ACSI 2019 Promo Paper 2

FINAL EXAMINATION 2019 YEAR 5 IB DIPLOMA PROGRAMME MATHEMATICS HIGHER LEVEL PAPER 2 26th September 2019 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 / 2019/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: 5] Consider the ΔABC with 18BAC = ° , 6AC = units and 3BC = units. Find the possible values of the length of AB .

ACS (Independent) / Mathematics Department / Mathematics HL / 2019/Final Exam / Paper 2 2 2. [Maximum mark: 6] (a) Given that * 22 13 iz i −= −+ , find the values of z and arg(z). [4] (b) Hence, find the value of arg(– z). [2]

ACS (Independent) / Mathematics Department / Mathematics HL / 2019/Final Exam / Paper 2 3 3. [Maximum mark: 4] Consider the system of equations: 21 23 22 0 xy z xyz x y kz −+ = − +−= −+= (a) Given k = 2, find the solution of the system. [2] (b) Comment on the system, with clear explanation, when k = 4. [2]

ACS (Independent) / Mathematics Department / Mathematics HL / 2019/Final Exam / Paper 2 4 4. [Maximum mark: 7] The