Seng Kang Sec Sch P2 2020

1 ··- .... , .• u ·- .. , le,_, (IJ SENG KANG SECONDARY SCHOOL PRELIMINARY EXAMINATIONS 2020 MATHEMATICS 4 NORMAL ACADEMIC Paper2 READ THESE INSTRUCTIONS FIRST Candidates answer on the Question Paper . Write your class, Index number and name on all the work you hand In. Wrtte In dal1< blue or black pen. You may use an HB pencil for any diagrams or graphs. Oo not use staples, paper clips, glue or correction fluid. Section A Ans- all questions. Section B - Answer one question . If wotklng Is needed for any question It must be shown with the answer. Omission of assentlal working will result In Iha loss of marks . The use of an approved scientific calculator la expected, where appropriate . 4045/02 13 August 2020 2 hours 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 rr, use either the calculator value or 3.142 , unless the question requires the answer In terms of"· Al the end of the examination, fasten all your work securely together. The number of marks Is given In brackets [ ] at the end of each quest ion or part question . The total of the marks for this paper Is 60. Parent'• I Guardian'• Signature: This document consists of 17 printed pages and 1 blank page. [Tum Over 2 Mathemotlcal Formulae Compound lnlereJ/ Total amount = JI+~) • '~ 100 Geometry and Measurement Trigonometry Sta/Isl/cs Curved surface area of a cone= nrl Surface area ofa sphere= 4nr 2 Volume of a cone= .!. m-2 h 3 4 J Volume of a sphere= 3 nr Area of triangle ABC= .!_ ab sin C 2 Arc length= r8 , where 8 is in radians Sector area=½ r'B • where 8 is in radians Cl b C -- = -- = sinA sinB sinC a' =h' +c' -2hccosA Lfx Mean= LI Standarddeviation =./Llx' -(Llx)' LI LI

2 (a) (b) 3 s«tlon A (52 marb) Answer all the questions in this acction. Simplify . I Solve the equation 2' = _!_ . 4 (a) Express 1.3 x I 0'1 as a decimal. (21 [II [I] (b) Theami ofa piece of wrapping paper is 5.88 xi~ mm2• Calrulate the total area. in square millimetres, of 1.5 x I 02 pieces of wrapping paper, leaving your answer in standard fonn. [2] [Turn Over 3 4 (a) Factori,ie 7nc - Jc + 18b - 42ab completely. (b) Solve (y + 2) (2y - 5) = 0. (c) -8 Solve the equation - = x + 4. x-2 \2\ (21 l~l

4 5 A coach bus travels 270 km from Singapore to Malacca. It reaches Johor in I hour 30 minutes after travelling at I 00 km/h, and makes the rest of the journey at 120 km/h. Calculate its average speed in km/h for the entire journey . (a) (I) Express 120 as a product of its prime factors . (II) State the smallest integer value of k for which 120k is a perfect square. (b) Albert goes hiking every 12 days and swimming every 6 days. He did both kind of exercises today . How many days from now will he go hikin1 and swimming again on the same day? (4) [I) [I) [21 (Tum Over 6 6 The diaaram below shows a rcctanaular paper box without cover. The length. breadth and height of the box arc 23 cm, 18 cm and 15 cm rnpcctively . 23 cm (a) Find the area of paper needed to constJUcl the box. (b) The diagram below shows a tennis ball with diameter 4 cm. ® Calculate the volume of the tennis ball . (2) [2]

I 7 (c) The leftnis ball11111 -.,II 111111)' lnlD lllt bo• In ,_. column&. 0 Find the_,....,. Nlmber or lfflnla balla 111111 can he placed In the 11o ... 121 ITumOver I 7 n...,_.,,,. . ..,.._"'1,u,.._, ,rf10.o>-o10.8)1N1Sfl.o>- ¥ (11 Find the sndlent of line P(l. (b) The line RS haa the 11me padient as the line P(l . find the equation or the line RS. (t) Hence, state the coordinates or R. (d) Calculate the area of the trapezium P(lRS. 111 121 111 [2]

8 9 A building is 4S m tall. Mis a point at the top of the building. Given that the aeroplane is 120 m above the ground and the angle of elevation from the point M to the aeroplane is 68.2°. 120m " " J.,. " " " " " " " " dm (a) Find the horizontal distance, d. There is a car moving towards the building. (b) Find the angle of depression of the point M to the car when the car is SO m away from the [2] building. [2] [Tum Over 9 10 A projectile i• beina fired from a cliff. 111 hciaf,t, h mc1cn, above the ground during its night is rcprclClltcd by the equation /1 • 28 + 481 - I 2r, where I is the time in seconds when the projectile is being fired. The table below shows some corresponding h and I values for the equation h = 28 + 481 - I 2r. 0 I.S 2.S 4 ,, 28 64 73 73 64 p (a) State the height of the vertical cliff. (b) Calculate the value ofp. (c) On the srid opposite, draw the graph of h = 28 + 481 - 12t' for 0 :S, :s S. (d) Use your graph to find (I) the greatest height reached by the projectile from the ground. (II) the time taken for the projectile to hit the ground . -32 [I) [I] [3) [I] [I]

11 H ., n lJl I l [1l H "1 ' 1 IJ ., l -, j j u t -l l t II ff I 4 -- rt , I I I I 4 ti j t - j il j ! I~ - ill H ! · 11 I i "1 1 I i--'-tJ ! .II l rtl-4 I a 1 IJ 1: I j - j - #±\iliL L~~ll' t t I" 1 !l l:li J ! l j JL-f1!i j Hl:t1 1: 11 .. I i l~t\ 1\ o\ 11!! I\\ ' ' I 1.,1 111 j ,J : s!)jl !1ti:li l_, i _ I ii! j i; I 1 ! i , 1 'I 1 1 , I 1 Ii• ,' 11; 'l 1 t,-l-l---1 1 ~-4+1-+-+l-+--l--l-l--4-\ 1-+!-1--l-+1.J..!-i-!+++++-H+II \ H+ll +++l+t+-!--'-l i +It\+ -1-++11 1 1-1+!-:-I-W--I M \ i , 111 I I I 1 1 I ,,11_,il' I ll l 1i '\ l 1 11 l i· ,i [!I ; j \ 111 r : i . I; I l ! Ii: l it11 l WI~ \1 I . I ,j l ~! 4 11 ill! i (Tum Over 12 10 Mr Kim receivn an income ofSIOO 000 for the year 2019. The amount of tax he needs to pay i• calculated after deductln1 the relief. He is eligible for the following relief; Personal relief S1500 Child relief $4000 Parent relief S9000 CPF $20000 (a) Calculate the total amount of relief. [I) (b) Calculate the amount of income which is taxable. (2)

13 His taxable income after deducting the relief will be laxed as follows: CbarseaJ,le Income Income Tu Rate Groa Tu Payable ("lo) ($) Finl $20,000 0 0 Next $10,000 2 200 Finl $30,000 - 200 Next $10,000 3.50 350 Finl $40,000 - 550 Next $40,000 7 2,800 (c) How much tax docs be need to pay? (d) In order to save up for bis retirement. Mr Kim decided to deposit $15 000 into his Supplcmcnta,y Retirement Scheme account. which is not taxable. How much lcsacr tax docs he pay? 14 B (8 marb) Answer one question from this ICc:lion. Each question carries 8 marb. II (a) The diagram shows a triangular roctd X>'Z, where XY = 18 m. rz = 11 m and arz = eo•. (2) z (I) Calculate the length of XZ. [3) [3) (II) Calculate the area of triangular field X>'Z. (2) ITurnOver

IS t(b) 'The diagnim · snows a semi-circle with centre O and nidius '16 cm. CZ\ 0.5 nid A O E Given that angle £COE= 0 .S radians. find (I) the angle COA in nidians. [I) (II) the ll1C8 of the segment CDE. [2] ITurnOver 16 12 The cumulative frequency l!l"IPh lhows lhe ditln'bari<ln of wecldy .. ..,. of 800 worl<en. Cumulative frequency 800 600 400 200 20 (a) Estimate (I) the median WAI", (II) the interquanile ranae, (Ill) the 30"' percentile wage. 60 10 w..,..(SJ 100 [I] (21 Ill

17 (b) Jfthe company decides to increase the wages of each worlccr by 10%, describe how the cumulative frequency curve differs from the given curve. I I I (c) If two workers are selected at random, calculate the probability that (I) they both earn less than S40 each per week, (I I (II) one earns less than S40 per week and the other earns between S60 to $80 per week. [2] END OF PAPER !Tum Over 18 BLANK PAGE

2020 4NA PnUmlnary Examlnadon1 Paper 2 ANSWERS l . lhl,c = -2 lal ai 3 (a)(7a - 3)(c-6b) (b)y=-2 or y=2} lcl,c = 0 or ,c= -2 5 120= 23 X 3 XS 30· 12 davs 7 -i;y= -ix+zi: R ( 0, 2~); 36! units' 9 28m;p=28; greatest height - 76 m; time taken = 4.5 secs 11 19.4 m; 97.5 m2; 2.64 rad; 2.63 cm' 19 2 (1