Singapore Chinese Girls School Paper 1

SINGAPORE CHINESE GIRLS’ SCHOOL PRELIMINARY EXAMINATION 2022 SECONDARY FOUR O-LEVEL PROGRAMME CLASS 4 REGISTER NUMBER CENTRE NUMBER S INDEX NUMBER MATHEMATICS 4048/01 PAPER 1 Monday 22 August 2022 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class, register number, centre number 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/tape. 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 π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. 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. This document consists of 19 printed pages and 1 blank page. CANDIDATE NAME [Turn over For Examiner’s Use www.KiasuExamPaper.com 663

2 Mathematical Formulae Compound Interest Total amount = 1 100 nrP§·¨¸©¹ Mensuration Curved surface area of a cone = rlS Surface area of a sphere = 24 rS Volume of a cone = 21 3 rhS Volume of a sphere = 34 3 rS Area of triangle ABC = 1 sin2 ab C Arc length = rT , where T is in radians Sector area = 21 2 r T , where T is in radians Trigonometry sin sin sin abc ABC 22 2 2c o sabc b c A Statistics Mean = fx f 6 6 Standard Deviation = 22fx fx ff §·66 ¨¸66 ©¹ www.KiasuExamPaper.com 664

3 [Turn Over 1 Expressed as the product of its prime factors, 321224 2 3 17 uu . (a) The number 1224 m ny , where m and n are prime numbers, is a perfect cube. Write down the value of m and of n. Answer m = ………………………. n = ………………………. [1] (b) The highest common factor and lowest common multiple of three numbers are 6 and 1224 respectively. Two of these numbers are 36 and 102, and the third number lies between 50 and 500. Find two possible values of the third number. Answer ................. and ………..…. [2] 2 A town is represented by an area of 20 cm2 on a map of scale 1 : 400 000. On a second map, the town is represented by an area of 51.2 cm2. Express the scale of the second map in the form 1 : n. Answer 1 : ………...………………. [2] www.KiasuExamPaper.com 665

4 3 The estimated number of rhinoceroses in the wild decreased from 70 000 in 1970 to 27 000 in 2021. The number decreased by r % every year. Find the value of r. Answer r = ………...…..……………. [2] 4 The graph shows the daily average number of passengers using the MRT system in Singapore from 2015 to 2019. Rapid rise in daily average number of passengers (a) State one misleading feature of the graph. Answer ……………………………………………………………………………………….. ……………………………………………………………………………………….. ……………………………………………………………………………………….. [1] (b) Explain how this feature affects the reader’s interpretation of the graph. Answer ……………………………………………………………………………………….. ……………………………………………………………………………………….. ……………………………………………………………………………………….. [1] 130 120 Daily average number of passengers (ten thousands) 60 110 100 90 70 80 2015 2019 2016 2017 2018 Year www.KiasuExamPaper.com 666

5 [Turn Over 5 Arnold purchased a bicycle from a shop at a discount of 20 % off the marked price. After a week, he sold it at $2205 and made a profit of 125 %. Calculate the marked price of the bicycle at the shop. Answer $ …………………..………. [2] 6 (a) Express 220 9 xx in the form 2 xp q . Answer ……………………………. [2] (b) Hence, solve 2 20 9xx . Answer x = ……...... or ………..... [2] www.KiasuExamPaper.com 667

6 7 When a number is first decreased by p % and then increased by p % , where p is a positive integer, the overall percentage decrease is 4 %. Find p. Answer p = ………………..…….. % [2] 8 The area of triangle LMN is 796.6 m2. LM = 62 m and MN = 52 m. Find the two possible sizes of the angle LMN. Answer …..…......... or …………..... [2] www.KiasuExamPaper.com 668

7 [Turn Over 9 (a) The first four terms of a sequence are 1, 5, 12 and 22. Find an expression, in terms of n, for the nth term of the sequence. Answer ……………………………. [1] (b) A series of rectangles was drawn. The table shows the width and the area of the first four rectangles drawn. Width (cm) Area (cm2) 2 10 4 36 6 78 8 136 (i) Find an expression, in terms of w, for the length of the rectangle with width w cm. Answer ……………………………... [1] (ii) Would it be possible for the perimeter of a rectangle in this sequence to be 596 cm? Explain your answer clearly. Answer …………………………………………………………………………………. …………………………………………………………………………………. …………………………………………………………………………………. …………………………………………………………………………………. …………………………………………………………………………………. …………………………………………………………………………………. [2] www.KiasuExamPaper.com 669

8 10 The sketch shows the graph of xyk a . The points (0, 1.5) and (5, 48) lie on the graph. Find the value of a and of k. Answer a = ………………………. k = ………………………. [2] 11 (a) Simplify 1 4 3 3343 e f

§· ¨¸ ©¹ . Answer …………………………..…. [1] (b) Solve

1 2 3 15 225 27 5 x xx . Answer x = …………………..……. [3] (0, 1.5) (5, 48) y x O www.KiasuExamPaper.com 670

9 [Turn Over 12 A, B, C, D, E, … are some of the vertices of a regular polygon. ABX is a straight line and angle BCA = 11.25q . (a) Calculate (i) angle CBX, Answer …………………………..…. [1] (ii) angle BED. Answer …………………………..…. [1] (b) A, C and E are consecutive vertices of a second regular polygon. Find the number of sides of this polygon.