Lacsap’s Fractions IB Math SL SL Type 1 December 11‚ 2012 Lacsap’s Fractions: Lacsap is Pascal backwards and the way that Lacsap’s fractions are presented is fairly similar to Pascal’s triangle. Thus‚ various aspects of Pascal’s triangle can be applied in Lacsap’s fraction. To determine the numerators: To determine the numerator (n)‚ consider it in relation to the number of the row (r) that it is a part of. Consider the five rows below: Row 1
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Math Portfolio HL- Type 1 INVESTIGATINGRATIOS OF AREAS AND VOLUMES The purpose of this portfolio is to investigate the ratios of areas and volumes when a function y= xn is graphed between two arbitrary parameters x=a and x=b such that a‹b. Task 1 The general formula to find area A is [pic] The general formula to find area B is [pic] Therefore‚ the ratio of Area A to Area B is- = [pic] ÷ [pic] = [pic] × [pic] = n : 1 n:1 is the general conjecture formed. The given
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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 that there is a vertical
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Complex Number System Arithmetic A complex number is an expression in the form: a + bi where a and b are real numbers. The symbol i is defined as √ 1. a is the real part of the complex number‚ and b is the complex part of the complex number. If a complex number has real part as a = 0‚ then it is called a pure imaginary number. All real numbers can be expressed as complex numbers with complex part b = 0. -5 + 2i 3i 10 real part –5; imaginary part 2 real part 0; imaginary part 3 real part 10; imaginary
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Topic 1- Exam Style Notes 1.1 Nature of Business Activity What is a business? * Business- decision making organisation using inputs to produce goods and services which satisfy the needs and wants of a customer * Factors of production- “CELL” 1. Capital- used to produce goods (non natural‚ eg machinery) 2. Enterprise- management/planning of factors of production 3. Land- natural resources; renewable and non renewable 4. Labour- physical and mental efforts of people
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dropping ruler for calculation of length of the neural pathways (Visual‚ Auditory and Sensual) Trial# | Visual | Auditory(Sound) | Sensual(Pressure) | | (cm±0.1cm) | (cm±0.1cm) | (cm±0.1cm) | | John | Arthur | John | Arthur | John | Arthur | 1 | 43.9 | 24.1 | 33.1 | 34.6 | 50.1 | 50.5 | 2 | 73.7 | 45.6 | 66.1 | 49.2 | 29.2 | 75.2 | 3 | 47.4 | 31 | 80.2 | 25.3 | 54.4 | 41 | 4 | 32 | 24.7 | 23.1 | 39.6 | 25.6 | 47.4 | 5 | 23.5 | 29.1 | 32.9 | 35.1 | 26.2 | 30.8 | 6 | 38.6 | 27.6 |
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MATH PORTFOLIO NUMBER OF PIECES Kanishk Malhotra 003566-035 (May 2012) In physics and mathematics‚ the ‘DIMENSION’ of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it (for
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1. Introduction The purpose of this research paper is to introduce the topic of “Complex and Imaginary Numbers” and its applications. I chose the topic “Complex and Imaginary Numbers” because I am interested in mathematics that is hard to be pictured in your mind‚ unlike geometry or equations. An imaginary number is the square root of a negative number. That is why they are called imaginary‚ what René Descartes called them‚ because he thought such a number could not exist. In this paper‚ I will
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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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Level The portfolio - tasks For use in 2012 and 2013 © International Baccalaureate Organization 2010 7 pages For final assessment in 2012 and 2013 2 MATME/PF/M12/N12/M13/N13 C O N T E N TS T y p e I t as k s Circles T y p e I I t as k s Fish Production Gold Medal Heights INTRODUC TI ON W h a t is t h e p u r p ose of t h is d oc u m e n t ? This document contains new tasks for the portfolio in mathematics SL. These tasks have been produced by the IB‚ for teachers
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