2017 O Level Math 4048 Paper 2 SUGGESTED MS

General Certificate of Education Ordinary Level 2017 Mathematics 4048/02 Syllabus 4048 Paper 2 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 1 1 (a) 42 53 3 12 10 5 xx xx +−  +− M1 Remove fraction 82 1 4 x x − − A1 o.e. (b) 2 2 (5 2 ) 3 (5 2 ) y y y y −− − M1 Join fraction 2 2 2 2 10 4 3 (5 2 ) 74 (5 2 ) y y y y yy y −−= − −= − A1 (c) 3 3 2 35 18 10 53 h j j k h k M1 Flip fraction or M0 5 24 12 j hk= A1 or B1 for 12 or B1 for 5 24 j hk (d) 1 12 4 816 v t   M1 Flip fraction or M0 3 22 v t= A1 or B1 for 1 2 o.e. or B1 for 3 2 v t (e) 2 2( 4) 3( 2) 1( 2)( 4) 2 8 3 6 2 4 8 xx xx x x x x x + + − =−+ + + − = − + − M1 Remove fraction 2 3 10 0 ( 2)( 5) 0 xx xx − − = + − = M1 Factorise o.e. 2x=− or 5x= A1 A1 for both [11]

General Certificate of Education Ordinary Level 2017 Mathematics 4048/02 Syllabus 4048 Paper 2 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 2 2 (ai) Mean 75.41 10 12 = M1 664.5083333 10 4.51 10=  =  (3 s.f.) 4.51 million A1 (aii) Percentage 6 7 5.09 10 100%5.41 10 =  M1 9.408502773% 9.41%== (3 s.f.) A1 (b) Number of people 61.591 10 101.6%=   M1 o.e. 61.616456 10= A1 c.a.o. (c) Number of visitors 7100 1.509 1097=   M1 771.555670103 10 1.56 10=  =  (3 s.f.) A1 o.e. [8] 3 (a) 50 bacteria B1 (b) 70.7p= (3 s.f.) B1 c.a.o. (c) Refer to graph on page 3 Correct scale used to draw graph S1 Plotting of all 8 points correctly P1 Smooth curve passing through all points C1 (d) 3.325 hours B1 Accept ± 0.05 (ei) Drawing of reasonable tangent at (2, 200) M1 Gradient 450 20 138.7096774 139 (3 s.f.)3.8 0.7 −= = =− A1 Accept ± 5 (eii) It represents the rate of growth of bacteria on the 2nd hour to be 139 bacteria per hour. B1 FT from (e)(i) [9]

General Certificate of Education Ordinary Level 2017 Mathematics 4048/02 Syllabus 4048 Paper 2 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 3 t 50 2 ty=

General Certificate of Education Ordinary Level 2017 Mathematics 4048/02 Syllabus 4048 Paper 2 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 4 4 (a) ( ) 22( 4 4) 10 ( 2)AB= − − + − − M1 14.4222051 14.4== units (3 s.f.) A1 (b) Gradient 10 ( 2) 3 4 4 2 −−= =−−− M1 3 2 310 ( 4) 42 y x c cc =− + =− − +  = 3 42yx=− + A1 o.e. (ci) 3 2 5 2 3 5 35 (1)22 xy yx yx += =− + =− + −−− M1 Express in the form y mx c=+ or find gradient Since th