ACSI 2014 Y3 Core Mathematics Paper 1

ACS(Independent)/Y3IPCoreMathsP1/2014/Final Year 1 Anglo - Chinese School (Independent) FINAL EXAMINATIONS 2014 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 Friday 3rd OCTOBER 2014 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 nu merical 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 13 printed pages. [Turn over Candidate Index Number

ACS(Independent)/Y3IPCoreMathsP1/2014/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 writte n working. You are therefore advised to show all working. Answer all the questions in the spaces provided. 1 [Maximum mark: 5] (a) Evaluate 5 45 35 32    . [3 marks] (b) Factorise 925 2x completely. [2 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2014/Final Year 3 2 [Maximum mark: 4] Which of the following is the graph of (a) xy 43 [1 mark] (b) 2 22 xxy  [2 marks] (c) 12 xy [1 mark] Answer: (a) Figure ________ (b) Figure ________ (c) Figure ________ y x Figure 1 y x Figure 2 Figure 3 xy x 1 Figure 4 y x Figure 5 x2y x Figure 6 y x

ACS(Independent)/Y3IPCoreMathsP1/2014/Final Year 4 3 [Maximum mark: 8] (a) Simplify     2 43 22 632 2 20 pq qp pq qp    . [4 marks] (b) If     2 9 7 2 3log 1ln256loglog       ex , find the value of 𝑥. [4 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2014/Final Year 5 ………………………………………………………………………………………… 4 [Maximum mark: 7] (a) Given that b a yx byax   43 , express y in terms of a , b and x . [4 marks] (b) Simplify 2 3 73 2        . [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2014/Final Year 6 5 [Maximum mark: 10] (a) Solve 32logloglog2 21255  yy . [4 marks] (b) Solve the following simultaneous equations xyx 1 4 16324  1log3577  yx [6 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2014/Final Year 7 6 [Maximum mark: 7] Given that 322  xxy . (a) Express y in the form khxy  2)( , where h and k are constants. [2 marks] (b) Hence, sketch the graph of 322  xxy , clearly labelling the coordinates of the x and y intercepts and turning points, if any. [3 marks] (c) Given that 𝑤 = 12 𝑦 , calculate the largest possible value of 𝑤. [2 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2014/Final Year 8 7 [Maximum mark: 6] Given that o148sinsin  and o52tantan  . (a) State an acute angle  and an obtuse angle  . [2 marks] (b) Hence, calculate  o22sin2 cos3          , using as much information given in the table below as it is necessary. sin cos tan o176 0.0698 −0.9976 −0.0699 o30 0.5000 0.8660 0.5774 [4 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2014/Final Year 9 8 [Maximum mark: 10] The roots of the equation 0542  xkx , where k is an integer, are  and  . (a) Write down the value of  and  in terms of k . [2 marks] (b) Gi