3 Correct for u 2c (i) not cont if x = 0, 1 (ii) not diff if x = 0, 1, 4 (iii)not defined if x = 0 5 Correct for r lim f(x) = 1 (iv) x 0 lim f(x) = not defined (v) x 1 f(1) = 3 (vi) 2d V = 16 t 16 (t + 1) 1 – – – dV = - 1 + 16(t + 1) 2 = 0 for max V – dt 16 = 1 so (t + 1)2 = 16 (t+1)2 15 so t = 3 or -5 but 0 t ≤ ≤ t + 1 = ±4 subs t = 3 max V = 16 3 4 = 9cm3 – – Correct equation dx = 2cm/sec Area = base×height 2e for area of dt = (10 x)× x2 – rectangle for u 10 A = A = x2 x3 = (10 x)× x2 – – 10 10 dA = 2x 3x2 – Correct chain of dx 10 derivatives for r dA = dA × dx = (2x 3x2 ) × 2 – dt dx dt 10 Correct derivatives with correct sub x = 5 , dA = (10 7.5) ×2 = 5 cm2/sec – solution for t dt Question Evidence Achievement (u) Merit (r) Excellence (t) THREE Apply Apply differentiation Apply differentiation differentiation methods, using methods, using methods in solving relational thinking, in extended abstract problems. solving problems. thinking, in solving problems. y = (x3 + 2)–4 /5 3a = 4 (x3 + 2) -9/5 3x2 yꞌ – Correct 5 derivative.
2c (i) not cont if x = 0, 1 (ii) not diff if x = 0, 1, 4 (iii)not defined if x = 0 (iv) lim f(x) = 1 x 0 (v) lim f(x) = not defined x 1 (vi) f(1) = 3 3 Correct for u 5 Correct for r 2d V = 16 – t – 16 (t + 1) – 1 dV = - 1 + 16(t + 1) – 2 = 0 for max V dt 16 = 1 so (t + 1)2 = 16 (t+1)2 t + 1 = ±4 so t = 3 or -5 but 0 ≤ t ≤ 15 subs t = 3 max V = 16 – 3 – 4 = 9cm3 2e dx = 2cm/sec Area = base×height dt = (10 – x)× x2 10 A = x2 – x3 10 dA = 2x – 3x2 dx 10 dA = dA × dx = (2x – 3x2 ) × 2 dt dx dt 10 sub x = 5 , dA = (10 – 7.5) ×2 = 5 cm2/sec dt Correct equation for area of rectangle for u A = = (10 – x)× x2 10 Correct chain of derivatives for r Correct derivatives with correct solution for t Question THREE Evidence Achievement (u) Merit (r) Excellence (t) 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. 3a y = (x3 + 2)–4 /5 yꞌ = – 4 (x3 + 2) -9/5 3x2 5 Correct derivative.