ACSI 2023 Promo Paper 2

FINAL EXAMINATION 2023 YEAR 5 IB DIPLOMA PROGRAMME MATHEMATICS : ANALYSIS AND APPROACHES HIGHER LEVEL PAPER 2 Monday 25 September 2023 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 should 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] This question paper consists of 11 printed pages including this cover page. Section A (55 Marks) Section B (55 Marks) Question Marks Question Marks 1 9 2 3 4 10 5 6 7 11 8 Subtotal Subtotal TOTAL / 110 Candidate Session Number 0 0 2 3 2 9

ACS (Independent) / Mathematics Department / Mathematics AA HL / Year 5 / 2023 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: 7] Consider the geometric sequence 2,8,32,… (a) Write down the common ratio of the sequence. [1] (b) Find the largest term of the sequence that has only four digits. [3] (c) The sum of n terms of this geometric series is less than 100000. Find the largest possible value of n. [3]

ACS (Independent) / Mathematics Department / Mathematics AA HL / Year 5 / 2023 Final Examination / Paper 2 3 2. [Maximum mark: 7] (a) Prove that 2log log . aa mm= [3] (b) Hence, solve the equation 2log 3log 2 5, xx+= giving your answer in exact form. [4]

ACS (Independent) / Mathematics Department / Mathematics AA HL / Year 5 / 2023 Final Examination / Paper 2 4 3. [Maximum mark: 8] A quadratic function 𝑓𝑓(𝑥𝑥) = 𝑎𝑎(𝑥𝑥 − 𝜆𝜆)