ACSI 2021 Y3 Core Mathematics Paper 1 Solution

ACS(Independent)/Y3IPCoreMathP1/2021/FinalExamination 1 Anglo - Chinese School (Independent) FINAL EXAMINATION 2021 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 Friday 1st October 2021 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. Paper 1 containts more straight-forward questions, but many students made careless mistakes in expansion, simplification and factorisation. They do not check the workings and verify the answers with the knowledge or the facts they learned. Many students still could not give the form of equation properly and they wrote expression instead. _______________________________________________________________________________________ This paper consists of 15 printed pages and 1 blank page. [Turn over For Examiner’s Use Candidate Index Number

ACS(Independent)/Y3IPCoreMathP1/2021/FinalExamination 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: 9] (a) Evaluate 34 33 33 4 − − − . [3 marks] (b) Make q the subject of the formula, 32 .5 qpp q −= + [3 marks] (c) Factorise 3 2 2 2 12 4 3x x y xz yz− − + completely. [3 marks] 1 (a) 3344 3333 393 44 3 4 43 3 3 4 5 3 9 4 5 11 5 − = − −− − =− − =− =− = (b) ( ) 2 22 22 2 2 32 5 32 5 5 3 2 3 2 5 25 3 qpp q qpp q p q p q p q p p p ppq p −= + −= + + = − − =− − −−= − © ( ) ( ) ( )( ) ( )( )( ) 3 2 2 2 22 22 12 4 3 4 3 3 43 2 2 3 x x y xz yz x x y z x y x z x y x z x z x y − − + = − − − = − − = + − − Students made careless mistake in simplifying the fraction in fraction. Students did not factorise completely the last step. Since the question wants q to be subject, q must not appear on the right hand side of the equation.

ACS(Independent)/Y3IPCoreMathP1/2021/FinalExamination 3 2. [Maximum mark: 8] (a) Sketch the graph of 2 9yx= − clearly labelling the coordinates of the axes -intercepts and turning point. [2 marks] (b) The curve 2 9yx= − meets the line 26yx=+ at points P and Q. Find the coordinates of P and Q.