2024 HYSS_S4-5 G3 MA Prelim_Paper 1_MS

[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. MARKING SCHEME 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_PRELIMINARY EXAMINATION_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_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 1 [Turn Over 1 (a) Calculate ( ) ( ) ( ) 211.8 11 7 16 40 2 16 − − − − −   −  . 1.750958 1.75 (3 s.f.) ----- B1− =− 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. 750 people ----- B1 Answer …………….… people [1] ________________________________________________________________________________ 2 (a) Express 1400 as the product of its prime factors. 321400 2 5 7 ----- B1=   Answer ………………………. [1] (b) Write down the smallest positive integer k such that 1400k is a perfect cube. 3 2 3 2 21400 2 5 7 2 5 7 (5 7 ) 245 ----- B1 kk k =    =     = 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. n = ?2 5 7 ?   1400 = 322 5 7 HCF = 5 7 35= By guess-and-check, 5 7 11 385 2nB=   = −−− [Condition: largest possible value between 300 – 400] Answer n = .…………………. [2]

4 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 1 [Turn Over 3 (a) Simplify 0 2 79y x x − . 2 0 2 7 7 9 9 1 1 9 19 xy x x x M x A −  =   −−− = −−− Answer ………………………. [2] (b) Simplify ( ) 5 12 481a . ( ) ( ) 55 5 1212 4 44 15 81 81 243 1 aa aB  = = −−− Answer ………………………. [1] ________________________________________________________________________________ 4 (a) Express as a single fraction in its simplest form 74 2 18 3 5 81 bb c  . 7 4 7 2 2 4 3 2 18 3 18 81 5 81 5 3 486 486 M1 for , 1 for full answer55 b b b c c b b Ac  =  = −−−  Answer ………………………. [2] (b) Use the laws of indices to show that 426 100 116 36 +  can be expressed as a single power o