ACSI 2019 Y3 Core Mathematics Paper 1

ACS(Independent)/Y3IPCoreMathsP1/2019/Final Year 1 FINAL EXAMINATIONS 2019 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 WEDNESDAY 2nd OCTOBER 2019 1 h 30 min Candidates answer on the Question Paper. No additional materials are required. 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 numerical 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 17 printed pages. [Turn over Candidate Index Number

ACS(Independent)/Y3IPCoreMathsP1/2019/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. Wher e 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: 8] (a) (i) Simplify ( )( ) 2 22m m n m n− + − . [2 marks] (ii) Hence, evaluate 220189 20193 20185− . [2 marks] (b) If 22 2ab+= and 22 3cd+= , find the value of ( ) ( ) 22 ac bd ad bc+ + − . [4 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… ……………………………………………………………………[Working may be continued next page]

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ACS(Independent)/Y3IPCoreMathsP1/2019/Final Year 4 2 [Maximum mark: 10] (a) Simplify the following: (i) 11 11 nnaa −+++ , [3 marks] (ii) 215 1 243 3 93 n n nn + −   . [3 marks] (b) Given that 52x=+ , express 2 4 1x + in the form of 5ab+ . [4 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… ……………………………………………………………………[Working may be continued next page]

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ACS(Independent)/Y3IPCoreMathsP1/2019/Final Year 6 3 [Maximum mark: 4] (a) Solve the simultaneous equations 3xy= and 2 32y x= . [2 marks] (b) On the same axes, draw the graphs of 3xy= and 2 32y x= , labelling the point of intersection clearly on your sketch. [2 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2019/Final Year 7 4 [Maximum mark: 8] (a) Given that 82 a−   and 18 b−   , and a and b are integers. Find (i) the smallest possible value of 2ab− , [1 mark] (ii) the greatest possible value of ( ) 2 46 b a++ . [2 marks] (b) Solve the inequality 12 3 3 4 6 14x x x−  −  − and hence state the smallest even number that satisfies the inequal