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International Baccalaureate: Maths

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  1. Maths IA Type 2 Modelling a Functional Building. The independent variable in this investigation is the height of the building. The maximum volume of a cuboid under the roof depends on the height of the roof, which is the dependant variable.

    The intercept will be modelled at the maximum height of the parabola Let intercept ? The roof is at a maximum turning point ? ? The form of the model quadratic is: To solve for , substitute in the known fixed values (the root) for and (36,0): Substitute all these values into the general form of the quadratic to obtain the general formula of the roof: Modelling at Minimum Height: Below in Fig 1 is a model of the roof structure with the minimum height of 36m, where the fa�ade is designed at the width.

    • Word count: 3051
  2. Mathematics Higher Level Internal Assessment Investigating the Sin Curve

    It can be seen that when you have a fraction that is smaller than 1 for your value the height of the sine curve ill decrease to the height of . On the other hand, having a bigger fraction than 1 increases the height of the sine curve to the value as can be seen from Graph 1.2. From these two graphs, it can be said that when is bigger than 1 the graph stretches outwards, whereas when is smaller than one the graph will stretch inwards.

    • Word count: 3010
  3. Maths Project. Statistical Analysis of GCSE results at my secondary school summer 2010

    U 0 This data is part of the main data showing just the English Language & Literature GCSE points for each student. I am going to compare the total score for each child against their alphabetical order numbering to see if we get any correlation and to prove if my hypothesis is right or wrong. Scope: National Curriculum Year Export Date : 10/06/2011 Name Entries English Language & Literature FEMALE GENDER MALE GENDER Total score Alphabetic Position Number of Results 181 Ab 9 34 m 34 181 Ab 9 40 m 40 180 An 8 28 m 28 179 Ar

    • Word count: 5192
  4. Stellar Numbers. In this task geometric shapes which lead to special numbers will be considered.

    Sequence and n2 1 2.5 4 5.5 7 8.5 10 11.5 Second difference This second difference illustrates the value for 'b' which is equal to. However the value of 'c' has not yet been determined. It was calculated using an example: Using n=2: n2 + n + c = 6 (2)2 + (2) + c = 6 5 + c=6 c=1 From the example we can verify that 'c' must be equal to 1 to reach the desired figure. To check that these are the correct values two more examples were used: --> Using n=5 n2 + n + 1 = 21 (5)2 + (5)

    • Word count: 5627
  5. Math portfolio: Modeling a functional building The task is to design a roof structure for the given building. The building has a rectangular base 150 meters long and 72 meters wide. The height of the building should not exceed 75% of its width

    I know that the length of the cuboid is 150 meters. So I have to find out the height and the width of the cuboid. The diagram below shows a cuboid which is fitted inside the curve roof structure. Let ABCD be the largest possible cuboid which can be fitted inside this curved roof structure I will let "2V" be the width of the cuboid and "H" be the height. The parabola is symmetrical structure, so do the cuboid, so I have taken the width as "2V" that is the width "V" is on the left side and "V" is on the right side of the axis of symmetry of the parabola.

    • Word count: 3774
  6. Fishing Rods

    other > The overall length of the fishing rod - it cannot be negative or too long as this will reduce efficiency The data points given above can then be plotted onto a graph using Microsoft excel. Using Matrix methods we can find a quadratic function to model the situation from the given data points: A quadratic equation is in the form. As there are 3 unknown variables (a, b, c) we can create a 3 x 3 matrix and a 3 x 1 matrix to model the given information.

    • Word count: 3755
  7. Ib math HL portfolio parabola investigation

    In the 1st part of my portfolio I will only consider a>o, giving me a minimum point for each parabola rather than a maximum. The 2nd would include values of a < 0. We know that for a graph to have its turning point in the first quadrant and a>0, it should have no real roots. This means that the parabola would not cut with the x-axis and its determinant would be greater than zero. Hence: ,where a >0 .

    • Word count: 3129
  8. Artificial Intelligence & Math

    claim that exploitations of the Internet have doubled from 1999. If such a trend continues the Internet will be too unsafe to be used without taking an unreasonable risk. As the Internet becomes more commonly used as a tool in criminal, terrorist and cyber terrorist activity governments around the world are beginning to re-evaluate their stance on its surveillance (Miller 2001,Kane 2002). Some trends but no developments. The ISP, provider of direct access to the Internet backbone, is essential in the surveillance. All Australian use of the Internet will be continually monitored by automated ISP computer mainframes for specific security flags.

    • Word count: 5042
  9. Population trends. The aim of this investigation is to find out more about different functions that best model the population of China from 1950 to 1995.

    Doing so has made the health care system be more effective which leads to more prevention of diseases and death. The investigation consists in finding a model that fits as close as possible the data given. This can be useful because the model can determinate how, if the parameters stay the same, the population numbers will be like in the future. However as parameters do change the models that are found will not be very precise to what the future could be, the past that is given can be modeled but that doesn't mean it will be similar to it.

    • Word count: 4397
  10. Math 20 Portfolio: Matrix

    The variables are as follows: tn = triangular number (numbers of dots) n = the stage In order to modify the expression for the previous series of 100 consecutive positive numbers into the general formula for the triangular pattern, we can simply replace the number 100 within the expressing (50)(100+1) by n. The reason for which is because within the context of the series of 100 consecutive numbers, there is 100 terms and therefore the 100th stage. Also, as you can see the 50 within the expression is derived by dividing 100 by 2.

    • Word count: 3011
  11. The speed of Ada and Fay

    Furthermore, after finding the time of Ada running 100 meters, I need to define the speed Ada runs in the experiment. To find the velocity, I will apply an equation that I use both in Physic and in Mathematic, which is . Therefore, by plugging the "s" and "t" values, then the result of the calculation will be the velocity. The calculation will be as follow, After calculation, I found that the velocity of Ada is 5.988 m/s. Due to further easier calculation; I decide to round up Ada's speed to one significant figure.

    • Word count: 3314
  12. This essay will examine theoretical and experimental probability in relation to the Korean card game called Sut-Da. First, a definition of probability and how it is used in general life will be examined. Each hand of Sut-Da provides the theore

    Hence came to decision to make this as my extended essay topic. I will first introduce what is probability and the game called "Sut-Da". Everyone has different definition for probability and it depends on which perspective the people looks from, but generally, probability is the measure of how likely for an event to occur. Throughout this essay, these two games will be set under few conditions. These conditions are; 1. Number of players are 2 2. The deck is shuffled 10 times after the game in order to create a fair deck every round My research question becomes: What are the possibilities of winning in "Sut-Da" and how does the theoretical value compare with the experimental value?

    • Word count: 5446
  13. Investigating Divisibility

    = n (n + 1) (n - 1) divisible by 3? When n = 1 n (n + 1) (n - 1) = 1 (2) (0) = 0 As 0�3 = 0, P(n) is divisible by 3 when x = 3 and n = 1 Assume n = k is correct k (k + 1) (k - 1) = k (k2 - 1) = k3 - k = 3M (where M s any natural number) Then considering n = k + 1 (k + 1) {(k + 1) + 1} {(k + 1) - 1} = (k + 1)

    • Word count: 3562
  14. Math Studies I.A

    We cannot say what strong or weak correlation is because everyone describes it differently. Hence, we can only measure the degree of correlation in terms of a numerical value. We will then test the significance of the value based on our selected data. Background information Systemic Information/Measurement x Y xy Countries GDP per capita (PPP) Life expectancy Afghanistan 800 43.8 35040 640000 1918.44 Algeria 7,000 72.3 506100 49000000 5227.29 Andorra 42,500 82.67 3513475 1806250000 6834.3289 Anguilla 8,800 77.46 681648 77440000 6000.0516 Argentina 14,200 75.3 1069260 201640000 5670.09 Aruba 21,800 74.2 1617560 475240000 5505.64 Austria 39,200 79.21 3105032 1536640000 6274.2241 Bahamas,

    • Word count: 6579
  15. Math Portfolio: trigonometry investigation (circle trig)

    By using theta, if it goes counter clock wise it will become positive while going in the direction of clockwise it becomes negative. Further more, based on our knowledge on Math Honor 1, we always know that hypotenuse in right triangles are the longest of among three sides. And thus since R is the hypotenuse, as explained before x and y can be any number as long as it is less than the radius. Therefore leading radius R always positive and real number.

    • Word count: 7447
  16. Investigating ratio of areas and volumes

    Area A is now the area contained between the graph and the x-axis between the arbitrary points x = an and x = bn and area B is the area contained between the graph and the y-axis between the arbitrary points x = an and y = bn. By this the ratio area A: area B can more readily be investigated. Area A is the area contained in between the graph of y = x1/n and the x-axis between the two arbitrary points x = an and x = bn such that a<b.

    • Word count: 4319
  17. Logan's logo

    X 0 1 2 3 4 5 6 7 8 9 10 Y 3.45 1.69 1.35 2.00 3.47 5.12 6.85 8.25 8.95 8.71 7.15 Table 2: observed data points for the curve g(x) The points of these curves are graphed on the following graph: Graph 1: Observed points of logo In the graph above the points were plotted in a coordinate system with a domain of and a range of, this was done according to the size of the diagram of the logo given.

    • Word count: 4567
  18. Math IA- Type 1 The Segments of a Polygon

    Therefore 62.0 cm2/19.1cm2 = 13:4 The ratio between the areas of the equilateral ?ABC to ?DEF when the segment divides the side in the ratio 1:3 is 13:4. Ratio of Sides = 1:4 For ?ABC = 62.1 cm2 For ?DEF = 26.6 cm2 In order to find the ratio, one needs to divide the area of ?ABC by the area of the ?DEF which will give one the ratio of the area of the bigger triangle to the smaller triangle.

    • Word count: 3048
  19. Math Portfolio Type II

    Therefore, un = 60,000 ---------------------- (3) * r is the growth factor as mentioned in the description. As found out in (3) that un = 60,000 which shows that the population has reached its long term sustainable limit where population is stable. Therefore, rn = 1 ---------------------- (4) So the second ordered pair (un , rn) as shown in (3) and (4) would be (60000,1) A general linear equation has the form (y-y1) = m(x-x1) where y and x are variables, y1 and x1 are the coordinates of a point on the curve and m is the slope of the curve.

    • Word count: 5981
  20. Barbara & Allen's Compound Interest

    = 1000(1+ 0.12) 10= 1000(1.12) 10� 1000(3.10585)� 3105.85 t=20, A= 1000( 1+ 0.12/1)(1)(20) = 1000(1+ 0.12) 20= 1000(1.12) 20� 1000(9.64629)� 9646.29 t=30, A= 1000( 1+ 0.12/1)(1)(30) = 1000(1+ 0.12) 30= 1000(1.12) 30� 1000(29959.92)� 29959.92 *Final answers rounded to the nearest hundredth in order to comply with the general money standard of cents. Table 1 Alan's Investment of $1000 at an Interest Rate of 12% Per Year Compounded Yearly t 0 1 2 5 10 20 30 A 1000 1120 1254.40 1762.34 3105.85 9646.29 29959.92 Table 1 represents Alan's investment of $1000 at an interest rate of 12% per year over a period of 1, 2, 5, 10, 20, and 30 years.

    • Word count: 3492
  21. Math HL portfolio

    - (- ) = 0.4235 - 2.4235= 2 The fourth parabola I used in the form of y=ax�+bx+c is Y=2x�-3x+1.2 = {0,26893} = {0,36754} = {1,6325} = {2,2311} D= - =( - ) - (- ) = 0.09861 - 0.59861= 0.5 The fifth parabola I used in the form of y=ax�+bx+c is y=2.5x�-3x+1 = {0,2254} = {0,3101} = {1,2899} = {1,7746} D= - =( - ) - (- ) = 0.0847 - 0.4847= 0.4 The sixth parabola I used in the form of y=ax�+bx+c is y=?x�-3x+1 = {0,23457} = {0,3417} = {0,93154} = {1,357} D= - =( - )

    • Word count: 4480
  22. The Population of Japan and Swaziland

    The results of these trials will then be averaged. I'll demonstrate this process using the first two consecutive values in the data table with the use of my TI-84 Plus Silver Edition Graphics Display Calculator (GDC). To begin with, I will use the two population values of 100 and 112.8. Since the values are taken from the year 1911 and 1921 the change will be 10. 1.01 is the approximate rate of change in population between the years 1911 and 1921. I will keep repeating this process using each group of two successive data values in the table.

    • Word count: 3743
  23. The segment of a polygon

    and the other two sides of PB and QC is 1.5 cm (obtained from ). The side of the smaller (inner) triangle is 3.32 cm. It has the ratio of 1.81:1 or 1:0.55 to the side length of the outer triangle (outer:inner) . The outer equilateral triangle's area obtained from the "Geometer's Sketchpad" is 15.59 cm� while the inner equilateral triangle's area is 4.77cm�. The sketchpad ratio of the two area is 3.268:1 or 13:4 (outer : inner). SIDES RATIO 1 : 4 This is the results of the drawings of the ratio 1:4 (length of sides).

    • Word count: 3050
  24. Math IA Type 1 In this task I will investigate the patterns in the intersection of parabolas and the lines y = x and y = 2x.

    First I will the graph the functions then I will use my GDC to find the four intersections points as illustrated on the graph.[example 1] Graph showing the equations: [In blue] [In brown ] [In green] Example 1 ] I will find the values for x1, x2,x3,x4 for the function, using the 'calculate intersect' feature on a GDC[ TI - 84 plus] 2. Now I will look at different parabolas of the form with values of a greater than 1.

    • Word count: 3001
  25. Math IA type 2. In this task I will be investigating Probabilities and investigating models based on probabilities in a game of tennis.

    Part 1 The ratio of the points won by Adam and Ben are 2:1 respectively. Therefore Adam wins twice as many points as Ben does. Therefore Adam wins of the points and subsequently Ben wins of the points. The distribution of X, the number of points won by Adam would be derived by using the binomial probability function and substituting variables and constants to arrive at an appropriate model for the distribution of X, the number of points won by Adam. The distribution chosen is the binomial probability distribution because in the case of the games of tennis, * There is a repetition of a number of independent trials in which there are two possible results, success [the event occurs ex.

    • Word count: 4036
"

"If I have seen further, it is by standing on the shoulders of giants."

-Isaac Newton

(IB) diploma students are required to take at least one course in mathematics. This furthers your IB education in two major ways: it teaches you to think critically about problems - even those you encounter outside mathematics - and it enhances your international credentials, since maths is a true lingua franca.

That said, between the symbols and greek letters, there's still a lot of English to be written. If your writing needs a bit of help, never fear. You can brush up with Marked by Teachers' collection of IB mathematics papers. Study the teacher-marked and peer-reviewed assignments to learn how to write papers that earn top marks. Before long, excellent writing will come naturally to you.

IB students who excel in maths will find themselves well-placed to choose a universitydegree from within the physical sciences or mathematical and computer sciences.

"

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