ACSI 2022 Y6 Math HL Prelim P1 Question Paper

PRELIMINARY EXAMINATION 2022 YEAR 6 IB DIPLOMA PROGRAMME MATHEMATICS: ANALYSIS AND APPROACHES HIGHER LEVEL PAPER 1 Tuesday 13 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. • You are not permitted access to any calculator for this paper. • Section A: answer all questions. Answers must be written within 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: 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 & 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 AA HL / Year 6 / 2022 Preliminary Examination / 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. 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. Do not write solutions on this page. 1. *[Maximum Mark: 7] (a) Given that 1sin 3 A= and that A is acute. (i) Find the exact value of tan .A (ii) Hence, find the value of tan 2 A  in the form ,mn− where m and n are integers. [4] (b) Solve the equation 2sin tanxx= for .22 xππ−<< [3] -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------

ACS (Independent) / Mathematics Department / Mathematics AA HL / Year 6 / 2022 Preliminary Examination / Paper 1 2 2. *[Maximum Mark: 5] Consider the expression 2 n kx x  + where k and n are positive integers. (a) Given that there are 11 terms in the expansion, state the value of .n [1] (b) For this value of ,n find the value of k given that the coefficient of 14x is 180. [4] -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------

ACS (Independent) / Mathematics Department / Mathematics AA HL / Year 6 / 2022 Preliminary Examination / Paper 1 3 3. *[Maximum Mark: 7] Consider the function () , 6 xfx cx= + where 0.c≠ (a) The line 2x=− is a vertical asymptote to the graph of ( ).y fx= Find the value of .c [1] (b) State the equation of the horizontal asymptote to the graph of ( ).y fx= [1] (c) On the set of axes below, sketch the graph of ( ),y fx= indicating all asymptotes and any axial intercept(s). [3] (d) Hence, solve the inequality 0 ( ) 2.fx<< [2] -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------

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