ACSI 2017 Y3 Core Mathematics Paper 1

ACS(Independent)/Y3IPCoreMathsP1/2017/Final Year 1 FINAL EXAMINATIONS 2017 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 WEDNESDAY 4th OCTOBER 2017 1 h 30 min 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)/Y3IPCoreMathsP1/2017/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: 3] (i) Simplify ( )( ) 2papap −−+ . [1 mark] (ii) Hence, evaluate 2489164891348919 − . [2 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2017/Final Year 3 2 [Maximum mark: 7] (a) Evaluate 12 3 112 12 −      −−     − . [2 marks] (b) Simplify the following (i) ( ) 3212 −−−     x , leaving your answer in the positive power. [2 marks] (ii) ( ) 12 73 42 32 −− −  zxy yx zy yx , giving your answer in the from rqp zyx , where p , q and r are rational numbers. [3 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2017/Final Year 4 3 [Maximum mark: 9] (a) Given that 2 14 −− x and 71 − y , find (i) the smallest possible value of 3xy− , [2 marks] (ii) the greatest possible value of x y 2 . [2 marks] (b) Solve 2 1 4 65 2 3 +−− xxx and state the integer that satisfies the inequality. [5 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2017/Final Year 5 4 [Maximum mark: 10] Three points A, B and C have coordinates ( )1,2 − , ( )3,6 and ( )3,2 −− respectively. If D is the mid-point of AB, find (i) the coordinates of D, [1 mark] (ii) the equation of the line 1L which passes through D and is parallel to BC, [3 marks] (iii) the coordinates of E, the point where 1L cuts xy =+ 42 . [3 marks] (iv) the area of BCED. [3 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… ……………………………………………………………………[Working may be continued next page]

ACS(Independent)/Y3IPCoreMathsP1/2017/Final Year 6 …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2017/Final Year 7 5 [Maximum mark: 3] It is given that x and y are related by       −= y xx 53ln . If a straight line PQ is obtained by plotting ye x against xy , find the gradient of the line PQ. …………………………………………………………………………………………….…………… ………………