ACSI 2018 Promo Paper 2

FINAL EXAMINATION 2018 YEAR 5 IB DIPLOMA PROGRAMME MATHEMATICS HIGHER LEVEL PAPER 2 Wednesday 10th October 2018 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 11 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 / 2018/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] The hours of sunlight in each day of a year, ()ht , where t is the day of the year, is given by ( ) 2.4sin(0.0172 1.38) 12, 1 365h t t t= − +   . (a) Find the maximum hours of sunlight and the minimum hours of sunlight in a day. (b) Find the number of days where there is less than 12 hours of sunlight.

ACS (Independent) / Mathematics Department / Mathematics HL / 2018/Final Exam / Paper 2 2 2. [Maximum mark: 4] Planes 1 , 2 and 3 have equations 2 3 9x y z+ + = , 2x y z k− + = and 33x kz+= respectively, where k is a constant. (a) Given that k = 2, find the point of intersection of 1 , 2 and 3 . (b) Given instead that k = 3, describe the relationship between 1 , 2 and 3 .

ACS (Independent) / Mathematics Department / Mathematics HL / 2018/Final Exam / Paper 2 3 3. [Maximum mark: 5] (a) Find the complex