ACSI 2018 Y3 Core Mathematics Paper 1

ACS(Independent)/Y3IPCoreMathsP1/2018/Final Year 1 FINAL EXAMINATIONS 2018 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 WEDNESDAY 3rd OCTOBER 2018 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 16 printed pages. [Turn over Candidate Index Number

ACS(Independent)/Y3IPCoreMathsP1/2018/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) Evaluate 53 53 53 3 − − − . [3 marks] (b) Make x the subject of the formula, 2 1 xy x −= + . [2 marks] (c) Factorize 2 2 2()x y x y+ − + completely. [3 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… ……………………………………………………………………[Working may be continued next page]

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ACS(Independent)/Y3IPCoreMathsP1/2018/Final Year 4 2 [Maximum mark: 7] (a) Given that 14 2x−  − and 71 − y , and x and y are integers. Find (i) the smallest possible value of 3yx− , [1 mark] (ii) the greatest possible value of 2 x y . [1 mark] (b) Solve 1 6 1 3 2 4 2 xxx −−   + and state the largest integer that satisfies the inequality. [5 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2018/Final Year 5 3 [Maximum mark: 6] Solve the simultaneous equations xyx 1 4 16324 =− , 1log3577 = yx . …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2018/Final Year 6 4 [Maximum mark: 6] (a) Simplify ( ) 2 9321 32 64 xx − −−−    . [3 marks] (b) Solve for x if ( ) 2 2 129 3 10 3 10xx +− = + . Leave your answer in the form of lgab where a and b are rational numbers. [3 marks] ……………………………………………………………………………………………………….… ……………………………………………………………………………………………………….… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2018/Final Year 7 5 [Maximum mark: 6] It is given that x and y are related by the equation pxxq y−= where p and q are constants. When y is plotted against y x , a straight-line graph is obtained. The line has gradient 3 and it passes through ( )1, 5 . (a) Find