ACSI 2019 Prelim Exam Y6 HL Paper 2 (Questions)

PRELIMINARY EXAMINATION 2019 YEAR 6 IB DIPLOMA PROGRAMME MATHEMATICS HIGHER LEVEL PAPER 2 24 September 2019 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 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 13 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 6 / 2019 Prelim Exam / 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. 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: 5] ACD is a triangle and B is a point on AC such that BC x= cm and ( )2AB x=+ cm . 48 and 50ooBCD BDCÐ= Ð= . If the area of ∆ 23.06ABD = cm2, find the value of x . B A C D

ACS (Independent) / Mathematics Department / Mathematics HL / Year 6 / 2019 Prelim Exam / Paper 2 2 2. [Maximum mark: 7] Find the value of n if the coefficient of 𝑥𝑥3 in the expansion of (2 + 3𝑥𝑥 + 𝑥𝑥2)𝑛𝑛 is 1560 .

ACS (Independent) / Mathematics Department / Mathematics HL / Year 6 / 2019 Prelim Exam / Paper 2 3 3. [Maximum mark: 5] Solve the following system of equations: ln 2xy= − ln 2yx= −

ACS (Independent) / Mathematics Department / Mathematics HL / Year 6 / 2019 Prelim E