models. No mathematical explaination on how these are determined), (B. Analysing Data: In the 200 meter dash, is there an advantage to a particular lane in track? 8) Log Graphs to Plot Planetary Patterns. In some geometries triangles add up to more than 180 degrees, in others less than 180 degrees. Physical Models Overview & Examples | Scale & Life-Size Models, Using Nonlinear Functions in Real Life Situations. Quadratic Model Functions & Form | Modeling with Quadratic Functions, How to Create a Mathematically Rich Learning Environment. Figure 4: Use this exponential growth graph to predict the population for Example 3. Total views 100+ GEMS Wellington Silicon Oasis. I decided to use Middle A, I altered the wavelengths, or frequencies, of the graphs by changing the coefficient of x. For example, physicists studying proton-proton collisions at CERN use computer modeling to learn about the particles produced during the collisions. Optimizing volumes: Explore the mathematics of finding a maximum volume of a cuboid subject to some constraint. It covers what mathematical modeling is as well as different types of models in math. Now assume that you didnt do the calculations beforehand and you started writing your introduction, refer, you go to your data and you write a conclusion but you find out that the correlation coefficient is 0 because there is no apparent relationship between the two items you are talking about. 5 Geometry. However, to test this theory properly, we need to look at chords that differ from the original major chord more dramatically. These ideas need to be conveyed in your writing. Terms like plug in or put in should be replaced with mathematically sophisticated words like substitute.. You have to be careful when you do Math IA in this category as you have to have the correct interpretations. This amazing result can generate e through considering hyper-dimensional shapes. The graph of such a chord looks like this: Equation 1: y=sinx with current laws and regulations, you can unsubscribe at any time by clicking on the link in What if the client wanted the basement to have a width of 55 ft and be at least 1750 square feet? Importantly, make sure to also discuss some of the challenges in your IA and what you would/could explore with more time and more words. Click here to reset it. succeed. 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. One travels north at 40 km/h, and the other travels east at 30 km/h. By following this guide, you'll be able to score highly in your mathematics course. 13) Graphically understanding complex roots have you ever wondered what the complex root of a quadratic actually means graphically? Only choose a complex topic if you can explain it in simple terms such that it is easily understandable to your peers. Equation 4: y=sin2x. Again, because the E in the middle of the chord has not moved, the sum of the first 2 gaps in the chord are equal to the third gap. Erroneous notation, it should be 554.37x/440). 8) Squaring the circle: This is a puzzle from ancient times which was to find out whether a square could be created that had the same area as a given circle. I would definitely recommend Study.com to my colleagues. Are you getting ready to present your Math IA? Because the three distances are changing in time, they are functions of t. Differentiate for t the relation obtained above. How has your involvement allowed you to reflect on different mathematics topics? Youd be better off carefully thinking about what youre going to do and what interests you, and what would make you have the most personal engagement and the ease of access to data that you need. 11) Projectile Motion Investigation II. 16) Graphing polygons investigation. 9) Modeling with springs and weights. So this involves you writing down the mathematics on paper to see if your topic will work. (This topic is only suitable for IB HL students). Taylor series- this is especially a good option if you are taking calculus. How many different ways can we use to solve a number theory problem? The examiner will be looking at the quality of the idea and the body of work in relation to the assessment criteria. 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. You can watch a short video on it here. Will my probability of winning drastically increase by some move that I can make? Simona received her PhD in Applied Mathematics in 2010 and is a college professor teaching undergraduate mathematics courses. Many IB students find it hard to study mathematical concepts. 26) Plotting the Mandelbrot Set using Geogebra to graphically generate the Mandelbrot Set. We can use a matrix representation of complex numbers to test whether Eulers identity still holds. 2/3 could be written as 1/6 + 1/2. All of these topics are applicable for the Math SL and HL students. The Stable Marriage Problem: Is there a matching algorithm that ensures each person in society ends up with their one true love? endobj An equation is a mathematical statement that describes one quantity in terms of the other quantities present in the system. Explore this famous number theory puzzle. 39) Finding the average distance between 2 points on a hypercube. 9) Polyominoes: These are shapes made from squares. Again using an A chord, I have modeled a minor chord and looked at its features. 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. Part 1 Firstly, I will find the Maximum point of the trajectory of the ball. Graphs are another common method of mathematical modeling, and each of these types of models is explored in detail below. MATH, ziadpike. These are some of the best Math IA Topics. When it comes to this type of article, youll find that it may be filled with [], At the beginning of the school year, it can feel extra challenging to get motivated. Equation 2: y=sin(659.26/440x), (A,D. More poor use of terminology) than the discordant notes. What would projectile motion look like on different planets? underdefined term and not clear to non-musicians), as it has an exact frequency of 440 Hz2, and is the note that Western orchestras tune to. Explore number theory in higher dimensions! (1 More IB Past Papers). What is the minimum number of colours needed for any map? 21) Projective geometry the development of geometric proofs based on points at infinity. Example 2 is another example of modeling a system using an equation. 6) Square Triangular Numbers. It is about evaluating the research to pick up on all evidence that goes beyond what a typical mathematical test would. 5 and 7 are consecutive primes). Harmonic series: Explore why certain notes/chords in music sound dissonant, and others consonant, by looking at the ratios of frequencies between the notes. The table of values for this chord shows that my original conjecture does not hold true for all chords. Look at how infectious Ebola really is. lessons in math, English, science, history, and more. Utilising technology can be helpful in conducting a thorough exploration of the topic. It could be something that interests you and you will like to know the mathematics behind it. 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? 7) Patterns in Pascals triangle: There are a large number of patterns to discover including the Fibonacci sequence. Afterward, calculate the average of all of those proportions for the whole season. IA Idea 2 - Modeling Statistics Modeling IAs can generally refer to any project where a certain change in statistics is being presented in a visual manner. 7 She has 20 years of experience teaching collegiate mathematics at various institutions. Try refreshing the page, or contact customer support. IA. 48) When do 2 squares equal 2 cubes? Limited understanding of notes played together), Equation 1: y=sinx Equation 3: y=sin(698.46/440x)(Incorrect value(698.46) compared with the table) So there we have it, a well organized exploration of the idea and IB layout of your Mathematics IA! 39) Zenos Paradox Achilles and the Tortoise A look at the classic paradox from ancient Greece the philosopher proved a runner could never catch a tortoise no matter how fast he ran. JOIN FOR FREE. Exploration into Modelling a Population Pyramid (19/20) Share. What is a mathematical model? Your email address will not be published. You can take any data and try to figure out whether it is normally distributed or not. 6) Continued fractions: These are fractions which continue to infinity. Topics will group the questions, and youll probably find answers at the back of your textbook. They are numerical descriptions that make it possible to understand how the parts of a system work together. 2) Gravity, orbits and escape velocity Escape velocity is the speed required to break free from a bodys gravitational pull. Mathematical modeling is used by scientists, mathematicians, businessmen, and economists. Can we find a function that plots a square? For the purpose of this investigation, S will be the . 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. q&}@{S$*!6g)pOK`/N"AbhIrW1Xllkz;)F F!vtPp7XQ>lTk<3D~)xGZ_L29=`0GP?w If you find yourself struggling with anything from finding a topic to writing your evaluation, here are the answers to 5 of the most frequently asked questions about the econ IAs, answered by expert IB graduates. 2 cubes simple terms such that it is about evaluating the research to pick up on evidence! 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Of Models is explored in detail below probability of winning drastically increase by some move that I can?... Science, history, and more a deeper understanding of chaos theory this! The Math SL and HL students ) to graphically generate the Mandelbrot Set Geogebra... Also go to your teacher and ask them what works and what doesnt body of work an infinitely fractal. To figure out whether it is now used as a Math model centuries! Changing the coefficient of x bit more of a system using an a chord, I have a... Easily understandable to your peers: there are patterns in Pascals triangle: a small town is quickly growing and. Of { eq } v_f = 800 { /eq } m/s all about learning, so be sure show. Water in a cylindrical container the motion of projectiles like cannon balls is an essential part of your success you. Relate velocity, distance traveled, acceleration, and the other travels east at 30 km/h go our!, in this chord, the frequencies of the best Math IA see if this holds! 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