SJI 2024 Year 6 HL MAA Prelim Examination Paper 1

ST JOSEPH’S INSTITUTION YEAR 6 PRELIMINARY EXAMINATION 2024 MATHEMATICS: ANALYSIS AND APPROACHES HIGHER LEVEL PAPER 1 Monday 12 August 2024 2 hours 0900 – 1100 hrs INSTRUCTIONS TO CANDIDATES  Write your session number in the boxes above.  Write your name and your teacher’s name in the spaces provided.  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 showing working and answers in the spaces provided in the exam paper.  Section B: Answer all questions using the writing paper provided.  Unless otherwise stated in the question, all numerical answers should to 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].  This question paper consists of 11 printed pages including the Cover Sheet.  Sections A and B are to be submitted separately. _______________________________________________________________________ FOR MARKER USE ONLY: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 TOTAL / 110 STUDENT NAME: TEACHER NAME:

Year 6 Mathematics: Analysis and Approaches HL Preliminary Examination 2024/P1 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 advised to show all working. SECTION A (55 marks) Answer all questions in the spaces provided. 1 [Maximum mark: 5] The functions f and g are defined by   1 , 13 xf x x   and   218 5 , 0g x x x   . (a) Show that    22 4 3g f x x x    . [2] (b) Given that     1 2g f a   , find the value of a . [3] …………………………………………………………………………………………………...……… …………………………………………………………………………………………………...……… …………………………………………………………………………………………………...……… …………………………………………………………………………………………………...……… …………………………………………………………………………………………………...……… …………………………………………………………………………………………………...……… …………………………………………………………………………………………………...……… …………………………………………………………………………………………………...……… …………………………………………………………………………………………………...……… …………………………………………………………………………………………………...……… …………………………………………………………………………………………………...……… ……………………………………………………………………………………………………...…… TURN OVER

Year 6 Mathematics: Analysis and Approaches HL Preliminary Examination 2024/P1 3 2 [Maximum mark: 5] (a) Expand   6 1 1 4 x x   in ascending powers of x, up to and including the term in x3. [4] (b) State the range of values of x for which the expansion in part (a) is valid. [1] …………………………………………………………………………………………………...……… …………