ACSI 2017 Promo Paper 2 ans

ACS (Independent) / Mathematics Department / Mathematics HL / 2017 / Final Exam / Paper 2 / Solutions 1 FINAL EXAMINATION 2017 YEAR 5 IB DIPLOMA PROGRAMME MATHEMATICS HIGHER LEVEL Paper 2 Solutions with Marker’s Comments Qn Solution Marker’s Comments Section A 1) [6 marks] Solving with GDC (Solving with Linear Equations Function and Log Function) or alternative Most students used graphical method to solve. Final answer

ACS (Independent) / Mathematics Department / Mathematics HL / 2017 / Final Exam / Paper 2 / Solutions 2 Qn Solution Marker’s Comments 2) [7 marks] At the end of year 1 The total in bank account At the end of second year At the end of seven years Many students were unable to find the general expression for S7 Using nsolve on GDC (or plotting graphs) 3) [6 marks] (a) (b) Observe that has argument (giving bearing of ) and a modulus of 4, giving a distance of 4 km from A Very few students were able to make this observation. Hence the complex number representing B Coordinates of B is A majority of those who found the coordinates of B correctly did not use complex numbers to obtain the answer. 4) [5 marks] Consider first number odd, no of ways 4 23 3 108P× ×= Consider first number even, no of ways 4 22 2 48P× ×= Total number of ways = 108 48 156+= Most students were able to do this question.

ACS (Independent) / Mathematics Department / Mathematics HL / 2017 / Final Exam / Paper 2 / Solutions 3 Qn Solution Marker’s Comments Alternative method: No. of 4-digit numbers ending with 0 = 5P3 x 1 = 60 No. of 4-digit numbers ending with 2 or 4 = 4 x 4P2 x 2 = 96 Total number of ways = 60 +96 = 156 5) [5 marks] For an even function Generally well done. But a minority of students do not know the definition of an even function. Equating , 6) [7 marks] (a) Use GDC to plot and Many attempt to solve the problem manually, without using the GDC which can solve this problem graphically which is more efficient. or

ACS (Independent) / Mathematics Department / Mathematics HL / 2017 / Final Exam / Paper 2 / Solutions 4 Qn Solution Marker’s Comments (b) Plot graph of The graph is concave downwards where Many students confuse point of inflexion with stationary points, wrongly finding the range by setting '( ) 0fx < 7) [7 marks] (a) A possible unit vector Students did not follow instruction and did not find the unit vector and the plane equation in the requested form. Equation of plane (b) Possible equations of plane or Students not heeding the hence requirement and taking a much longer method to solve the problem.

ACS (Independent) / Mathematics Department /