Sample Math IA. We hope this will give you the push you need to realise your potential and understand complex and unfamiliar mathematics. So there we have it: 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! It is clear then, that there is a difference in the mathematical relationship of notes within chords in harmony and discordant chords. Katherine has a bachelor's degree in physics, and she is pursuing a master's degree in applied physics. Copyright 2023 Get the grade you deserve. 10 Topology and networks. The Risk of Insurance: An investigation into asymmetric information and how being unsure about the future state of the world may lead us to be risk-averse, Gabriels Horn: This figure has an infinite surface area but a finite volume, can you p. Voting Systems: What voting system ensures that the largest amount of people get the official that they would prefer? You need to know what will be in the y-axis and what will be in the x axis so this can be something like a velocity time graph. 35) Sphere packing how to fit spheres into a package to minimize waste. ScienceFusion Intro to Science & Technology Unit 1.1: What Is Science? For example, recall the kinematic equation from Example 1. I would definitely recommend Study.com to my colleagues. First try the linear model and assess whether it works well or not and then do the same with the quadratic model. 14) Circular inversion what does it mean to reflect in a circle? If any points are chosen at random in a square what is the expected distance between them? We prioritize IAs based on the number of requests. 46) Ramanujans Taxi Cab and the Sum of 2 Cubes. 18)Waging war with maths: Hollow squares. Math Studies IA Relationship Between Crime Rate and Unemployment Kaitlin Snyder February 20, 2013 Central Academy; Des Moines Public Schools. Two variable function . They are numerical descriptions that make it possible to understand how the parts of a system work together. 10) Is Intergalactic space travel possible? We need to assign starting values for S, I and R - the numbers of people susceptible, infectious, recovered (immune) from measles. Game theory as it is easy and overdone. Linear regressions: Run linear regressions using OLS to predict and estimate the effect of one variable on another. 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 A key feature of equations and graphs that makes them useful models is their ability to make predictions about the future of the system in question. What is a mathematical model? What is a mathematical model used for? It involves understanding the modulo operation. the You can test whether something is normally distributed or not. 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. Mathematical Card Tricks: Look at the probabilities at play in the famous 3 card monte scam. This is a nice way to link some maths history with studying an interesting function. 14 Advice from an IB Examiner on topics you should avoid. The following sections explore these other types of mathematical modeling in detail. The area of this basement is {eq}A = 50 * 35 = 1750 {/eq} square feet. This process can help you reflect on new relevant logic that you may not have known previously. 9) Polyominoes: These are shapes made from squares. endobj Nice to see you here. We look forward to joining the Lanterna and being part of your success. Relationships: Do BMI ratings and country wealth share a significant relationship? 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. She currently teaches struggling STEM students at Lane Community College. Modelling COVID 19 using SIR Model. 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. 13) Different number systems Learn how to add, subtract, multiply and divide in Binary. To model this problem, we need the following tools. Examples are given. 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. Only choose a complex topic if you can explain it in simple terms such that it is easily understandable to your peers. Harmonic series: Explore why certain notes/chords in music sound dissonant, and others consonant, by looking at the ratios of frequencies between the notes. Unfortunately these equations are very difficult to solve - but luckily we can use a computer program to plot what happens. The soundwaves produced by oscillators are in the same form as notes produced by mechanical instruments, so the same note ultimately sounds the same, or very similar, to our ear. You can try to find the volume of a complicated object like a wineglass through different methods. To extend this investigation, I would like to look at the area between the waves in relation to the semitone difference and frequency ratios. 2. Graphs are another common method of mathematical modeling, and each of these types of models is explored in detail below. The great Indian mathematician Ramanujan discovered some amazing examples of these. Can you find the pattern behind it? Example 2 is another example of modeling a system using an equation. (C. Im going to select several topics and describe them for you so that you can have a topic and some guidance on the approach you should take. ~gv;pg9;{eF4"_=}GiRpfg)ZS-7q-25+0Zj9Ga!Q
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Q`;|':OO/Vk!&rgXC`ERY). This is a puzzle that was posed over 1500 years ago by a Chinese mathematician. 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. How can we use computers to gain a deeper understanding of sequences? coursework papers, [url=https://tenormin.site/]tenormin 25 mg tablet[/url], Your email address will not be published. 2) Gravity, orbits and escape velocity Escape velocity is the speed required to break free from a bodys gravitational pull. 5 and 7 are consecutive primes). An equation writes the relationship between quantities, and a graph is a visual representation of that relationship. 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. I will now look at some discordant notes and see how they compare with the chords I have already looked at. Enrolling in a course lets you earn progress by passing quizzes and exams. 14) Galileos Inclined Planes. 8) Finding prime numbers: The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics. Equation 3: y=sin(659.26/440x)
>> Optimizing areas: Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon? Also, ensure that you look at our article on Tips to get a 7 in the Math Internal Assessment. Try refreshing the page, or contact customer support. There are two fundamental questions that you can ask yourself at the beginning of this process. 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. 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. succeed. The graph of such a chord looks like this: Equation 1: y=sinx
These are some of the best Math IA Topics. This client is so picky that unless the basement has exactly 1750 square feet he absolutely will not buy the house. Can all fractions with a numerator of 2 be written as 2 Egyptian fractions? 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. Equation 3: y=sin(739.99/440x)
It could be something that interests you and you will like to know the mathematics behind it. Familiarise yourself with the steps below, and then dive into your chosen topic. 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. It should show personal engagement with the topic at hand. % It is now used as a saying to represent something impossible. An inversion chord is the same as a major chord, but the notes are in a slightly different order. For the purpose of this investigation, S will be the . The ratio of the gaps is 1:1:2. 5) Elliptical orbits Planets and comets have elliptical orbits as they are influenced by the gravitational pull of other bodies in space. 23) Perfect Numbers: Perfect numbers are the sum of their factors (apart from the last factor). Get unlimited access to over 84,000 lessons. Example 3: A small town is quickly growing, and the mayor is worried. This chord, like the first inversion, is another different rearrangement of the notes in a major chord. This graph looks very similar to the major graph, but the actual values, shown in the The following table, are slightly different. I started by working out how to model a single note. 1) Radiocarbon dating understanding radioactive decay allows scientists and historians to accurately work out somethings age whether it be from thousands or even millions of years ago. This is a nice geometry puzzle solved using a variety of methods. This is a lovely result which uses parametric functions to create a beautiful example of mathematical art. A nice starting point for students good at coding who want to put these skills to the test mathematically. 12 Other Math IA Ideas. Fourier transforms have an essential part to play in modern life and are one of the keys to understanding the world around us. 34) The Tusi circle how to create a circle rolling inside another circle using parametric equations. Start with the IA format! A post which looks at the maths behind this particularly troublesome series. All rights reserved. terms of service. 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. 12) Four colour map theorem a puzzle that requires that a map can be coloured in so that every neighbouring country is in a different colour. IA Review. Football topics such as exploring the probability of penalty kicks being saved, or the best position of the goalkeeper. 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. 2) Hexaflexagons: These are origami style shapes that through folding can reveal extra faces. How strange things happen when we start to manipulate divergent series. ie 6 is a perfect number because 1 + 2 + 3 = 6. 14, Advice from an IB Examiner on topics you should avoid. dS/dt = -2.14 I S. dI/dt = 2.14 I S - 0.14 I. dR/dt = 0.14 I. 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. The first criterion is about the presentation, with the aim of assessing the general organization and coherence of your IA. What would projectile motion look like on different planets? 5 Geometry. Recently, computer modeling has become a popular method for understanding large data sets and for running statistical analysis such as using Bayes' formula. The internal assessment is an individual evaluation that focuses on subject-related work. Equation 2: y=sin(587.33/440x), Equation 1: y=sinx
So in this method you are testing the difference between two means and you are checking whether there is a significant difference. Computers can take in a large data set, perform statistical analysis on the data, and generate plots within minutes. What does the future hold? Exemplars. Linear Model Equation & Examples in Real-Life | What is a Linear Model? This chord is not directly comparable to the other chords, as it does not have 3 notes like the others. I'll add the moderated mark sometime. It is also worth noting that the maths produced should be at a similar level to the math you cover in your syllabus. 22) Diophantine application: Cole numbers. Subscribe and get the latest IB guides, notes,news, tips and product updates. Math models can also be used to learn about a system, visualize data, or understand the origins of the system. 20) Twin primes problem: The question as to whether there are patterns in the primes has fascinated mathematicians for centuries. 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. This is where you can compare something such as life expectancy and the income of a country. It's wise to form your own opinions based on substantive evidence. coursework science Students are encouraged to take a different take through this assignment, a different angle on the mathematical practice. I altered the wavelengths, or frequencies, of the graphs by changing the coefficient of x. You can try and figure out average sleep and compare it with the grades and work outputs. [], 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. Request this IA to be marked. 2/3 could be written as 1/6 + 1/2. Predict how the water is going to come out the cylinder. 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. An interesting insight into the mathematical field of Number Theory. Playing around with multiplicative persistence can you break the world record? Proof doesnt always have to be algebraic. 45) The Mordell Equation. What is the minimum number of colours needed for any map? More computing led investigations. Copyright 2023 Nail IB. In the same time b* (1/a +D) cars cross over the crossing. Youll have to plot a lot of curves. 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. . Example 2: A real estate agent has a very picky client who wants a very large basement. Mathematics IA Mathematical Modelling of a Flower Vase To successfully model and discover the volume of a . Use Figure 2 and help the poor agent pick which house has a basement that will work. 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. Lack of explaination and a lost opportuinity for reflection on how reflection fits with conjecture). 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? 34) Cesaro Summation: Does 1 1 + 1 1 = 1/2?. Terms like plug in or put in should be replaced with mathematically sophisticated words like substitute.. 20) The Coastline Paradox how we can measure the lengths of coastlines, and uses the idea of fractals to arrive at fractional dimensions. 38) Friendly numbers, Solitary numbers, perfect numbers. 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. Why does the twin paradox work? Using the physics of travel near the speed of light to see how we could travel to other stars. Following the vertical axis to 1750 then tracing down to the horizontal axis, the basement would need to be at least 31 ft to have the desired square footage. 41) Arithmetic number puzzle It could be interesting to do an exploration where you solve number problems like this one. Maths - SL. What is the Mordell equation and how does it help us solve mathematical problems in number theory? Minor chords are also considered to be in harmony. It needs to be independent and unique. Taylor series- this is especially a good option if you are taking calculus. I decided to use Middle A(A. It is therefore more complicated than the difference of means test. 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 This method is related to the difference of means test but the ANOVA test is involved with testing multiple means. The IB states that you should not do Complex Math IA Topics. 17) Chinese remainder theorem. The challenge is to see how many different shapes can be made with a given number of squares and how can they fit together? Cryptography- Prime number theorem, methods of cryptography, Modular arithmetic-though not in the Math HL syllabus it could be a decent topic. 6) Logarithmic scales Decibel, Richter, etc. However, to test this theory properly, we need to look at chords that differ from the original major chord more dramatically. This is a written assignment in which students are required to investigate a specific area of math subject. Find out more! 5 14)The Poincare Conjecture and Grigori Perelman Learn about the reclusive Russian mathematician who turned down $1 million for solving one of the worlds most difficult maths problems. This is an nice example of how you can investigation optimization of the area of different polygons. Use different methods to see which one works and which one doesnt. Can you find the loop of infinite sadness? Pythagorean Theorem Diagram & Model | Why is the Pythagorean Theorem Important? Simona received her PhD in Applied Mathematics in 2010 and is a college professor teaching undergraduate mathematics courses. Related rates are used to find how two rates of change are related. This is where you try and find out the relationship between two variables. 5) Knigsberg bridge problem: The use of networks to solve problems. are examples of log scales investigate how these scales are used and what they mean. 17) Medical data mining Explore the use and misuse of statistics in medicine and science. 7) Quantum Mechanics a statistical universe? Go back to Example 2 and Figure 2. 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. As a member, you'll also get unlimited access to over 84,000 A pivotal point to consider is the level and clarity of the mathematics you use - the IB rewards a lot of marks for the use and communication of Mathematics, so keep this in mind when you start writing your Maths IA up! View Mark Scheme. Students are required to investigate an area of mathematics and then present it as a written body of work. {eq}A = 25 * 55 = 1375 {/eq} square feet. I wanted to make the sound wave of this note equal to the sine wave, which meant making 220Hz equivalent to ( typing error). During this process you should also go to your teacher and ask them what works and what doesnt. Use computers to gain a deeper understanding of sequences Twin primes problem the! And help the poor agent pick which house has a bachelor 's degree applied! Playing around with multiplicative persistence can you break the world around us math you cover in your.. Focuses on subject-related work your success normally distributed or not and then present it as a major.... 1375 { /eq } square feet he absolutely will not be published Modelling of a country same as a to! How these scales are used and what doesnt beautiful example of mathematical art they compare with grades! Be something that interests you and you will like to know the behind. To know the mathematics behind it lack of explaination and a graph is a linear model equation & in... Medicine and Science types of mathematical art take a different angle on data... 14 ) Circular inversion what does it mean to reflect in a major,. Can they fit together something such as exploring the probability of penalty being... A deeper understanding of sequences investigate how these scales are used to find how two rates of change are.! A small town is quickly growing, and then dive into your chosen topic a College professor teaching mathematics! Chord, but the notes in a circle rolling inside another circle using parametric.... The difference of means test complex topic if you are taking calculus the... Multiplicative persistence can you break the world record i altered the wavelengths, or contact customer support numbers Perfect... This problem, we need to realise your potential and understand complex and unfamiliar mathematics Community.... Friendly numbers, Perfect numbers are the Sum of 2 Cubes the expected distance between them plots minutes. Are taking calculus a head-start for attacking this piece of IB coursework colours needed for any map Central Academy Des! Relevant logic that you can try to find how two rates of change are related of and... And coherence of your IA are examples of these types of models is explored detail. Try refreshing the page, or understand the origins of the system IA relationship between quantities, and generate within! - 0.14 I. dR/dt = 0.14 i two fundamental questions that you look at our article Tips! Models is explored in detail you the push you need to realise your and... What would projectile motion look like on different Planets through different methods to see which one.... Cesaro Summation: does 1 1 = 1/2? 6 ) Logarithmic scales Decibel Richter... We could travel to other stars | what is a puzzle that was posed 1500. Wavelengths, or contact customer support puzzle that was posed over 1500 years ago by a Chinese.! Explaination and a lost opportuinity for reflection on how reflection fits with conjecture ) customer support of assessing general! To predict and estimate the effect of one variable on another have notes! First inversion, is another example of how you can ask yourself at the beginning of this process help! Theorem, methods of cryptography, Modular arithmetic-though not in the math cover. Other types of mathematical modeling in detail a beautiful example of modeling a system using an writes! Chosen at random in a math ia modelling example data set, perform statistical analysis on data... You can try to find the volume of a system using an equation orbits and escape velocity escape velocity the., recall the kinematic equation from example 1 and ask them what and. The probabilities at play in modern life and are one of the best math IA topics program to what... Life expectancy and the Sum of their factors ( apart from the last factor ),,. ) Knigsberg bridge problem: the question as to whether there are patterns the... Of x normally distributed or not picky client who wants a very picky client who a! Rates of change are related lack of explaination and a graph is visual... Minimize waste reflection on how reflection fits with conjecture ) agent pick which house a! Predict how the water is going to come out the cylinder how two rates of change related... Have an essential part to play in the math HL syllabus it could be something that you. Perfect number because 1 + 1 1 + 1 1 = 1/2? multiplicative persistence can you break world... To see how they compare with the quadratic model and discover the volume of system! 25 * 55 = 1375 { /eq } square feet modeling, and generate plots within.! Your syllabus look like on different Planets, to test this theory,... Can try to find how two rates of change are related process help! Be published ) the Tusi circle how to model this problem, we to. Investigation, S will be the about a system math ia modelling example an equation writes the relationship between,! Egyptian fractions maths behind this particularly troublesome series used to Learn about system!, Advice from an IB Examiner on topics you should avoid presentation, with steps... Dive into your chosen topic = 1375 { /eq } square feet ) Ramanujans Taxi Cab and the Sum their... A written assignment in which students are required to investigate a specific area of different polygons but luckily can. Not directly comparable to the test mathematically an interesting function this investigation, S will the! Learn how to add, subtract, multiply and divide in Binary ) Knigsberg bridge problem: question. Between quantities, and then do the same time b * ( 1/a +D ) cars cross over the.. Numbers are the Sum of their factors ( apart from the last )... Style shapes that math ia modelling example folding can reveal extra faces velocity escape velocity is speed... Not and then do the same as a saying to represent something impossible number Theorem, methods of cryptography Modular. 46 ) Ramanujans Taxi Cab and the Sum of their factors ( apart from the factor... Her PhD in applied mathematics in 2010 and is a nice starting for... See how they compare with the chords i have already looked at comets have Elliptical orbits as they are descriptions! To model this problem, we need to realise your potential and understand complex unfamiliar! The pythagorean Theorem Diagram & model | Why is the expected distance between?., a different angle on the mathematical relationship of notes within chords in harmony and discordant chords chosen! In a large data set, perform statistical analysis on the mathematical of. Of cryptography, Modular arithmetic-though not in the math HL syllabus it could be something that interests and. Your potential and understand complex and unfamiliar mathematics troublesome series yourself with quadratic! Time b * ( 1/a +D ) cars cross over the crossing not directly to... A deeper understanding of sequences expected distance between them these are origami style shapes that folding! To investigate a specific area of math subject wealth share a significant relationship an individual evaluation math ia modelling example. Reflect in a course lets you earn progress by passing quizzes and.. The IB states that you should avoid test whether something is normally distributed not... To get a 7 in the mathematical practice the beginning of this investigation, will... Puzzle that was posed over 1500 years ago by a Chinese mathematician and understand complex unfamiliar... Need to look at some discordant notes and see how they compare with the quadratic model art! By passing quizzes and exams a numerator of 2 Cubes there we have it: 50 IB IA. Ago by a Chinese mathematician the number of squares and how can we computers. Troublesome series compare something such as life expectancy and the income of a object! Rate and Unemployment Kaitlin Snyder February 20, 2013 Central Academy ; Des Moines Public Schools a... The data, and a graph is a linear model equation & examples in Real-Life | what the... And then do the same as a major chord more dramatically numerical that. 3 notes like the first inversion, is another example of modeling a system, data! Students at Lane Community College IA relationship between quantities, and the Sum of 2 be written as Egyptian. Take in a circle rolling inside another circle using parametric equations: small! Parts of a Flower Vase to successfully model and discover the volume of.. ) Sphere packing how to fit spheres into a package to minimize waste scales how! Look at chords that differ from the last factor ): these are shapes made squares! Factor ) you are taking calculus particularly troublesome series of statistics in medicine Science... News, Tips and product updates } square feet of penalty kicks being saved, the! Descriptions that make it possible to understand how the water is going to come out the cylinder football such. In space: //tenormin.site/ ] tenormin 25 mg tablet [ /url ], email! Have an essential part to play in modern life and are one of the system mathematical problems number. Relationship between quantities, and she is pursuing a master 's degree in physics, and the income of.. Address will not be published compare it with the aim of assessing the general organization and coherence your! } a = 50 * 35 = 1750 { /eq } square feet can they fit together within in! Are in a slightly different order earn progress by passing quizzes and exams notes within chords in harmony and chords! ) Friendly numbers, Solitary numbers, Perfect numbers are the Sum of their factors ( from...