Mathematics HL - May 2002 - P2

Mathematics HL - May 2002 - P2 - M02/510/H(2) IB DIPLOMA...

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MATHEMATICS HIGHER LEVEL PAPER 2 Wednesday 8 May 2002 (morning) 3 hours 222–237 12 pages M02/510/H(2) INSTRUCTIONS TO CANDIDATES Do not open this examination paper until instructed to do so. Answer all five questions from Section A and one question from Section B. Unless otherwise stated in the question, all numerical answers must be given exactly or to three significant figures. Write the make and model of your calculator on the front cover of your answer booklets e.g. Casio fx-9750G , Sharp EL-9600, Texas Instruments TI-85. IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI
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Please start each question on a new page. You are advised to show all working, where possible. Solutions found from a graphic display calculator should be supported by suitable working eg if graphs are used to Fnd a solution, you should sketch these as part of your answer. Incorrect answers with no working will normally receive no marks. SECTION A Answer all fve questions from this section. 1. [Maximum mark: 16] The points A, B, C, D have the following coordinates A : (1, 3, 1) B : (1, 2, 4) C : (2, 3, 6) D : (5, – 2, 1) . (a) (i) Evaluate the vector product AB 3 AC , giving your answer in terms of the unit vectors i , j , k . (ii) Find the area of the triangle ABC . [6 marks] The plane containing the points A, B, C is denoted by Π and the line passing through D perpendicular to is denoted by L . The point of intersection of L and is denoted by P . (b) (i) Find the cartesian equation of . (ii) Find the cartesian equation of L . [5 marks] (c) Determine the coordinates of P . [3 marks] (d) Find the perpendicular distance of D from . [2 marks] – 2 – M02/510/H(2) 222–237
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2. [Maximum mark: 12] The function y = f ( x ) satisFes the differential equation (a) (i) Using the substitution y = n x , show that (ii) Hence show that the solution of the original differential equation is , where c is an arbitrary constant. (iii) ±ind the value of c given that y = 2 when x = 1. [7 marks] (b) The graph of y = f ( x ) is shown below. The graph crosses the x -axis at A . (i) Write down the equation of the vertical asymptote. (ii) ±ind the exact value of the x -coordinate of the point A . (iii) ±ind the area of the shaded region. [5 marks] y x 0 5 1 A yx x xc = + (ln ) 2 21 2 x x d d = (–). 20 22 2 x y x xy x d d =+ > () 222–237 Turn over – 3 – M02/510/H(2)
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3. [Maximum mark: 14] (i) (a) Find the determinant of the matrix [1 mark] (b) Find the value of λ for which the following system of equations can be solved.
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This note was uploaded on 05/06/2010 for the course MATH 1102 taught by Professor Chang during the Spring '10 term at Savannah State.

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Mathematics HL - May 2002 - P2 - M02/510/H(2) IB DIPLOMA...

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