2020 4E5N Prelim QP1

Name: Register Number: Class: 4E 5N BEDOK GREEN SECONDARY SCHOOL Preliminary Examination 2020 4E 5N MATHEMATICS 4048/01 Paper 1 28 August 2020 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and register 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 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 80. For Examiner’s Use This document consists of 21 printed pages including the cover page. © BGSS 2020 No part of this document may be reproduced in any form or transmitted in any form or by any means without the prior per mission of Bedok Green Secondary School [Turn over 80

2 © BGSS 2020 Mathematical Formulae Compound interest Total amount 1 100 nrP     Mensuration 2 2 3 2 Curved surface area of a cone Surface area of a sphere 4 1Volume of a cone 3 4Volume of a sphere 3 1Area of triangle sin 2 Arc length , where is in radians 1Sector area , where 2 rl r r h r ABC ab C r r                is in radians Trigonometry 2 2 2 sin sin sin 2 cos a b c A B C a b c bc A      Statistics 22 Mean Standard deviation fx f fx fx f f               

3 © BGSS 2020 [Turn over Answer all the questions. 1 x is a number which has 4 significant figures. x = 7 (nearest integer), x = 7.5 (1 decimal place) x = 7.49 (2 decimal places) Find (a) the least possible value of the number x, Answer ……… …….. …....……………… [1] (b) the greatest possible value of the number x. Answer ……… …….. …....……………… [1] 2 Given that sin  = 0.875, find the values of  where 0 ≤  ≤ 180. Answer  = ………… …. . or ………… …. . [2] 3 (a) 3 x pp p p   Find the value of x. Answer x = ………… …. ....……………… [ 1] (b) Simplify 1 2( )25 m  . Answer ……… …….. …....……………… [1]

4 © BGSS 2020 4 Write as a single fraction in its simplest form 3 2 5 7 1x x   . Answer ……… ……..…....……………… [2 ] 5 (a) The cube root of n is 26  53. Find n as a product of its prime factors. Answer n = …… ..…..…....……………… [1 ] (b) A roll of wire A is 156 cm long. A roll of wire B is 390 cm long. Both rolls of wire A and B are cut into pieces of equal length. Find the maximum possible length of each piece of wire. Answer ……… …….. ….....……… … cm [1]

5 © BGSS 2020 [Turn over 6 A two-digit number, x, where 10 ≤ x ≤ 99, is written down at random. Find the probability that the number is (a) a multiple of 10, Answer ……… …….. …....……………… [1] (b) a perfect square. Answer ……… …….. …....……………… [1] 7 y = x3 + 2 y = x3 – 2x2 – x + 2 y = 2 – x3 xy 2 xy 2 y = 2x Write down a possible equation for each of the given sketch graphs. In each case, select one of the equations from the given table. Answer ……………..…....……………… ……………..…....… …………… [2] y x O y x O

6 © BGSS 2020 8 y is inversely proportional to x3. When x has a certain value, y = 5. Find the value of y when x is doubled. Answer y = ……… … …....……………… [ 2] 9 On a particular day, the lowest temperature recorded was 5 C. The difference between the highest and lowest temperature recorded that day was 6 C. (a) Find the highest temperature on that day. Answer ……… ……..…....……… …… C [1] (b) The lowest temperature was recorded at 0400. The highest temperature was recorded at 1200. The temperature is assumed to increase at a constant rate between 0400 and 1200 that day. Find the time when the temperature was 1.5 C. Answer ……… …….. …....……………… [ 2]

7 © BGSS 2020 [Turn over 10 Solve the simultaneous equations 3x – 4y = –16, 5x + 6y = 5. Answer x = ………… …. ....…………… y = ………… …. ....……… .…… [ 3] 11 (a) Solve the inequalities 8 ≤ 7  3x < 10. Answer ……… …….. …....……………… [ 2] (b) Write down the smallest integer which satisfy 8 ≤ 7  3x < 10. Answer … …… …….. …....……………… [ 1]

8 © BGSS 2020 12 The pie chart represents the amount of time that Alicia spent on cycling, swimming and playing badminton in a particular week. The total amount of time that she spent on the three sports that week was 15 hours. The angle representing the amount of time that she spent on playing badminton was 154. (a) That week, Alicia spent 5 hours swimming. Calculate the angle of the sector representing the amount of time spent on swimming. Answer ……… ……..….... …… ………  [1] (b) On each of the seven days that week, Alicia spent the same amount of time playing badminton. Calculate the amount of time, in minutes, she spent on playing badminton each day. Answer ……… ……..…...…………min [2 ] 154

9 © BGSS 2020 [Turn over 13 VABCD is a rectangular pyramid with vertex V directly above C of the base ABCD. AB = 15 cm, BC = 8 cm and VC = 6 cm. Find (a) the volume of the pyramid, Answer …… .….. …....……………… cm3 [1] (b) the length of AC, Answer ……… …….. …....… ………… cm [1] (c) angle VAC. Answer ……… …….. … ...………………  [1] V A B C D 15 cm 8 cm 6 cm

10 © BGSS 2020 14 Use the factorisation method to solve the equation (3x – 1)(x + 1) = 4. Answer x = ………… …. . or ………… …. . [3] 15 The price of an apartment at the end of 2010 was 7% higher than that at the end of 2009. The price of the same apartment at the end of 2011 was 5% higher than that at the end of 2010. Calculate the price of the apartment at the end of 2011 as a percentage of the price at the end of 2009. Answer ……… ……..…....………… … % [3]