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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and Advanced Level 9707/02 For Examination from 2011 Paper 2 Data Response SPECIMEN PAPER 1 hour 30 minutes Additional Materials: Answer Booklet/Paper READ THESE INSTRUCTIONS FIRST If you have been given an Answer Booklet‚ follow the instructions o the front cover of the Booklet. Write your Centre number‚ candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples‚ paper clips‚ highlighters‚ glue or correction fluid. Answer all
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IB Chemistry Summary- By Paul Li & Silvia Riggioni TABLE OF CONTENTS Table of Contents............................................................................................................................................................ 1 Atomic Theory................................................................................................................................................................ 3 The Electromagnetic Spectrum.............................................
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2.1.1 Distinguish between biotic and abiotic components of an ecosystem * Biotic factors in an ecosystem are living‚ biological factors that may influence an organism in an ecosystem * Abiotic factors are non-living‚ physical factors that may influence an organism in an ecosystem 2.1.2 Define the term trophic level * The position that an organism occupies in a food chain‚ or a group of organisms in a community that occupy the same position in food chains 2.1.3 Identify and explain
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International General Certificate of Secondary Education FIRST LANGUAGE ENGLISH Paper 2 Reading Passages (Extended) 0500/02 For Examination from 2015 SPECIMEN PAPER 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your Centre number‚ candidate number and name in the spaces provided. Write in dark blue or black pen. Do not use staples‚ paper clips‚ glue or correction fluid. Answer all questions in the space provided. If additional
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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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International Baccalaureate | Gold Medal Heights SL Math IA- Type II | Turner Fenton Secondary School | Completed by: Harsh Patel Student Number: 643984 IB number: Teacher: Mr. Persaud Course Code: MHF4U7-C Due Date: November 16th‚ 2012 Introduction This report will investigate the winning heights of high jump gold medalists in the Olympics. The Olympics composed of several events evaluating
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A M I N AT I O N Mathematics General Instructions • Reading time – 5 minutes • Working time – 3 hours • Write using black or blue pen • Board-approved calculators may be used • A table of standard integrals is provided at the back of this paper • All necessary working should be shown in every question Total marks – 120 • Attempt Questions 1–10 • All questions are of equal value 212 BLANK PAGE – 2 – Total marks – 120 Attempt Questions 1–10 All questions are of equal value
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your name here Surname Other names Centre Number Candidate Number Edexcel GCSE Mathematics A Paper 2 (Calculator) Foundation Tier Thursday 8 November 2012 – Afternoon Time: 1 hour 45 minutes Paper Reference 1MA0/2F You must have: Ruler graduated in centimetres and millimetres‚ protractor‚ pair of compasses‚ pen‚ HB pencil‚ eraser‚ calculator. Tracing paper may be used. Total Marks Instructions Use black ink or ball-point pen. Fill in the boxes at the top of
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Walking into the Morris Morrison presentation I thought to myself “wow this is going to be boring”. To my surprise it was anything but boring. Morrison truly is an amazing speaker. From the second he walked out on stage I had such interest in everything he had to say. As Morrison opens his speech he begins to talk about his childhood. He was and orphan‚ his father a drug dealer and his mother a prostitute‚ in Brooklyn New York. Shortly after he was adopted by his uncle. He and his uncle
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