There has been a recent breakthrough in this problem. This is a lovely result which uses parametric functions to create a beautiful example of mathematical art. What is the minimum number of colours needed for any map? Pages 15. 23) Perfect Numbers: Perfect numbers are the sum of their factors (apart from the last factor). The ratio of the gaps is 1:1:2. For more personal engagement, feel free to reach out to your instructor or tutor. A mathematical model is commonly written as an equation. 6) Batman and Superman maths how to use Wolfram Alpha to plot graphs of the Batman and Superman logo. Its a HL Math IA. Browse thousands of Internal Assessment, Extended Essay, and TOK examples. 7) Explore the Si(x) function a special function in calculus that cant be integrated into an elementary function. copyright 2003-2023 Study.com. An interesting topic can also stem from liking a particular topic of subject in math such as calculus and then you can find something in relation to even Formula 1 or a real life situation that involves calculus. 23) Measuring the Distance to the Stars. 13) The Tusi couple A circle rolling inside a circle. Minor chords are also considered to be in harmony. 19) Natural logarithms of complex numbers. How strange things happen when we start to manipulate divergent series. This can help you avoid so very many problems. Modelling COVID 19 using SIR Model. Mathematics SL and HL teacher support material 1 Example 4: Student work Modelling musical chords using sine waves Introduction From the stimulus word "Harmony", I chose to look at the transmission of sound waves in music. 16) Hyperbolic functions These are linked to the normal trigonometric functions but with notable differences. Many IB students find it hard to study mathematical concepts. A chemical formula is a mathematical model that relates the relative amounts of composite chemicals in a molecule. Then you found out the difference between the proportions of three point shots vs two point shorts. Click here to reset it. So this involves you writing down the mathematics on paper to see if your topic will work. The example gives the acceleration of the car and the driver as 80 {eq}m/s^2 {/eq} and the time that both travel as 10 seconds. 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 evidence would suggest that notes which are traditionally considered to be in harmony are mathematically neater than those that are not in harmony. We also have similar ideas for Biology, Chemistry, Economics, History, Physics, TOK. It is therefore more complicated than the difference of means test. JOIN FOR FREE . You may present your work in a word processing software (like Microsoft Word or Pages), or it can be handwritten. Plus, get practice tests, quizzes, and personalized coaching to help you 20) The Coastline Paradox how we can measure the lengths of coastlines, and uses the idea of fractals to arrive at fractional dimensions. This is the graph of A = l*55. IA. To solve the problem, complete the following steps. Using Mathematical Models to Solve Problems, How Mathematical Models are Used in Business, Static Vs Dynamic Simulation in Quantitative Analysis. This problem can be modeled with the equation {eq}A = l*55 {/eq}, and Figure 3 illustrates this problem with the length on the horizontal axis and area on the vertical axis. However, the gaps are still in a neat ratio of 1:2:2. Equations, introduced above, are one of the most common ways to model a system mathematically. However, this is just a theory and would have to be tested more thoroughly. Investigate some rocket science! What is a mathematical model? Also, ensure that you look at our article on Tips to get a 7 in the Math Internal Assessment. Whatever you choose, remember that you will create a new exploration of complex ideas. 15) Modelling epidemics/spread of a virus what is the mathematics behind understanding how epidemics occur? 32) Soap Bubbles, Wormholes and Catenoids. I decided to use Middle A, I altered the wavelengths, or frequencies, of the graphs by changing the coefficient of x. JOIN FOR FREE. Exemplars. In order to get the most accurate graph, I used the original frequencies of the other notes3. The IB is all about learning, so be sure to show the marker your growth throughout the IA. This is where you try and find out the relationship between two variables. 6) Continued fractions: These are fractions which continue to infinity. Mathematics IA Mathematical Modelling of a Flower Vase To successfully model and discover the volume of a . The planets follow a surprising pattern when measuring their distances. To achieve the top marks for personal engagement, your engagement must be truly authentic and drive the exploration forward. It helps to understood the marking criteria before deciding on your topic to ensure you use premium content in your work that can help you score highly. Online Private Tuition: One-on-one support from the comfort of your own home, whenever and wherever you need it. I will now look at the augmented 6th, another discordant chord. 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. This is a written assignment in which students are required to investigate a specific area of math subject. 14) Galileos Inclined Planes. Transitioning back into the mindset of full days at school can be overwhelming. Straight lines are not straight, parallel lines meet and angles in a triangle dont add up to 180 degrees. 26) Fermats little theorem: If p is a prime number then a^p a is a multiple of p. 28) Recurrence expressions for phi (golden ratio): Phi appears with remarkable consistency in nature and appears to shape our understanding of beauty and symmetry. 1. It covers what mathematical modeling is as well as different types of models in math. Exploration into Modelling a Population Pyramid (19/20) Share. ), Continued fractions- Use of continued fractions as representations of real numbers.. Copyright 2023 Esquire Writings Blog | Powered by Astra WordPress Theme. Figure 2: Use the length and width for each basement to find each area. In this video. 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. Math IA Topic Examples and Ideas. You can try and figure out average sleep and compare it with the grades and work outputs. 8 Calculus/analysis and functions. 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. Playing around with multiplicative persistence can you break the world record? Your email address will not be published. I will now look at some discordant notes and see how they compare with the chords I have already looked at. (This topic is only suitable for IB HL students). These ideas need to be conveyed in your writing. Equation 3: y=sin(659.26/440x) 8) Hollow Cubes and Hypercubes investigation. Maths is closely connected with astronomy see how we can work out the distance to the stars. You may also include any personalised problem statements and explain how you aim to achieve a solid investigation on the topic. However, to test this theory properly, we need to look at chords that differ from the original major chord more dramatically. You can watch a short video on it here. So an advantage of choosing such a topic is you can do the investigation at home. Optimization Problems Steps & Examples | What is Optimization in Calculus? Are there functions which plot any polygons? For more info on how to write the exploration, check out our completeMath IA Guide. So its that time of your IB program when you need to start working on your IA. 36) Can we prove that 1 + 2 + 3 + 4 . Start with the IA format! 14) Circular inversion what does it mean to reflect in a circle? lessons in math, English, science, history, and more. 13 chapters | 16) Graphing polygons investigation. 4) Tesseract a 4D cube: How we can use maths to imagine higher dimensions. The area of this basement is {eq}A = 50 * 35 = 1750 {/eq} square feet. Login. 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. 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. The examiner will be looking at the quality of the idea and the body of work in relation to the assessment criteria. For example, physicists studying proton-proton collisions at CERN use computer modeling to learn about the particles produced during the collisions. 26) Plotting the Mandelbrot Set using Geogebra to graphically generate the Mandelbrot Set. Explore number theory in higher dimensions! Follow in the footsteps of a genius! Statistical Modeling Purpose & Types | What is Statistical Modeling? Will my probability of winning drastically increase by some move that I can make? This amazing result can generate e through considering hyper-dimensional shapes. Two variable function . Afterward, calculate the average of all of those proportions for the whole season. 15 Closing. Find out more! 10) Tangrams: Investigate how many different ways different size shapes can be fitted together. There are many ideas you can explore for the assessment, including graph theory, surface area, geometry, calculus equations, statistics, linear regression, modelling statistics, the SIR model, etc. This can be like the proportion of people who dropped out of high school. Mathematical modeling is used by scientists, mathematicians, businessmen, and economists. xKO@+Mtt 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. Equation 2: y=sin(659.26/440x), (A,D. (1 More IB Past Papers). Algebraic Model Overview & Examples | What is the Algebraic Model? Equation 2: y=sin(622.25/440x). This produces the following graph: Using an A major chord, I can look at the relationship between the notes in a major chord. Proving of Fermats little theorem.. Nice to see you here. Models for the height of water in a cylindrical container, Advice from an IB Examiner on topics you should avoid, Differential Equations-the use of differential equations to model things in engineering or physics (ensure you do not talk much about the science. Subscribe and get the latest IB guides, notes,news, tips and product updates. Familiarise yourself with the steps below, and then dive into your chosen topic. It needs to be independent and unique. We look forward to joining the Lanterna and being part of your success. You can compare income and life expectancy in a country. Maths - SL. Can we use a mixture of pure maths and computing to solve this problem? xU]hU>3;yCmK+u!aR&MM6Ut'3 } The Stable Marriage Problem: Is there a matching algorithm that ensures each person in society ends up with their one true love? 7) When do 2 squares equal 2 cubes? It is now used as a saying to represent something impossible. Figure 1: Throwing a baseball can be described using the kinetic equations which are a type of mathematical model. Topics that rely more on natural sciences such as physics and put less emphasis on Math. She has 20 years of experience teaching collegiate mathematics at various institutions. Why do magic squares work? 10) Mathematical card tricks investigate some maths magic. 3) Projectile motion: Studying the motion of projectiles like cannon balls is an essential part of the mathematics of war. 37) Generating e through probability and hypercubes. Example 2 is another example of modeling a system using an equation. This assessment is a great way for students to expand their knowledge and learn valuable skills. 25) Eulers 9 Point Circle. How fast are the car and driver going when the driver stops pushing the gas pedal to the floor? An essential component of JPEG, DNA analysis, WIFI signals, MRI scans, guitar amps find out about the maths behind these essential technologies. Scored 16 out of 20. 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 graph of such a chord looks like this: Equation 1: y=sinx How did Galileo achieve his breakthrough understanding of gravity? 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. Updated: 01/07/2022 Table of Contents. 45) The Mordell Equation. 7) Mbius strip: An amazing shape which is a loop with only 1 side and 1 edge. Get a cylindrical container (with a valve), fill it with water, release the valve and measure how long it takes for the height of water to reduce to zero. How many different ways can we use to solve a number theory problem? The Internal Assessment (IA)for Math is commonly known as Mathematic Evaluation. The great Indian mathematician Ramanujan discovered some amazing examples of these. This will help to keep your data analysis focused. The approximate ratio for this chord shows that the ratio is not as precise, This evidence would suggest that notes which are traditionally considered to be in harmony are mathematically neater than those that are not in harmony. IA Review. oZWE|-jT (XA Students are required to investigate an area of mathematics and then present it as a written body of work. Example 2: A real estate agent has a very picky client who wants a very large basement. The IB states that you should not do Complex Math IA Topics. The ratio of the gaps is now 2:3:5. 16) Eulers identity: An equation that has been voted the most beautiful equation of all time, Eulers identity links together 5 of the most important numbers in mathematics. One example is modeling the radioactive decay of chernobyl, and determining if conditions are suitable for living. 38) Friendly numbers, Solitary numbers, perfect numbers. << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 612 792] The following ' SUVAT' displacement formula and the Kinematics initial velocity formulae will be used as a medium. By following this guide, you'll be able to score highly in your mathematics course. This chord, however, has 3 notes, so it can be more easily compared to the other chords I have looked at. While there are different perspectives when it comes to formatting your maths IA, we recommend the steps outlined below. Exemplars. Browse thousands of Internal Assessment, Extended Essay, and TOK examples. Understanding What Math IA is All About Students are required to investigate an area of mathematics and then present it as a written body of work. View Mark Scheme. /TT2 9 0 R >> >> 13) Graphically understanding complex roots have you ever wondered what the complex root of a quadratic actually means graphically? Explore this famous number theory puzzle. Example 3: A small town is quickly growing, and the mayor is worried. 2, How to come up with an idea or a topic. Math models can also be used to learn about a system, visualize data, or understand the origins of the system. Utilising technology can be helpful in conducting a thorough exploration of the topic. 9) Optimization of area an investigation. As it is only 2 notes, it cannot be modeled in exactly the same way as the other chords, but can still be graphed: Equation 1: y=sinx How much safer does a password get by adding symbols or numbers? Essential knowledge for future astronauts. There are many different uses for mathematical models such as understanding relationships or making predictions about the future, and there are many different types of mathematical models that can be used depending on the needs of the scientist. You can put it in a bucket of water to assess the water it displaces. What if the client wanted the basement to have a width of 55 ft and be at least 1750 square feet? All of these topics are applicable for the Math SL and HL students. 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 1: y=sinx Explores unfamiliar maths and devises own approach to area under curve. October 29, 2021. Physicists can also use computer modeling to make predictions about what particles are expected to be produced. 5) Stacking cannon balls: An investigation into the patterns formed from stacking canon balls in different ways. An example of modeling is presenting the rate at which a country's population changes relative to external factors. Lost your password? 5) Elliptical orbits Planets and comets have elliptical orbits as they are influenced by the gravitational pull of other bodies in space. Gain a deeper understanding of chaos theory with this investigation. B. Investigate how to solve them. 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. 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. 6) Mandelbrot set and fractal shapes: Explore the world of infinitely generated pictures and fractional dimensions. Look at how infectious Ebola really is. IA. You can test whether something is normally distributed or not. 21) Projective geometry the development of geometric proofs based on points at infinity. . Can we extend our investigation above to a multi-dimensional cube? For this reason, this theory does not only apply to sound coming to electronic instruments but every kind of instrument. Although that might sound easy, thats not always the case! lanchester s combat model ia maths sl 7 exploring an alternative method of calculating the volume of a star 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. Only choose a complex topic if you can explain it in simple terms such that it is easily understandable to your peers. This chord is also known as The Devils Chord, as it is considered to be the most the unpleasant sounding chord in music. Equation 1: y=sinx Student created own way of looking for patterns in the chords). 4) Applications of complex numbers: The stunning graphics of Mandelbrot and Julia Sets are generated by complex numbers. What conclusions did you reach, and did you succeed in exploring the aim that you set out at the beginning of the Math IA! 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. The ratios of frequencies of chords in harmony are more concise(B. 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. Again using an A chord, I have modeled a minor chord and looked at its features. This chord is not directly comparable to the other chords, as it does not have 3 notes like the others. Rock Paper Scissors: If I played and won with rock already, should I make sure to change what I play this time? 1b) The shape of the universe non-Euclidean Geometry is at the heart of Einsteins theories on General Relativity and essential to understanding the shape and behavior of the universe. 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: This client is so picky that unless the basement has exactly 1750 square feet he absolutely will not buy the house. Similarly, it could be that the third gap is double the first or second gap. endobj Equation 3: y=sin(698.46/440x)(Incorrect value(698.46) compared with the table) MATH, ziadpike. Be sure to account for your interest in the top, its relevance in your life, your prior knowledge about it, what you wish to achieve, and how you'll arrive at an answer. 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. A nice starting point for students good at coding who want to put these skills to the test mathematically. An Augmented 6th is also known as a dominant 7th, which was one of the first discordant chords to be used in music in the West. The Greeks used a very different approach to understanding quadratics and as a result had a deeper understanding of their physical properties linked to light and reflection. Exemplars. I will now look at different chords to see if this conjecture holds true. You can think of the IA as a written mathematical presentation that will impact your final grade. Equation 4: y=sin2x. Students are encouraged to take a different take through this assignment, a different angle on the mathematical practice. In SL youll be required to find two variables and look for some kind of relationship whether its. 1) Modular arithmetic This technique is used throughout Number Theory. The gaps in the ratios do not directly relate to the difference in semitones, as the semitones do not have equal frequencies-the frequencies of semitones diverge as the frequencies increase, and the notes get higher in pitch. Computer modeling may be new, but chemical formulas as a math model are centuries old. Using x'(t)=30, y'(t)=40 and the distance of each car after two hours, we obtain: 4. Subject to the conditions provided for by applicable Optimizing areas: Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon? 9) Coding Hailstone Numbers. The challenge is to see how many different shapes can be made with a given number of squares and how can they fit together? Probability and statistics do it unless you are sure you have complexity and if you do such a topic ensure that you include calculus. These are some of the best Math IA Topics. 8) The Remarkable Dirac Delta Function. 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. 32) RSA code the most important code in the world? Examples are given. The kinematic equations can be used to describe the motion of any moving object, and because they relate different quantities present in a single system to describe another aspect of the system, the kinematic equations are considered a mathematical model. As with all mathematics, personal involvement by means of practising is best if you want to score highly in your hl syllabus. Revision Courses: These offer a helping hand when it matters the most to boost your grades! Youve likely spent weeks relaxing and thinking about anything other than school! All other trademarks and copyrights are the property of their respective owners. Two cars start moving from the same point. What is the geometric shape of soap bubbles? 5 Geometry. Create your account. Equation 2: y=sin(523.27/440x) In this article, we're breaking down the best way to format yours in a way that promotes independent thinking and personal engagement. So Im not just going to give you a list of 50 Math IA Topics though we have that if you want. 41) Chaos and strange Attractors: Henons map. 11) Mersenne primes: These are primes that can be written as 2^n -1. Sample Math IA. IB Math IA Examples and Ideas IA Idea 1 - Modeling Statistics Modeling statistics is a pretty broad concept for an IA, but it can refer to any project where a change in statistics is presented in a visually effective manner. 2) Hexaflexagons: These are origami style shapes that through folding can reveal extra faces. A good use of your calculus skills. So in this method you are testing the difference between two means and you are checking whether there is a significant difference. the IA Review. This particular problem was solved by Euler. endobj 11) Projectile Motion Investigation II. If any points are chosen at random in a square what is the expected distance between them? Graphs not related to tables). Using the physics of travel near the speed of light to see how we could travel to other stars. Equation 1: y=sinx Equation 2: y=sin (554.37/440x) Equation 3: y=sin (659.26/440x) Equation 4: y=sin2x ( A. Equation 3: y=sin(739.99/440x) 14 Advice from an IB Examiner on topics you should avoid. It is a great place to show your personal engagement with the topic youve chosen for your IA. Recently, computer modeling has become a popular method for understanding large data sets and for running statistical analysis such as using Bayes' formula. 41) Arithmetic number puzzle It could be interesting to do an exploration where you solve number problems like this one. Lets take a look at the criteria for your Math IA. Nonetheless, if you feel like you want to search for your topics, an excellent place to start would be the IB Mathematics textbook. succeed. 1, Models for the height of water in a cylindrical container. Evaluating limits: Exploring LHpitals rule. This takes the usual projectile motion ideas and generalises them to investigate equations of ellipses formed. math ia (and 1 more) Submitted January 14, 2018 Type I: Sequences Grade awarded: 18/20 Updated July 17, 2009 Type II: Tide modelling Grade awarded: 16/20 Updated July 17, 2009 Type I: Roots of i Grade awarded:18 Updated December 2, 2009 Type II: Bloodstream Grade: Updated July 18, 2009
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