Mathematics HL - May 2004 -TZ2 - P2

Mathematics HL - May 2004 -TZ2 - P2 - c 3 hours IB DIPLOMA...

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MATHEMATICS HIGHER LEVEL PAPER 2 Friday 7 May 2004 (morning) 3 hours M04/512/H(2) c IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI 224-239 12 pages INSTRUCTIONS TO CANDIDATES y Do not open this examination paper until instructed to do so. y Answer all five questions from Section A and one question from Section B. y Unless otherwise stated in the question, all numerical answers must be given exactly or to three significant figures. y Write the make and model of your calculator in the appropriate box on your cover sheet e.g. Casio fx-9750G , Sharp EL-9600, Texas Instruments TI-85.
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Please start each question on a new page. You are advised to show all working, where possible. Where an answer is wrong, some marks may be given for correct method, provided this is shown by written working. Solutions found from a graphic display calculator should be supported by suitable working, e.g. if graphs are used to find a solution, you should sketch these as part of your answer. SECTION A Answer all five questions from this section. 1. [Maximum mark: 13] The points and are mapped to and A(1, 2) B(4, 5) A (2, 3) B (5, 6) respectively by a linear transformation M . (a) (i) Find the matrix M which represents this transformation. [7 marks] (ii) Find the image of under M . A The point is mapped to by a translation T . C(1, 3) C (2, 2) [2 marks] (b) Find the vector which represents T . (c) Find the image of under the following transformations. D(5, 7) (i) T followed by M ; [4 marks] (ii) M followed by T . – 2 – M04/512/H(2) 224-239
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2. [Maximum mark: 14] (i) Jack and Jill play a game, by throwing a die in turn. If the die shows a 1, 2, 3 or 4, the player who threw the die wins the game. If the die shows a 5 or 6, the other player has the next throw. Jack plays first and the game continues until there is a winner. [1 mark] (a) Write down the probability that Jack wins on his first throw. [2 marks] (b) Calculate the probability that Jill wins on her first throw. [3 marks] (c) Calculate the probability that Jack wins the game. (ii) Let be the probability density function for a random variable X , where ( ) f x 2 , for 0 2 ( ) 0, otherwise. kx x f x = [2 marks] (a) Show that . 3 8 k = (b) Calculate (i) ; E( ) X [6 marks] (ii) the median of X .
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