If the slant height of a cone is 8√3 cm 1e prove that the maximum volume is when = 8 cm and = cm h r 8√2 r2+ h2 = 192 r2= h 192 – h2 8√3 r Correct Equ for V by eliminating r (192 h2)h = (192h h3) π – π – V = or h but 3 3 preferably r dV = (192 3h2) = 0 for max vol π – dh 3 Correct derivative 192 = 3h2 so h2 = 64 and solving for h = 8 (not -8) derivative = 0 and r2= 192 h2 – = 192 64 – Correct r and h = 128 found for t = 64×2 So r = 8√2 Question Evidence Achievement (u) Merit (r) Excellence (t) TWO 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 = ln(x2 + 1) Correct 3x + 4 2a derivative. =(3x + 4)× 2x ln(x2 + 1) ×3 yꞌ – (x2 + 1) . (3x + 4)2 where y = 3e2x 8 x = 4 – Correct = 6e2x 8 yꞌ – 2b derivative and sub x = 4 sub to get 6 x = 4 = 6e0 = 6×1 = 6 yꞌ for u
1e If the slant height of a cone is 8√3 cm prove that the maximum volume is when h = 8 cm and r = 8√2 cm r2+ h2 = 192 r2= 192 – h2 h 8√3 r V = π (192 – h2)h = π (192h – h3) 3 3 dV = π (192 – 3h2) = 0 for max vol dh 3 192 = 3h2 so h2 = 64 h = 8 (not -8) and r2= 192 – h2 = 192 – 64 = 128 = 64×2 So r = 8√2 Correct Equ for V by eliminating r or h but preferably r Correct derivative and solving for derivative = 0 Correct r and h found for t Question TWO 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. 2a y = ln(x2 + 1) 3x + 4 yꞌ =(3x + 4)× 2x – ln(x2 + 1) ×3 (x2 + 1) . (3x + 4)2 Correct derivative. 2b y = 3e2x – 8 where x = 4 yꞌ = 6e2x – 8 sub x = 4 yꞌ = 6e0 = 6×1 = 6 Correct derivative and sub x = 4 to get 6 for u
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