Outram Sec 4E5N Maths P2 Prelim 2022 Solutions

1 1a 3500 12 38000percentage increase = 100%38000 10.5% −  = 1b A = 101.85000(1 )100+ =5976.51 Interest earned = 5976.51 – 5000 =$976.51 (nearest cent) 1c Cost of hotel in Switzerland = 140 4 101.8 0.7 100   =$814.40 Cost of hotel in London = 101.8120 3 1.73 100   =$634.01 Total cost = $814.40 + $634.01 =$1448 (nearest dollar) 2a 43 132 x x+ − 4 3 2 6 10 1 1 10 xx x x +  − − − 2b 3 2 3 1 10 18 12 233 24 10 37 3 15 10 15 4 39 52 4 3 1 2 xy xy xy xy x x y + =− −− − =− −− − =− −− + =− −− =− =− = 2c 22 22 2 36 25 2 3 3 (2 3) 6( 5) 2( 5)(2 3) ( 5)(2 3) 3 (2 3) 6( 5) 2( 5)(2 3) 6 9 6 30 2(2 10 3 15) 6 15 30 4 14 30 2 29 0 (2 29) 0 290or 2 x xx x x x x x x x x x x x x x x x x x x x x x x xx xx xx +=−+ +− +=− + − + + + − = − + + + − = − + − + − = − − += += = =− M1 A1 A1 M1 M1 M1 M1 M1 A1 A1 M1 A1 A1 M1 M1 M1 A1 each

2 2d 500 5(100) 100 300 3(100) 100 200 2(100) 100 200 300 500 2 2 32 3 3 27 4 4 16 4 3 2 == == ==  2e 24 6 8 12 12 8 x y x y y x − − −   = = 3a 4.5 3c 53 12 53 4 8 8 x x x x y += + − = = 0.40 3.60x or= 3dii 1.10 2.80x or= 3diii 22 2 3 4 5 342 103 4 6 8 3 4 6 10 8 3 12 10 0 12; 10 x x x xx x x x x x xx AB + = + − + = + − + = + − − + = =− = 4a In 1 min, larger pipe fills 1 x of tank. In 1 min, smaller pipe fills 1 10x+ of tank. In 1 min, both pipes fill 11 10xx+ + of tank. 2 2 1 1 1 10 20 ( 10) 1 ( 10) 20 20(2 10) ( 10) 40 200 10 30 200 0( ) xx xx xx x x x x x x x x shown += + ++ =+ + = + + = + − − = M1 A1 M1 A1 M1 A1 each M1 M1 M1 M1 A1 A1 each

3 4b 2( 30) ( 30) 4(1)( 200) 2(1) 30 1700 2 35.6 5.62( ) x or rej − −  − − −= = =− 4c 1 2045.61 43.9%  = 5ai sin 27.5 15.3 7.06 AD AD = = 5aii 2215.3 7.06 13.6 AC=− = 5aiii 13.6tan 35.6 13.6 tan 35.6 19.0 AB AB = =  = 5b Angle of depression = angle of elevation of D from B 7.06tan 19.0 20.4 AOE AOE =  =  5c 2213.6 19.0 23.37 11 23.37 13.6 19.022 11.1m BC AP AP = + =   =   = 5d 22 2 2 2 7.06 19.0 20.27 20.27 23.37 15.3 2(23.37)(15.3)cos 58.9 BD BCD BCD = + = = + −   =  6a TD= s TC TD DC=+ = s + 4r 6bi Since 3TC PQ= , so TC//PQ. () () TCD PQD corr s CTD QPD corr s  =   =  By AA property, triangles TCD and PQD are similar. M1 A1 each M1 A1 M1 M1 M1 M1 A1 M1 A1 M1 M1 M1 A1 M1 A1 M1 M1 M1

4 6bii 2 3 9 1 6 : : log 1 : 9 1 : 12 1 : 9 : 108 Area TCD PQ Area PQD PQ Area TCD TD Area CAD AD Area PQD Area TCD Area of paralle ram == == 1 : 108 7ai ( ) ( ) 37 ( ) 180 37 37 106 106 2 53 at centre = 2 at circumference OAB isos AOB sumof sin a ADB  =    = − − =     =  =    7aii 180 22 37 37 53 31 (sum of s in a ) OBD = − − − − =    7aiii 180 37 31 112 (opp angles of a cyclic quad) AED = − − = 7b Let the radius be r. 2 2 2 22 2 Area of sector 106 360 106Area of sector 360 1Area of AOB = sin1062 106 122.5 sin106360 2 22.5 0.4444 7.12 AOB r AOB r r rr r r cm    = =   =  −  = = 7c sin 37 7.116 4.28 OF OF cm = = 8ai 40.5 minutes 8aii Q3=46 Q1=39 IQR=7 8aiii 15 100%140 10.7%  = 8b 1. The women generally ran slower than the men as their median timing (43.4 min) is greater compared to the men (40.5 min). 2. The timings of the women are more consistent as their IQR (4) is lower compared to the men (7). M1 for either Q1 or Q3 M1 A1 M1 M1 A1 M1 M1 A1 M1 A1 M1 M1 A1 M1 A1 M1 A1 M1 M1

5 8ci 62 31 280 140= 8cii 78 39 280 140= 8d 123 122 280 279 0.192  = 9a 7 9b 40 35 30    9c 4012 15 16 3510 13 14 30 1485 1275 =  =   = M HF 9d Each element represents the total amount earned by the fitness studio for the morning and afternoon sessions respectively. 9e 5(1485 1275) $13800+= 10a 0.8 3700 $2960= 10b 0.4 40000100 $160  = 10c DBS Multiplier Salary credited = 0.8 4500 $3600= Eligible transactions = $4100 - $4300 Interest earned 0.4 40000100 $160 = = OCBC 360 1.2 0.3 0.05 1.55%+ + = Interest earned 1.55 40000100 $620 = = M1 M1 M1 A1 A1 A1 A1 each A1 A1 M1 M1 A1 M1 M1 M1 M1

6 UOB One Interest earned first $15000 0.5 15000100 $75 = = Interest earned next $15000 0.55 15000100 $82.50 = = Interest earned next $10000 0.65 10000100 $65 = = Total interest = 75 82.50 65 $222.50+ + = Mr Lim should change to the OCBC account as it pays higher interest on his $40000 savings. M1 M1 M1