ACSI 2012 Y3 Core Mathematics Paper 1

ACS(Independent)/Y3IPCoreMathsP1/2012/Final Year 1 Anglo - Chinese School (Independent) FINAL EXAMINATIONS 2012 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 TUESDAY 2ND OCTOBER 2012 1 h 30 min Additional Material Graph Paper (1 sheet) INSTRUCTIONS TO CANDIDATES  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 question, all numeric al answers must be given exactly or correct to three significant figures.  The maximum mark for this paper is 80. For Examiner’s Use _______________________________________________________________ This paper consists of 14 printed pages. [Turn over Candidate Index Number

ACS(Independent)/Y3IPCoreMathsP1/2012/Final Year 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) Given that 2 53   y yx , express y in terms of x . [3 marks] (b) Simplify 2222 44   nn nn xyx xy . [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2012/Final Year 3 2 [Maximum mark: 4] Given that 25  x , 61  y and x and y are integers, find (a) the least possible value of 3yx . [2 marks] (b) the least possible value of x y . [2 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2012/Final Year 4 3 [Maximum mark: 4] In the diagram, PQR is a straight line, QR = 2 cm and RS = h cm. Find the following in terms of h . (a) SRQsin , [2 marks] (b) PQStan . [2 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… P Q R S 2 cm h cm

ACS(Independent)/Y3IPCoreMathsP1/2012/Final Year 5 4 [Maximum mark: 9] (a) A, B and C are points on level ground, with A due north of C. oBAC 45 , oBCA 60 and AB = 48 m. Calculate the length of BC, leaving your answer in the form ba where a, b and c are constants. [ 2 3120sin o , 2 1120cos o , 3120tan o , 2 145sin o , 2 145cos o , 145tan o ] [3 marks] (b) In the diagram, A, B, C and D are four towns. Find the bearing of (i) A from D, (ii) D from C, (iii) A from B. [6 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… A B C D 48o 100o 96o 72o N

ACS(Independent)/Y3IPCoreMathsP1/2012/Final Year 6 5 [Maximum mark: 5] Given that 3 1cos A and oo A 18090  , find the value of (a) Atan , [2 marks] (b) A AA sin32 tancos3   , leaving your answer in the form 2ba where a and b are constants. [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2012/Final Year 7 6 [Maximum mark: 8] Joel and Gabriel started together on a 7 km race at the same constant speed of y km/h. After 1 km, Joel increased his speed by 1 km/h and ran the remaining 6 km at the new speed. Gabriel walked at a constant speed of y km/h all the way. (a) Write down the time, in terms of y , Joel took to complete the 7 km race. [1 mark] (b) Given that Joel finished the race 12 minutes earlier than Gabriel, form an equation in y and show that it reduces to 0302  yy . [3 marks] (c) Solve the equation 0302  yy . [2 marks] (d) Calculate Joel’s average speed, in km/h, for the whole journey. [2 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2012/Final Year 8 7 [Maximum mark: 5] (a) Express 16123 2  xxy in the form khxay  2)( . [2 marks] (b) Hence, sketch the curve 16123 2  xxy , indicating clearly, the points of intersection with the axes (if any) and the turning point. [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………