5) Diophantine equations: These are polynomials which have integer solutions. 3. Figure 3: A graph is a visual representation of a system. Lets take a look at the criteria for your Math IA. 8) The Remarkable Dirac Delta Function. 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. [], 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. Example 2 is another example of modeling a system using an equation. So this involves you writing down the mathematics on paper to see if your topic will work. A model in math can be different depending on the type of model or what the model is describing, and some of the uses of mathematical models are: An error occurred trying to load this video. stream Figure 4: Use this exponential growth graph to predict the population for Example 3. You can compare income and life expectancy in a country. 34) Cesaro Summation: Does 1 1 + 1 1 = 1/2?. 25) Eulers 9 Point Circle. 13 40 Mathematics Internal Assessment Ideas. 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. 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. 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) 6) Batman and Superman maths how to use Wolfram Alpha to plot graphs of the Batman and Superman logo. 1) The harmonic series: Investigate the relationship between fractions and music, or investigate whether this series converges. 15. Youd be better off carefully thinking about what youre going to do and what interests you, and what would make you have the most personal engagement and the ease of access to data that you need. 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. Simplifying this expression gives the final answer of {eq}v_f = 800 {/eq} m/s. It's wise to form your own opinions based on substantive evidence. The following ' SUVAT' displacement formula and the Kinematics initial velocity formulae will be used as a medium. 29) The Riemann Hypothesis one of the greatest unsolved problems in mathematics worth $1million to anyone who solves it (not for the faint hearted!). Maths Exploration (IA) ideas 28452 March 19, 2021 Predicting fire spread in wildlife fields: This mathematical model of fire presented in this paper offers for the first time a method for making the quantitative evaluation of both rates of spread and fire intensity in fuels that qualify for the assumptions made on the model. Equation 3: y=sin(659.26/440x) This is an area of maths that is not strictly bound to the number! math ia (and 1 more) Submitted January 14, 2018 Type I: Sequences Grade awarded: 18/20 Updated July 17, 2009 Type II: Tide modelling Grade awarded: 16/20 Updated July 17, 2009 Type I: Roots of i Grade awarded:18 Updated December 2, 2009 Type II: Bloodstream Grade: Updated July 18, 2009 You may also include any personalised problem statements and explain how you aim to achieve a solid investigation on the topic. Login. Knigsberg bridge problem: Using networks to solve problems. q&}@{S$*!6g)pOK`/N"AbhIrW1Xllkz;)F F!vtPp7XQ>lTk<3D~)xGZ_L29=`0GP?w Predict how the water is going to come out the cylinder. It covers what mathematical modeling is as well as different types of models in math. 19) Natural logarithms of complex numbers. Transitioning back into the mindset of full days at school can be overwhelming. 14, Advice from an IB Examiner on topics you should avoid. Monty Hall problem: How does Bayesian probability work in this real-life example, and can you add a layer of complexity to it? Two variable function . Many IB students find it hard to study mathematical concepts. 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. 1) Modular arithmetic This technique is used throughout Number Theory. Topics that rely more on natural sciences such as physics and put less emphasis on Math. 13) The Tusi couple A circle rolling inside a circle. 13 chapters | You should include relevant graphs, tables, and diagrams. It involves understanding the modulo operation. I will now look at different chords to see if this conjecture holds true. newsletters and promotional offers. Familiarise yourself with the steps below, and then dive into your chosen topic. 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. 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. It is now used as a saying to represent something impossible. 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. 15) Modelling epidemics/spread of a virus what is the mathematics behind understanding how epidemics occur? An example of modeling is presenting the rate at which a country's population changes relative to external factors. Can you find the loop of infinite sadness? Mathematical models are used in nearly every field of mathematics, but what is model in math? Start with the IA format! This is a written assignment in which students are required to investigate a specific area of math subject. 12) Four colour map theorem a puzzle that requires that a map can be coloured in so that every neighbouring country is in a different colour. 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. This may indicate the start of a pattern. Equation 2: y=sin(587.33/440x), Equation 1: y=sinx The IB is measuring relevancy by checking that you only included maths that is directly intended to answer the research question. Equation 3: y=sin(739.99/440x) Math models have been around for centuries, and they can describe everything from moving objects to chemical formulas. 48) When do 2 squares equal 2 cubes? The three main types of mathematical models are equations, graphs, and computer modeling, and each of these can be used to learn about different aspects of a system. Look at the inherent probabilistic nature of the universe with some quantum mechanics. 31) The Shoelace Algorithm to find areas of polygons. 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. Use your calculus to get another areas of mathematics. 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. Copyright 2023 Nail IB. How accurately can be approximate irrationals? As with all assessments, you also need to include a solid conclusion that summarises the research and work youve done. ScienceFusion Intro to Science & Technology Unit 1.1: What Is Science? succeed. Game theory as it is easy and overdone. Can all fractions with a numerator of 2 be written as 2 Egyptian fractions? 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. This problem asks you to explore a sliding ladder. As a member, you'll also get unlimited access to over 84,000 Topics will group the questions, and youll probably find answers at the back of your textbook. Are you getting ready to present your Math IA? Pythagorean triples: Can you find patterns in what numbers form a pythagorean triple? 1. 5 Are there functions which plot any polygons? 6) Mandelbrot set and fractal shapes: Explore the world of infinitely generated pictures and fractional dimensions. 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 By following this tried and tested structure for your math IA, each student will be able to present their findings consistently and optimally. 10) Tangrams: Investigate how many different ways different size shapes can be fitted together. 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. 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. Related rates are used to find how two rates of change are related. So there you have it. 37) Generating e through probability and hypercubes. Equations are one form of mathematical modeling, and the physical kinematic equations relate velocity, distance traveled, acceleration, and time. 22) The Folium of Descartes. Personal connection and engagement with the subject matter are key. Interesting: The chosen topic needs to be exciting enough to elicit not only your interest but that of your audience. You can take any data and try to figure out whether it is normally distributed or not. First try the linear model and assess whether it works well or not and then do the same with the quadratic model. 23) Measuring the Distance to the Stars. 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. Solving math word problems. For this reason, this theory does not only apply to sound coming to electronic instruments but every kind of instrument. A chemical formula is a mathematical model that relates the relative amounts of composite chemicals in a molecule. To find out more, see our. By submitting this form, I agree to the data entered being used by Nail IBNSW for sending 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. 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