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 1 5045 Contents Prior learning Topics Topic 1—Algebra Topic 2—Functions and equations Topic 3—Circular functions and trigonometry Topic 4—Vectors Topic 5—Statistics and probability Topic 6—Calculus 2 3 3 4 4 5 5 6 Mathematics SL formula booklet 1 Formulae
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Alma Guadalupe Luna Math IA (SL TYPE1) Circles Circles Introduction The objective of this task is to explore the relationship between the positions of points within circles that intersect. The first figure illustrates circle C1 with radius r‚ centre O‚ and any point P. r is the distance between the centre O and any point (such as A) of circle C1. Figure 1 The second diagram shows circle
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generate an equation for the numerator of the fraction‚ the fraction data must be organized and graphed. The table below shows the relationship between the row number and numerator being relative to an exponential function as the sequence goes on. N(n+1)-Nn represents the equation for the graph that increases more evenly as the sequence advances. Using excel to graph the points and loggerpro to generate an equation‚ the general statement for finding the numerator N=0.5n2+0.5n‚ n having to be greater
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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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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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Math Magic – Matrices Page 1 Working With Matrices: A. Number Sense only deals with small matrices‚ usually 2 x 2 matrices. This page will look at 3 ways of manipulating matrices: Multiplying Matrices‚ Inverses‚ and Determinants. B. Multiplying Matrices 1. Unlike general multiplication‚ matrix multiplication is not commutative. Multiplying A x B and B x A will give different results. 2. The following will show how to multiply two 2x2 matrices: a. In other words‚ you multiply the row of
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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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be used; For the first calculations‚ r=1 and OP =2. By finding the ∠O in one triangle‚ I have found the ∠O in both triangles‚ allowing me a complete ration to perform the sine law. Side Note: All Final Answers are rounded to 3 Significant Figures. For the first calculations‚ r=1 and OP =2. By finding the ∠O in one triangle‚ I have found the ∠O in both triangles‚ allowing me a complete ration to perform the sine law. Side Note: All Final Answers are rounded to 3 Significant Figures. When a
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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 to use in the examination sessions in 2012 and 2013. It should be noted that most tasks previously produced and published by the IB will no longer be valid for assessment after the November 2010 examination session. These include all the tasks in any teacher support material (TSM)‚ and
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