ACSI 2011 Y3 Core Mathematics Paper 2

Anglo - Chinese School (Independent) FINAL EXAMINATIONS 2011 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 Monday 10 October 2011 1 h 30 min INSTRUCTIONS TO STUDENTS 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, fasten the answer sheets together. Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. INFORMATION FOR STUDENTS The maximum mark for this paper is 80. ___________________________________________________________ __________ This question paper consists of 07 printed pages. [Turn over

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2011/FinalExamination 2 A 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 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) Solve 2 500323 xx  , giving your answer correct to 2 decimal places. [4 marks] (b) Find the range of values of x for which x (1 – x) < x² – 6. [3 marks] 2 [Maximum mark: 4] A cuboid has a square base of side )51(  m and a volume of )152)(25(  m3 . Find the height of the cuboid in the form ).5( ba 3 [Maximum mark: 4] The figure shows a right circular cone inscribed in a sphere with centre O and radius of 1 cm. The cone has a height AB and a base radius AC. Given that AOC radians, express the volume of the cone in terms of . [Volume of a Sphere= ,3 4 3r Volume of a cone= ]3 1 2hr C O B ѳ A 1 cm

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2011/FinalExamination 3 4 [Maximum mark: 7] Singapore Airlines has a fleet of aircraft consisting of 50 aircraft of type A, 80 of type B and 70 of type C. Each type has 3 classes of seat known as Economy, Business and First Class. The table below shows the number of these seats in each of the 3 types of aircraft. Type of Aircraft Economy Business First Class A 350 80 50 B 200 50 30 C 120 25 10 (a) Write down the two matrices whose product shows the total number of seats in each class. [2 marks] (b) Evaluate the product of the two matrices. [2 marks] On a typical day, each aircraft made one flight. It was found that 5%, 10% and 20% of the Economy, Business and First Class seats respectively were em