SOTA 2023 Prelim MAA HL Paper 1

Yr6/5/MATAA/HP1/Aug2023 13 p a g e s © School of the Arts, Singapore Year 6 Mathematics: analysis and approaches Higher level Paper 1 Preliminary Examinations Friday 25 August 2023 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 and attach them to this examination paper. • 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/Aug2023 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] (a) Show that , where . [2] (b) Hence, prove that is a multiple of 4. [2]

- 3 - Yr6/5/MATAA/HP1/Aug2023 Turn over 2. [Maximum mark: 5] The following diagram shows the graph of a function , with domain 0 ≤ x ≤ 4 . (a) (i) Write down ; (ii) Find . [3] (b) On the same digram, sketch the graph of . [2]

- 4 - Yr6/5/MATAA/HP1/Aug2023 3. [Maximum mark: 6] Consider the function , where m is a constant. (a) Find the value of m for which the x–axis is a tangent to the graph of f. [4] (b) Find the range of values of m for which the graph of f has a positive y–intercept. [2]

- 5 - Yr6/5/MATAA/HP1/Aug2023 Turn over 4. [Maximum mark: 5] The derivative of the function f is given by . The graph of has an x–intercept at x = 3. Find an expression for .

- 6 - Yr6/5/MATAA/HP1/Aug2023 5. [Maximum mark: 9] The following table shows the probability distribution of a discrete random variable X. x 0 1 2 P(X = x) (a) Explain why . [1] (b) Show that . [5] (c) Hence, find E(X). [3] sinθ23−cos2θcos2θ<23sinθ=12

- 7 - Yr6/5/MATAA/HP1/Aug2023 Turn over 6. [Maximum mark: 6] A particle moves along a straight line so that after seconds, its displacement , in metres, satisfies the equation . (a) Show that its velocity, . [3] (b) Find its acceleration, in terms of . [3]