2025 A Level H2 Math 9758 Paper 1 SUGGESTED MS

General Certificate of Education Advanced Level 2025 Higher 2 Mathematics 9758/01 Syllabus 9758 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 1 1 (a) 2 35ua=+ B1 c.a.o. 3 9 20ua=+ B1 FT from 2u (b) 4 3(9 20) 5 27 65u a a= + + = + M1 s.o.i. 3 5 9 20 27 65 110a a a a+ + + + + + = M1 Know to sum 1u to 4u s.o.i. 140 20 2aa=  = A1 o.e. [5] 2 (a) Let the first term be a and common difference be d. ( )20 2 19 652 ad+= ( )28 2 27 65 302 ad+ − =− M1 Attempt to use AP sum formula s.o.i. 10(2 19 ) 65 20 190 65 ad ad += += 14(2 27 ) 35 28 378 35 ad ad += += M1 Simplify to either equation By GC, 8a= and 1 2d =− . First term 8= and common difference 1 2=− . A1 Conclude, o.e. (b) ( 2) 1 ( 1) e ee kn kn kn n u u + + +== M1 Find 1n n u u + o.e. As the ratio of subsequent terms is a constant, the sequence is geometric. A1 Ratio is a constant o.e. [5]

General Certificate of Education Advanced Level 2025 Higher 2 Mathematics 9758/01 Syllabus 9758 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 2 3 (a) 3 i 3 i 3 i 3 i z ++= −+ M1 Attempt to multiply by conjugate s.o.i. 2 2 3 i 1 3 i3 1 2 2z += = ++ M1 Find z o.e. 22 13 122z = + =    A1 ( ) ( ) 1 πarg tan 3 3z −== A1 Radians only Alternatively: 3i3i 3i 3i ++ = − − M1 Uses 11 22 zz zz = s.o.i. 1z = A1 ( ) ( ) 3iarg arg 3 i arg 3 i 3i  + = + − − − M1 Uses ( ) ( ) arg arg arg z w zw   =− ( ) ( ) ( )( ) 11 πarg tan 3 tan 3 3z −−= − − = A1 Radians only (b) Plotting of A correctly with modulus and argument B1 Plotting of B correctly relative to A B1 Since B is obtained by rotating A by π 2 radians in the anti-clockwise direction, the complex number represented by A is multiplied by i. Hence, the complex number represented by B is iz. B1 Alternatively (using exponential form): Since B is obtained by rotating A by π 2 radians in the anti-clockwise direction, the complex number represented by B is ππ π πi i i62 6 2e e e i z  + =  = . B1 [7]

General Certificate of Education Advanced Level 2025 Higher 2 Mathematics 9758/01 Syllabus 9758 Paper 1 SUGGESTED Solutions & Marking Scheme Mark Allocation Prepared by: Jordan Tew (@math_stuff_here) 3 4 (a) 1 213 1 (3 10) ( 1)d 2 d1 x x xy xx − + − +  + = + M1 Know to use product rule s.o.i. 33 3 1031 6 6 3 10 3 421 1 2 ( 1) 2 ( 1) xx x x xx x xx ++− + − − −+= = = + ++ A1 Simplify x-coordinate of turning point 4 3= A1 o.e. (b) 3 1 2 32 2 d2 ( 1) 3 4 d 3 d d2 ( 1) 2 ( 1) 32 d d yxx x yyxx xx + = −   + + + = M1 Reasonable attempt to differentiate wrt x When 4 3x= , d 0d y x = . 3 2 2 4d2 1 3 0.420848... 0.421 (3 s.f.)3d y xx 