Achievement Merit (r) Excellence (t) Question Evidence (u) TWO Apply integration Apply integration Apply integration methods in methods, using methods, using solving problems. relational extended abstract thinking, in thinking, in solving problems. solving problems. Correct A =2 3+ 1 + 4(9 + 15 +5) + 2(13+11) calculation. 3 2a = 112 Correct 2b = = 4 y 4x3 + 3x2 4x + c sub x = 1, y ꞌ – ꞌ integrations and 4 = 4 + 3 4 + c so c = 1 constants – evaluated and y = x4 + x3 2x2 + x + d sub x = 1, y = 2 – solution found 2 = 1 + 1 2 + 1 + d so d = 1 – = u. y = x4 + x3 2x2 + x + 1 – A + B = dx = 8ln(8) 2c Correct value So A = 4ln(8) for total area for u. A = dx = 8ln(k) Solving 8ln(k) = 4 ln(8) ln(k) = ½ ln(8) = ln( 8 ½) Correct k = 8 ½ integration with correct value for k. 1 when 1, find when x = y = y x = 2 2d Correct integration with = correct constant. = ln(y) = 3 + c – x2 Correct sub 1 and 1 x = y = integration with 0 = –3 + c so c = 3 correct constant ln(y) = 3 + 3 – and value y x2 found. sub x = 2 ln(y) = – ¾ + 3 = 2 ¼ y = e 2.25 ≈ 9.49
Question TWO Evidence Achievement (u) Merit (r) Excellence (t) A =2 3+ 1 + 4(9 + 15 +5) + 2(13+11) 3 = 112 Apply integration methods in solving problems. Apply integration methods, using relational thinking, in solving problems. Apply integration methods, using extended abstract thinking, in solving problems. 2a Correct calculation. 2b y ꞌ = 4x3 + 3x2 – 4x + c sub x = 1, y ꞌ = 4 4 = 4 + 3 – 4 + c so c = 1 y = x4 + x3 – 2x2 + x + d sub x = 1, y = 2 2 = 1 + 1 – 2 + 1 + d so d = 1 y = x4 + x3 – 2x2 + x + 1 Correct integrations and constants evaluated and solution found = u. 2c A + B = dx = 8ln(8) So A = 4ln(8) A = dx = 8ln(k) Solving 8ln(k) = 4 ln(8) ln(k) = ½ ln(8) = ln( 8 ½) k = 8 ½ Correct value for total area for u. Correct integration with correct value for k. 2d x = 1 when y = 1, find y when x = 2 = = ln(y) = – 3 + c x2 sub x = 1 and y = 1 0 = –3 + c so c = 3 ln(y) = – 3 + 3 x2 sub x = 2 ln(y) = – ¾ + 3 = 2 ¼ y = e 2.25 ≈ 9.49 Correct integration with correct constant. Correct integration with correct constant and y value found.
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