Greendale Sec 4048_01 Answer Scheme

2022 4E5A Preliminary Examination Paper 1 Mark Scheme 1 22 33 3 3 5 ( 5) 5 25 25 5 55 55 25 125 55 150 55 0.475235 0.475 (3 )sf − −− × −−×= −× −× −−= −× −= −× = = B1 2 38 2( at centre = 2 times at circumferenc e) 76 180 76 (base angles of isosceles triangle)2 52 QOS OSQ ∠ =×∠ ∠ = ° −∠= = ° M1 A1 3 Diagram 4 B1 4a The size of the picture is different over the years. B1 (o.e) 4b The reader may be misled to think that a bigger picture represents more people. B1 (o.e) 5a 3 33 9 27 (3 ) 3 = = B1 5b 23 4 23 4 4 22 24 5 25 2 25 54 5 2 xy xz zy xy y z xz y xz ÷ = × = M1 (for any simplification of constants or variable) A1 6 Worker : Hours : Footbridge 18: 60 : 3 18: 20 : 1 1 : 360 : 1 1 : 2520 : 7 63 : 40 : 7 Additional workers = 63 18 45 workers−= M1 A1 7 6, 6, 9, 11, 18 B1 for any 3 B2 for all 5

8 41 125 20 5 2 110 10 18 5 10 5 6 xx xx x x + −= − + −= − += − =− M1 M1 A1 9a + 2 3 5 7 11 2 4 5 7 9 13 3 5 6 8 10 14 5 7 8 10 12 16 7 9 10 12 14 18 11 13 14 16 18 22 B1 for all correct 9bi 6 25 B1 (ecf) 9bii 5 25 B1 (ecf) 9c The spinner has to be fair so that the probabilities of obtaining each outcome is equal. B1 (o.e) 10a 2 22 2 2 2 75 7775 22 7 29 24 113724 xx xx x x −+  =−+ − +    = −− = −− M1 A1 10b 113,724  − B1 11a p = 7 q = –2 B1 B1 11b 7 2 100 7 102 14.571 n n n −< < < Largest n is14 B1 12a 4u -> 7.2 1u-> 1.8 3u-> $5.40 B1 12b 700 : 1750 2 : 5 B1

13a 2 2 17 1 7 ( 3) 1 116 16 r q r r r =+ =+− = = B1 13b 2 2 2 17 7 7 7 r q rq qr qr =+ = + = − = ±− M1 A1 14 Let the initial cost be $x. Cost price = 1.08x Selling price = 1.15 (1.08x) = 1.242x 1.242x -> $465.75 1.242 465.75 $375 x x → → M2 for 465.75 ()1.08 1.15 oe× B1 for 1.08 or 1.15 (oe seen) 15 3 3 511576.25 (1 ) 100 11576.25 (1.05) $10000 P P P = + = = B1 for 5% seen B1 for power 3 B1 16ai 3 , 4 , 5 , 7 , 10 , 11 B1 16aii 4 , 10 B1 16b ( )AB ′∪ or AB′′∩ B1 17 2228.6 5 5 2(5)(5)cos 118.63317 180 118.63317 61.36683 8cos 61.36683 16.69449 16.69449 5 11.69449 11.7 DCE DCE ACB AC AC AE m =+− ∠ ∠= ∠= − = = = = − = = M1 M1 M1 A1

18a 224.8 ( ) 7.5 ( ) 4.8 ( ) 7.5 ( ) 4.8 ( ) 7.5 1000 100 ( ) 7.5 1000 1001 () ( ) 4.8 1:125000 cm map km actual cm map km actual cm map cm actual cm map cm actual → → →×× ××→ M1 A1 18b 4.8 ( ) 7.5 ( ) 7.51 () ( ) 4.8 7.59 () 9 ( ) 4.8 11.25 cm map km actual cm map km actual cm map km actual km → → →× = B1 19a 12(2 ) 5( 4 )32 254 2032 3 58 23 xxy y xxy y xy −−− =−−+ = + M1 A1 19b 4 5 16 20 (4 5 ) 4 (4 5 ) (4 5 )( 4 ) am bm an bn m ab n ab a bm n −−+ = −− − = −− M1 A1 20ai 2495 3 5 11= ×× B1 20aii 2495 3 5 11= ×× N = ? HCF 15 3 5= ×