ACSI 2017 Y3 Core Mathematics Paper 2

FINAL EXAMINATION 2017 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 MONDAY 9th October 2017 1 hour 30 minutes 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 5 printed pages. [Turn over

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2017/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: 10] (a) It is given that 2 2 1 atuts += . (i) Express a in terms of s , u and t . [2] (ii) Find the value of a when 4.12=s , 256.0=u and 25.0=t , leaving your answer corrected to the nearest whole number. [2] (b) Solve the equation 8 1 1 4 −=− y y , leaving your answers in the simplest surds. [3] (c) A man bought m pencils at r dollars per dozen. He sold them for k cents each. Find an expression, in terms of m , r and k , for the profit, in cents, that he made. [3] 2 [Maximum mark: 6] Find the value(s) of k for which the line kyx =+ is a tangent to the curve 53 22 =+− yxx . [6] 3 [Maximum mark: 11] Solve the following equations: (a) 7323 6482 +−+ = xxx [3] (b) 3 122loglog 82 =+ xx [4] (c) Solve the equation t t ee 721 =+− , giving your answer correct to 2 decimal places. [4]

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2017/FinalExamination 3 4 [Maximum mark: 7] (a) The sum S of the first n integers is given by the formula )1(2 1 += nnS . What is the minimum number of integers required in order for the sum to exceed 325? [3] (b) Find the values of the integers a and b such that 52 525 525 5 + += + + ba . [4] 5 [Maximum mark: 10] In the diagram, the points A, B, C and D are on level ground. The point D is equidistant from A and C and ∠ADC = 90o. C is due north of A, AC = 37 m, BC = 40 m and ∠BCA = 55o. Calculate (a) the area of △ 𝐴𝐵𝐶, [2] (b) ∡𝐶𝐵𝐴, [4] (c) the distance AD, [2] (d) the bear