2024 HYSS S4-5 G3 MA Prelim Paper 1 QP

[Turn Over HUA YI SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 4-G3 / 5-G2 NAME CLASS INDEX NUMBER MATHEMATICS 4052/01 PAPER 1(XX) 13 August 2024 2 hour 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class, and index number 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. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of the marks for this paper is 90. 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. For Examiner’s Use 90 This document consists of 22 printed pages. © HYSS 2024 No part of this document may be reproduced in any form or transmitted in any form or by any means without the prior permission of Hua Yi Secondary School. Setter: Ms Jasmine Tan

2 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn over Mathematical Formulae Compound interest Total Amount = 1 100 n rP+ Mensuration 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 = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean =   f fx Standard deviation = 22       −     f fx f fx

3 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn over 1 (a) Calculate ( ) ( ) ( ) 211.8 11 7 16 40 2 16 − − − − −   −  . Answer ………………………. [1] (b) There are 800 people in an auditorium, correct to the nearest hundred. State the minimum number of people that could be in the auditorium at this time. Answer …………….… people [1] ________________________________________________________________________________ 2 (a) Express 1400 as the product of its prime factors. Answer ………………………. [1] (b) Write down the smallest positive integer k such that 1400k is a perfect cube. Answer k = ...………………. [1] (c) n is a number between 300 and 400. The highest common factor of n and 1400 is 35. Find the largest possible value for n. Answer n = .…………………. [2]

4 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn over 3 (a) Simplify 0 2 79y x x − . Answer ………………………. [2] (b) Simplify ( ) 5 12 481a . Answer ………………………. [1] ________________________________________________________________________________ 4 (a) Express as a single fraction in its simplest form 74 2 18 3 5 81 bb c  . Answer ………………………. [2] (b) Use the laws of indices to show that 426 100 116 36 +  can be expressed as a single power of six. Answer [2]

5 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn over 5 In a greenhouse, the estimated number of flowering plants increased from 4100 in January 2024 to 4980 in June 2024. The number increased by c% every month. Find the value of c. Answer c = .…………………. [3] ________________________________________________________________________________ 6 Kyle runs a tennis club. 54 of the members are adults and 31 are children. His aim is that at least 60% the members should be children. Form an inequality to find the smallest number of children that Kyle would still need to recruit achieve his aim. Answer ……….…… children [3]

6 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn over 7 A car travels at an average speed of 74.5 km/h for 2.25 hours. (a) Convert 75 km/h to m/s. Answer ………………..… m/s [1] (b) By rounding the numbers correct to 1 significant figure, find an estimate of the distance travelled by the car. Show your working clearly. Answer ………………..… km [2] (c) Without doing any calculation, explain why the actual distance travelled by the car is greater than the answer to (b). Answer [1] ………………………………………………………………………………………….……….. ………………………………………………………………………………………….……….. ………………………………………………………………………………………….……….. ………………………………………………………………………………………….……….. ________________________________________________________________________________ 8 Isha has written down five numbers. The mean of these numbers is 13.2, the median is 12 and the mode is 7. The largest number is three times the smallest number. Find the five numbers in ascending order. Answer ……. , ……. , ……. , ……. , ……. [2]

7 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn over 9 Factorise completely (a) 442 32ps− , Answer ………………………. [3] (b) 12 9 6 8cd cx xy dy− + − . Answer ………………………. [2] ________________________________________________________________________________ 10 (a) Express 298 xx−+ in the form 2()a x b++ . Find the value of a and of b. Answer a = .…………………. [1] b = .…………………. [1] (b) Explain why when 4x= , the expression 298 xx−+ has its minimum value. Answer [1] ………………………………………………………………………………………….……….. ………………………………………………………………………………………….……….. ………………………………………………………………………………………….……….. ………………………………………………………………………………………….………..

8 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn over 11 Solve the equation 2052 1x x+= + . Answer x = ……… or ………. [3] ________________________________________________________________________________ 12 The points ( )4,20 and ( )10, 4− satisfy the curve given by the equation 2 4y ax bx= + − . Use an algebraic method to determine the values of a and b. Answer a = ……… , b = …..…. [4]

9 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn over 13 {integers :1 16}xx =   {1, 2, 4, 8,16}V = {1, 4, 7, 9,10,14}W = Some of the information is shown on the Venn diagram. (a) Complete the Venn diagram by representing all the elements in the given sets. Answer in above Venn diagram [1] (b) Describe the elements of Set V. Answer [1] ………………………………………………………………………………………….……….. ………………………………………………………………………………………….……….. ………………………………………………………………………………………….……….. (c) List the elements contained in the set 'VW . Answer ………………………. [1] (d) Find the number of elements in ( ) ( )''V W V W   . Answer ………………………. [1] (e) Use one of the symbols below to complete each statement. =      (i) {2,16} ……… V (ii) 13 ……… W Answer (e) (i) ………... [1] (ii) …...…… [1] 3 5 6 11 12 13 15 V W

10 2024_4-G3 / 5-G2_PRELIMS_ MATHEMATICS _PAPER 1 [Turn over 14 In grocery mart G, water costs $1.80 per litre, fresh milk costs $2.90 per litre and juice costs $2.30 per litre. In grocery mart H, water costs $0.20 more per litre, fresh milk costs $0.40 less per litre and juice costs $0.10 less per litre. This information can be represented by the matrix Q = 1.8 0.2 W 2.9 0.4 M 2.3 0.1 J GH   − − . (a) Rayyen and Zinnie went shopping together. Rayyen bought 4 litres of water, 2 litres of milk and 3 litres of juice. Zinnie bought 3 litres of water and 4 litres of juice. Represent their purchases in a 23 matrix P. Answer P = ……………………. [1] (b) Evaluate the matrix R = PQ. Answer R = ……………………. [2] (c) State what the elements in the second column of mat