SOTA 2023 Prelim MAA HL Paper 2 Solutions

Yr6/5/MATAA/HP2/Aug2023 14 pages © School of the Arts, Singapore Year 6 Mathematics: analysis and approaches Higher level MARK SCHEME 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. • 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 No Solutions Mark scheme 1(a) BC = 3.42166 BC = 3.42 Attempt to use cosine rule (M1) Correct substitution (A1) BC = 3.42 (3s.f.) A1 1(b) Attempt to use sine rule (M1) Correct substitution (A1) A1 2(a) a = 30.5 (3 s.f.) b = – 419.462 b = – 419 (3 s.f.) a = 30.5 (3 s.f.) A1 b = – 419 (3 s.f.) A1 2(b) A1 2(c) y = 30.4932(29) – 419.462 y = 464 841 $465 000 Correct substitution of 29 into their regression equation (M1) $465 000 or 466 000 A1 2(d) EITHER correlation does not imply causation (there is an association but not causation) OR there could be another factor involved. EITHER correlation does not imply causation OR there could be another factor involved (eg other factors may affect profits or advertising not the sole factor affecting profits.) R1 NOT More money spent on ads will affect profits. 3 -------------- (1) ---------- (2) Attempt to use or (M1) Attempt to solve simultaneous equations (M1) A1 A1

- 3 - Yr6/5/MATAA/HP2/Aug2023 Turn Over Turn over [exact value] (M1) [must be exact value] (A1) 4(a) Both graphs are decreasing functions. hours hours < 23.105 hours Since Betacold took a shorter time for concentration to