It needs to be independent and unique. Equation 4: y=sin2x. The internal assessment is an individual evaluation that focuses on subject-related work. . 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. Cryptography- Prime number theorem, methods of cryptography, Modular arithmetic-though not in the Math HL syllabus it could be a decent topic. Equation 2: y=sin(659.26/440x), (A,D. 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. 2) Hexaflexagons: These are origami style shapes that through folding can reveal extra faces. Putting it all together gives: {eq}v_f = v_i + at {/eq} -> {eq}v_f = 0 + 80*10 {/eq}. Fourier transforms have an essential part to play in modern life and are one of the keys to understanding the world around us. The Chinese Remainder Theorem: An insight into the mathematics of number theory, Sum of all positive integers is -1/12? 4) Genetics Look at the mathematics behind genetic inheritance and natural selection. 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. So, where do you even begin your IA? 18. In this video. 2) How to Design a Parachute looking at the physics behind parachute design to ensure a safe landing! What conclusions did you reach, and did you succeed in exploring the aim that you set out at the beginning of the Math IA! With these Topics ensure that you are not heavily reliant on the Physics aspect; put more emphasis on Mathematics. Bookmark Download. 15) Modelling epidemics/spread of a virus what is the mathematics behind understanding how epidemics occur? By siging up, I agree to Lanternas 44) Modelling Chaos how we can use grahical software to understand the behavior of sequences. Unfortunately these equations are very difficult to solve - but luckily we can use a computer program to plot what happens. << /Length 5 0 R /Filter /FlateDecode >> 2) Solving maths problems using computers computers are really useful in solving mathematical problems. 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. Using x'(t)=30, y'(t)=40 and the distance of each car after two hours, we obtain: 4. An inversion chord is the same as a major chord, but the notes are in a slightly different order. 39) Finding the average distance between 2 points on a hypercube. This chord is also known as The Devils Chord, as it is considered to be the most the unpleasant sounding chord in music. 6) Continued fractions: These are fractions which continue to infinity. However, this is just a theory and would have to be tested more thoroughly. 3) Mathematical methods in economics maths is essential in both business and economics explore some economics based maths problems. 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. 7) Sierpinksi triangle: a fractal design that continues forever. [], or you can call us here at: +44 20 4571 0455. Although that might sound easy, thats not always the case! Can we use a mixture of pure maths and computing to solve this problem? 15 Closing. View Mark Scheme. It may be that maths can help determine which chords, and sequences of chords, will work together and be most pleasing to the ear. Scored 16 out of 20. Equations are one form of mathematical modeling, and the physical kinematic equations relate velocity, distance traveled, acceleration, and time. A chemical formula is a mathematical model that relates the relative amounts of composite chemicals in a molecule. 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. 5 Algebra and number. By doing this, you can determine findings throughout the process. 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. Math models have been around for centuries, and they can describe everything from moving objects to chemical formulas. The planets follow a surprising pattern when measuring their distances. 14, Advice from an IB Examiner on topics you should avoid. It is therefore more complicated than the difference of means test. The first criterion is about the presentation, with the aim of assessing the general organization and coherence of your IA. 2 0 obj This assessment is a great way for students to expand their knowledge and learn valuable skills. Equation 2: y=sin(554.37/440x) 7) When do 2 squares equal 2 cubes? In this article, we're breaking down the best way to format yours in a way that promotes independent thinking and personal engagement. Did your learning affect your life in any way, or how might it affect the lives of others? Then you found out the difference between the proportions of three point shots vs two point shorts. So in this method you are testing the difference between two means and you are checking whether there is a significant difference. 1678+ Video tutorials, 1226+ PDF IB Resources, 195+ Sample IAs, 148+ EEs, 8777+ Sample questions, 653+ quizzes, IB No mathematical explaination on how these are determined), (B. Equation 3: y=sin(698.46/440x)(Incorrect value(698.46) compared with the table) What does the future hold? 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. 3. 2) Step two is to calculate the area of basement 2 which has a length of 50 ft and a width of 35 ft. Will my probability of winning drastically increase by some move that I can make? It solves about 90% as many problems as real kids: a small sample of 9-12 year olds scored 60% on a test from our dataset, while our system scored 55% on those same problems. A classic problem in number theory which can be solved through computational power. Optimizing volumes: Explore the mathematics of finding a maximum volume of a cuboid subject to some constraint. What is a Mathematical Model? A nice starting point for students good at coding who want to put these skills to the test mathematically. 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. In addition to a bibliography at the end, you must acknowledge all direct quotes that you use throughout your essay. 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. Use Figure 4 to help the mayor find out how fast her town is growing. For example, the common chemical formula for water, {eq}H_20 {/eq}, means that there are two hydrogen atoms for every one oxygen atom in a molecule of water. Also, ensure that you look at our article on Tips to get a 7 in the Math Internal Assessment. Equation 1: y=sinx Equation 2: y=sin (554.37/440x) Equation 3: y=sin (659.26/440x) Equation 4: y=sin2x ( A. These are some of the best Math IA Topics. An interesting insight into the mathematical field of Number Theory. In this mathematical exploration, the students attempts to study the mathematical relationship of notes within chords inn harmony and discordant chords. Students are encouraged to take a different take through this assignment, a different angle on the mathematical practice. You may present your work in a word processing software (like Microsoft Word or Pages), or it can be handwritten. What would projectile motion look like on different planets? They are numerical descriptions that make it possible to understand how the parts of a system work together. One example is modeling the radioactive decay of chernobyl, and determining if conditions are suitable for living. They have data and different comparisons that may be great for you. 38) Friendly numbers, Solitary numbers, perfect numbers. This is a nice way to link some maths history with studying an interesting function. 3) Galileo: Throwing cannonballs off The Leaning Tower of Pisa Recreating Galileos classic experiment, and using maths to understand the surprising result. 10) Mathematical card tricks investigate some maths magic. 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. We have a complete cycle of time 1/a + D+T. The IB is measuring relevancy by checking that you only included maths that is directly intended to answer the research question. coursework science Equation 2: y=sin(622.25/440x). ), Continued fractions- Use of continued fractions as representations of real numbers.. JOIN FOR FREE. In this time 1 + a*D pedestrians arrive and then cross. 9) Designing bridges Mathematics is essential for engineers such as bridge builders investigate how to design structures that carry weight without collapse. Lets take a look at the criteria for your Math IA. 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. Pages 15. Are there functions which plot any polygons? It is essential that you select the appropriate topic for you that aligns with your interests and you dont pick a topic just because very many people have done it. These statistical analyses and plots model the input data and allow the researcher to understand different attributes of the data set. 36) Sierpinski triangle an infinitely repeating fractal pattern generated by code. Apart from the dreadedmathematics exam, you're also expected to write up the exploration of a topic. Essential knowledge for future astronauts. Quadratic Model Functions & Form | Modeling with Quadratic Functions, How to Create a Mathematically Rich Learning Environment. 10) Is Intergalactic space travel possible? Equation 2: y=sin(523.27/440x) 12) Towers of Hanoi puzzle This famous puzzle requires logic and patience. Analysing Data: In the 200 meter dash, is there an advantage to a particular lane in track? with current laws and regulations, you can unsubscribe at any time by clicking on the link in 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. 9) Coding Hailstone Numbers. 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. 1a) Non-Euclidean geometries: This allows us to break the rules of conventional geometry for example, angles in a triangle no longer add up to 180 degrees. An Augmented 6th is also known as a dominant 7th, which was one of the first discordant chords to be used in music in the West. 1, Models for the height of water in a cylindrical container. Share. Optimization Problems Steps & Examples | What is Optimization in Calculus? 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. How much safer does a password get by adding symbols or numbers? Use your calculus to get another areas of mathematics. 10) Pythagorean triples: A great introduction into number theory investigating the solutions of Pythagoras Theorem which are integers (eg. You can test whether something is normally distributed or not. The table of values for this chord shows that my original conjecture does not hold true for all chords. The distance between the two cars is changing at the rate: Mathematical models are numerical or quantitative representations of a real-world system.There are many different types of math models, and they common involve constants and variables. 18) Hyperbolic geometry how we can map the infinite hyperbolic plane onto the unit circle, and how this inspired the art of Escher. However, there is not necessarily a difference in chords that are in harmony and discordant chords. Investigate how to solve them. 408 In order to get the most accurate graph, I used the original frequencies of the other notes3. View Math IA Final.docx from MATH, HL at GEMS Wellington Silicon Oasis. Lost your password? The area of this basement is {eq}A = 50 * 35 = 1750 {/eq} square feet. Harmonic series: Explore why certain notes/chords in music sound dissonant, and others consonant, by looking at the ratios of frequencies between the notes. So lets say you decide to assess Lewis Hamiltons speed at a certain velocity of a given time. By year three, the population is almost 300,000. It is also worth noting that the maths produced should be at a similar level to the math you cover in your syllabus. The use of mathematics to prove and explain concepts is applicable to various contexts. 4, 40 Mathematics Internal Assessment Ideas. Personal connection and engagement with the subject matter are key. 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. It involves understanding the modulo operation. 1. 11) Flatland by Edwin Abbott This famous book helps understand how to imagine extra dimension. Example 2 is another example of modeling a system using an equation. 3. 3) Projectile motion: Studying the motion of projectiles like cannon balls is an essential part of the mathematics of war. 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 approximate ratio for this chord shows that the ratio is not as precise (B. Computers can take in a large data set, perform statistical analysis on the data, and generate plots within minutes. Equation 3: y=sin(659.26/440x) Math models can also be used to learn about a system, visualize data, or understand the origins of the system. 4 0 obj Gain a deeper understanding of chaos theory with this investigation. I started by working out how to model a single note. Here is a geometric proof. 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. 49) Rational approximations to irrational numbers. Why do magic squares work? Simplifying this expression gives the final answer of {eq}v_f = 800 {/eq} m/s. Login. All of these topics are applicable for the Math SL and HL students. Graphs are another common method of mathematical modeling, and each of these types of models is explored in detail below. Go back to Example 2 and Figure 2. Two cars start moving from the same point. MATH, ziadpike. Instead of comparing means, youll be comparing proportions. Interestingly, the graphs of these intervals show that the notes in the perfect fourth cross at exactly 3, and the notes in the perfect fifth cross at 2. By year four the town's population will be larger than 1,400,000. The ratio of the gaps is now 2:3:5. Graphs not related to tables). Are you getting ready to present your Math IA? 14) Egyptian fractions: Egyptian fractions can only have a numerator of 1 which leads to some interesting patterns. Maths IA - Maths Exploration Topics: Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. See {eq}A = 25 * 55 = 1375 {/eq} square feet. 15) Julia Sets and Mandelbrot Sets We can use complex numbers to create beautiful patterns of infinitely repeating fractals. You can check whether there is a significant difference in the salary of someone who studied in a community college and one who went to an Ivy League school. 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. Even if they do understand the mathematics, the restriction on length does not allow such students to address the target audience when explaining the mathematics. We hope this will give you the push you need to realise your potential and understand complex and unfamiliar mathematics. Minor chords are also considered to be in harmony. Using the physics of travel near the speed of light to see how we could travel to other stars. Game theory as it is easy and overdone. How can we find the area of any polygon? 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. What is the next best alternative if this is not viable? 1) Step one is to calculate the area for basement 1. Your report should include afull bibliographywith all sources at the end of the report. A good use of your calculus skills. The ratios of frequencies of chords in harmony are more concise. This may indicate the start of a pattern. Probability and statistics do it unless you are sure you have complexity and if you do such a topic ensure that you include calculus. Interesting: The chosen topic needs to be exciting enough to elicit not only your interest but that of your audience. ~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). 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. Examples are given. 19) Natural logarithms of complex numbers. For example, to find how fast the distance between two cars increases, if we know the speeds of two cars that travel away from a 90-degree intersection, we will use the related rates model. So there you have it. 6. << /Length 11 0 R /N 1 /Alternate /DeviceGray /Filter /FlateDecode >> The following sections explore these other types of mathematical modeling in detail. 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End, you can test whether something is normally distributed or not 2 points a... Chords inn harmony and discordant chords the internal assessment is a great introduction into number theory ) ( value. This assignment, a different take through this assignment, a different take through this assignment a! Use a mixture of pure maths and computing to solve this problem independent thinking and personal engagement topic!
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