ACSI 2020 Y3 Core Mathematics Paper 1

Confidential – for internal circulation only FINAL EXAMINATIONS 2020 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 FRIDAY 2nd OCTOBER 2020 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 and 1 blank page. [Turn over Candidate Index Number

ACS(Independent)/Y3IPCoreMathsP1/2020/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: 4] (a) Evaluate ( )( )2 10002 10002 2−+ [2 marks] (b) If 2ab ab − =+ , find the value of a b . [2 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2020/Final Year 3 2 [Maximum mark: 6] (a) Express 23 42mm ++− as a single fraction. [2 marks] (b) Make y the subject of the formula yzx yz += − . [4 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2020/Final Year 4 3 [Maximum mark: 7] (a) Simplify 2 3 5( 1) 43 x x x xx  −+   − . [3 marks] (b) (i) Hence, solve 2 3 5( 1)05 43 x x x xx  −+   − . [3 marks] (ii) State the largest integer value of x that satisfy the inequalities. [1 mark] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2020/Final Year 5 4 [Maximum mark: 5] A cuboid consisting of a rectangular base of breadth 35− cm and length 51+ cm has a volume of 48 16 5− cm3. Find the height of the cuboid in the form ( 5 1)a − , where a is an integer to be determined. [5 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….……………

ACS(Independent)/Y3IPCoreMathsP1/2020/Final Year 6 5 [Maximum mark: 9] Consider the equation 2 6 15y x x=− − + , (a) Write the expression 2 6 15xx− − + in the form 2()x h k− + + , where h and k are constants to be determined. [2 marks] (b) State the coordinates of the turning point of 2 6 15y x x=− − + . [1 mark] (c) Solve the equation 2 6 15xx− − + , simplifying your answers and leaving them in surd form. [3 marks] (d) Sketch the graph of 2 6 15y x x=− − + , stating the coordinates of the points of intersection with the axes and turning point clearly. [3 marks] …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… …………………………………………………………………………………………….…………… ……………………………………………………………………[Working may be continued next page]

ACS(Independent)/Y3IPCoreMathsP1/2020/Final Year 7 [Continuation of working space for Question 5]………………………………………….…………… …………………………………………………………………………