BDKSS 4N Prelim P2 2023 MS

2023 4N Prelim P2 MS 1a 5.75 (3sf) B1 1b 78.71 10 B1 1c 0.0543 B1 1d 4 1 3 36 2(4 1) 3 6 8 2 3 6 xx xx xx −+− − − −= − − −= = 75 6 x−= M1 A1 2a 5 25 25 49 7 7 7 7 7 77 25 3 n n n n n − = = = −= =− M1 (make all same base) A1 2b 11 3 33 3 8 8 x x −  =  = 2 x M1 (make positive index or apply power of -1/3 into brackets A1 3ai 6cos 10QPR= = 3 5 B1 3aii 6sin 10PRT= = 3 5 B1 3b Area = 13(10)(3)( )25 =9 units2 OR 1 (3)(6) 92 = B1 4a 504 399 100%504 −  = 520 %6 M1 A1 4b Balance = 90% of 399 = 359.10 Int = 359.1(5)(1) 17.955100 = M1 M1

Extra = 17.955 100%399  =4.5% A1 5ai 225 1 (5 1)(5 1)x x x− = + − B1 5aii 4 10 6 15 2 (2 5) 3 (2 5) ax x ay y x a y a − + − = − + − (2 5)(2 3 )a x y= − + M1 A1 5b 2 2 2 11 113 31 1( 1)(3 ) 4 3 3 4 2 3 2 1 0 0 ( 1)( 1) xx xx xx x x x xx xx xx +=+− − + + =+− = − + − =− + + − + = = − − x = 1 M1 (combine) M1 (obtain quad eqn/ attempt) M1 (solve eqn) A1 6a 22 2 2 2 2 5.2 27.04 4.5 2 24.25 XZ XY YZ == + = + = Since 2 2 2XZ XY YZ+ , the converse of Pythagoras’ Theorem is not true. The triangle is not right angled triangle. M1 (working) A1 (conclude stmt) 6b 2 2 2 1 5.2 2 4.5cos 2(5.2)(2) cos (0.51875) XZY XZY − +−= = =58.8° (1dp) M2 A1 7 See graph [9] 8ai Vol = 23 2(5) (8) (5)3 − =367 cm3 (3sf) M1 (either formula) A1 8aii Total area = 22(5) 2 (5)(8) 2 (5)  ++ = 487 cm2 M1, M1 (cylinder & Hemis) A1 8b Max = 8 x 5 x 1 = 40 B1

9a 2 3 14 (1) 4 7 (2) (1) 2 : 4 6 28 (2) : 4 7 7 21 3 2.5 xy xy xy xy y y x + = −−−− − = −−−−  + = −= = = = M1 A1 A1 9bi 2 22 2 (3 7)( 2) 3 6 7 14 0 2 14 x x x x x x x xx = + − = − + − = + − M1 M1 A1 9bii 22 14 0xx+ − = 21 1 4(2)( 14) 2(2)x −  − −= = 2.41 or -2.91 M1 A1, A1 9biii Length cannot be negative. B1 10a Electricity 0.2794(793) 221.5642 Gas 0.2166(70) 15.162 Water services 1.21(36.5) 44.165 Waterborne 0.92(36.5) 33.58 50conservation tax (44.165) 22.0825100 refuse removal 9 == == == == == = Total = $345.5537 After GST = 108345.5537 100 =$373.20 (2dp) M1 (find water services) M1(electricity or gas) A1

10b SP Group (no contract) Total for a month = 29.62 x 793 = $234.8866 Total over 12 mths =234.8866 x 12 – 50 = 2768.6392 Sembcorp (12 mth) Total for a month = 100 22.5 (29.61)(793)100 181.9757 − = Total over 12 mths =181.9757 x 12 – 100 = 2083.7084 Senoko (12 mth) Total for a month = 100 19 (28.98)(793)100 186.1472 − = Total over 12 mths =186.1472 x 12 – 50 = 2183.7664 Since the cost over 1 year is the cheapest for Sembcorp, Get the 12 months plan from Sembcorp. M1: SPgroup M1: Sembcorp M1: Senoko M1 A1 11ai angle ACD = 90° - 20° = 70° (right angle in semicircle) B1 11aii Angle AOB = 40° (angle at centre = 2x