ACSI 2017 Promo Paper 2

FINAL EXAMINATION 2017 YEAR 5 IB DIPLOMA PROGRAMME MATHEMATICS HIGHER LEVEL PAPER 2 Monday 16th October 2017 2 hours _________________________________________________________________________ INSTRUCTIONS TO CANDIDATES • Write your session number in the boxes above. • Do not open this examination paper until instructed to do so. • A graphic display calculator is required for this paper. • Section A: answer all questions in the boxes provided. • Section B: answer all questions on the writing paper provided. Fill in your session number on each answer sheet, and attach them to this examination paper using the string provided. • Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. • A clean copy of the Mathematics HL and Further Mathematics HL formula booklet is required for this paper. • The maximum mark for this examination paper is [100 marks] This question paper consists of 12 printed pages including this cover page. Section A (50 Marks) Section B (50 Marks) Question Marks Question Marks 1 9 2 3 10 4 5 6 11 7 8 Subtotal Subtotal TOTAL / 100 Candidate Session Number 0 0 2 3 2 9

ACS (Independent) / Mathematics Department / Mathematics HL / 2017/Final Exam / Paper 2 1 Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. In particular, solutions found from a graphic display calculator should be supported by suitable working, e.g. if graphs are used to find a solution, you should sketch these as part of your answer. 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. Section A Answer all questions in the boxes provided. Working may be continued below the lines if necessary. 1. [Maximum mark: 6] Solve the following equations ( ) 3 2 12 log 3 xy e xy e + = +=

ACS (Independent) / Mathematics Department / Mathematics HL / 2017/Final Exam / Paper 2 2 2. [Maximum mark: 7] At the start of the first year, a student puts in 1000 dollars into a new savings account. At the end of that year, he earned a fixed interest of 1.2% after which he withdraws a sum of p dollars. The student continues with this practice of withdrawing p dollars annually for a total of 7 years. If the total balance in the account at the end of 7 years is $439.52, find p .

ACS (Independent) / Mathematics Department / Mathematics HL / 2017/Final Exam / Paper 2 3 3. [Maximum mark: 6] Given that 1 34zi= + and ( )3 44 3zi = ++ , (a) Find 2z if 12 3zz z+= . [2] (b) Hence find the coordinates of a point B which is on a bearing of 330° and a distance of 4 km from poi