Lacsap’s Fractions IB Math SL Internal Assessment Paper 1 Lacsap’s Fractions Lacsap is Pascal spelled backward. Therefore‚ Pascal’s Triangle can be used practically especially with this diagram. (Diagram 1) This diagram is of Pascal’s Triangle and shows the relationship of the row number‚ n‚ and the diagonal columns‚ r. This is evident in Lacsap’s Fractions as well‚ and can be used to help understand some of the following questions. Solutions Describe how to find
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Introduction In this task‚ I will develop model functions representing the tolerance of human beings to G-force over time. In general‚ humans have a greater tolerance to forward acceleration than backward acceleration‚ since blood vessels in the retina appear more sensitive in the latter direction. As we all know‚ the large acceleration is‚ the shorter time people can bear. Using the data shown in the task and Mat lab analysis‚ we can get several model functions to represent the tolerance
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Predictability of Social Media Usage to Grade Averages IB Math Studies Spring 2013 Table of Contents: Introduction/Purpose……………………………………………………………..p.3 Data Collection Method……………………………………………………….....p. 3 - 4 Data Analysis: Chi-Squared Statistic Frequency Table…………………………………………………………p. 4 - 5 Contingency Table……………………………………………………….p. 5 – 6 Chi – Squared Statistic…………………………………………………...p. 7 Degrees of Freedom………………………………………………………p. 7 Critical Value……………………………………………………………
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Purpose of Investigation The purpose of this investigation is to find out the general trends of the Olympic gold medal height each time the event is held. It also could be used to predict the next gold medal height in the upcoming Olympic events. We could know as well what functions can be used to plot the graphs. People could also analyze the pattern of rise or decrease in height of the winning height in the Olympic game. This investigation also allows future participants to find out
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In Lacsap’s Fractions‚ when looking for a general pattern for the numerator‚ it can be noted that it does not increase linearly but exponentially. Numerators are 3‚6‚10‚ and 15‚ each preceding numerator added by one plus the row number. Using this general statement it can be concluded that the numerator in the 6th row is 21 (15+6)‚ and 28 for the 7th. Generating a Statement for the Numerator: To generate an equation for the numerator of the fraction‚ the fraction data must be organized and
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1. (a) Let A be the set of all 2 × 2 matrices of the form ‚ where a and b are real numbers‚ and a2 + b2 0. Prove that A is a group under matrix multiplication. (10) (b) Show that the set: M = forms a group under matrix multiplication. (5) (c) Can M have a subgroup of order 3? Justify your answer. (2) (Total 17 marks) 3. (a) Define an isomorphism between two groups (G‚ o) and (H‚ •). (2) (b) Let e and e be the identity elements of groups G and H respectively. Let f be
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Exploration of Lacsap’s Fractions The following will be an investigation of Lacsap’s Fractions‚ that is‚ a set of numbers that are presented in a symmetrical pattern. It is an interesting point that ‘Lacsap’ is ‘Pascal’ backwards‚ which hints that the triangle below will be similar to “Pascal’s Triangle”. 1 1 1 1 1 1 1 1 1 1 There are many patterns evident in this triangle‚ for instance I can see
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Algebraic Fractions An algebraic fraction can always be expressed in different‚ yet equivalent forms. A fraction is expressed in its simplest form by cancelling any factors which are common to both the numerator and the denominator. Algebraic Fractions can be simplified by cancelling down. To do this‚ numerators and denominators must be fully factorised first. If there are fractions within the numerator/denominator‚ multiply by a common factor to get rid of these and create an equivalent fraction:
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1. Report Writing Check List The written report should have the following sections‚ each starting on a new page: Title page (mandatory) Title of assignment Unit number and name Student’s name Date of submission Submission or Resubmission Name of assessor Table of contents (mandatory) Use page numbers Title page‚ table of contents page and appendices do not need page numbers. Introduction (mandatory) The introduction describes the background‚ purpose and scope of the assignment; it explains
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IB Maths SL TYPE I Lacsap’s Fractions Portfolio Lacsap’s fraction Introduction: Lacsap’s fraction is a symmetrical triangle that has the following pattern in the first five rows The shape is similar to Pascal triangle. It has the same quantity of symmetrical triangle as Pascal triangle. And Lacsap is the inverse alphabet order of Pascal. These make me think about Pascal triangle and I made an assumption that elements in Lacsap triangle may have the same relationship as in Pascal triangle
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