ACSI 2023 Y3 Core Mathematics Paper 1

ACS(Independent)/Y3IPCoreMathP1/2023/Final Exam Anglo - Chinese School (Independent) FINAL EXAMINATION 2023 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 Friday 29 th September 2023 1 hour 30 minutes 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. _______________________________________________________________________________ This paper consists of 16 printed pages. [Turn over For Examiner’s Use Candidate Index Number

ACS(Independent)/Y3IPCoreMathP1/2023/Final Exam 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: 5] (a) Evaluate 312 42 11 4 − − . [2] (b) Simplify ( ) 342 26 164 2 1 14 7 ab bc b − − ÷ , leaving your answer in positive index. [3] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

ACS(Independent)/Y3IPCoreMathP1/2023/Final Exam 3 2. [Maximum mark: 4] The graph ( ) 2 23 4yx m= − +− has a minimum point at ( )3, 8 ,− where m is a constant. (a) Find the value of m. [1] (b) Hence, sketch the graph of ( ) 2 23 4yx m= − +− . Label the coordinates of the axes - intercepts and turning point clearly. [3] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ y O x

ACS(Independent)/Y3IPCoreMathP1/2023/Final Exam 4 3. [Maximum mark: 7] (a) Simplify 108 4 2718 333 +− . [2] (b) (i) Given that the points ( ) ( ) ( ), 1 , , and , 5 5 353P Qx R lie on the same straight line, find the value of x. [3] (ii) Find the length of PR, in the form unitsab , where a and b are integers. [2] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ......................................................................................................................