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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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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IB Mathemetics SL Portfolio: Logarithmic Bases In this portfolio task‚ I will investigate the rules of logarithms by identifying the logarithmic sequences. After identifying the pattern‚ I will produce a general statement which defines the sequence. I will then test the validity of my general statement by using other values. I will finally conclude the portfolio task by explaining how I arrived to my general statement and its limitations. Consider the following sequences. Write down the next
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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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SL TYPE 1-LACSAP’S FRACTIONS * INTRODUCTION This investigation is going to do research patterns relates to the Lacsap’s Fractions. For its external structure‚ Lacsap’s Fraction is analogous to Pascal’s Triangle. Lacsap’s Fraction presents the way of generating and organizing the binomial coefficients. Within this investigation‚ the work is planning to be divided into two parts. In the first part‚ the content will relate to the pattern of numerators. In the second part‚ I am going to do the
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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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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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Diploma Programme Mathematics SL formula booklet For use during the course and in the examinations First examinations 2014 Published March 2012 © International Baccalaureate Organization 2012 Mathematical studies SL: Formula booklet 5045 1 Contents Prior learning 2 Topics 3 Topic 1—Algebra 3 Topic 2—Functions and equations 4 Topic 3—Circular functions and trigonometry 4 Topic 4—Vectors 5 Topic 5—Statistics and probability 5 Topic 6—Calculus
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In Lacsap’s Fractions‚ En(r) refers to the (r+1)th term in the nth row. The numerator and denominator are found separately‚ therefore to find the general statement‚ two different equations‚ one for the numerator and one for the denominator‚ must be found. Let M=numerator and let D=denominator so that En(r) = M/D. To find the numerator for any number of Lacsap’s Fractions‚ an equation must be made that uses the row number to find the numerator. Because the numerator changes depending on the row
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IB Math SL Type II Internal Assessment High Jump Heights Aim: The aim of this task is to consider the winning height for the men’s high jump in the Olympic Games. The table below gives the height (in centimeters) achieved by the gold medalists at various Olympic Games. Year | 1932 | 1936 | 1948 | 1952 | 1956 | 1960 | 1964 | 1968 | 1972 | 1976 | 1980 | Height(cm) | 197 | 203 | 198 | 204 | 212 | 216 | 218 | 224 | 223 | 225 | 236 | Note: The Olympic Games were not held in 1940 and
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