So an advantage of choosing such a topic is you can do the investigation at home. 2, How to come up with an idea or a topic. For example, recall the kinematic equation from Example 1. You can go to gapminder.org and go through the data they have. View Mark Scheme. I feel like its a lifeline. 14) Circular inversion what does it mean to reflect in a circle? Use your calculus to get another areas of mathematics. 7) Sierpinksi triangle: a fractal design that continues forever. The picky client needs the basement to have a specific area, and the area of a rectangle can be modeled mathematically with the equation {eq}A = lw {/eq} where A stands for area, l stands for length, and w stands for width. This means, that perhaps in the future music can be created entirely mathematically. 50) Square triangular numbers. I wanted to make the sound wave of this note equal to the sine wave, which meant making 220Hz equivalent to ( typing error). Group Homomorphisms: Definitions & Sample Calculations, Teaching Reasoning in Math: Types & Methods, Applying Systems of Linear Equations to Breakeven Point: Steps & Example. Graphs not related to tables). This will also give you personal engagement points. The second criterion looks largely at the mathematical language you have used, such as: Ensure that these three components are accurate and consistent throughout your IA. The IB needs us to do more than just show what weve done. ScienceFusion Intro to Science & Technology Unit 1.1: What Is Science? 9) Optimization of area an investigation. Maths - HL. 35) Fermats Theorem on the sum of 2 squares An example of how to use mathematical proof to solve problems in number theory. Proof doesnt always have to be algebraic. Investigate what makes a number happy or sad, or sociable! ie 6 is a perfect number because 1 + 2 + 3 = 6. It should show personal engagement with the topic at hand. 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. Many IB students find it hard to study mathematical concepts. With these Topics ensure that you are not heavily reliant on the Physics aspect; put more emphasis on Mathematics. Probabilistic Models Overview & Uses | What is Probalistic Modeling? 10) Codes and ciphers: ISBN codes and credit card codes are just some examples of how codes are essential to modern life. lanchester s combat model ia maths sl 7 exploring an alternative method of calculating the volume of a star 27) Volume optimization of a cuboid how to use calculus and graphical solutions to optimize the volume of a cuboid. 1) The Monkey and the Hunter How to Shoot a Monkey Using Newtonian mathematics to decide where to aim when shooting a monkey in a tree. Use Figure 4 to help the mayor find out how fast her town is growing. 1, Models for the height of water in a cylindrical container. For the purpose of this investigation, S will be the . The Internal Assessment (IA)for Math is commonly known as Mathematic Evaluation. You should do some research before you embark on this Math IA Idea and learn everything you need to know. Optimization Problems Steps & Examples | What is Optimization in Calculus? 6) Handshake problem: With n people in a room, how many handshakes are required so that everyone shakes hands with everyone else? However, this is just a theory and would have to be tested more thoroughly. In this mathematical exploration, the students attempts to study the mathematical relationship of notes within chords inn harmony and discordant chords. 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! This is an area of maths that is not strictly bound to the number! 41) Arithmetic number puzzle It could be interesting to do an exploration where you solve number problems like this one. and many many more tips and tricks on securing those top marks on our free resources page - just click the 'Maths resources' button! This is a function which is used in Quantum mechanics it describes a peak of zero width but with area 1. We also have similar ideas for Biology, Chemistry, Economics, History, Physics, TOK. IA Review. The mathematics of deceit: How con artists use pyramid schemes to get rich quick! Or is it better to switch? Katherine has a bachelor's degree in physics, and she is pursuing a master's degree in applied physics. 7) Quantum Mechanics a statistical universe? The internal assessment is an individual evaluation that focuses on subject-related work. There has been a recent breakthrough in this problem. Probability: Are Oxford and Cambridge biased against state-school applicants? 22) Diophantine application: Cole numbers. During the reflective stage, connect the results with the initial aims. Harmonic series: Explore why certain notes/chords in music sound dissonant, and others consonant, by looking at the ratios of frequencies between the notes. The chain rule and differentiation rule of polynomials. q&}@{S$*!6g)pOK`/N"AbhIrW1Xllkz;)F F!vtPp7XQ>lTk<3D~)xGZ_L29=`0GP?w Also, ensure that you look at our article on Tips to get a 7 in the Math Internal Assessment. 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. legislation, you have rights in relation to your data. So, where do you even begin your IA? 1) The Van Eck Sequence The Van Eck Sequence is a sequence that we still dont fully understand we can use programing to help! No mathematical explaination on how these are determined) ( B. This assessment is a great way for students to expand their knowledge and learn valuable skills. oZWE|-jT (XA 5) Stacking cannon balls: An investigation into the patterns formed from stacking canon balls in different ways. A great introduction to some of the ideas behind non-euclidean geometry. Equation 3: y=sin(659.26/440x) Using trignometric graphs but nothing is done with them. In order to get the most accurate graph, I used the original frequencies of the other notes3. Game theory as it is easy and overdone. Copyright 2023 Nail IB. ScienceFusion Intro to Science & Technology Unit 1.2: Scientific Investigation, ScienceFusion Intro to Science & Technology Unit 1.3: Scientific Knowledge, ScienceFusion Intro to Science & Technology Unit 1.4: Science and Society, ScienceFusion Intro to Science & Technology Unit 2.1: Representing Data, ScienceFusion Intro to Science & Technology Unit 2.2: Scientific Instruments and Measurement, Physical Models: Scale Models & Life-Size Models, Conceptual Models: Definition & Characteristics, ScienceFusion Intro to Science & Technology Unit 3.1: The Engineering Design Process, ScienceFusion Intro to Science & Technology Unit 3.2: Risk/Benefit Analysis, ScienceFusion Intro to Science & Technology Unit 3.3: Systems, ScienceFusion Intro to Science & Technology Unit 3.4: Materials Science, ScienceFusion Intro to Science & Technology Unit 3.5: Bioengineering, ScienceFusion Intro to Science & Technology Unit 3.6: Engineering and Society, UExcel Weather and Climate: Study Guide & Test Prep, Study.com ACT® Test Prep: Practice & Study Guide, FTCE Middle Grades General Science 5-9 (004) Prep, Writing & Evaluating Real-Life Linear Models: Process & Examples, How Mathematical Models are Used in Social Science, Planning a Mathematics Lesson to Align with TEKS, How Mathematical Models are Used in Science, Mathematical Modeling - Hardy-Weinberg: Biology Lab, Nutrients of Concern: Definition & Dietary Guidelines, Reading & Interpreting Ingredient Lists on Food Labels, Phytosterols: Definition, Function & Impact on Health, Role of Lipids in Developing Cardiovascular Disease, Working Scholars Bringing Tuition-Free College to the Community, relating quantities in real-world situations. 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. 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. Here are some examples solved using Python. 10) Mathematical card tricks investigate some maths magic. Bookmark Download. Math models can also be used to learn about a system, visualize data, or understand the origins of the system. This investigates a generalized version of projectile motion discover what shape is created. Can you find the loop of infinite sadness? All of these topics are applicable for the Math SL and HL students. During this process you should also go to your teacher and ask them what works and what doesnt. See Other examples of math models are the Pythagorean theorem and line graphs. So its that time of your IB program when you need to start working on your IA. 11) Mersenne primes: These are primes that can be written as 2^n -1. Linear Model Equation & Examples in Real-Life | What is a Linear Model? Interestingly, in this chord, the frequencies of the notes are evenly spaced, as the ratio of the gaps is 1:1:1. 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. Give us the email address you use to log in to Lanterna and well send you instructions for resetting your password. Equation 1: y=sinx This client is so picky that unless the basement has exactly 1750 square feet he absolutely will not buy the house. Based on this, it is clear that the student needs to know the appropriate mathematical language and relevant key terms to engage in the topic. 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. Equation 2: y=sin(622.25/440x). Student created own way of looking for patterns in the chords). The examiner will be looking at the quality of the idea and the body of work in relation to the assessment criteria. Create your account. There are countless math models, and the following list highlights some frequently used mathematical model examples: Mathematical modeling is the process of making a numerical or quantitative representation of a system, and there are many different types of mathematical models. View Math IA Final.docx from MATH, HL at GEMS Wellington Silicon Oasis. No explaination of how approx frequency ratio values are determined. IA. . 3) Mathematical methods in economics maths is essential in both business and economics explore some economics based maths problems. 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? 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. 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. 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. In this time 1 + a*D pedestrians arrive and then cross. JOIN FOR FREE. 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 Whatever you choose, remember that you will create a new exploration of complex ideas. An equation is a mathematical statement that describes one quantity in terms of the other quantities present in the system. 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. 2) Gravity, orbits and escape velocity Escape velocity is the speed required to break free from a bodys gravitational pull. Optimizing areas: Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon? Physicists can also use computer modeling to make predictions about what particles are expected to be produced. Why do magic squares work? Recently, computer modeling has become a popular method for understanding large data sets and for running statistical analysis such as using Bayes' formula. 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. This section looks at the quality of the maths and how relevant it is to the exploration. << /ProcSet [ /PDF /Text ] /ColorSpace << /Cs1 7 0 R >> /Font << /TT1 8 0 R You can try and figure out average sleep and compare it with the grades and work outputs. 18) Fermats last theorem: A problem that puzzled mathematicians for centuries and one that has only recently been solved. Based on this, it is clear that the student needs to know the appropriate mathematical language and relevant key terms to engage in the topic. A chemical formula is a mathematical model that relates the relative amounts of composite chemicals in a molecule. This mathematical equation has been described as the most important in all of physics. Evaluating limits: Exploring LHpitals rule. One travels north at 40 km/h, and the other travels east at 30 km/h. Can we use a mixture of pure maths and computing to solve this problem? You can put it in a bucket of water to assess the water it displaces. Equation 2: y=sin(523.25/440x) 12) Towers of Hanoi puzzle This famous puzzle requires logic and patience. The ratio of the gaps is 1:1:2. More poor use of terminology) than the discordant notes. 408 No mathematical explaination on how these are determined), (B. (16 More IB Resources), See Because the three distances are changing in time, they are functions of t. Differentiate for t the relation obtained above. You can also model everything from Angry Birds to stunt bike jumping. Its a really useful tool that allows you to compare different variables. Lets take a look at the criteria for your Math IA. 5 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. Equation 1: y=sinx Equation 2: y=sin (554.37/440x) Equation 3: y=sin (659.26/440x) Equation 4: y=sin2x ( A. 12 Other Math IA Ideas. 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. By submitting this form, I agree to the data entered being used by Nail IBNSW for sending 10/29/2020. 15. 2/3 could be written as 1/6 + 1/2. The following graph demonstrates how this chord travels through the air: Equation 1: y=sinx 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. 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