Partial Fractions A way of "breaking apart" fractions with polynomials in them. What are Partial Fractions? We can do this directly: Like this (read Using Rational Expressions to learn more): 2 + 3 = 2·(x+1) + (x-2)·3 x-2 x+1 (x-2)(x+1) Which can then be simplified to: = 2x+2 + 3x-6 = 5x-4 x2+x-2x-2 x2-x-2 ... but how do we go in the opposite direction? That is what we discover here: How to find the "parts" that make the single fraction (the "partial fractions")
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Internal Assessment IB Physics-7 Mr. Parent 14 January 2012 I. Design • Purpose: o To determine how the surface area of a coffee filter affects the average velocity of the coffee filter from the same height. • Variables: o Independent Variable ▪ Surface area- The area of the surface after the folds have been made o Dependent Variable ▪ The Average velocity- calculated by measuring the time and dividing by
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IB Business & Management 2013 Internal Assessment Standard Level Guidelines booklet Mark Lewis Jan 2013 Page 1 of 77 IB Business & Management Internal Assessment Guidelines Standard Level – 2013 Index Page • Templates • IB Commentary on report structure • IB SL IA criteria and mark bands from syllabus • IB general commentary on SL IA from syllabus • Sample IA’s with marks (IB sourced) • General guide comments (IB Sourced) • Recent IA questions at Carey • General guide comments (IB Sourced) • Subject
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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 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
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What’s So Hard About Fractions? Fractions as we know them today‚ the symbols and the algorithms for performing operations‚ have developed over thousands of years‚ beginning with ancient Egyptians. Through research of the origins‚ the development of fractions to appearing symbolically as we know them today‚ and of the developments of how we operate with them today and then connecting that knowledge with the observations of contemporary math education experts and personal interviews and observation
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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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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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Math SL Investigation Type 2 Stellar Numbers This is an investigation about stellar numbers‚ it involves geometric shapes which form special number patterns. The simplest of these is that of the square numbers (1‚ 4‚ 9‚ 16‚ 25 etc…) The diagram below shows the stellar triangular numbers until the 6th triangle. The next three numbers after T5 would be: 21‚ 28‚ and 36. A general statement for nth triangular numbers in terms of n is: The 6-stellar star‚ where there are 6 vertices‚ has
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M10/5/MATHL/HP2/ENG/TZ1/XX 22107204 mathematics higher level PaPer 2 Thursday 6 May 2010 (morning) 2 hours iNsTrucTioNs To cANdidATEs Write your session number in the boxes above. not open this examination paper until instructed to do so. do graphic display calculator is required for this paper. A section A: answer all of section A in the spaces provided. section B: answer all of section B on the answer sheets provided. Write your session number on each answer sheet‚ and attach
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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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