ACSI 2011 Y3 Core Mathematics Paper 1

Anglo - Chinese School (Independent) FINAL EXAMINATIONS 2011 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 Tuesday 4 October 2011 1 h 30 min INSTRUCTIONS TO STUDENTS Write your index number in the boxes above. Do not open this examination paper until instructed to do so. You are not permitted access to any calculator for this paper. Answer all questions in the spaces provided. Unless otherwise stated in the ques tion, all numerical answers must be given exactly or correct to three significant figures. INFORMATION FOR STUDENTS The maximum mark for this paper is 80. _____________________________________________________________________ This question paper consists of 14 printed pages. [Turn over Candidate Index Number

ACS(Independent)MathDept/Y3IPCoreMathPaper1/2011/FinalExamination 2 Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. You are therefore advised to show all working. Answer all the questions in the spaces provided. 1 [Maximum mark: 6] (a) Solve .9107223  xxx (b) Simplify 22 )3( 2 93 1 123 26     y x yx y . [3 marks] [3 marks] Answer: a) ______________________________ b) ______________________________ 2 [Maximum mark: 3] Solve 01622  xx by completing the square, leaving your answer in the surd form. Answer: ______________________________

ACS(Independent)MathDept/Y3IPCoreMathPaper1/2011/FinalExamination 3 3 [Maximum mark: 7] Both Alan and Benny invested in some stocks. Alan lost $84 in x months and Benny lost the same amount 4 months later . i) Write an expression for the average monthly losses incurred by Alan. ii) Write an expression for the average monthly losses incurred by Benny. iii) If Alan lost $16 more than Benny per month, form an equation in x and show that it reduces to .02142  xx iv) Hence, calculate the average monthly losses incurred by Benny. [1 mark] [1 mark] [3 marks] [2 marks] Answer: i) ______________________________ ii) ______________________________ iii) ______________________________ iv) ______________________________

ACS(Independent)MathDept/Y3IPCoreMathPaper1/2011/FinalExamination 4 4 [Maximum mark: 6] Simplify each of the following: i) 2 1 4124 )4()8)((   yyy ii) 12 12 33 33     xx xx [3 marks] [3 marks] Answer: i) ______________________________ ii) ______________________________

ACS(Independent)MathDept/Y3IPCoreMathPaper1/2011/FinalExamination 5 5 [Maximum mark: 5] John spent a total of $7 on two burgers and three sandwiches. Each burger costs $x and each sandwich costs $y. Given that seven burgers cost $13 more than a sandwich, (a) Write down two equations connecting x and y. (b) Use the matrix method to find the price of each burger and each sandwich. [2 marks] [3 marks] Answer: a) __________________________________ b) 1 burger is $_____, 1 sandwich is $ _____

ACS(Independent)MathDept/Y3IPCoreMathPaper1/2011/FinalExamination 6 6 [Maximum mark: 7] The line 1 b y a x passes through the points A )0,3( and B )4,0(  . The point O is the origin. Find i) the value of a and of b; ii) the gradient of the line AB ; iii) the area of the triangle OAB; iv) the shortest distance between the origin O and the line AB. [2 marks] [2 marks] [1 mark] [2 marks] Answer: i) ______________________________ ii) ______________________________ iii) ______________________________ iv) ______________________________

ACS(Independent)MathDept/Y3IPCoreMathPaper1/2011/FinalExamination 7 7 [Maximum mark: 8] (a) Find the range of values of p for which the line xpy 122  will meet the curve .)3( 2xpy  (b) Find the range of values of k for which kxx  42 2 is always positive for all real values of x. [4 marks] [4 marks] Answer: a)______________________________ b)______________________________

ACS(Independent)MathDept/Y3IPCoreMathPaper1/2011/FinalExamination 8 8 [Maximum mark: 6] In the diagram, WZY is a straight line,  XYZ is a right angled triangle and VY is perpendicular to XZ. XZ = 4 cm and  YXZ = 30. Using the information given , find i) YZ; ii) XY and iii) VY 30⁰ 60⁰ sin 2 1 2 3 cos 2 3 2 1 tan 3 1 3 [2 mark] [2 mark] [2 mark] Answer: i) ______________________________ ii) ______________________________ iii) ______________________________ Y 30⁰ X V Z W 4 cm

ACS(Independent)MathDept/Y3IPCoreMathPaper1/2011/FinalExamination 9 9 [Maximum mark: 4] The diagram shows three points A, B and C on level ground. Given that AB = AC,  40ACB and the bearing of B from A is 115 , calculate the bearing of i) C from A , ii) A from B , [2 marks] [2 marks] Answer: i) ______________________________ ii) ______________________________ 115⁰ A B C N 40⁰

ACS(Independent)MathDept/Y3IPCoreMathPaper1/2011/FinalExamination 10 10 [Maximum mark: 7] If the roots of the equation 0122  xx are α and β where α > β, find (a) α + β and αβ ; (b)   and (c) the quadratic equation whose roots are α2 and β2 . [2 marks] [2 marks] [3 marks] Answer: a) α + β = ______ and αβ= ________ b) ______________________________ c) ______________________________