N2: 1 u A3: 2 u A4: 3 u M5: 1 r M6: 2 r E7: 1 t with minor errors ignored E8: 1 t with full excellence criteria Judgement Statement Achievement with Not Achieved Achievement Achievement with Excellence Merit 0 - 6 7 - 13 14 - 18 19 -24 Score range Achievement Question Evidence Merit (r) ONE (u) Apply Apply differentiation Apply differentiation differentiation methods, using methods, using methods in relational thinking, in extended abstract solving problems. solving problems. thinking, in solving problems. y = 8sin(4x) Correct = 32cos(4x) yꞌ 1a derivative. Correct answer y = (x3 + 2x)2 = u = 2(x3 + 2x)(3x2+2) = 2×3×5 = 30 yꞌ 1b so gradient of normal = -1 30 and Correct up to x = cos(2t) y = 2sin(t) 1c dy = 2cos(t) dx = dy = 2cos(t) –2sin(2t) dx -2sin(2t) dt dt Correctly = u dy = 2cos(t) = cos(t) = 1 – simplified = r . dx sin(t) –2sin(2t) –cos(t)sin(t) y = e 8 4x + 4x – 1d -4e8 4x + 4 = 0 at stat pts yꞌ= – so 4 = 4e8 4x – 1 = e8 4x – Correct dy for u 0 = 8 4x – dx So x = 2 and state that Correct answer for dx = 0 for r dt
N2: 1 u A3: 2 u A4: 3 u M5: 1 r M6: 2 r E7: 1 t with minor errors ignored E8: 1 t with full excellence criteria Judgement Statement Not Achieved Achievement Achievement with Merit Achievement with Excellence Score range 0 - 6 7 - 13 14 - 18 19 -24 Question ONE Evidence Achievement (u) Merit (r) Apply differentiation methods in solving problems. Apply differentiation methods, using relational thinking, in solving problems. Apply differentiation methods, using extended abstract thinking, in solving problems. 1a y = 8sin(4x) yꞌ = 32cos(4x) Correct derivative. 1b y = (x3 + 2x)2 yꞌ = 2(x3 + 2x)(3x2+2) = 2×3×5 = 30 so gradient of normal = -1 30 Correct answer = u 1c x = cos(2t) and y = 2sin(t) dx = –2sin(2t) dy = 2cos(t) dt dt dy = 2cos(t) = cos(t) = – 1 . dx –2sin(2t) –cos(t)sin(t) sin(t) Correct up to dy = 2cos(t) dx -2sin(2t) = u Correctly simplified = r 1d y = e 8 – 4x + 4x yꞌ= -4e8 – 4x + 4 = 0 at stat pts so 4 = 4e8 – 4x 1 = e8 – 4x 0 = 8 – 4x So x = 2 Correct dy for u dx and state that dx = 0 dt Correct answer for for r
4b_practice_examination__number_4_schedule.docx