SOTA 2022 Year 6 MAAHL Prelim Paper 1

Yr6/5/MATAA/HP1/Aug2022 16 pages © School of the Arts, Singapore Year 6 Mathematics: analysis and approaches Higher level Paper 1 Preliminary Examinations Monday 29 August 2022 2 hours Instructions to candidates • 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 answer boxes provided. • Section B: answer all questions on the answer sheets provided. Write your name and class on each answer sheet. • Unless otherwise stated in the question, all numerical answers should 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]. Section A Section B Question Marks Question Marks 1 10 2 11 3 12 4 5 6 7 8 9 Name: 110 Class: Index:

- 2 - Yr6/5/MATAA/HP1/Aug2022 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. 1. [Maximum mark: 4] Given that and when , find y in terms of x. d sin 2d y xx= 1 2y= 0x=

- 3 - Yr6/5/MATAA/HP1/Aug2022 Turn Over Turn over 2. [Maximum mark: 5] Audrey rolls a biased 6-sided dice with faces labelled as 1, 2, 3, 4, 5 and 6. The probabilities of obtaining odd numbers are all the same, and the probabilities of obtaining even numbers are also all the same. The probability of obtaining an even number is twice the probability of obtaining an odd number. (a) Find the probability of obtaining a 1. [2] Audrey rolls the die three times. (b) Find the probability of Audrey obtaining two 1s and one 2. [3]

- 4 - Yr6/5/MATAA/HP1/Aug2022 (This question continues on the following page) 3. [Maximum mark 5] The function f is defined by , where , and a is a constant (a) Write down the equation of the vertical asymptote of the graph of . [1] (b) Given that the horizontal asymptote of the graph of is , state the value of a. [1] 3() 32 axfx x -= + ff2y=

- 5 - Yr6/5/MATAA/HP1/Aug2022 Turn Over Turn over (Question 3 continued) (c) Sketch the graph of in the axes below, indicating clearly all asymptotes and axial intercepts.. [3] f

- 6 - Yr6/5/MATAA/HP1/Aug2022 4. [Maximum mark: 7] The function f is define