SCSS 2024 EM Prelim P1 QP

SWISS COTTAGE SECONDARY SCHOOL SECONDARY FOUR AND FIVE PRELIMINARY EXAMINATION O Name: ( ) Class: MATHEMATICS Paper 1 Candidates answer on the Question Paper. 4052/01 Monday 26 August 2024 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your class, index number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. For Examiner’s Use Section A 72 Section B 18 Total 90 This document consists of 22 printed pages and 2 blank pages. Setter: Mr Ang Hanping Vetter: Mdm Zoe Pow [Turn over Home of Thoughtful Leaders: Serve with Honour, Lead with Humility

2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Measurement Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length r= , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22f x f x ff  −  

3 Section A (72 marks) Answer all the questions. 1 In the triangle, PQ = QR, PR = 15 cm and angle PQR = 90o. Calculate PQ. Answer PQ = .………………... cm [2] 2 A bag contains 8 red balls, 5 green balls and 7 yellow balls. (a) A ball is chosen at random and then replaced. What is the probability that it is not a red ball? Answer .……………….................. [1] (b) x yellow balls are removed from the bag. The probability of choosing a green ball is now 1 3 . Find the value of x. Answer x = .………………............ [1] 15 P Q R

4 3 In 2023, the population in Singapore was 5 920 000, correct to the nearest ten thousand. The population increased by 4% from 2020 to 2023. Calculate the population in Singapore in 2020, giving your answer correct to the nearest ten thousand. Answer .……………….................. [2] 4 Write as a single fraction in its simplest form ( )322 34 xx −− . Answer .……………….................. [2] 5 Simplify 4 3 3 627 x y   . Answer .……………….................. [2]

5 6 Peter has many cuboid blocks with dimensions 24 cm by 20 cm by 15 cm. He wishes to manufacture a box in the shape of a cube to pack the blocks such that there is no empty space in the box. Find the smallest possible length of the box. Answer .………………............ cm [2] 7 The students in a school participate in exactly one CCA each. The table shows information on the type of CCA which students in a class participate in. Clubs and Society Sports Uniformed Groups TOTAL Males 6 Females 10 5 3 18 TOTAL 16 12 40 (a) How many males participate in uniformed groups? Answer .……………….................. [1] (b) A pie chart is to be drawn showing the data for the females. Calculate the angle representing females participating in uniformed groups. Answer .……………….................. [1]

6 8 The mass of Jupiter is approximately 271.90 10 kg. The mass of Earth is approximately 245.97 10 kg. (a) Giving your answer in standard form, calculate how many times Jupiter’s mass is, compared to that of Earth’s. Answer .……………….................. [1] (b) Density refers to the mass per unit volume. Given that the volume of Jupiter is 241.43 10 m3 and that of Earth ’s is 211.08 10 m3, calculate and determine which planet has a higher density. Answer .……………….................. [2] 9 Elva invested a sum of money in an account paying compound interest at 4% per year. After 3 years, there was $89 989.12 in her account. How much did Elva invest in the account? Answer $ …….…………………... [3]

7 10 A metal sphere has a mass of 197 grams, correct to the nearest gram. (a) Find the least possible mass of the metal sphere. Answer …….…………………... g [1] (b) The volume of the metal sphere is 25 cm3, correct to the nearest cubic centimetre. Find the greatest possible mass of 1 cubic centimetre of the metal. Answer …….…………………... g [2] 11 A class of 10 boys and 10 girls took a test. The girls’ marks were 4, 5, 6, 7, 7, 7, 8, 8, 8 and 10. (a) State the modal mark for the girls. Answer .……………….................. [1] (b) Find the mean mark for the girls. Answer .……………….................. [1] (c) The mean mark for the whole class was 7.5. Aaron claims that the boys did better in the test. Do you agree? Justify your answer. Answer ...…………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………... [1]

8 12 (a) Factorise 42ab− . Answer .……………….................. [1] (b) Factorise completely 8 1 4 2xy x y− − + . Answer .……………….................. [2] 13 (a) On the Venn Diagram shown in the answer space, shade the set AB ' . [1] (b)        : is an integer and 1 100} : is a perfect square : is a multiple of 3 : is an integer ending in 2 x x x P x x Q x x R x x  =   = = = (i) List the elements contained in the set QR . Answer .……………….................. [1] (ii) Write down ( )n PR . Answer .……………….................. [1] A B

9 14 (a) A regular polygon has interior angles of 140o. Find the number of sides of the polygon Answer .……………….................. [2] (b) The diagram shows a sketch of a regular octagon and an equilateral triangle. Calculate x. Answer x = …………..................... [2] xo

10 15 The graph shows information about the waste generated in Singapore from 2013 to 2023. (a) Estimate the waste recycled in 2021. Answer .………………....... tonnes [1] (b) Make one comment about the total waste generated in the 2020s compared with the 2010s. Answer ...…………………………………………………………………………………… ………………………………………………………………………………………... [1] (c) There was a significant drop in the amount of construction and demolition waste, which is usually completely recycled, over the last decade. Brian claims that this contributed to a decline in the percentage of waste recycled in the 2020s compared with the 2010s. Does the graph support his claim? Justify your answer with reference to the graph. Answer ...…………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………... [2] 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 Tonnage ('000 tonnes) Year Total Waste Ge