IGCSE Additional Mathematics Paper2 2011

This document consists of 16 printed pages. © UCLES 2010 [Turn over For Examiner's Use 1 2 3 4 5 6 7 8 9 10 11 12 Total UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/02 Paper 2 For Examination from 2011 SPECIMEN PAPER 2 hours Candidates answer on the Question Paper. Additional Materials: Electronic calculator READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an electronic calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 80. 2 © UCLES 2010 0606/02/SP/11 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, a ac b b x 2 4 2 − ± − = . Binomial Theorem (a + b)n = an +    1n an–1 b +     2n an–2 b2 + … +     rn an–r br + … + bn, where n is a positive integer and     rn = ! )! ( ! r r n n − . 2. TRIGONOMETRY Identities sin2 A + cos2 A = 1. sec2 A = 1 + tan2 A. cosec2 A = 1 + cot2 A. Formulae for ∆ABC C c B b A a sin sin sin = = . a2 = b2 + c2 – 2bc cos A. ∆ = 21 bc sin A. 3 © UCLES 2010 0606/02/SP/11 [Turn over For Examiner's Use 1 Given that A =     4 7 6 13 , find the inverse matrix A–1 and hence solve the simultaneous equations 13x + 6y = 41, 7x + 4y = 24. [4] 2 Variables x and y are connected by the equation y = (2x – 9)3. Given that x is increasing at the rate of 4 units per second, find the rate of increase of y when x = 7. [4] 4 © UCLES 2010 0606/02/SP/11 For Examiner's Use 3 Find the set of values of m for which the line y = mx + 2 does not meet the curve y = x2 – 5x + 18. [5] 4 (a) A sports team of 3 attackers, 2 centres and 4 defenders is to be chosen from a squad of 5 attackers, 3 centres and 6 defenders. Calculate the number of different ways in which this can be done. [3] 5 © UCLES 2010 0606/02/SP/11 [Turn over For Examiner's Use (b) How many different 4-digit numbers greater than 3000 can be formed using the six digits 1, 2, 3, 4, 5 and 6 if no digit can be used more than once? [3] 5 (i) Differentiate x ln x with respect to x. [2] (ii) Hence find ∫ ln x dx. [3] 6 © UCLES 2010 0606/02/SP/11 For Examiner's Use 6 Solve the following equations. (i) 3 4 5 82 24 − − = x x x x [3] (ii) lg (2y + 10) + lg y = 2 [3] 7 © UCLES 2010 0606/02/SP/11 [Turn over For Examiner's Use 7 QP 1.4 ms –1 48 m The diagram shows a river with parallel banks. The river is 48 m wide and is flowing with a speed of 1.4 ms–1. A boat travels in a straight line from a point P on one bank to a point Q which is on the other bank directly opposite P. It is given that the boat takes 10 seconds to cross the river. (i) Find the speed of the boat in still water. [4] (ii) Find the angle to the bank at which the boat should be steered. [2] 8 © UCLES 2010 0606/02/SP/11 For Examiner's Use 8 The function f is defined, for 0 Y x Y 2π, by f(x) = 3 + 5 sin 2x. State (i) the amplitude of f, [1] (ii) the period of f, [1] (iii) the maximum and minimum values of f. [2] Sketch the graph of y = f(x). [3] 9 © UCLES 2010 0606/02/SP/11 [Turn over For Examiner's Use 9 The line y = 2x – 9 intersects the curve x2 + y2 + xy + 3x = 46 at the points A and B. Find the equation of the perpendicular bisector of AB. [8] 10 © UCLES 2010 0606/02/SP/11 For Examiner's Use 10 y x O y = x − 8x + 16x 3 2 The diagram shows part of the curve y = x3 – 8x2 + 16x. (i) Show that the curve has a minimum point at (4, 0) and find the coordinates of the maximum point. [4] 11 © UCLES 2010 0606/02/SP/11 [Turn over For Examiner's Use (ii) Find the area of the shaded region enclosed by the x-axis and the curve. [4] 12 © UCLES 2010 0606/02/SP/11 For Examiner's Use 11 The table shows experimental values of two variables x and y. x 2 4 6 8 y 2.25 0.81 0.47 0.33 (i) On the graph paper below, plot xy against x1 and draw a straight line graph. [3] xy x1 13 © UCLES 2010 0606/02/SP/11 [Turn over For Examiner's Use (ii) Use your graph to express y in terms of x. [5] (iii) Estimate the value of x and of y for which xy = 4. [3] 14 © UCLES 2010 0606/02/SP/11 For Examiner's Use 12 Answer only one of the following two alternatives. EITHER O DC B A 6 cm 0.6 rad 2 cm The diagram shows a sector AOB of a circle with centre O and radius 6 cm. Angle AOB = 0.6 radians. The point D lies on OB such that the length of OD is 2 cm. The point C lies on OA such that OCD is a right angle. (i) Show that the length of OC is approximately 1.65 cm and find the length of CD. [4] (ii) Find the perimeter of the shaded region. [3] (iii) Find the area of the shaded region. [3] OR A particle moves in a straight line so that t seconds after passing a fixed point O its acceleration, a ms–2, is given by a = 4t – 12. Given that its speed at O is 16 ms–1, find (i) the values of t at which the particle is stationary, [5] (ii) the distance the particle travels in the fifth second. [5] Start your answer to Question 12 here. Indicate which question you are answering. EITHER OR 15 © UCLES 2010 0606/02/SP/11 [Turn over For Examiner's Use Continue your answer to Question 12 here. 16 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. © UCLES 2010 0606/02/SP/11 For Examiner's Use Continue your answer here if necessary.