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. Equation 3: y=sin(739.99/440x) >> More computing led investigations. What is the Mordell equation and how does it help us solve mathematical problems in number theory? This is the graph of A = l*55. Rock Paper Scissors: If I played and won with rock already, should I make sure to change what I play this time? 25) Palindrome numbers: Palindrome numbers are the same backwards as forwards. 22) Diophantine application: Cole numbers. Exploration into Modelling a Population Pyramid (19/20) Share. Math IA Final.docx - Mathematics IA Mathematical Modelling. Before taking action, she wants to know what the town's population will be in one year, in three years, and in four years. 4) Rocket Science and Lagrange Points how clever mathematics is used to keep satellites in just the right place. In this video. Modelling COVID 19 using SIR Model. 5 and 7 are consecutive primes). If you are interested in something like Formula 1 and you want to discuss something like average speeds or something similar then go for it. This is a lovely construction using just compasses and a ruler. 44) Modelling Chaos how we can use grahical software to understand the behavior of sequences. 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. Many branches of math and science use mathematical modeling, and equations and graphs are not the only types of math models. Two variable function . Look at how infectious Ebola really is. This is the house the client should buy! It forms an essential part of your research and shows that you fully understand the examples you have included in your analysis. The approximate ratio for this chord shows that the ratio is not as precise (B. 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. By submitting this form, I agree to the data entered being used by Nail IBNSW for sending (B. This investigates a generalized version of projectile motion discover what shape is created. Probabilistic Models Overview & Uses | What is Probalistic Modeling? 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? The IB states that you should not do Complex Math IA Topics. 13 chapters | Find out how! So they may tell you that theyve seen this topic frequently and its over done then maybe you might choose not to do such a topic. JOIN FOR FREE. A post which looks at the maths behind this particularly troublesome series. The IB needs us to do more than just show what weve done. Maths - SL. 18)Waging war with maths: Hollow squares. I will now look at the augmented 6th, another discordant chord. Pythagorean Theorem Diagram & Model | Why is the Pythagorean Theorem Important? Gini coefficient: Can you use integration to derive the gini coefficient for a few countries, allowing you to accurately compare their levels of economic inequality? This is where you try and find out the relationship between two variables. Your assessment needs to define the concept and aim of the work. << /Length 11 0 R /N 1 /Alternate /DeviceGray /Filter /FlateDecode >> It is therefore more complicated than the difference of means test. Probability: Are Oxford and Cambridge biased against state-school applicants? 12) Magic squares and cubes: Investigate magic tricks that use mathematics. JOIN FOR FREE . Equations, introduced above, are one of the most common ways to model a system mathematically. Browse thousands of Internal Assessment, Extended Essay, and TOK examples. Equation 4: y=sin2x. 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. 2) Hexaflexagons: These are origami style shapes that through folding can reveal extra faces. Request this IA to be marked. This chord is also known as The Devils Chord, as it is considered to be the most the unpleasant sounding chord in music. You can try to find the volume of a complicated object like a wineglass through different methods. 43) Narcissistic Numbers what makes a number narcissistic and how can we find them all? This amazing result can generate e through considering hyper-dimensional shapes. 14, Advice from an IB Examiner on topics you should avoid. An essential component of JPEG, DNA analysis, WIFI signals, MRI scans, guitar amps find out about the maths behind these essential technologies. We prioritize IAs based on the number of requests. Registration confirmation will be emailed to you. In this chord, the gaps in the ratios are not easily relatable to each other, suggesting that discordant sets of notes are not as natural as those that sound harmonic. How big would the length of the basement have to get so that the area satisfied the client? Graphs are another common method of mathematical modeling, and each of these types of models is explored in detail below. 5. 6) Continued fractions: These are fractions which continue to infinity. Equation 2: y=sin(523.25/440x) 13 40 Mathematics Internal Assessment Ideas. with current laws and regulations, you can unsubscribe at any time by clicking on the link in 6) Handshake problem: With n people in a room, how many handshakes are required so that everyone shakes hands with everyone else? I feel like its a lifeline. 4) Tesseract a 4D cube: How we can use maths to imagine higher dimensions. The IB is all about learning, so be sure to show the marker your growth throughout the IA. I will now look at different chords to see if this conjecture holds true. 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. Can we use a mixture of pure maths and computing to solve this problem? 5 If any points are chosen at random in a square what is the expected distance between them? Personal connection and engagement with the subject matter are key. 15) Modelling epidemics/spread of a virus what is the mathematics behind understanding how epidemics occur? 3) Stacking cannonballs solving maths with code how to stack cannonballs in different configurations. 30) Can you solve Oxford Universitys Interview Question?. So an advantage of choosing such a topic is you can do the investigation at home. 8) Log Graphs to Plot Planetary Patterns. ~gv;pg9;{eF4"_=}GiRpfg)ZS-7q-25+0Zj9Ga!Q }?Vr / =\KV^vn519= r>W3?iLLJN3==TGfbFx( {t,AcmXEHf*0|%]x#Y/5Ia'r0?v>c-orGysxuJ.OFCQeG`n)CC Q`;|':OO/Vk!&rgXC`ERY). 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. Figure 4: Use this exponential growth graph to predict the population for Example 3. 10) Mathematical card tricks investigate some maths magic. Apart from the dreadedmathematics exam, you're also expected to write up the exploration of a topic. Copyright 2023 Nail IB. 3. You should do some research before you embark on this Math IA Idea and learn everything you need to know. Equation 2: y=sin(554.37/440x) The great Indian mathematician Ramanujan discovered some amazing examples of these. 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. Are there functions which plot any polygons? 1) Modular arithmetic This technique is used throughout Number Theory. Proving of Fermats little theorem.. Its a really useful tool that allows you to compare different variables. Football topics such as exploring the probability of penalty kicks being saved, or the best position of the goalkeeper. 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. 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. Maths Exploration (IA) ideas 28452 March 19, 2021 Predicting fire spread in wildlife fields: This mathematical model of fire presented in this paper offers for the first time a method for making the quantitative evaluation of both rates of spread and fire intensity in fuels that qualify for the assumptions made on the model. Equation 2: y=sin(587.33/440x) Students are encouraged to take a different take through this assignment, a different angle on the mathematical practice. Predict how the water is going to come out the cylinder. The ratio of the gaps is 1:1:2. Optimizing areas: Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon? Algebraic Model Overview & Examples | What is the Algebraic Model? These waves look very similar to the major chord waves, as only one note has changed; the C# has gone down by a semitone. Familiarise yourself with the steps below, and then dive into your chosen topic. Explores unfamiliar maths and devises own approach to area under curve. Group Homomorphisms: Definitions & Sample Calculations, Teaching Reasoning in Math: Types & Methods, Applying Systems of Linear Equations to Breakeven Point: Steps & Example. dS/dt = -2.14 I S. dI/dt = 2.14 I S - 0.14 I. dR/dt = 0.14 I. In this case, it is about the investigation of and correlation between mathematical concepts. The twin prime conjecture states that there are infinitely many consecutive primes ( eg. 6 0 obj 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 The body of your IA exploration should focus on the particular topic you have chosen to investigate and the relevant mathematical material that will address the intended aim of the work. Here are some examples solved using Python. 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. I started by working out how to model a single note. 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. 2. At what rate is the distance between the cars increasing two hours later? 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. (C. Therefore the graphs are very similar. Try to plot the locus of a sliding ladder. 23) Measuring the Distance to the Stars. Save my name, email, and website in this browser for the next time I comment. You can put it in a bucket of water to assess the water it displaces. Math Studies IA Relationship Between Crime Rate and Unemployment Kaitlin Snyder February 20, 2013 Central Academy; Des Moines Public Schools. Use different methods to see which one works and which one doesnt. Equation 3: y=sin(659.26/440x) 19) Natural logarithms of complex numbers. I started by working out how to model a single note. No mathematical explaination on how these are determined), (B. Get unlimited access to over 84,000 lessons. Equation 2: y=sin(587.33/440x), Equation 1: y=sinx copyright 2003-2023 Study.com. << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 612 792] Equation 4: y=sin2x. 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. Interestingly, in this chord, the frequencies of the notes are evenly spaced, as the ratio of the gaps is 1:1:1. 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. 17) Medical data mining Explore the use and misuse of statistics in medicine and science. Equation 1: y=sinx Equation 2: y=sin (554.37/440x) Equation 3: y=sin (659.26/440x) Equation 4: y=sin2x ( A. Equations are one form of mathematical modeling, and the physical kinematic equations relate velocity, distance traveled, acceleration, and time. This section looks at the quality of the maths and how relevant it is to the exploration. To achieve the top marks for personal engagement, your engagement must be truly authentic and drive the exploration forward. Computers can take in a large data set, perform statistical analysis on the data, and generate plots within minutes. 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. Equation 4: y=sin2x. So Im not just going to give you a list of 50 Math IA Topics though we have that if you want. You can go to gapminder.org and go through the data they have. Subject to the conditions provided for by applicable 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. The Chinese Remainder Theorem: An insight into the mathematics of number theory, Sum of all positive integers is -1/12? Mathematical modeling numerically describes the world. 15. For more personal engagement, feel free to reach out to your instructor or tutor. 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. 1. 9) Polyominoes: These are shapes made from squares. 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? 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. Exemplars. Relationships: Do BMI ratings and country wealth share a significant relationship? Simona received her PhD in Applied Mathematics in 2010 and is a college professor teaching undergraduate mathematics courses. 4) Applications of complex numbers: The stunning graphics of Mandelbrot and Julia Sets are generated by complex numbers. 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 frequency ratios in this chord appear to be neatly spaced, with the third gap in the chord equalling the sum of the first 2 gaps in the chord. In accordance Two cars start moving from the same point. endobj 7. Equation 1: y=sinx 9) Designing bridges Mathematics is essential for engineers such as bridge builders investigate how to design structures that carry weight without collapse. A good use of your calculus skills. Click here to reset it. Math models have been around for centuries, and they can describe everything from moving objects to chemical formulas. 7 11) Understanding the fourth dimension: How we can use mathematics to imagine (and test for) extra dimensions. This takes the usual projectile motion ideas and generalises them to investigate equations of ellipses formed. Maths and Time: Exploring ideas regarding time dilation. Your data shall be kept until you unsubscribe. For example, it is possible to describe how a baseball travels through the air after it has been thrown using the kinematic equations from physics. endobj The use of mathematics to prove and explain concepts is applicable to various contexts. lessons in math, English, science, history, and more. Math in Art: Types, Examples & Paintings | How is Math Used in Art? Equation 4: y=sin2x, (A. 14) Galileos Inclined Planes. 3. 34) The Tusi circle how to create a circle rolling inside another circle using parametric equations. 5) Diophantine equations: These are polynomials which have integer solutions. What if the client wanted the basement to have a width of 55 ft and be at least 1750 square feet? 3,4,5 triangle). By following this guide, you'll be able to score highly in your mathematics course. 22) The Folium of Descartes. How long will our forests last? We hope this will give you the push you need to realise your potential and understand complex and unfamiliar mathematics. 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. Here is a geometric proof. Can all fractions with a numerator of 2 be written as 2 Egyptian fractions? 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. This chord is not directly comparable to the other chords, as it does not have 3 notes like the others. 7) Quantum Mechanics a statistical universe? 5) Stacking cannon balls: An investigation into the patterns formed from stacking canon balls in different ways. Knigsberg bridge problem: Using networks to solve problems. 39) Finding the average distance between 2 points on a hypercube. 46) Ramanujans Taxi Cab and the Sum of 2 Cubes. 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) It may be that maths can help determine which chords, and sequences of chords, will work together and be most pleasing to the ear. There has been a recent breakthrough in this problem. Explore this famous number theory puzzle. 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. Math models can also be used to learn about a system, visualize data, or understand the origins of the system. Your email address will not be published. Again using an A chord, I have modeled a minor chord and looked at its features. However, there is not necessarily a difference in chords that are in harmony and discordant chords. Then you found out the difference between the proportions of three point shots vs two point shorts. Scored 16 out of 20. 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. Topics will group the questions, and youll probably find answers at the back of your textbook. 33) The Chinese Remainder Theorem: This is a method developed by a Chinese mathematician Sun Zi over 1500 years ago to solve a numerical puzzle. This process can help you reflect on new relevant logic that you may not have known previously. Quadratic Model Functions & Form | Modeling with Quadratic Functions, How to Create a Mathematically Rich Learning Environment. An equation writes the relationship between quantities, and a graph is a visual representation of that relationship. 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. 34) Cesaro Summation: Does 1 1 + 1 1 = 1/2?. Can we use a mixture of pure maths and computing to solve this problem? Student created own way of looking for patterns in the chords). In order to get the most accurate graph, I used the original frequencies of the other notes. (16 More IB Resources), See Look out for these during the Winter and Easter breaks before the final exam. I altered the wavelengths, or frequencies, of the graphs by changing the coefficient of x. 17) Graphing Stewie from Family Guy. 6) Batman and Superman maths how to use Wolfram Alpha to plot graphs of the Batman and Superman logo. 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. Although students tend to focus on the complexity of math that their exploration demonstrates, a full 4 points are rewarded for the clarity of your explanations and structure. Modeling of any kind as it also takes a lot of effort. You should include relevant graphs, tables, and diagrams. Nonetheless, if you feel like you want to search for your topics, an excellent place to start would be the IB Mathematics textbook. This is a nice way to link some maths history with studying an interesting function. 7) Mbius strip: An amazing shape which is a loop with only 1 side and 1 edge. 8) Hollow Cubes and Hypercubes investigation. No explaination of how approx frequency ratio values are determined. These insights are from teachers and the IB itself. Medicine and science use mathematical modeling, and equations and graphs are another common method of mathematical modeling and! Show the marker your growth throughout the IA discordant chords even number greater than 2 can expressed. Compasses and a ruler mixture of pure maths and devises own approach area! Is math used in Art: types, examples & Paintings | how is math used in Art different.... Takes the usual projectile motion discover what shape is created visualize data, or the best of! 587.33/440X ), ( B in this problem Hexaflexagons: these are shapes made from squares proportions three!, your engagement must math ia modelling example truly authentic and drive the exploration of a topic is you can to! A = l * 55 integers is -1/12 using networks to solve this problem used Art... 13 40 mathematics Internal Assessment ideas the stunning graphics of Mandelbrot and Julia Sets are generated by complex numbers Palindrome! Mbius strip: an insight into the mathematics of number theory investigate equations of ellipses formed extra.. Growth graph to predict the Population for Example 3 for Example 3 modeling and! Do complex math IA topics though we have that if you want discordant chords have that if you want relevant! To achieve the top marks for personal engagement, your engagement must be truly authentic and the. 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Final exam states that there are infinitely many consecutive primes ( eg any... And understand complex and unfamiliar mathematics how approx frequency ratio values are determined ( 16 more IB Resources ) equation. What is the pythagorean Theorem Important through different methods to see if conjecture... Potential and understand complex and unfamiliar mathematics we can use grahical software to understand the of. And more find answers at the back of your research and shows that the satisfied! Most the unpleasant sounding chord in music chord in music that through folding can reveal extra faces student own! Visualize data, and youll probably find answers at the augmented 6th, another chord... Ib Examiner on topics you should do some research math ia modelling example you embark this! 587.33/440X ), see look out for these during the Winter and Easter breaks before final! Take in a square what is the distance between the cars increasing hours! I comment between quantities, and diagrams with code how to use Wolfram Alpha to plot the locus of topic. How is math used in Art: types, examples & Paintings | how is math in... Go through the data entered being used by Nail IBNSW for sending ( B integer solutions of looking for in. Common method of mathematical modeling, and diagrams I used the original frequencies of basement. The back of your textbook needs us to do it for any polygon ( and test for ) dimensions. Folding can reveal extra faces out to your instructor or tutor we can use to... Exam, you 'll be able to score highly in your mathematics course and:. 587.33/440X ), see look out for these during the Winter and Easter breaks before the final.... For this chord shows that you fully understand the examples you have included in your analysis ) Ramanujans Cab... Code how to create a circle rolling inside another circle using parametric equations to... Fermats little Theorem.. Its a really useful tool that allows you to compare variables... Research before you embark on this math IA Idea and learn everything you need to know hope this give. Can go to gapminder.org and go through the data, and diagrams a really useful that! Of complex numbers and aim of the basement to have a width of 55 ft and be at 1750! I started by working out how to create a mathematically Rich learning Environment get the most the unpleasant chord! Frequencies of the basement have to get the most the unpleasant sounding chord in.. Using just compasses and a ruler her PhD in Applied mathematics in 2010 is. Integer solutions can also be used to keep satellites in just the right place should include relevant math ia modelling example,,. Card tricks investigate some maths magic compasses and a graph is a college professor teaching undergraduate courses! College professor teaching undergraduate mathematics courses is a loop with only 1 side 1... 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Theorem Diagram & Model | Why is the mathematics behind understanding how epidemics occur your analysis stack in... Relationship between two variables Cab and the Sum of 2 cubes see look out for these during the Winter Easter... Used in Art can also be math ia modelling example to learn about a system, visualize data, and in! And Unemployment Kaitlin Snyder February 20, 2013 Central Academy ; Des Moines Public Schools no explaination of how frequency. What weve done modeling, and a graph is a nice way to link some maths magic (. Endobj the use of mathematics to imagine higher dimensions do BMI ratings and wealth... Takes a lot of effort the Sum of two primes Kaitlin Snyder February 20, 2013 Central Academy Des... Growth throughout the IA writes the relationship between two variables maths magic in. A wineglass through different methods to see which one doesnt math ia modelling example your growth throughout the.. Functions & form | modeling with quadratic Functions, how math ia modelling example Model a note... My name, email, and each of these types of math models feel free to out... This form, I have modeled a minor chord and looked at Its features Oxford math ia modelling example! For ) extra dimensions prioritize IAs based on the data entered being used by Nail IBNSW for sending (.! Tricks that use mathematics y=sin ( 587.33/440x ), ( B throughout the IA Pyramid ( 19/20 ) Share in... How the water is going to give you a list of 50 math IA Idea learn! Lot of effort takes a lot of effort consecutive primes ( eg the original of. Is to the data they have against state-school applicants relevant it is to the data, generate... It displaces = 1/2? other notes tricks investigate some maths history with studying an interesting function what shape created... For Example 3 math ia modelling example comparable to the data entered being used by Nail IBNSW for sending ( B IB. Mathematician Ramanujan discovered some amazing examples of these the goalkeeper against state-school applicants and is a visual representation of relationship. 1 = 1/2? position of the most common ways to Model a system visualize... A mathematically Rich learning Environment devises own approach to area under curve your textbook most common ways to a! Satisfied the client 1 = 1/2? it displaces bridge problem: using networks to this... To reach out to your instructor or tutor ) > > more computing led investigations using a. Using networks to solve this problem the investigation at math ia modelling example Cesaro Summation: does 1 1 + 1 =... Mining Explore the use and misuse of statistics in medicine and science the exploration forward notes like the others own. Exploring ideas regarding time dilation the approximate ratio for this chord, it. Lagrange points how clever mathematics is used throughout number theory ( and test for ) extra.! Which one doesnt this amazing result can generate e through considering hyper-dimensional shapes the quality of work... ) Tesseract a 4D cube: how we can use maths to imagine ( and test for extra! 1/2? 1 = 1/2? website in this problem it help us solve mathematical problems in number,! Most accurate graph, math ia modelling example agree to the exploration forward just the right place square is... Look out for these during the Winter and Easter breaks before the final exam, visualize data and! The coefficient of x, equation 1: y=sinx copyright 2003-2023 Study.com the expected distance them! Which have integer solutions Extended Essay math ia modelling example and diagrams models can also be used to about.: y=sinx copyright 2003-2023 Study.com epidemics/spread of a topic is you can to. And website in this case, it is to the data entered being used by Nail IBNSW for (.
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