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. Probability and statistics do it unless you are sure you have complexity and if you do such a topic ensure that you include calculus. How mathematical formations were used to fight wars. 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. 3) Projectile motion: Studying the motion of projectiles like cannon balls is an essential part of the mathematics of war. Nice to see you here. As a member, you'll also get unlimited access to over 84,000 11) Mersenne primes: These are primes that can be written as 2^n -1. 7) Patterns in Pascals triangle: There are a large number of patterns to discover including the Fibonacci sequence. are examples of log scales investigate how these scales are used and what they mean. This takes the usual projectile motion ideas and generalises them to investigate equations of ellipses formed. Equation 1: y=sinx
2 0 obj An equation is a mathematical statement that describes one quantity in terms of the other quantities present in the system. So an advantage of choosing such a topic is you can do the investigation at home. xKO@+Mtt 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. Or is it better to switch? 13) Telephone Numbers these are numbers with special properties which grow very large very quickly. The great Indian mathematician Ramanujan discovered some amazing examples of these. The first criterion is about the presentation, with the aim of assessing the general organization and coherence of your IA. 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. 20) The Coastline Paradox how we can measure the lengths of coastlines, and uses the idea of fractals to arrive at fractional dimensions. 33) Can you solve an Oxford entrance question? How strange things happen when we start to manipulate divergent series. Proving of Fermats little theorem.. You can go to gapminder.org and go through the data they have. Graphs are another common method of mathematical modeling, and each of these types of models is explored in detail below. This evidence would suggest that notes which are traditionally considered to be in harmony are mathematically neater than those that are not in harmony. More poor use of terminology) than the discordant notes. What would projectile motion look like on different planets? The IB is measuring relevancy by checking that you only included maths that is directly intended to answer the research question. Equation 2: y=sin(523.27/440x)
Lanterna also offers the following to support students: The IAs make up 20% of your final grade in IB Economics, so you cannot underestimate their importance! 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 ratio of the gaps is 1:1:2. It involves understanding the modulo operation. Pythagorean triples: Can you find patterns in what numbers form a pythagorean triple? Tic Tac Toe: What is the optimal strategy in this legendary game? 10 Topology and networks. 38) Find the average distance between 2 points on a square. These insights are from teachers and the IB itself. 10) Mathematical card tricks investigate some maths magic. I will now look at different chords to see if this conjecture holds true. 30) Can you solve Oxford Universitys Interview Question?. For example, recall the kinematic equation from Example 1. Physicists can also use computer modeling to make predictions about what particles are expected to be produced. Years are on the horizontal axis and population is on the vertical axis. You can try and figure out average sleep and compare it with the grades and work outputs. 36) Sierpinski triangle an infinitely repeating fractal pattern generated by code. endobj lessons in math, English, science, history, and more. << /ProcSet [ /PDF /Text ] /ColorSpace << /Cs1 7 0 R >> /Font << /TT1 8 0 R Share. Examples are given. The chain rule and differentiation rule of polynomials. 5) Project Euler: Coding to Solve Maths Problems. 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. For the purpose of this investigation, S will be the . 6) Bullet projectile motion experiment using Tracker software to model the motion of a bullet. Online Private Tuition: One-on-one support from the comfort of your own home, whenever and wherever you need it. 11) Flatland by Edwin Abbott This famous book helps understand how to imagine extra dimension. JOIN FOR FREE. As with all assessments, you also need to include a solid conclusion that summarises the research and work youve done. 49) Rational approximations to irrational numbers. ScienceFusion Intro to Science & Technology Unit 1.1: What Is Science? Using the relation obtained in 2, solve for z'(2). What is a mathematical model used for? The next step in this process is to do the math. 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. A mathematical model is commonly written as an equation. These are some of the best Math IA Topics. 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. Knowing how youre being graded will make it much easier to make sure you're ticking all the boxes. Revision Courses: These offer a helping hand when it matters the most to boost your grades! 8) Finding prime numbers: The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics. 7) Explore the Si(x) function a special function in calculus that cant be integrated into an elementary function. 7) Quantum Mechanics a statistical universe? 3) Galileo: Throwing cannonballs off The Leaning Tower of Pisa Recreating Galileos classic experiment, and using maths to understand the surprising result. B. 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. Fermats Last Theorem is one of the most famous such equations. 27) Volume optimization of a cuboid how to use calculus and graphical solutions to optimize the volume of a cuboid. IA Review. 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) 14 Advice from an IB Examiner on topics you should avoid. 14) Galileos Inclined Planes. 40) Finding focus with Archimedes. Quadratic Model Functions & Form | Modeling with Quadratic Functions, How to Create a Mathematically Rich Learning Environment. It is now used as a saying to represent something impossible. We need to assign starting values for S, I and R - the numbers of people susceptible, infectious, recovered (immune) from measles. (1 More IB Past Papers). 7 However, this is just a theory and would have to be tested more thoroughly. 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. 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. Use different methods to see which one works and which one doesnt. You can think of the IA as a written mathematical presentation that will impact your final grade. Analysing Data: In the 200 meter dash, is there an advantage to a particular lane in track? This is a lovely construction using just compasses and a ruler. Computer modeling may be new, but chemical formulas as a math model are centuries old. 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. Are you getting ready to present your Math IA? 14) Circular inversion what does it mean to reflect in a circle? Here are some of the best topics in which you can get a good idea for your Math IA. [], 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. 7) Sierpinksi triangle: a fractal design that continues forever. Your assessment needs to define the concept and aim of the work. Use your calculus to get another areas of mathematics. It is clear then, that there is a difference in the mathematical relationship of notes within chords in harmony and discordant chords. 7. Math models can also be used to learn about a system, visualize data, or understand the origins of the system. 13) Different number systems Learn how to add, subtract, multiply and divide in Binary. Lost your password? For this reason, this theory does not only apply to sound coming to electronic instruments but every kind of instrument. 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. No mathematical explaination on how these are determined), (B. What is a mathematical model? 38) Friendly numbers, Solitary numbers, perfect numbers. 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. ~gv;pg9;{eF4"_=}GiRpfg)ZS-7q-25+0Zj9Ga!Q
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Q`;|':OO/Vk!&rgXC`ERY). than the discordant notes. 10) Is Intergalactic space travel possible? Simona received her PhD in Applied Mathematics in 2010 and is a college professor teaching undergraduate mathematics courses. Can we extend our investigation above to a multi-dimensional cube? IB Math IA: Modelling a Skateboard Ramp Mr. Flynn IB 3.6K subscribers Subscribe 200 Share 11K views 1 year ago IB Math IA ideas Access all videos at https://mrflynnib.com . endobj 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. Investigate what makes a number happy or sad, or sociable! We have a complete cycle of time 1/a + D+T. Doc Preview. 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. 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. 40) Stellar Numbers This is an excellent example of a pattern sequence investigation. Go back to Example 2 and Figure 2. 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. stream 36) Can we prove that 1 + 2 + 3 + 4 . So lets say you decide to assess Lewis Hamiltons speed at a certain velocity of a given time. Real-world problems often include tens of thousands, if not hundreds of thousands data points, and computer modeling has become the popular method for understanding these large data sets because of the speed and accuracy with which a computer can process information. Optimizing areas: Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon? 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