#### LAcsap fractions - it is clear that in order to obtain a general statement for the pattern, two different statements will be needed

Jonghyun Choe March 25 2011 Math IB SL Internal Assessment – LASCAP’S Fraction The goal of this task is to consider a set of fractions which are presented in a symmetrical, recurring sequence, and to find a general statement for the pattern. The presented pattern is: Row 1 1 1Row 2 1 32 1Row 3 1 64 64 1Row 4 1 107 106 107 1Row 5 1 1511 159 159 1511 1 Step 1: This pattern is known as Lascap’s Fractions. En(r) will be used to represent the values involved in the pattern. r represents the element number, starting at r=0, and n represents the row number starting at n=1. So for instance, E52=159, the second element on the fifth row. Additionally, N will represent the value of the numerator and D value of the denominator. To begin with, it is clear that in order to obtain a general statement for the pattern, two different statements will be needed to combine to form one final statement. This means that there will be two different statements, one that illustrates the numerators and another the denominators, which will be come together to find the general statement. To start the initial pattern, the pattern is split into two different patterns; one demonstrating the numerators and another denominators. Step 2: This pattern demonstrates the pattern of the numerators. It is clear

#### Maths Project. Statistical Analysis of GCSE results at my secondary school summer 2010

Statistical Analysis of GCSE results at my secondary school summer 2010 Introduction For my maths project, I requested for the summer 2010 GCSE Exam results from St Bede's secondary school Exam moderator; so as to analyse it. Having received the data, I made the names of the students anonymous, to keep their information private. I kept the data in alphabetical order so that my hypothesis would make sense. I identified the gender for the 186 students that wrote the exam; which took a lot of time to get the data ready and to make it private. I had to search on the internet for the equivalent GCSE grade points so that I could change the grades to points so as to have a good set of data for my analysis. My hypothesis for my maths project base on the GCSE result summer 2010 is the lower down you are in the alphabetical order of the registration the less you do well in the exams and by that having low GCSE results at the end, while the higher up you are in the register the better you do and having a good GCSE result at the end. So by my hypothesis the graphs that I am going to produce base on my data results should have a negative trend (line of best fit) and for it to have a negative trend showing my hypothesis, what I did was numbered the students starting from the last student on the alphabetical order in the register numbering him/her number 1 and numbering the first

#### The purpose of this investigation is to explore the various properties and concepts of matrix cryptography.

Danny Aburas ________________ Year 12 Maths Studies ________________ ________________ Investigation ________________ ________________ ________________ ________________ Matrix Cryptography ________________ Topic: Working with Linear Equations and Matrices Subtopics: 3.3 Matrices 3.4 The Inverse of a Matrix A completed investigation should include: . an introduction that outlines the problem to be explored, including its significance, its features, and the context 2. the method required to find a solution, in terms of the mathematical model or strategy to be used 3. the appropriate application of the mathematical model or strategy, including . the generation or collection of relevant data and/or information, with details of the process of collection 2. mathematical calculations and results, and appropriate representations 3. the analysis and interpretation of results 4. reference to the limitations of the original problem . a statement of the results and conclusions in the context of the original problem 2. appendices and a bibliography, as appropriate. Learning Requirements Assessment Design Criteria Capabilities 1. understand fundamental mathematical concepts, demonstrate mathematical skills, and apply routine mathematical procedures 2. use mathematics as a tool to analyse data and other information elicited

#### Artificial Intelligence & Math

International Baccalaureate Information Technology in a Global Society Portfolio Big Brother is watching: what are the impacts on society? (Politics and Government) June 2003 Student No. 1 XY International School News Item: Mackenzie, Kate 2002, Data-spying deal between police, ISPs, http://australianit.news.com.au/articles/0,7204,4180888%5E15306%5E%5Enbv%5E,00.html [May 2003] Presentation of the Issue Whilst the Internet has become a valuable resource for much of the Australian community, it has also been misused, and has led to numerous Internet assisted crimes against families and businesses alike. Dubbed 'The Telecommunications Interception Amendment Bill', the new law will provide the Government with greater access to Internet surveillance through the cooperation between ISPs and Australian law enforcement agencies (Mackenzie 2003). Australian ISPs are now required to aid in the interception of sensitive data and are obliged to work openly with government departments, such as federal police and ASIO (Australian Security Intelligence Organisation). The amendment bill proposes to counter the increasingly prevalent problem of electronic criminal activity by providing more practical, widespread and efficient surveillance over the Internet's usage. By closely monitoring Internet usage, the Government aims to intercept criminal activity before damage can be dealt.

#### Math Studies - IA

IB MATHEMATICAL STUDIES Internal Assessment "An investigation into the value of Ryder Cup as a reflection of the US and Europe's comparative strength in the sport of golf." Peter Frederiksen Svane St. Mary's International School IB Candidate Number: 000134 - 039 March 10th, 2008 INTRODUCTION The Ryder Cup takes place every other year in September, and is supposed to determine whether Europe or the US is the best in the sport of golf. Each side is represented by twelve golf players, who get the chance to play against each other over the course of three days. Contrary to regular tournaments, the Ryder Cup is played in a match play format1 rather than using stroke play2. The question therefore arises if the Ryder Cup is a true reflection of which region (US or Europe) has the best group of golfers. Are Europeans really better golfers than Americans, since they have won all the meets since the new millennium? To put a final answer to this debate, the investigation will focus on performances in regular tournaments, in which the Ryder Cup players have all competed, and their performance in the Ryder Cup. Various mathematical processes will be carried out within the scope of relevance in order to reach a conclusion to the mentioned task. The performance of the Ryder Cup team players in regular stroke play tournaments on their seasonal tours, where the players come in direct

#### Develop a mathematical model for the placement of line guides on Fishing Rods.

Math Summative: Fishing Rods Fishing Rods A fishing rod requires guides for the line so that it does not tangle and so that the line casts easily and efficiently. In this task, you will develop a mathematical model for the placement of line guides on a fishing rod. The Diagram shows a fishing rod with eight guides, plus a guide at the tip of the rod. Leo has a fishing rod with overall length 230 cm. The table shown below gives the distances for each of the line guides from the tip of his fishing rod. Guide Number (from tip) 1 2 3 4 5 6 7 8 Distance from Tip (cm) 10 23 38 55 74 96 120 149 Define suitable variables and discuss parameters/constraints. Using Technology, pot the data points on a graph. Using matrix methods or otherwise, find a quadratic function and a cubic function which model this situation. Explain the process you used. On a new set of axes, draw these model functions and the original data points. Comment on any differences. Find a polynomial function which passes through every data point. Explain you choice of function, and discuss its reasonableness. On a new set of axes, draw this model function and the original data points. Comment on any differences. Using technology, find one other function that fits the data. On a new set of axes, draw this model function and the original data points. Comment on any differences. Which of you

#### SL Math IA: Fishing Rods

Math Summative: Fishing Rods Fishing Rods A fishing rod requires guides for the line so that it does not tangle and so that the line casts easily and efficiently. In this task, you will develop a mathematical model for the placement of line guides on a fishing rod. The Diagram shows a fishing rod with eight guides, plus a guide at the tip of the rod. Leo has a fishing rod with overall length 230 cm. The table shown below gives the distances for each of the line guides from the tip of his fishing rod. Guide Number (from tip) 1 2 3 4 5 6 7 8 Distance from Tip (cm) 10 23 38 55 74 96 120 149 Define suitable variables and discuss parameters/constraints. Using Technology, pot the data points on a graph. Using matrix methods or otherwise, find a quadratic function and a cubic function which model this situation. Explain the process you used. On a new set of axes, draw these model functions and the original data points. Comment on any differences. Find a polynomial function which passes through every data point. Explain you choice of function, and discuss its reasonableness. On a new set of axes, draw this model function and the original data points. Comment on any differences. Using technology, find one other function that fits the data. On a new set of axes, draw this model function and the original data points. Comment on any differences. Which of you

#### sunrise over newyork

IB Standard Level Type II Math Portfolio Sunrise over New York Student Names: Nam Vu Nguyen Set Date: Thursday, December 20, 2007 Due Date: Wednesday, January 09, 2008 School Name: Father Lacombe Senior High School Teacher: Mrs. Gabel I CERTIFY THAT THIS PORTFOLIO ASSIGNMENT IS ENTIRELY MY OWN WORK Nam Vu Nguyen: ___________________________________ IB Standard Level - Type II - Math Portfolio Sunrise over New York Mathematics is a study of the concepts of quantity, structure, space and change. It is a type of science that draws conclusions and connections to the world around us. Mathematicians would call math a science of patterns and these patterns are discovered in numbers, space, science, computers, imaginary abstractions, and everywhere else. Mathematics is also found in numerous natural phenomena's that occurs around us. Today math is used all around us and is applied to many educational fields, through this people have become inspired to discover and make use of their mathematical knowledge which will then lead to entirely new disciplines. Math is present in wherever there are difficult problems that involve quantity, structure, space or change; such problems appear in various forms such as commerce, land measurement and especially astronomy. The purpose of this paper is to examine the data on the times of the sunrise over New York, over a period of 52

#### IB MATH TYPE I Portfolio - LOGARITHM BASES

LOGARITHM BASES ________________ Purpose: My purpose for this investigation was to find the general statement that expresses logabx, in the terms of c and d. I was able to achieve this goal through the process of finding the expression for the nth term in various different sequences. In the beginning stages of my investigation I came across the sequence of Log28, Log48, Log88, Log168, Log328....... While I was looking at this sequence I came to the realization that the base of the log form was increasing at a constant pattern. I realized that the base of 2 was being raised to the power of the term number. Therefore the second term has a base of 4 due to the fact that 2 raised to the power of 2(term number) equals 4. Even though the base changes the 8 stays constant and this also means that I would be able to continue the pattern. 6th term = log(2˄6)8 7th term = log(2˄7)8 = log648 = log1288 After continuing the pattern I realized the next step would be to solve this problem and discover what exponent we need to raise to base to, in order to achieve the answer of 8. So I decided to change my pattern from log form into exponential form. 2x=8, 4x=8, 8x=8, 16x=8, 32x=8, 64x=8, 128x=8 After successfully converting into exponential form I decided to take this a

#### Tide Modeling

felpTide Modeling . Using Microsoft Excel, plot the graph of time versus height. Describe the result using the terminology you have acquired in the study of circular functions. In order to come up with a plot graph for the bay of Fundy in Noca Scotia, Cana it was necessary to use Microsoft Excel and the data from www.lau.chs-shc.dfo-mpo.gc.ca.com. In order to plot the graph in excel all of the data had to be entered in the spreadsheet. Once that was done a scatter graph was created. Once it was done it was possible to analyze the graph. The first thing that is possible to notice is that this is a periodical graph. However, the graph is not completely periodical since the lines don't always have the same height. Sometimes it is greater or lower. This can be attributed to the fact that it is a real life situation. Therefore, it would not be expected for it to be perfect. However, the graph is still periodical since it follows the same shape throughout. 2. Use your understanding of circular functions and their transformations to develop a mathematical model for the behavior noted in the graph. Explain your method and reasoning in detail. In order to come up with the equation I had to come up with a series of averages. This was necessary since the graph is not completely periodical. In order for me to find the vertical translation of the graph, meaning how much the