2006 O Level Add Math 4018 Paper 1 SUGGESTED MS

General Certificate of Education Ordinary Level 2006 Additional Mathematics 4018/01 Syllabus 4018 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 1 1 NOT within the 4049 syllabus (i) xA B1 (ii) ( )n ' 16B = B1 (iii) CD = B1 [3] 2 (i) 2a= B1 (ii) 360 360120 3 120bb =  = =  B1 (iii) 1c=− B1 [3] 3 (i) ( ) 2 8 3 4yx − =− ( ) 3d ( 2) 8 3 4 3d y xx − = −  −  M1 ( ) 3 d 48 d 34 y x x =− − A1 When 2x= , gradient is 6− . A1 (ii) NOT within the 4049 syllabus E2 [5]

General Certificate of Education Ordinary Level 2006 Additional Mathematics 4018/01 Syllabus 4018 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 2 4 NOT within the 4049 syllabus (i) Unit vector of 22 33113 4 = 44 53 ( 4)    −=    −−+−     ij Unit vector of 22 44114 3 = 33 534    +=    +     ij M1 Attempt to find either unit vector s.o.i. 3 3 610 24 4 85 68 OP OP      = = =     − − −       = − ij   A1 4 4 1215 33 3 95 12 9 OQ OQ      = = =            = + ij   A1 (ii) 12 6 6 9 8 17PQ      = − =     −       M1 Find QP  o.e. 226 6 1717PQ = = +  M1 Apply distance formula o.e. 325 5 13 5 PQ  == =  A1 [6]

General Certificate of Education Ordinary Level 2006 Additional Mathematics 4018/01 Syllabus 4018 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 3 5 NOT within the 4049 syllabus (i) Let A and B represent the number of aircrafts for each type and the number of Economy, Business and First seats in each type of aircraft respectively. ( )5 8 4 10=A B1 300 60 40 150 50 20 120 40 0 100 0 0   =   B B1 (ii) Let C represent the total number of seats in each class. ( ) ( ) 300 60 40 150 50 205 8 4 10 4180 860 360120 40 0 100 0 0   ==    C B2 B1 for any two correct B1 for all correct (iii) Let D represent the percentage of empty seats for Economy, Business and First seats on that particular day. 0.05 0.1 0.2  = D B1 (iv) ( ) ( ) 0.05 4180 860 360 0.1 367 0.2  ==  CD 367 seats B1 [6]

General Certificate of Education Ordinary Level 2006 Additional Mathematics 4018/01 Syllabus 4018 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 4 6 62 6 6 1 6 2 3 63 2 662 2 (2) (2) 122 2 2 6 (2) ...3 2 64 96 60 ... x x x x xx −− −         − = + − + −                   + − +  = − + + B3 B1 for each simplified term Coefficient of 2 60