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

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- 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 cause annual profit to increase. Give a reason why this statement is not correct. [1] (This question continues on the following page)

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- 6 - Yr6/5/MATAA/HP2/Aug2023 3. [Maximum mark: 6] In an arithmetic sequence, the sum of the first 10 terms is 375 and the sum of the first 30 terms is 3525. Find the 45th term of the sequence.

- 7 - Yr6/5/MATAA/HP2/Aug2023 Turn Over Turn over Please do not write on this page. Answers written on this page will not be marked.

- 8 - Yr6/5/MATAA/HP2/Aug2023 4. [Maximum mark: 7] On Monday at noon, Kenny took an injection that combines two drugs, Anticold and Betacold. At time t hours, after the injection, the concentrations, measured in units, of Anticold and Betacold in Kenny’s bloodstream can be modelled as and respectively. Each drug becomes ineffective when its concentration falls below 1 unit. (a) Show that Betacold becomes ineffective before Anticold. [2] Fifteen hours after the first injection, Kenny took a second injection. (b) (i) Find the concentration of Betacold from the first injection in Kenny’s bloodstream on Tuesday at noon. (ii) Hence, find the total concentration of Betacold in Kenny’s bloodstream on Tuesday at noon. [5] (This question continues on the following page)

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- 10 - Yr6/5/MATAA/HP2/Aug2023 5. [Maximum mark: 6] Consider the expansion of , where . The coefficient of the term in is 448. Find the value of k.