SOTA 2022 Year 6 MAA HL Prelim Paper 2 Solutions

Yr6/5/MATAA/HP2/Aug2022 18 pages © School of the Arts, Singapore Year 6 Mathematics: analysis and approaches Higher level Paper 2 Preliminary Examinations Tuesday 30 August 2022 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 the 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: Solution

- 2 - Yr6/5/MATAA/HP2/Aug2022 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. (a) Or (b) Mtd 1 Yes. From (a), when , Mtd 2 Let Then and . Thus is a solution to (a). x=3−λ,y=10−2λ,z=λλ∈!λ=−1(x,y,z)=(4,12,−1)x=3−λ=4⇒λ=−1y=10−2(−1)=12z=λ=−1(4,12,−1) 1. [Maximum mark: 5] (a) Solve the system of linear equations: [3] ()(b) (b) Determine whether is a solution to (a). [2] 4x−3y−2z=−18y+2z=10x+z=3(4,12,−1)

- 3 - Yr6/5/MATAA/HP2/Aug2022 Turn over (a) (shown) (b) = 2.206356… f(w)dw05∫=1kw2+25dw05∫=1k[15tan−1(w5)]05=115k[(π4)−0]=1k=20π 2. [Maximum mark: 5] The probability density function of the continuous random variable is defined by (a) Show that . [3] (b) Find , the expected value of . [2] Wf(w)=kw2+250≤w≤5,0otherwise.⎧⎨⎪⎩⎪k=20πE(W)W

- 4 - Yr6/5/MATAA/HP2/Aug2022 3. [Maximum mark: 7] A company manufactures washing detergent. They gave a number of identical coloured shirts to some customers and asked them to keep a record of how often the shirts were washed. After four months, the company went back to the customers and note down how many times the shirts had been washed, and the colour intensity of the shirt. Number of washes, N 5 7 9 4 13 8 7 Co