2021 O Level Math 4048 Paper 1 SUGGESTED MS

General Certificate of Education Ordinary Level 2020 Mathematics 4048/01 Syllabus 4048 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 1 1 Total value $2500 $2500 1.6% 3= +   M1 Calculates annual interest s.o.i. $2620 A1 [2] 2 By Pythagoras’ Theorem, 2 2 220.5 13.3 AB=+ M1 Attempt to use PT s.o.i. 2220.5 13.3 15.6 cmAB= − = A1 [2] 3 (a) Distance 80 3 240 km=  = B1 ‘80’ and ‘3’ must be seen in working (b) The speed and time are both rounded down ; thus the actual distance is greater than the estimated value. B1 Rounded down mentioned o.e. [2] 4 (a) 0.32 B1 o.e. (b) 42 White Marbles B1 c.a.o. [2] 5 3 2( 4) 9 8( 4) 4 3 12 x x x x − − −−= M1 Join fraction 9 8 32 12 32 12 xx x −+= += A1 [2] 6 1 2 15 21 21 B2 B1 Any 3 correct B1 All 5 correct [2] 7 Height of cuboid 1200 8 cm150== M1 s.o.i. 15 cm by 10 cm by 8 cm A1 c.a.o. [2] 8 Number of visitors in 2018 7690000 240.6%= M1 240% o.e. 18502140 18500000 (3 s.f.) = = A1 Accept nearest ten thousand [2]

General Certificate of Education Ordinary Level 2020 Mathematics 4048/01 Syllabus 4048 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 2 9 (a) 5 2x=− B1 o.e. (b) 8 5 6 9a b a b− − − M1 Expand 2 14ab=− A1 c.a.o. [3] 10 Frequency Sector angle Walk 24 160 Bus 21 140 Cycle 9 60 Sector angle Frequency 36054=   B3 OR M1 A2 B1 for each angle OR M1 Attempt to find any angle A1 for any angle correct A1 for all angles [3] 11 Exterior angle 1 180 22.58=  =  M1 Find exterior angle Number of sides 360 22.5= M1 16 sides A1 Alternative (longer) method: Interior angle 7 180 157.58=  =  M1 Find interior angle ( 2) 180 157.5nn−  = M1 Form equation 180 360 157.5 22.5 360 16 nn nn −= =  = 16 sides A1 [3] 12 (a) The elements of A are the factors of 12. B1 (b)  ' ' 7, 8, 9, 10, 11, 13, 14AB= B1 (c) 6 B1 [3]

General Certificate of Education Ordinary Level 2020 Mathematics 4048/01 Syllabus 4048 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 3 13 (a) 475000 B1 Accept ± 5000 (b) The number of people aged 0 –9 has fallen ( 2017 bar is shorter than 2007) from 2007 to 2017. B1 Accept length of bar o.e. (c) In general, the population of residents aged above 40 has increased and the population of residents aged below 40 has decreased. M1 Must define ages clearly Hence, the mea n age of the resident population has increased. A1 [4] 14 (a) Angle Angle (Given) Angle Angle (Shared angle) ABC ADE EAD CAB = = M1 Hence, triangles ABC and ADE are similar. (AA Similarity Test) A1 (b) 9 10 12 AD = M1 9 10 7.5 cm12 12 7.5 4.5 cm (Shown) AD CD =  = = − = A1 AG [4] 15 (a) 224 12 9x px p++ B2 B1 for any two correct terms B1 for all correct (b) 3p=− B1 [3] 16 (a) 4t = B1 (b) 2E kv= (k is a constant) Let the initial and new speed be 1v and 2v respectively. 2 1 1 1 1 2 2 1 1 2 2 2 0.25 1 2 EE kv v k E E EE kv v k k k =  = =  = = = M1 Find expression for new speed in terms of old energy s.o.i. 50% reduction A1 A0 for –50% [3]

General Certificate of Education Ordinary Level 2020 Mathematics 4048/01 Syllabus 4048 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 4 17 4 2 16x y B2 B1 for 16 B1 for 4 2 x y [2] 18 (a) 31081 litres/km or 1090 litres/km ( 3 s.f.)37 B1 o.e. (bi) 5.5 m B1 (bii) 3 6 Volume of fuel tank 1 1.228 10 60 =  M1 3 61Volume of fuel tank 1.228 1060 5.685185185 5.69 litres (3 s.f.) =   == A1 [4] 19 Angle ACB 180 82 56 42= − − =  M1 s.o.i. Using sine rule, 15.6 sin 42 sin 56 AB = M1 15.6sin 42 12.59103062 cmsin 56AB ==  Area 1 (15.6)(12.59103062)sin 822= M1 2297.25426547 cm 97.3 cm (3 s.f.)== A1 [4] 20 (ai) 4223 B1 (aii) 36 B1 48 B1 (b) 2p= B1 7q= B1 [5]

General Certificate of Education Ordinary Level 2020 Mathematics 4048/01 Syllabus 4048 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 5 21 (a) 26 3 2 3 (2 ) (2 ) x xy x y x x y x y + − − = + − + M1 or M0 (3 1)(2 )x x y= − + A1 or B1 per term (b) (4 3)(2 3) 0xx+ − = M1 33 or 42x=− A2 A1 for each value [5] 22 (a) 5 4 2 63 y = M B1 (b) 476 286 5 336 68 117 6 65 x y x y += + + + P B2 B1 Any two correct B1 All elements (c) It represents Tom’s total cost of buying garden centre A. B1 (d) 38x= B1 (e) 4y= B1 [6]

General Certificate of Education Ordinary Level 2020 Mathematics 4048/01 Syllabus 4048 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 6 23 (a) Drawing of a suitable tangent at (2, 1) M1 Gradient 5 ( 5) 43 0.5 −−== − A1 Accept ±0.1 (bi) 32 32 60 8 6 2 6 x x x x x x x + − = + − + =− + M1 Attempt to manipulate s.o.i. 32 86 32 3 x x x x yx + − + =− + =− + A1 (bii) Drawing of straight line with three relevant points M1 FT from (b)(i) 3 or 0 or 2x=− A1 [6]

General Certificate of Education Ordinary Level 2020 Mathematics 4048/01 Syllabus 4048 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 7 3yx=− +

General Certificate of Education Ordinary Level 2020 Mathematics 4048/01 Syllabus 4048 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 8 24 (a) 0.25 m/s2 B1 (bi) 8T m B1 (bii) Distance travelled by A 1 (5 10)(20) (10)( 20)2 T= + + − M1 150 10 200 8 90TT+ − = + M1 Form equation 2 140T = M1 Isolate or simplify 70T = A1 [6] END OF MARKING SCHEME