ACSI 2020 Y3 Core Mathematics Paper 2

FINAL EXAMINATION 2020 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 WEDNESDAY 7th October 2020 1 hour 30 minutes ADDITIONAL MATERIALS: Answer Paper (7 sheets) Graph Paper ( 1 sheet) 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. Answers in degrees are to be given to one decimal place. INFORMATION FOR STUDENTS The maximum mark for this paper is 80. _____________________________________________________ This question paper consists of 4 printed pages. [Turn over

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2020/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 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. Begin each question on a new page. 1. [Maximum mark: 6] (a) Evaluate 2 4 (0.3578) 7.647 43.96  , leaving your answer correct to 3 significant figures. [2] (b) Express 2 1 1 10 3 2 2 4 x x x x ++++ − − as a single fraction in its simplest form. [4] 2 [Maximum mark: 7] (a) Solve the equation 923 2x x−= , giving your answers correct to two decimal places. [4] (b) Expand and simplify 2 1 2 1 2 4 3 3 3 3 3 3p q q q p p  + − +      . [3] 3 [Maximum mark: 9] (a) Simplify ( ) ( ) 32 12 44 2 3 24 (4 ) xx xx − −  , expressing your answer in positive indices. [3] (b) Given that 1 2 2 21 16 2(2 ) 28 xx xx k + −+ + = , find the value of k . [3] (c) Find the value of 1 1 1 log log logpqrpqr pqr pqr++ . [3]

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2020/FinalExamination 3 4 [Maximum mark: 15] The diagram shows four towns A, B, C and D. Given that Town C and Town D lie west of B, AB = 8.2 km, BC = 8.8 km, CD = 9.3 km and 118oACD= , calculate (a) ABC , [4] (b) the bearing of B from A, [2] (c) the distance AD. [3] A cyclist starts from D at 1030 and travels towards A at a constant speed of 15 km/h. (d) Find the time, to the nearest minute, when he will be nearest to Town C. [6] 5 [Maximum mark: 13] (a) The equation of a curve is 23 3 12y qx px q= − + where p and q are positive i