SJI 2022 Year 6 HL MAA Prelim Examination Paper 2

STUDENT NAME: _____________________________ TEACHER NAME: _____________________________ ST. JOSEPH’S INSTITUTION YEAR 6 PRELIMINARY EXAMINATION 2022 MATHEMATICS: ANALYSIS AND APPROACHES HIGHER LEVEL PAPER 2 Friday 19 August 2022 2 hours 1400 – 1600 hrs INSTRUCTIONS TO CANDIDATES  Write your session number in the boxes above.  Write your name and teacher’s name in the spaces provided.  Do not open this examination paper until instructed to do so.  Section A: Answer all questions showing working and answers in the spaces provided in the exam paper.  Section B: Answer all questions using the foolscap paper provided.  The use of a scientific or examination graphical calculator is permitted in this paper.  TI-Nspire calculators must be in Press-to-Test mode and cleared of all previous data.  TI-84+ graphical calculators must only have permitted apps and be ram cleared.  A clean copy of the Mathematics: Analysis and Approaches formula booklet is required for this paper.  Unless otherwise stated in the question all numerical answers must be given exactly or correct to three significant figures.  The maximum mark for this examination paper is [110 marks].  Number of printed pages = 14.  Sections A and B are to be submitted separately. ___________________________________________________________________________ FOR MARKER USE ONLY: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 TOTAL /110

Year 6 Mathematics: Analysis and Approaches HL Preliminary Examination 2022/P2 2 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, for example, 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 advised to show all working. SECTION A (53 marks) Answer all questions in the spaces provided. 1 [Maximum mark: 6] The graph of the function 7logh x x a b   passes through the points 0,1 and 3 7e , 1 log 2 . Find the value of a and the value of b. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… TURN OVER

Year 6 Mathematics: Analysis and Approaches HL Preliminary Examination 2022/P2 3 2 [Maximum mark: 7] For 3 4 4x   , find the value of x for which the sum to infinity 2 3 1 1 1 tan tan tanx x x    equals to tanx. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… TURN OVER

Year 6 Mathematics: Analysis and Approaches HL Preliminary Examination 2022/P2 4 ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… TURN OVER

Year 6 Mathematics: Analysis and Approaches HL Preliminary Examination 2022/P2 5 3 [Maximum mark: 7] The functions f and g are defined by  2 2 15,f x x x    for 5 1x   ,g x x c  for ,x c. (a) Find 1 2f  [4] (b) Find the range of f. [1] (c) Given that 0g f x  for 5 1,x    determine the set of possible values for c. [2] ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… TURN OVER

Year 6 Mathematics: Analysis and Approaches HL Preliminary Examination 2022/P2 6 4 [Maximum mark: 6] Alex and Bobby have each been given $1000 to save for university. Alex invests his money in an account that pays a nominal annual interest rate of 2.35% compounded half-yearly. (a) Calculate the amount Alex will have in his account after 5 years. Give your answer correct to 2 decimal places. [3] Bobby wants to invest his money in an account such that his investment will increase to 2 times the initial amount in 5 years. Assume the account pays a nominal annual interest of p% compounded quarterly. (b) Determine the value of p. [3] ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… TURN OVER

Year 6 Mathematics: Analysis and Approaches HL Preliminary Examination 2022/P2 7 5 [Maximum mark: 5] Six vectors 2 3 4 5 6, , , , ,1v v v v v v are each chosen to be either 1 1     or 3 2     with equal probability, with each choice made independently. Find the probability that the sum 2 3 4 5 6    1v v v v v v is equal to the vector 10 8     . ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… …………………………………………………………………