25 2 M Using trigonometry: cos = α = cos–1 α = 33.557 31° α Area of segment of one circle = πr2 – r2sinθ = sin r2(π – θ) where = 2 × 33.6° = 67.2° and = 6 cm. θ r Area = 62(π –sin67.2°) = 36(0.586 431 67.2°) –sin M1 M1 for correct trigonometric statement for angle = 36(0.586 431 0.460 931 6) – = 4.517 979 cm2 A1 A1 for any rounded answer to 2 or more sf Area of overlap = 2 × 4.517 979 cm2 = 9.035 959 cm2 M1 M1 for correct segment formula M1 M1 for correct factorisation A1 A1 for correct substitution of radius and a correct angle A1 A1 for correct answer to 2 or more sf M1 M1 for multiplying by 2 A1 9.0 cm2 A1 for correct answer to either 1 or 2 sf C1 C1 for use of mathematical language and diagrams to support solution 9
25 Using trigonometry: cos α = α = cos–1 α = 33.557 31° Area of segment of one circle = πr2 – r2sinθ = r2(π – sin θ) where θ = 2 × 33.6° = 67.2° and r = 6 cm. Area = 62(π –sin67.2°) = 36(0.586 431 –sin 67.2°) = 36(0.586 431 – 0.460 931 6) = 4.517 979 cm2 Area of overlap = 2 × 4.517 979 cm2 = 9.035 959 cm2 9.0 cm2 M1 A1 M1 M1 A1 A1 M1 A1 C1 2 M1 for correct trigonometric statement for angle A1 for any rounded answer to 2 or more sf M1 for correct segment formula M1 for correct factorisation A1 for correct substitution of radius and a correct angle A1 for correct answer to 2 or more sf M1 for multiplying by 2 A1 for correct answer to either 1 or 2 sf C1 for use of mathematical language and diagrams to support solution M 9
Higher_Skills_Geometry_MarkScheme_Edexcel.docx