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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Mixed Fractions (Also called "Mixed Numbers") | | A Mixed Fraction is a whole number and a proper fraction combined. such as 1 3/4. | 1 3/4 | | | (one and three-quarters) | | | Examples 2 3/8 | 7 1/4 | 1 14/15 | 21 4/5 | See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number). Names We can give names to every part of a mixed fraction: Three Types of Fractions There are three types
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Type I – Mathematical Investigation Lacsap’s Fractions The focus of this investigation is surrounding Lascap’s Fractions. They are a group of numbers set up in a certain pattern. A similar mathematical example to Lacsap’s Fractions is Pascal’s Triangle. Pascal’s Triangle represents the coefficients of the binomial expansion of quadratic equations. It is arranged in such a way that the number underneath the two numbers above it‚ is the sum. Ex. 1 1 1 1 2 1 1
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Adding & subtracting fractions 1. Where in life is this useful? a) Cooking: [pic] b) Measurements (construction‚ remodeling‚ etc): [pic] c) Time: [pic] d) Money: [pic] 2. Fractions with the same (“common”) denominators Example: (without converting back & forth from mixed numbers): [pic] [pic] 3. Fractions with different denominators In order to add (or subtract) fractions with different denominators
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IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI M07/5/MATHL/HP1/ENG/TZ1/XX/M MARKSCHEME May 2007 MATHEMATICS Higher Level Paper 1 16 pages -2- M07/5/MATHL/HP1/ENG/TZ1/XX/M This markscheme is confidential and for the exclusive use of examiners in this examination session. It is the property of the International Baccalaureate and must not be reproduced or distributed to any other person without the authorization of IBCA. -3- M07/5/MATHL/HP1/ENG/TZ1/XX/M
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Iva Rhiana C. Santiago 4218 “Man is like a fraction whose numerator is what he is and whose denominator is what he thinks. The greater the denominator‚ the lesser the fraction.” –Lev Tolstoy We should take note that in a fraction‚ as the denominator becomes larger‚ the value of the fraction becomes lesser. Man is also like a fraction as what Lev Tolstoy said in his quotation. Life is full of choices‚ full of situations. Where sometimes all our way to run away is by pretending. Pretending is one
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Population Trends in China The goal of this mathematical study is to explore the different functions that best model the population of China from the years 1950 to 1995. Year | 1950 | 1955 | 1960 | 1965 | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | Population in Millions | 554.8 | 609.0 | 657.5 | 729.2 | 830.7 | 927.8 | 998.9 | 1070.0 | 1155.3 | 1220.5 | Using the Chinese population data from 1950 to 1995‚ let us construct a graph using technology. Before graphing the data though‚ we must
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1. Be very particular about the subject you choose for prelims‚ as you will be appearing for an objective type of paper. History‚ maths‚ geography may prove to be very scoring. Choose subjects which have availability of books‚ reading material and guidance. In recent years engineering subjects like civil and electrical can be chosen‚ giving BEs and IITians an edge (yes! even here they are giving the BAs and BScs a tough fight!)(more content follows the advertisement below) A D V E R T I S E M E
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Basic Concepts on Fraction Fraction – is defined as a part of a whole. In some other books‚ it is defined as a number written in the form ab ‚ where “a” and “b” are numbers and “b” is not equal to zero. Basic Parts of a Fraction * Numerator – the number above tells how many parts are taken. * Denominator – the number below tells how many equal parts the whole is divided. * Fraction bar – line that separates the two numbers. It also indicates division. There are several kinds
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M11/5/MATME/SP1/ENG/TZ1/XX 22117303 mathematics staNDaRD level PaPeR 1 Wednesday 4 May 2011 (afternoon) 1 hour 30 minutes iNSTrucTioNS To cANdidATES candidate session number 0 0 Examination code 2 2 1 1 – 7 3 0 3 Write your session number in the boxes above. not open this examination paper until instructed to do so. do are not permitted access to any calculator for this paper. You Section A: answer all questions in the boxes provided. Section B: answer all questions on the
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