ACSI 2022 Promo Paper 1

FINAL EXAMINATION 2022 YEAR 5 IB DIPLOMA PROGRAMME MATHEMATICS : ANALYSIS AND APPROACHES HIGHER LEVEL PAPER 1 Tuesday 20 September 2022 2 hours _________________________________________________________________________ INSTRUCTIONS TO CANDIDATES • Write your session number in the boxes above. • Do not open this examination paper until instructed to do so. • You are not permitted access to any calculator for this paper. • Section A: answer all questions. Answers must be written within 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 : 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 & SL papers This question paper consists of 14 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 / 2022 Final Examination / Paper 1 1 Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. 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: 5] Solve the following equation. 9 12 3 27 0xx−  + =

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2022 Final Examination / Paper 1 2 2.* [Maximum mark: 6] Given that 33 2 9 9log 1 log lg lg 2lg 9 125 5xy= + = − + , find the values of x and y .

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2022 Final Examination / Paper 1 3 3.* [Maximum mark: 6] (a) Show that ln x , 2ln x and 3ln x are 3 consecutive terms of an arithmetic progression. [2] (b) Solve 10 1 ln 55k k x = = . [4]

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2022 Final Examination / Paper 1 4 4.* [Maximum mark: 7] (a) Find the term independent of x in the expansion of 6 2 1px x  + in terms of p . [5] (b) Given that the term independent of x is 60, find the value