ACSI 2017 Promo Paper 1

FINAL EXAMINATION 2017 YEAR 5 IB DIPLOMA PROGRAMME MATHEMATICS HIGHER LEVEL PAPER 1 11th October 2017 2 hours _________________________________________________________________________ INSTRUCTIONS TO CANDIDATES  Write your session number in the boxes above.  Do not open this examination paper until instructed to do so.  No calculators are allowed 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 12 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 / Year 5 / 2017 Final Exam / 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. 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: 6] (a) Find the term independent of x in the expansion of 6 2 2x x   . [3] (b) Prove that 11 nn nr rr r          . [ 3 ]

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2017 Final Exam / Paper 1 2 2. [Maximum mark: 5] The diagram shows the graph of f . (a) On the same diagram, sketch the graph of 1f . [4] (b) Hence find the point of intersection of ()f x and 1()f x . [1]

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2017 Final Exam / Paper 1 3 3. [Maximum mark: 5] The cubic polynomial ()f x and quadratic polynomial ()p x are related by the following equation: () ()( 1 ) 4fx p x x   . The roots of ()f x are at 2x and 3x . Find 32()f x x Ax Bx C   , where A , B and C are constants to be determined.

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2017 Final Exam / Paper 1