2 Negative quadratic curve G1 Intercept (0,9) G1 Through (3,0) and (-3,0) G1 3 Any correct y value calculated B1 (0,5), (1,1), (2,-1), (3,-1), (4,1) B1 and (5,5) calculated Above points plotted G1 Smooth parabola through the G1 points 8 1 y = (x 2)2 - 4 B2 M1 if y omitted, or for y = (x + 2)2 - 4 – 2(i) Translation of B1 () B1 2(ii) y = f(x 2) B2 B1 for y = f(x + 2) – 3(i) Translation of B1 () B1 3(ii) sketch of parabola right way up B1 min at (0,-4) and graph through B1 (-2,0) and (2,0) 9 1(i) 15.5 M1 Use of Pythagoras A1 1(ii) x = 75.5° M1 (cos x = ) correct ratio and substitution A1 2 or (but not ± M1 Use iof pythagoras √8 2√2 √8) M1 use of = opp / adj tan Ɵ A1 3 Smooth curve between y = 1 G1 and y = -1 (90,0) and (270,0) G1 (0,1), (180,-1), (360,1) G1 10 1(i) 9.0 or 8.96 or 8.960 M1 for use of cosine rule M1 for square-rooting 80.2(8) ‘their’ A1 1(ii) 13.3 or better (13.2577..) M1 use of 0.5 x 4.1 x 6.6 x sin 108 ‘their’ A1 correct values A1 ans 2 BC = 384 (or better) M1 recognisable attempt at cosine rule M1 BC2 = 3482 + 3022 2x348x302xcos72 – Total length = 1034m A1 BC = 383.86….. (or better) A1 Total length = BC + 650 ft
2 Negative quadratic curve Intercept (0,9) Through (3,0) and (-3,0) G1 G1 G1 3 Any correct y value calculated (0,5), (1,1), (2,-1), (3,-1), (4,1) and (5,5) calculated Above points plotted Smooth parabola through the points B1 B1 G1 G1 8 1 y = (x – 2)2 - 4 B2 M1 if y omitted, or for y = (x + 2)2 - 4 2(i) Translation of () B1 B1 2(ii) y = f(x – 2) B2 B1 for y = f(x + 2) 3(i) Translation of () B1 B1 3(ii) sketch of parabola right way up min at (0,-4) and graph through (-2,0) and (2,0) B1 B1 9 1(i) 15.5 M1 A1 Use of Pythagoras 1(ii) x = 75.5° M1 A1 (cos x = ) correct ratio and substitution 2 √8 or 2√2 (but not ± √8) M1 M1 A1 Use iof pythagoras use of tan Ɵ = opp / adj 3 Smooth curve between y = 1 and y = -1 (90,0) and (270,0) (0,1), (180,-1), (360,1) G1 G1 G1 10 1(i) 9.0 or 8.96 or 8.960 M1 M1 A1 for use of cosine rule for square-rooting ‘their’ 80.2(8) 1(ii) 13.3 or better (13.2577..) M1 A1 A1 use of ‘their’ 0.5 x 4.1 x 6.6 x sin 108 correct values ans 2 BC = 384 (or better) Total length = 1034m (or better) M1 M1 A1 A1 recognisable attempt at cosine rule BC2 = 3482 + 3022 – 2x348x302xcos72 BC = 383.86….. Total length = BC + 650 ft