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International Baccalaureate: Maths
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Graph 1: The winning men?s high jump heights in Olympic Games for years between 1932 and 1980. (Excluding 1940 and 1944) The x-axis represents the year of the Olympic Games. This begins at 1932. The y-axis represents the Gold Medalists high jump height in centimeters. Unfortunately, there are parameters to this graph. There were no Olympic Games in 1940 and 1944 due to the war. This meant that the data is not consistent as we are missing 2 years of Gold Medalist heights. The graph also only shows the heights of the 1932 to 1980 Olympic Games which is a small section of the overall Olympic Games data, beginning in 1986.
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work towards and so may not have had the same improvement in their skills as if the Olympic Games had continued to happen in even four year intervals. This may explain why the height of the winning high jump in 1948 is less than that of the winning high jump at the previous Olympic Games in 1936. For this reason I have decided to tests the various models for the data for both 1932 and 1936 included and excluded in the graphs showing the data gathered between 1932 and 1980.
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Stellar Numbers. In this folio task, we are going to determine difference geometric shapes, which lead to special numbers.
Finally, check it with the TI-84 calculator. After that, we could consider the special numbers for the geometric shapes in the task. Results/ Analysis Now, a diagrams show a triangular pattern of evenly spaced dots. The numbers of dots in each of them are (1, 3, 6, 10 and 15) and those numbers can be known as the square numbers. By seeing the diagram, we can know that one more row of dots will be added by the general term number increase 1, the new row will have 1 more dots then the pervious row.
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Then, I will try to link the patterns discovered to some pre-established mathematical concepts, such as the Maclaurin series. ________________ Part I Firstly, let us look at the sequence of terms when x=1 and a=2, as the value of n increases. n t n S n 0 1 1 1 0.693147 1.693147 2 0.240227 1.933374 3 0.055504 1.988878 4 0.009618 1.998496 5 0.001333 1.999829 6 0.000154 1.999983 7 0.000015 1.999999 8 0.000001 2.000000 9 0.000000 2.000000 10 0.000000 2.000000 When n=10, we can see that S n is equal to 2.000000.
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The investigation given asks for the attempt in finding a rule which allows us to approximate the area under a curve (I.e. between the curve and the x-axis) using trapeziums
Through the values on the graph, one is able to determine the variables. The second task assigned to this investigation is to increase the amount of trapeziums from the initial two trapeziums to five trapeziums, and then find a second approximation for the area. The five trapeziums use an identical method as the previous question. Using the method shown, the areas of each trapezium will be calculated and the values will then be added together to obtain the overall approximation of the area.
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The purpose of this investigation is to explore the various properties and concepts of matrix cryptography.
Mathematical Modelling and Problem-solving The specific features are as follows: MMP1 Application of mathematical models. MMP2 Development of solutions to mathematical problems set in applied and theoretical contexts. MMP3 Interpretation of the mathematical results in the context of the problem. MMP4 Understanding of the reasonableness and possible limitations of the interpreted results, and recognition of assumptions made. MMP5 Development and testing of conjectures, with some attempt at proof. MMP6 Contribution to group work. Communication of Mathematical Information The specific features are as follows: CMI1 Communication of mathematical ideas and reasoning to develop logical arguments. CMI2 Use of appropriate mathematical notation, representations, and terminology.
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