35) Fermats Theorem on the sum of 2 squares An example of how to use mathematical proof to solve problems in number theory. 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. What is the minimum number of colours needed for any map? 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. Fermats Last Theorem is one of the most famous such equations. Computer modeling has become a popular method for quantitively understanding real-world problems, and chemical formulas, which succinctly describe chemical reactions, have been around for centuries. Save my name, email, and website in this browser for the next time I comment. More computing led investigations. 5 0 obj 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. 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! Minor chords are also considered to be in harmony. 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 Can all fractions with a numerator of 2 be written as 2 Egyptian fractions? 4) Rocket Science and Lagrange Points how clever mathematics is used to keep satellites in just the right place. Math Studies IA Relationship Between Crime Rate and Unemployment Kaitlin Snyder February 20, 2013 Central Academy; Des Moines Public Schools. Although that might sound easy, thats not always the case! When the gun fires, she fully accelerates at 80 {eq}m/s^2 {/eq} for 10 seconds. It involves understanding the modulo operation. Terms like plug in or put in should be replaced with mathematically sophisticated words like substitute.. It covers what mathematical modeling is as well as different types of models in math. (C. 16 Math IA Ideas 6. This is the house the client should buy! Recently, computer modeling has become a popular method for understanding large data sets and for running statistical analysis such as using Bayes' formula. 6) Continued fractions: These are fractions which continue to infinity. We hope this will give you the push you need to realise your potential and understand complex and unfamiliar mathematics. All rights reserved. This analysis can be done in minutes or hours, but without a computer the same analysis could take decades. 52) Have you got a Super Brain? Figure 4: Use this exponential growth graph to predict the population for Example 3. The first criterion is about the presentation, with the aim of assessing the general organization and coherence of your IA. 12) Magic squares and cubes: Investigate magic tricks that use mathematics. You may also include any personalised problem statements and explain how you aim to achieve a solid investigation on the topic. We have a complete cycle of time 1/a + D+T. May 2022. 5 Algebra and number. 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. See 7) Explore the Si(x) function a special function in calculus that cant be integrated into an elementary function. Choose your own pattern investigation for the exploration. The most commonly used math models are equations and graphs. How many different ways can we use to solve a number theory problem? You have to be careful when you do Math IA in this category as you have to have the correct interpretations. These datasets can easily be found on Gapminder. What conclusions did you reach, and did you succeed in exploring the aim that you set out at the beginning of the Math IA! All rights reserved. 12) The Riemann Sphere an exploration of some non-Euclidean geometry. 22) The Folium of Descartes. 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. Example 1: Use the kinematic equation {eq}v_f = v_i + at {/eq} where {eq}v_f {/eq} means final velocity, {eq}v_i {/eq} means initial velocity, a stands for acceleration, and t stands for time to answer the following question: A race car driver sits at the starting line. Ib Math Studies Ia Thesis Example When somebody should go to the ebook stores, search initiation by shop, shelf by shelf, it is truly problematic. An interesting insight into the mathematical field of Number Theory. 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. How do you come up with a good math IA?. promotional emails that we send to you. This may indicate the start of a pattern. What is a mathematical model? 31) Grahams Number a number so big that thinking about it could literally collapse your brain into a black hole. 11 Math and computing. So there we have it, a well organized exploration of the idea and IB layout of your Mathematics IA! << /Length 5 0 R /Filter /FlateDecode >> Browse thousands of Internal Assessment, Extended Essay, and TOK examples. Optimizing areas: Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon? The examiner will be looking at the quality of the idea and the body of work in relation to the assessment criteria. Equation 4: y=sin2x. A first inversion chord starting on A will actually be in the key of F major. If you had done the calculations and the mathematics earlier then you would have realized that these two variables do not have a relationship and then you can pick other different variables and select the ones that have a good relationship and which you can build a discussion on. Use Figure 2 and help the poor agent pick which house has a basement that will work. Many IB students find it hard to study mathematical concepts. 14) Methods for solving differential equations Differential equations are amazingly powerful at modelling real life from population growth to to pendulum motion. What if the client wanted the basement to have a width of 55 ft and be at least 1750 square feet? For more info on how to write the exploration, check out our completeMath IA Guide. 47) Hollow cubes and hypercubes investigation. These waves look very similar to the major chord waves, as only one note has changed; the C# has gone down by a semitone. According to student reviews, IB Maths is a struggle for many students working towards getting their diplomas. The table below shows more information about the notes in this chord. 26) Plotting the Mandelbrot Set using Geogebra to graphically generate the Mandelbrot Set. 43) Narcissistic Numbers what makes a number narcissistic and how can we find them all? 10 Topology and networks. 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. 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. 38) Find the average distance between 2 points on a square. Cracking a Password: How long would it take to be able to correctly guess a password? I would definitely recommend Study.com to my colleagues. JOIN FOR FREE. Equation 1: y=sinx Equation 2: y=sin (554.37/440x) Equation 3: y=sin (659.26/440x) Equation 4: y=sin2x ( A. These insights are from teachers and the IB itself. With these Topics ensure that you are not heavily reliant on the Physics aspect; put more emphasis on Mathematics. I wanted to make the sound wave of this note equal to the sine wave, which meant making 220Hz equivalent to ( typing error). 1. This chord, however, has 3 notes, so it can be more easily compared to the other chords I have looked at. So this involves you writing down the mathematics on paper to see if your topic will work. These statistical analyses and plots model the input data and allow the researcher to understand different attributes of the data set. Math models have been around for centuries, and they can describe everything from moving objects to chemical formulas. Nonetheless, if you feel like you want to search for your topics, an excellent place to start would be the IB Mathematics textbook. This means, that perhaps in the future music can be created entirely mathematically. 33) Can you solve an Oxford entrance question? Friendly numbers, Solitary numbers, perfect numbers:Investigate what changes the condition of numbers, Force: Calculating the intensity of a climbers fall based upon their distance above where they last clamped in. Pythagorean Theorem Diagram & Model | Why is the Pythagorean Theorem Important? The Chinese Remainder Theorem: An insight into the mathematics of number theory, Sum of all positive integers is -1/12? 10) Mathematical card tricks investigate some maths magic. Related rates are used to find how two rates of change are related. dS/dt = -2.14 I S. dI/dt = 2.14 I S - 0.14 I. dR/dt = 0.14 I. During the reflective stage, connect the results with the initial aims. 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. Examples are given. 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 should do some research before you embark on this Math IA Idea and learn everything you need to know. No mathematical explaination on how these are determined), (B. 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. Maths is closely connected with astronomy see how we can work out the distance to the stars. Exploration into Modelling a Population Pyramid (19/20) Share. {eq}A = 25 * 55 = 1375 {/eq} square feet. 18) Fermats last theorem: A problem that puzzled mathematicians for centuries and one that has only recently been solved. Therefore the graphs are very similar. 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. In some geometries triangles add up to more than 180 degrees, in others less than 180 degrees. 18. the Are there functions which plot any polygons? In order to score in the top range here, make sure your IA is clearly structured. Your IA some non-Euclidean geometry also include any personalised problem statements and explain how you to. Any map big that thinking about it could literally collapse your brain a. 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