SOTA 2023 Prelim MAA HL Paper 2

Yr6/5/MATAA/HP2/Aug2023 18 pages © School of the Arts, Singapore Year 6 Mathematics: analysis and approaches Higher level Paper 2 Preliminary Examinations Monday 28 August 2023 2 hours Instructions to candidates • Do not open this examination paper until instructed to do so. • A graphic display calculator is required 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/HP2/Aug2023 Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. 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 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: 6] The following diagram shows triangle ABC, with , , and . (a) Find . [3] (b) Find [3] (This question continues on the following page) Diagram not to scale

- 3 - Yr6/5/MATAA/HP2/Aug2023 Turn Over Turn over (Question 1 continued)

- 4 - Yr6/5/MATAA/HP2/Aug2023 2. [Maximum mark: 6] A company wishes to assess whether there is a linear relationship between the annual amount spent on advertising, $x thousand, and the annual profit, $y thousand for seven years. The following table shows the data collected. Annual advertising amount ($x thousand) 24.0 25.9 30.0 27.0 32.4 37.0 33.0 Annual profit ($y thousand) 241 361 524 471 556 652 641 The regression line of y on x for this data can be written in the form . (a) Find the value of a and the value of b. [2] (b) Write down the value of the Pearson’s product-moment correlation coefficient, r. [1] (c) Use the equation of your regression line to estimate the annual profit, to the nearest thousand, during a year when $29 000 was spent on advertising. [2] (d) A manager commented that this correlation coefficient shows that spending more money on advertising will