A-LevelMathematicsCircular measure9709/12 · Feb/Mar 2019 · Q36 Marks
In the diagram, CXD is a semicircle of radius 7 cm with centre A and diameter CD. The straight line YABX is perpendicular to CD, and the arc CYD is part of a circle with centre B and radius 8 cm. Find the total area of the region enclosed by the two arcs. [Figure X.X]
- In the diagram, CXD is a semicircle of radius 7 cm with centre A and diameter CD. The straight line YABX is perpendicular to CD, and the arc CYD is part of a circle with centre B and radius 8 cm. Find the total area of the region enclosed by the two arcs.[6]
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Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [B1] Angle CBA = sin⁻¹(7/8) = 1.0654 or CBD = cos⁻¹(-17/32) = 2.13
- [M1] Sector BCYD = 1/2×8²×2×their1.0654(rad) soi
- [M1] ΔBCD = 7 × √8² −7² or 2×½×8²×sin(2×their1.0654) soi
- [M1] Semi-circle CXD = ½π×7² = 76.9(7)
- [M1A1] Total area = their68.19 – their27.11 + their76.97 = 118.0-118.1
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