A1 7 1 Cubic the correct way up G1 x-axis cuts at -1, 2, 4 shown G1 y-axis cuts at 8 shown G1 2 Sketch of cubic correct way up G1 Curve through (0,0) G1 Curve touches x-axis at x=3 G1 3 Correct graph with clear G2 (G1 for only one branch correct0 asymptote at x = 2 (0, -0.5) shown G1 4 10 B1 8 1 y = x2 8x + 5 B1 – 2 f(x 3) = (x 3)3 3) + B1 Substitution – – –5(x – 2 B1 Partial expansion of cubic term (x2 6x + 9)(x 3) – – f(x x3 3x2 6x2 + 18x A1 All correct unsimplified – – – + 9x 27 5x + 15 + 2 B1 Correct consolidation – – = x3 9x2 + 22x - 10 – 3 f(x-4) = 2(x-4)3 + 7(x-4)2 M1 Substitution – 7(x-4) 12 – M1 Correct expansion of one pair of brackets 2x3 17x2 + 33x M1 correct completion to given answer – 4 (x + 1 3)(x 2 3)(x 4 3) M1 Allow one slip – – – – – ie (x -2)(x 5)(x 7) A1 Oe – – 9 1 Tan 42° = M1 0.9004 = M1 13.5(06) m = height of pole A1 2 ± B3 B2 for either - or or ± oe or M1 for seen 3 (0, 0) B1 ( 90, 1) B1 (270, -1) B1 (360, 0) B1 10 1(i) C = M1 Correct attempt at cosine rule 141.1….. M1 Correct full method for C Bearing = 038. 8 (accept A1 C 038.9) A1 Bearing 1(ii) 3030 to 3050 acceptable M1 Correct use of 0.5xaxbxsinC A1 2 M1 Correct use of sine rule A1 AB AB = 7.80 (or better, 7.799…) M1 2 x 0.5 x x 11.4 x sin 36 ’their AB’ A1 Area Area = 52.2 to 52.3
A1 7 1 Cubic the correct way up x-axis cuts at -1, 2, 4 shown y-axis cuts at 8 shown G1 G1 G1 2 Sketch of cubic correct way up Curve through (0,0) Curve touches x-axis at x=3 G1 G1 G1 3 Correct graph with clear asymptote at x = 2 (0, -0.5) shown G2 G1 (G1 for only one branch correct0 4 10 B1 8 1 y = x2 – 8x + 5 B1 2 f(x – 3) = (x – 3)3 –5(x – 3) + 2 (x2 – 6x + 9)(x – 3) f(x – x3 – 3x2 – 6x2 + 18x + 9x – 27 – 5x + 15 + 2 = x3 – 9x2 + 22x - 10 B1 B1 A1 B1 Substitution Partial expansion of cubic term All correct unsimplified Correct consolidation 3 f(x-4) = 2(x-4)3 + 7(x-4)2 – 7(x-4) – 12 2x3 – 17x2 + 33x M1 M1 M1 Substitution Correct expansion of one pair of brackets correct completion to given answer 4 (x + 1 – 3)(x – 2 – 3)(x – 4 – 3) ie (x -2)(x – 5)(x – 7) M1 A1 Allow one slip Oe 9 1 Tan 42° = 0.9004 = 13.5(06) m = height of pole M1 M1 A1 2 ± B3 B2 for either - or or ± oe or M1 for seen 3 (0, 0) ( 90, 1) (270, -1) (360, 0) B1 B1 B1 B1 10 1(i) C = 141.1….. Bearing = 038. 8 (accept 038.9) M1 M1 A1 A1 Correct attempt at cosine rule Correct full method for C C Bearing 1(ii) 3030 to 3050 acceptable M1 A1 Correct use of 0.5xaxbxsinC 2 AB = 7.80 (or better, 7.799…) Area = 52.2 to 52.3 M1 A1 M1 A1 Correct use of sine rule AB 2 x 0.5 x ’their AB’ x 11.4 x sin 36 Area