2025 A Level H2 Math 9758 Paper 2 SUGGESTED MS

General Certificate of Education Advanced Level 2025 Higher 2 Mathematics 9758/02 Syllabus 9758 Paper 2 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 1 Section A: Pure Mathematics [40 marks] 1 (a) 8 11 5 114 5 14 7 112 9 9 4 110 c t b c t b c t b + + = + + = + + = M2 M1 for any correct equation M1 for all three 7, 3, 5c t b= = = A1 (b) Let x, y and z denote the number of cars, trains and boats Sam has. 7 3 5 113x y z+ + = M1 Set up equation Process of Guess and Check, Trial and Error, Algebraic manipulation, inequalities, o.e. M1 Any valid method seen and reason 6 cars, 7 boats, 10 trains A1 [6]

General Certificate of Education Advanced Level 2025 Higher 2 Mathematics 9758/02 Syllabus 9758 Paper 2 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 2 2 (a) 1 2 3 6 3 3 6 0 6 PQ −           = − =                 M1 Find PQ  s.o.i. 34 34 44 3433 68 QR PQ QR PQ =        = = =             M1 Attempt to find QR  o.e. 4 4 1 5 4 4 6 10 8 8 6 14 OR OQ OR                − =  = + =                       A1 (b) 1 1 2 6 2 8 66 SQ cc −           = − − =           −       M1 Find SQ  s.o.i. 23 0 8 3 0 66 6 24 36 6 0 6 66 11 SQ PQ c c cc         =   =      −    + + − = =  =  A1 (c) 1 2 1 2 3 5 11 0 11 PS −−           = − − = −                 M1 Find PS  s.o.i. 1 3 1 3 5 3 5 3 cos 11 6 11 6                 −  = −                      M1 Reasonable attempt to use dot product s.o.i. 54cos 52.7 (1 d.p.) or 0.920 rad (3 s.f.) 7938 =  =  A1 [8]

General Certificate of Education Advanced Level 2025 Higher 2 Mathematics 9758/02 Syllabus 9758 Paper 2 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 3 3 (a) 2 2 2 d 1 d sin 3 sin 3dd d sin 3 d yy y x xx y x y y x x− =  = = M1 Variable separable s.o.i. 1 cos3 3 x cy− =− + M1 Correct integration When πx= , 1y= . 141 33 cc− = +  =− M1 Find arbitrary constant o.e. 1 cos3 4 3 f ( )3 3 4 cos3 x xyx− =− −  = + A1 (bi) B2 B1 for correct maximum, minimum and y- intercept B1 for correct period and shape 1c= or 3 5c= B1 o.e. (bii) π ,3 kxk=  B2 B1 for equation B1 condition for k (biii) 3f( π) 4 cos3x x+= − B1 FT from (a) (c) 2 2 2 dd 2 sin 3 3 cos3dd yy y x y xxx =+ M2 M1 for attempt to use product rule M1 for implicit differentiation ( ) ( ) ( ) ( ) 2 22 2 2 2 2 3 2 d 3cos3 2 sin 3 sin 3d d 3cos3 2si