ACSBR 2023 4E5N Add Math Prelim P1 MS updated

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 1 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) 1 Height = = = = 2 (a) (shown) By factor theorem, is a factor of f(x) (b) Since f(x) has three real roots when f(x) = 0, has two real roots. 3 (a) (b) (c)

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 1 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) 4 (a) Sub (1,0) 5 (a) (b) For is an increasing function,

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 1 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) ---(1) ----(2) Alternative method (c) Gradient of normal is undefined (vertical line) 6 (a) or (reject, A is acute) or (shown) (b)

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 1 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) (c) From (b), is a negative ratio. So lies in the 2nd or 4th quadrant. Both and A are both acute, cannot exceed . Thus lies in the 2nd quadrant and is obtuse. 7 (a) (b) = = or 16.7 (3s.f) 8 (a)

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 1 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) or (reject) 8 (b) Coefficient of x4 = 9 (a) (b) (c) No solution 10 (a) Let y =

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 1 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) (reject) (b) M1 Largest value of the integer q = 9 A1 [8] 11 (a) DA = GC + x AD = T = 11+13 +26 + T = 50 + (b) = T = (c) Max T = 50 + =79.1 (3s.f) This is not possible as the maximum distance of T is 79.1 m.

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 1 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) 12 (a) a + 4 (b) centre = (rejected) or centre = (c) Gradient of radius = Gradient of line L = Equation of line L: 13 (a) = = Let Let

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 1 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) Let (b) = =