SJI 2023 Year 6 HL MAA Prelim Examination Paper 2

/110 Q7 Q8 Q9 Q10 Q11 TOTAL eparately. paper is [110 marks]. ysis and Approaches formula booklet is all numerical answers must be given FOR MARKER USE ONLY: Q1 Q2 Q3 Q4 Q5 Q6 Sections A and B are to be submitted se exactly or to three significant figures. The maximum mark for this examinatior Number of printed pages = 15. A clean copy of the Mathematics: Anal required for this paper. Unless otherwise stated in the questic -Test mode and cleared of all previous data. ave permitted apps and be ram cleared he foolscap paper provided. aphical calculator is permitted in this paper. the spaces provided. I instructed to do so. g working and answers in the spaces above. 0900 - 1100 hrs CHES 24 August 2023 2 hr TI-Nspire calculators must be in Press-to TI-84+ graphical calculators must only h provided in the exam paper. Section B: Answer all questions using t The use of a scientific or examination gr Write your name and teacher's name in Do not open this examination paper unti Section A: Answer all questions showin INSTRUCTIONS TO CANDIDATES Write your session number in the boxes PAPER 2 Thursday MATHEMATICS: ANALYSIS AND APPROA HIGHER LEVEL RY EXAMINATION 2023 TUTION 2 U L EXAMINATION CODE 8 8 2 3 7 1 0 2 CANDIDATE SESSION NUMBER YORAETLABORA. YEAR 6 PRELIMINAF ST. JOSEPH'S INSTI STUDENT NAME: TEACHER NAME:

2 TURN OVER ce. [2](c) each digit may be used at most twic [1] can be formed using the digits 1, 2 and 3 when A (54 marks) provided this is shown by written working. You In particular, solutions found from a graphic ble working, for example, if graphs are used to of your answer. Where an answer is incorrect, Approaches HL Preliminary Examination 2023/P2 eorrect answer with no workina Answers must (a) no repetitions are allowed, (b) any repetitions are allowed 1 [Maximum mark: 4] Find the number of 3-digit numbers that SECTION A Answer all questions in the spaces provided. some marks may be given for a correct method, are advised to show all working. be supported by working and/or explanations. display calculator should be supported by suita find a solution, you should sketch these as part Year 6 Mathematics: Analysis and Full marks are not necessarily awarded for a d

TURN OVER expansion. [4] [2] 45 the coefficient of xn-2 is 4 Approaches HL Preliminary Examination 2023/P2 (a) Find the value of n. (b) Hence find the middle term in the e 1 In the expansion of ( -)2 for n e Z+, Year 6 Mathematics: Analysis and IMaximum mark• 91

TURN OVER Approaches HL Preliminary Examination 2023/P2 Show that 4(cos+ 0+sin* 0) =3+cos 40 २ Year 6 Mathematics: Analysis and IMaximum mar 51

5 TURN OVER [3] [2] [2] 4 5 (c) Find E(Y) and Var(). (b) Find P(Y = y) for y = 1, 2, ..., 6. 4 5 6 4 5 6 are equal. h gives the possible outcomes of Y. non die 1 and die 2 respectively. mber shown on the two dice or the common neously. Approaches HL Preliminary Examination 2023/P2 2 2 2 2 X2 X1 21 3 number shown on the dice if the numbers (a) Complete the following table whic Let X and X₂ denote the number show1 The random variable Y is the larger nu Two fair cubical dice are thrown simultan 4 Year 6 Mathematics: Analysis and IMaximum mark• 71

5 TURN OVER e Approaches HL Preliminary Examination 2023/P2Year 6 Mathematics: Analysis and

TURN OVER [4] an Z BAС. [3] e length of the sides are in geometric sequence Approaches HL Preliminary Examination 2023/P2 (a) Find the value of r. (b) Hence find the possible values of t Triangle ABC is right-angled at B and th with common ratio r where r >1. Year 6 Mathematics: Analysis and IMaximum mark• 71

B TURN OVER B lationship between a and b? [2] [3] a positive constant, a and b are non-zero Approaches HL Preliminary Examination 2023/P2 (a) State and explain the geometrical re (b) Find the value of b in terms of 2 It is given that 2a =(a-b)b where 2 is vectors. Year 6 Mathematics: Analysis and IMaximum mar4• 51

TURN OVER 5 ween the mode and the mean. [2] as x→∞.] [5] [2] x>0, otherwise. pability density function Approaches HL Preliminary Examination 2023/P2 (c) Find the probability that X lies bety (b) Show that the mean of X is 4. 1 [You may assume that x²e 2 0 (a) Find the mode of X. I f(x)=xe4 0, 1 2 A continuous random variable X has prot Year 6 Mathematics: Analysis and 7 [Mavimum mar1• 61

0 N OVER 1 Approaches HL Preliminary Examination 2023/P2Year 6 Mathematics: Analysis and