ACSI 2021 Promo Paper 2

FINAL EXAMINATION 2021 YEAR 5 IB DIPLOMA PROGRAMME MATHEMATICS HIGHER LEVEL PAPER 2 FRIDAY 24 SEP 2021 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. Answers must be written within the answer 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 Analysis and Approaches formula booklet is required for this paper. • The maximum mark for this examination paper is [110 marks] • Questions with an asterisk (*) are common to both HL and SL papers This question paper consists of 12 printed pages including this cover page. Section A (55 Marks) Section B (55 Marks) Question Marks Question Marks 1 10 2 3 4 11 5 6 7 12 8 9 Subtotal Subtotal TOTAL / 110 Candidate Session Number 0 0 2 3 2 9

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2021 Final Examination / Paper 2 2 Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. Solutions found from a graphic display calculator should be supported by suitable working. For example, 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. Answers must be written within the answer boxes provided. Working may be continued below the lines, if necessary. 1. *[Maximum mark: 6] An infinite geometric sequence has the first term 1. The sum of the first three terms is 2. The terms in the sequence are all positive. (a) Find the common ratio. [3] (b) Find the sum of the infinite sequence. [3]

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2021 Final Examination / Paper 2 3 2. [Maximum mark: 6] (a) Express ( )( ) 5 13 12xx+− in partial fractions. [2] (b) Hence expand ( )( ) 5 13 12xx+− as a series of ascending powers of x up to and including the term in 3.x [4]

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2021 Final Examination / Paper 2 4 3. *[Maximum mark: 4] The moment magnitude scale, M, is a m