2020 4E5N Prelim QP2v2

Name: Register Number: Class: 4E 5N BEDOK GREEN SECONDARY SCHOOL Preliminary Examination 2020 4E 5N MATHEMATICS 4048/02 Paper 2 31 August 2020 2 hours 30 minutes 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 100. For Examiner’s Use This document consists of 25 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 wit hout the prior permission of Bedok Green Secondary School [Turn over 100

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 1 (a) The cash price of a camera is $1 880. Amelia bought the camera on hire purchase. She paid a deposit of one fourth of the cash price and paid the rest by 24 equal monthly instalments of $65. (i) Find the total amount that Amelia paid for the camera. Answer $…… …….. …....……………… [1] (ii) Calculate the extra cost of buying the camera on hire purchase as a percentage of the cash price. Answer …… …….. …....……………… % [1] (b) Alyssa bought an identical camera. In order for her to pay for the camera, she borrowed a sum of $1 880 for 3 years at a compound interest rate of 4% per year. Calculate the interest that Alyssa had to pay. Answer $…… …….. …....……………… [ 2] (c) On selling a camera at $1 880, the merchant made a profit of 113% of the cost which he paid for the camera. Find the cost price of the camera. Answer $…… …….. …....……………… [ 2]

4 © BGSS 2020 2 (a) Microspheres are small spherical particles which transport drugs in the human body. The surface area of one microsphere is 1.54  1010 m2. Find the radius of the microsphere. Give your answer in standard form. Answer …… …….. …....……………… m [1] (b) Simplify 4 2 20 12 3 5 m m n n . Answer …… …….. …....……………… … [1] (c) 1 2y q r p  (i) Evaluate y when 1 2p , q = 12 and r = –4. Answer y = …… … .....……………… … [1] (ii) Express r in terms of p, q and y. Answer r = …… ..…....……………… … [2]

5 © BGSS 2020 [Turn over 2 (d) A cylindrical water dispenser, with uniform cross section, has a capacity of 30 litres. (i) Water from Tap A fills the empty dispenser at a constant rate of x litres per second. Write down, in terms of x, the time taken by Tap A to fill up the empty water dispenser. Answer …… …….. …....……………… …s [1] (ii) Water from Tap B fills the same dispenser at a constant rate of (x + 2) litres per second. Write down, in terms of x, the time taken by Tap B to fill up the empty water dispenser. Answer …… …….. …....……………… …s [1] (iii) Tap B takes 25 seconds less than Tap A to fill up the empty dispenser. Write down an equation in x and show that it can be simplified to 5x2 + 10x – 12 = 0. Answer [2]

6 © BGSS 2020 2 (d) (iv) Solve the equation 5x2 + 10x – 12 = 0. Answer x = …… ….. ….... or …… ….. ….... [ 3] (v) Hence find the amount of time taken by Tap A to fill up the water dispenser. Answer ……… …….. …....….……… … s [1] (vi) The cylindrical water dispenser has a height of 40 cm. Sketch a graph showing how the depth of water varies with time as the empty water dispenser is filled up with water from Tap A. [1] Depth of water (cm) Time (s) 0

7 © BGSS 2020 [Turn over 3 Points A (8, 1), B (1, 1) and C( 4, 3) form a triangle as shown in the diagram. (a) Given that the points A, B, C and D are vertices of a parallelogram, find the coordinates of all three possible positions of D. Answer (……… , ……… ), (……… , … … … ) or (……… , ……… ) [3] (b) Find the length of BC. Answer ……… ……..…....….…….units [1 ] (c) Find, as a fraction in its simplest form, the value of cos ˆABC . Answer ……… ……..…....….…….……. [1 ] (d) Calculate the area of triangle ABC. Answer ……… ……....….…….…….unit 2 [1] (e) Point E (m, n) lies on AC such that AE : AC = 1 : 4. Find the values of m and n. Answer m = ………… …. ....…………… n = ………… …. ....……… .…… [ 2] y x A (8, 1) B (1, 1) C (4, 3) O

8 © BGSS 2020 4 (a) The cumulative frequency graph represents the masses of 200 eggs from Sunny Farm. The eggs are grouped according to their masses. Grade 1 : 62 g < mass ≤ 75 g Grade 2 : 51 g < mass ≤ 62 g Grade 3 : 40 g < mass ≤ 51 g Cumulative frequency Mass (g)

9 © BGSS 2020 [Turn over 4 (a) Use the graph to find (i) the median mass, Answer ……… ……..…....….…….……g [1 ] (ii) the percentage of eggs which are in Grade 2 category, Answer ……… ……..…....….…….……% [2 ] (iii) the interquartile range. Answer ……… ……..…....….…….……g [1 ] (b) The box and whisker plot shows the masses of 200 eggs from Happy Farm. Fiego made two comparisons between the masses of eggs from Happy Farm and Sunny Farm. State whether you agree with Fiego’s statements. Provide statistical evidence to support your answer. (i) Statement 1: Generally, eggs from Sunny Farm have more consistent masses than eggs from Happy Farm. ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ _____________________________________________________________ [1] 40 50 60 70 80 Mass (g)

10 © BGSS 2020 4 (b) (ii) Statement 2: Happy Farm has a higher percentage of eggs in Grade 1 category than Sunny Farm. ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ _____________________________________________________________ [1] (c) Thirty employees in Happy Farm work in either Administrative Department or Farming and Outdoors Department. The table shows the breakdown of males and females employees in the departments. Administrative Farming and Outdoors Males 1 20 Females 3 6 (i) Two employees are selected randomly from the 30 employees to be