ACSBR 2023 4E5N Add Math Prelim P2 - MS updated

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 2 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) 1 (a) $1000 (b) = (c) 3 months or August $4000 2 (a) Solving (1), (2) (b) Sub. (1) into (2): For the line to intersect the curve at two distinct points,

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 2 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) 3 (a) Alternative Method (b) ,

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 2 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) 4 (a) Using similar triangles (b) Using chain rule When h = 8, 5 (a) or (reject) (shown) Since

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 2 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) (b) Midpoint of PR = Gradient of QS = Equation of QS : Sub (1) into Subst. into (1) : (c) Area = =. or 28.6 (3sf) 6 (a) Given that AE = EB and CF = FB, E is the midpoint of AB and F is midpoint FB. Hence by mid-point theorem, AC and EF are parallel (b) angle AED = angle DCE (tangent chord theorem) angle DCE = angle CEF

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 2 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) (alternate angles, AC is parallel to EF) Hence angle AED = angle CEF (c) In triangle AED and triangle CEF Let angle CFE = Angle CDE = (angles in opposite segment) Angle ADE = (adjacent angles on a a straight line) Angle CFE = Angle ADE or Angle CFE = Angle ADE (exterior angle of cyclic quadrilateral ) or angle DAE = angle FEB (corresponding angles, AC parallel EF) Angle FEB = angle ECF (tangent chord theorem) Angle DAE = angle ECF From part (a) angle AED = angle CEF Triangle AED is similar to triangle CEF (AA similarity) 7 (a) t 0 10 20 30 40 V 8 000 17 500 38 000 83 000 190 000 3.90 4.24 4.58 4.92 5.28 Plot a straight line graph of against t. (b)

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 2 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) (c) years 1970 + 50.81 = 2020 (d) 2020 is outside range of values in the initial table. House prices may not grow in the same way after 2010. 2020 would be using extrapolation, so is not likely to be reliable. 8 (a) and (b)

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 2 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) 9 (a) Total surface area (b) For stationary cost (3s.f) (c) When , Since the cost is minimum, the company should choose r found in (b) .

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 2 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) 10 (a) (gradient of tangent) Gradient of normal = (b)

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 2 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) 11 (a) At B , v = 0 (b) when t = 0, s = 0,  c = 100 when t = 10 ln 2, Distance AB = 15.3 m Alternative Method: = = = 15.3 m (3s.f) (c) When t = 3, (3s.f) (d)

Marking Scheme Secondary 4 Express / 5 Normal (Academic) Additional Mathematics Paper 2 Preliminary Examination 2023 Anglo-Chinese School (Barker Road) when t = 15, when t = 16, Since the displacement changes from positive 2.69m at t = 15 to negative 0.1897 m at t = 16,  the particle was at A again during the sixteenth second.