ACSI 2022 Y6 HL Mathematics Prelim Exam Paper 2 (Questions)

PRELIMINARY EXAMINATION 2022 YEAR 6 IB DIPLOMA PROGRAMME MATHEMATICS: ANALYSIS AND APPROACHES HIGHER LEVEL PAPER 2 Wednesday, 14 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.  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 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 AA HL / Year 6 / 2022 Preliminary Examination / 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. 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: 4] (a) In a circle centre O, radius r, ABis any chord and AOB  where 0    . Find an expression for the area of the minor segment cut off by ABin terms of r and . [1] (b) If this area is one quarter of the area of the circle, show that 2 2sin    . [1] (c) Find the value of AOB . [2]

ACS (Independent) / Mathematics Department / Mathematics AA HL / Year 6 / 2022 Preliminary Examination / Paper 2 2 2. *[Maximum mark: 4] The derivative of a function f is given by ' sin cosf x x x , where x. The graph of f passes through the point ,03     . Find f x in exact form.

ACS (Independent) / Mathematics Department / Mathematics AA HL / Year 6 / 2022 Preliminary