Paper 1 QP

4048/1/GE2/22 [Turn Over] O JURONG SECONDARY SCHOOL 2022 GRADUATION EXAMINATION 2 SECONDARY 4 EXPRESS/ SECONDARY 5 NORMAL (ACADEMIC) CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4048/01 PAPER 1 26 Aug 2022 2 hours Candidates answer on the Question paper. READ THESE INSTRUCTIONS FIRST 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, glue or correction fluid. Answer all the 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. At the end of the examination, fasten all your work securely together. 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 23 printed pages, including this page. 80

2 4048/1/GE2/22 Mathematical Formulae Compound interest Total amount 1 100 n rP=+  Mensuration Curved surface area of a cone πrl= Surface area of a sphere 24πr= Volume of a cone 21 π3 rh= Volume of a sphere 34 π3 r= Area of triangle ABC 1 sin2 ab C= Arc length r= , where  is in radians Sector area 21 2 r = , where  is in radians Trigonometry C c B b A a sinsinsin == 2 2 2 2 cosa b c bc A= + − Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

3 4048/1/GE2/22 [Turn Over] 1 Simplify ( )2 3 4 5x− − − + . Answer ……………………..………….[1] ___________________________________________________________________________ 2 The ratio of interior angle : exterior angle of a regular polygon is 5:1 . Calculate the number of sides that the polygon has. Answer ...............................................sides [1] ___________________________________________________________________________ 3 A photocopier can photocopy at a rate of 30 double-sided papers per minute. Calculate (a) in minutes, the time taken to print 600 pages on double-sided setting, Answer ……………………..…minutes [1] (b) the number of double-sided papers that can be photocopied in 1 hour. Answer …………...double-sided papers [1] ___________________________________________________________________________

4 4048/1/GE2/22 4 A survey was conducted to find out the preferred brand of mobile phone that secondary school students like. State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. ............................................................................................................................................ …........................................................................................................................................ …………………………………………………………………………………………[2] ___________________________________________________________________________ 5 Solve the inequality 2 2 3 9 4x x x− +  −  + . Answer ................................................... [2] ___________________________________________________________________________

5 4048/1/GE2/22 [Turn Over] 6 Find a possible set of integer values of a and b such that t he lines 1xy+= and 1ax by+= (a) do not intersect, X X Answer a= ……………………..……….... b= ………...……………..……[1] (b) intersect at exactly one point. X X Answer a= ……………………..……….... b= ………...……………..……[1] ___________________________________________________________________________ 7 Factorise 2 2 2 24 4 2 2ax ay bx by− + − completely. Answer ……………………..………….[2] ___________________________________________________________________________

6 4048/1/GE2/22 8 Simplify 16 6 3 2a b−   . Answer ……………………..………….[2] ___________________________________________________________________________ 9 Given that 25 125 5x= , find the value of x. Answer x= ……………………..……...[2] ___________________________________________________________________________

7 4048/1/GE2/22 [Turn Over] 10 Solve ( ) 2 51 422 xx += −− . Answer x= ……………………..……...[3] ___________________________________________________________________________ 11 (a) Express 215 xx+− in the form of ( ) 2 x a b++ . Answer ……………………..………….[1] (b) Write down the equation of line of symmetry of the graph of 215y x x= + − . XX XX Answer ……………………..………….[1] (c) Write down the coordinates of intersection between the line of symmetry and the graph of 215y x x= + − . Answer (………....… , …………….) [1] ___________________________________________________________________________

8 4048/1/GE2/22 12 The area of triangle ABC is 7.5 cm 2. Two of the sides are of length 5 cm and 6 cm respectively. Find the length of the third side. Answer ……………………..………cm [3] ___________________________________________________________________________ 13 The Ideal Gas Law 8.3145PV nT= relates pressure P (measured in Pascal), volume V (measured in metres3), the number of moles of a gas n (measured in moles), and temperature T (measured in Kelvins). One mole of gas is found to exert a pressure of 101 325 Pascal at room temperature 293 Kelvins. Find the volume of the gas in cm3. Answer ……………………..……..cm3 [2] ___________________________________________________________________________

9 4048/1/GE2/22 [Turn Over] 14 A map of the United States of America has a scale of 1:8 000 000 . (a) The length of the Mississippi River is 3766 km. Calculate the length, in centimetres, of Mississippi River on the map. Answer ………..................................cm [1] (b) The area of California on the map is 66.25 cm2. Calculate the actual area, in square kilometres, of California. Answer ............................................km2 [2] ___________________________________________________________________________ 15 (a) n is a positive integer. Show that, for all n, 26 25 11nn++ is not a prime number. ............................................................................................................................................ …........................................................................................................................................ …………………………………………………………………………………………[2] (b) Hence, determine whether 16261 is a prime number. Show your working clearly. ............................................................................................................................................ …........................................................................................................................................ …………………………………………………………………………………………[2] ___________________________________________________________________________

10 4048/1/GE2/22 16 The diagram represents a plot of land, ABCD. The police is looking for a robber hiding in the land. Scale: 1 cm represents 1 km Here are the accounts from three witnesses: Witness 1: The robber is located more than 6 km away from A. Witness 2: The robber is located nearer to B than A. Witness 3: The robber