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] ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ………………………… ……………………………………………………………………………………..

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2020 FE/ Paper 1 3 2. *[Maximum mark: 6] 9, m, n are consecutive terms of a geometric progression and 9, 2m and 3n are consecutive terms of an arithmetic progression. Given that mn≠ , find the value of m and of n. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………..

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2020 FE/ Paper 1 4 3. *[Maximum mark: 6] Given that , find the value of x . ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. �[𝑘𝑘 + 𝑙𝑙𝑙𝑙𝑙𝑙2(𝑥𝑥)] 22 𝑘𝑘=3 = 170, 𝑥𝑥 ∈ ℝ

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2020 FE/ Paper 1 5 4. [Maximum mark: 6] , and αβ γ are roots of the equation 32 7 20 50 0zz z+ + += . Without solving for , and αβ γ find the polynomial of degree 3 whose roots are 1, 1 and 1αβ γ−− − . ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………..

ACS (Independent) / Mathematics Department / Mathematics HL / Year 5 / 2020 FE/ Paper 1 6 5. [Maximum mark: 7] The following diagram shows the graph of ()y fx= with x-intercepts at 2− and 0, minimum point (-1, -2) and asymptote 2y= (a) Sketch the graph of ( ) 1 fx in the same diagram above indicating the x-intercepts, turning point and asymptote(s) clearly. [5] (b) If the domain of another function ( )gx is [ ]0,8 and its range is [ ]4,11 , write down the domain and range of ( ) 1 gx whenever possible. [2] y = f(x) ……………………………………………………………………………………………………………….. ……………………………………………………