PLMGS 4E_5NA Math P1 Prelim 2017_Worked Solutions

Paya Lebar Methodist Girls’ School (Secondary) Department of Mathematics 2017 Preliminary Examination Mathematics Paper 1 (4048/1) Worked Solutions Qns No. Solution 1(a) )5(2)3(3  xyx = 10239  xyx = 1037  yx 1(b) 36)12( 2 x = )612)(612(  xx = )72)(52(  xx OR 36)12( 2 x = 36144 2  xx = 3544 2  xx = )72)(52(  xx 2 aybybxax 10142115  = )57(2)75(3 abybax  = )23)(75( yxba  3(a) 3(b) P = {1, 2, 3} Q = {2, 3, 4, 5, 6} Elements in P  Q are 2 and 3. 4 )516()34( 22  nn = 51692416 22  nnn = 424 n = )16(4 n Since the expression is a multiple of 4, it is divisible by 4. 5 Let the width be x cm. 288)9)(2)(( xx 28818 2 x 162 x 4x (4 is rejected) Length of base = 8 cm.  A B

Qns No. Solution 6 8.13 52sin 4.17 sin XZY       8.13 52sin4.17sin XZY = 83.5 or 96.5 7 3 1 45 45 3       h 3 3 1 45 45  h 453 145 3       h 80.13h (2 dp) OR Let the height of small pyramid be x cm. 3 1 45 3      x       3 3 145x 2013.31x 2013.3145h = 13.80 (2 dp) 8  Title is biased – Does not allow reader to make their own judgement  The width of cylindrical bars are not equal – exaggerates the difference between the years 9 xxx 21 2 472 3 2  = xxx 21 2 )4)(12( 3  = 12 2 )4)(12( 3  xxx = )4)(12( )4(23   xx x = )4)(12( 112   xx x 10(a)  50DAC ( at centre = 2 at circumference) 10(b)  70180ADO (s in the opp segs) = 110 10(c)  11050180ADO ( sum of ) = 20 2 100180 ADO (base  of isos )

Qns No. Solution = 40  2040ACO = 20 11(a) 21215 xx = 15122  xx = 2 2 2 1215)6(     x = 21)6( 2x 11(b) Minimum value is 21 11(c) Equation is 6x . 12(a) dP 100941001.1 5  d100941001.11022.2 55  10094 1001.11022.2 55 d = 12.0 m (3 sf) Depth of diver = 12.0 m 12(b) 1 5 1 100941001.1 dP  2 5 2 100941001.1 dP  )100941001.1()100941001.1(105.3 2 5 1 55 dd  )(10094105.3 21 5 dd  10094 105.3 5 21  dd = 34.7 m Difference in depths is 34.7 m 13 In Singapore, 10 grams of gold cost $567.40 1 gram costs $56.74 USD 1275.10 = $1.382  1275.10 = $1762.19 In Los Angeles, 31.10 grams of gold cost $1762.19 1 gram of gold costs $56.67 Gold is cheaper in Los Angeles. OR 1.382 Singapore dollars = 1 US dollar S$567.40 = USD 382.1 40.567 = USD 410.56 In Singapore, 10 grams of gold cost USD 410.56

Qns No. Solution 1 gram costs USD 41.06 In Los Angeles, 31.10 grams of gold cost USD 1275.10 1 gram of gold costs USD 41 Gold is cheaper in Los Angeles. 14 C(46, 24) 15(a) 5 6tan BCP  194.50BCP PCQ = 2  50.194 = 100.4 (1 dp) 15(b) 