ACSI 2020 Promo Paper 1

FINAL EXAMINATION 2020 YEAR 5 IB DIPLOMA PROGRAMME MATHEMATICS HIGHER LEVEL PAPER 1 TUESDAY 22 SEP 2020 2 hour _________________________________________________________________________ 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 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 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 / 2020 FE/ Paper 1 2 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 in the boxes provided. Working may be continued below the lines if necessary. 1. [Maximum mark: 7] The lengths of two sides of a triangle are 4 cm and 5 cm. Let θ be the angle between the two given sides. The area of the triangle is 5 15 2 2cm . (a) Show that 15sin 4θ = [2] (b) Find the two possible values of the length of the third side. [5] ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. …………………………