Mathematics — previous courses · 2001 · November · Paper 2 · HL · Question paper

MATHEMATICS HIGHER LEVEL PAPER 2 Monday 12 November 2001 (morning) 3 hours 881–237 11 pages INTERNATIONAL BACCALAUREATE BACCALAURÉAT INTERNATIONAL BACHILLERATO INTERNACIONAL N01/510/H(2) INSTRUCTIONS TO CANDIDATES •D o 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, as appropriate. •W rite 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. You are advised to start each new question on a new page. A correct answer with no indication of the method used will usually receive no marks. You are therefore advised to show your working. In particular, where graphs from a graphic display calculator are being used to find solutions, you should sketch these graphs as part of your answer. SECTION A Answer all five questions from this section. 1. [Maximum mark: 13] (a) Solve the following system of linear equations x +3 y –2 z = –6 2x + y +3 z = 7 3x – y + z = 6. [3 marks] (b) Find the vector v = (i +3 j –2 k) × (2i + j +3 k). [3 marks] (c) If a = i +3 j –2 k , b = 2i +j +3 k and u = ma + nb where m , n are scalars, and u ≠ 0, show that v is perpendicular to u for all m and n . [3 marks] (d) The line l lies in the plane 3x – y + z = 6, passes through the point (1, –1, 2) and is perpendicular to v . Find the equation of l . [4 marks] 2. [Maximum mark: 10] (i) Let y = sin(kx)– kx cos(kx), where k is a constant. Show that . [3 marks] (ii) A particle is moving along a straight line so that t seconds after passing through a fixed point O on the line, its velocity v(t)ms –1 is given by . (a) Find the values of t for which v(t) = 0, given that 0 ≤ t ≤ 6. [3 marks] (b) (i) Write down a mathematical expression for the total distance travelled by the particle in the first six seconds after passing through O . (ii) Find this distance. [4 marks] vt t t() =    sin π 3 d d y x kx k x= 2 sin( ) –2– N01/510/H(2) 881–237