Beatty Sec EM 4E5N P2 2020 QP

1 SUBJECT : Mathematics LEVEL : Sec 4E/5N PAPER : 4048 / 2 DURATION : 2 hour 30 minutes SETTER : Mr Lai Chee Kit Mrs Samsol DATE : 26 August 2020 CLASS : NAME : REG NO : READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces on the top of this page. 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. ____________________________________________________________________________ This paper consists of 26 printed pages (including this cover page) BEATTY SECONDARY SCHOOL PRELIMINARY EXAMINATION 2020 O For Examiner’s Use 100 [Turn over

2 Mathematical Formulae Compound Interest Total amount = nrP )1001( + Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 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 1 (a) It is given that ( ) 221 2A h a b=− . (i) Evaluate A when 4a= , 2.5b= and 6h= . Answer A = …………………… [1] (ii) Express b in terms of A, a and h. Answer b = ……………………. [2] (b) Express as a single fraction in its simplest form 2 72 4 4 1 2 1x x x −− + − . Answer ………………………… [3] [Turn over

4 (c) (i) Solve the inequality 5 4 4 72 xx−+  . Answer ………………………... [2] (ii) State the greatest integer value of x which satisfies 5 4 4 72 xx−+  . Answer x = ………….................. [1] (d) Solve the equation 72 25 xx x+ += . Answer x = …………………….. [2]

5 2 Ethan went on a journey of 80 km. For the first 3 5 of the journey, his average speed was x km/h. (a) Write down an expression, in terms of x, for the time taken in hours for the first part of the journey. Answer …………………. hours [1] He increased his average speed by 6 km/h for the remaining journey. The time taken for the second part of the journey is 18 minutes less than the first part of the journey. (b) Write down an equation in x to represent this information and show that it simplifies to 23 142 2880 0xx− − = . Answer [4] [Turn over

6 (c) Solve the equation 23 142 2880 0xx− − = , giving your solutions correct to two decimal places. Answer x = ……… or ……….... [3] (d) Calculate the time taken for the whole journey. Give y our answer in hours and minutes, correct to the nearest minute. Answer ……... hours…….. minutes [2]

7 3 (a) The following table shows the volume of mail handled by SingPost from 2009 to 2012. Number of mail 2009 2010 2011 2012 Domestic 876 114 663 497 669 543 655 317 International 126 548 116 851 110 944 109 463 https://data.gov.sg/dataset/volume-of-mail-handled-by-type-annual (i) Calculate the percentage decrease in the total volume of mail from 2009 to 2012. Answer ……………………… % [2] (ii) Calculate the mean number of mail per month for 201 2. Give your answer in standard form, correct to 3 significant figures. Answer ………………………… [2] [Turn over

8 (iii) In which two years are the ratio of the number of domestic mail to the number of international mail approximately the same? Justify your answer clearly. Answer Years …………… and ……….......................... [2] (b) A bank offers a saving account with an interest rate of 1.5% per year, compounded monthly. Shawn invests $8500 in this account. Calculate the total amount of interest he has earned at the end of 3 years. Give your answer correct to the nearest cent. Answer $....................... [2]

9 (c) The exchange rate between Singapore dollars ($) and Thai Baht (THB) is $1= THB 22.66. Mandy visited her friend in Thailand. She bought a watch for THB 5400 and paid using her credit card. The credit card company converts the price to Singapore dollars. She was charged a fee of 1.2% for the currency conversion. Calculate the total amount in Singapore dollars that Mandy has to pay the credit card company. Give your answer correct to the nearest dollar. Answer $....................... [3] [Turn over

10 4 The variables x and y are connected by the equation 3 314 xyx= − − . Some corresponding values of x and y are given in the table below. x 4− 3− 2− 1− 0 1 2 3 4 y 5− p 3 1.75 1− 3.75− 5− 3.25− 3 (a) Find the value of p. Answer p =…………………..... [1] (b) On the grid opposite, draw the graph of 3 314 xyx= − − for 44 x−   . [3] (c) The equation 3 3 3 04 x x− − = has three solutions. Explain how this can be seen from your graph. Answer [2] (d) By drawing a tangent, find the gradient of the curve at (3, 3.25)− . Answer ………………………. [2]