ACSI 2012 Y3 Core Mathematics Paper 2

ACS(Independent)/Y3IPCoreMathsP2/2012/Endyear 1 Anglo - Chinese School (Independent) FINAL YEAR EXAMINATION 2012 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 Monday 8 October 2012 1 hour 30 minutes Additional Materials Answer Paper ( 6 sheets) Graph Paper ( 1 sheet) INSTRUCTIONS TO CANDIDATES • Write your index number in the boxes on the cover page. • Do not open this examination paper until instructed to do so. • A calculator is required for this paper. • Answer all the questions on the answer sheets provided. • At the end of the examination, attach the answer sheets to the cover page 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 6 printed pages. [Turn over

ACS(Independent)/Y3IPCoreMathsP2/2012/Endyear 2 Full marks are not necessarily awarded for a co rrect 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 on the answer sheets provided. Please start each question on a new page. 1. [Maximum mark: 7] A triangular prism is shown in the diagram above. BCDE , ACDF and ABEF are rectangles. It is given that M is the midpoint of BC , 5 cmAB AC= = , 8 cmBC= and 12 cmCD= . (Volume of prism = Area of cross-section × Length) i) Find ADM∠ . [4 marks] ii) Find the volume of the prism. [3 marks] 2. [Maximum mark: 7] The two curves 33yx= and 2 5y x= intersect at the point A. i) Find the coordinates of the point A. [3 marks] ii) Hence sketch the graphs of 33yx= and 2 5y x= on the same diagram, indicating clearly the coordinates of Aand where the graphs cut the axes (if any). [4 marks] M 12 cm 5 cm F E D C B A 8 cm

ACS(Independent)/Y3IPCoreMathsP2/2012/Endyear 3 3. [Maximum mark: 8] The diagram above shows the cross-section of a ci rcular tube used in a wind instrument, with point Oas the centre. The regular octagon ABCDEFGH is a hollow section which fits exactly in the tube with all 8 vertices on the ci rcumference of the circle. It is given that the radius mmOB x= and the length of the chord 7 mmAB= . i) Find AOB∠ . [2 marks] ii) Show that 9.146 mmx= , correct to 3 decimal places. [3 marks] iii) Find the area of the octagon ABCDEFGH . [3 marks] B F G H E D C A O x mm 7 mm

ACS(Independent)/Y3IPCoreMathsP2/2012/Endyear 4 4. [Maximum mark: 10]