Outram Sec 4E5N Maths P2 Prelim 2022

Subject : Mathematics Paper No. : 4048/02 Level (Stream) : Secondary Four Express Five Normal (Academic) Date : 29 August 2022 Duration : 2 hour 30 minutes Marks : 100 READ THESE INSTRUCTIONS FIRST Candidates answer on the Question Paper. Write your name, class 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, highlighters, glue or correction fluid. Answer all questions. The number of marks is given in brackets [ ] at the end of each question or part question. 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. For Examiner’s Use 100 This document consists of 25 printed pages, including this cover page. Setter: Mr Jeremy Lum OUTRAM SECONDARY SCHOOL PRELIMINARY EXAMINATION 2022 Class Index Number Name: __________________________________________________

2 Mathematical Formulae Compound interest Total amount = 𝑃 (1 + 𝑟 100) 𝑛 Mensuration Curved Surface area of a cone = 𝜋𝑟𝑙 Surface area of a sphere = 4𝜋𝑟2 Volume of a cone = 1 3 𝜋𝑟2ℎ Volume of a sphere = 4 3 𝜋𝑟3 Area of triangle 𝐴𝐵𝐶 = 1 2 𝑎𝑏 sin 𝐶 Arc length = 𝑟𝜃, where  is in radians Sector area = 1 2 𝑟2𝜃, where  is in radians Trigonometry 𝑎 sin 𝐴 = 𝑏 sin 𝐵 = 𝑐 sin 𝐶 𝑎2 = 𝑏2 + 𝑐2 − 2𝑏𝑐 cos 𝐴 Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

3 Answer all the questions. 1 (a) In 2020, Tammy earned a total of $38000. In 2021, he earned $3500 each month. Calculate the percentage increase in his earnings from 2020 to 2021. Answer ……………………………...% [2] (b) A bank offers a savings account with a compound interest rate of 1.8 % per annum. On 1st January 2022, Tammy deposited $5000 in this account. Calculate the total interest earned on 31st December 2031. Give your answer correct to the nearest cent. Answer $ ……………………………... [3]

4 (c) The exchange rate between Singapore dollars (SGD) and Swiss franc (CHF) is 1 SGD = 0.7 CHF. The exchange rate between British pounds (GBP) and Singapore dollars is 1 GBP = 1.73 SGD. Tammy is planning a trip to Europe. She finds these hotel prices on a website. Tammy books 4 nights in the hotel in Switzerland and 3 nights in the hotel in London. She pays using her credit card. The credit card company converts the prices to Singapore dollars. Tammy is charged a fee of 1.8% of the total amount for the currency conversion. Calculate the total amount of money Tammy pays for the two hotels, including the credit card fee. Give your answer correct to the nearest dollar. Answer $ ……………………………... [4] Swiss Hotel CHF140 per night London Hotel GBP120 per night

5 2 (a) Solve the inequality 43 132 x x+ − . Answer ……………………………...... [2] (b) Solve these simultaneous equations. 3 2 3 10 18 12 33 xy xy + =− − =− Answer x = …………………………... y = …………………………... [3]

6 (c) Solve the equation 36 25 2 3 x xx +=−+ . Answer x =…………... or …………… [4]

7 (d) Arrange 500 300 2002 ,3 , 4 in ascending order. Show your reasoning clearly. Answer ………………………………... [2] (e) Simplify 24 6 x y −   , leaving your answer in positive indices only. Answer ……………………………....... [2]

8 y 3 (a) Complete the table of values for 534yx x= + − . Give your answer correct to 1 decimal place. x 0.5 1 1.5 2 3 4 5 6 7 y 7.5 4 3.8 6.7 9.3 12 14.8 17.7 [1] (b) On the grid, draw the graph of 534yx x= + − for 07 x . 0 x [3] 18

9 (c) Use your graph to find the solutions of the equation 53 12x x+= in the range 07 x . Answer x = …………... or …………… [2] (d) (i) On the grid in part (b), draw the line 2 3 4yx=+ for 07 x . [2] (ii) Write down the x-coordinates of the points where this line intersects the curve. Answer x = …………... or ………….... [2] (iii) These values of x are the solutions of the equation 230x Ax B+ + = . Find the values of A and B. Answer A = …………………………... B = …………………………... [3]

10 4 A water tank can be filled with water by two pipes in 20 minutes. The smaller pipe takes 10 minutes longer than the larger pipe to fill the tank. If the larger pipe takes x minutes to fill the tank, (a) write down an equation to represent this information and show that it reduces to 2 30 200 0xx− − = . Answer [3] (b) Solve the equation 2 30 200 0xx− − = . Answer x = …………... or …………… [3] (c) Find the percentage of the tank that can be filled by the smaller pipe in 20 minutes. Answer ………………………….......% [2]