A-LevelMathematicsCircular measure9709/12 · Feb/Mar 2017 · Q46 Marks
In the diagram, AB = AC = 8 cm and angle CAB = 2/7 π radians. The circular arc BC has centre A, the circular arc CD has centre B and ABD is a straight line. [Figure 4.1]
- (i)Show that angle CBD = 9/14 π radians.[1]
- (ii)Find the perimeter of the shaded region.[5]
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Mark scheme
Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.
- [B1] ABC = π / 2-π / 7 = 5π / 14. CBD = π – 5π /14 = 9π/14 AG Or other valid exact method.
- [M1] sin(π/7) / BC = sin(2π/7) / 8 or BC/sin(2π/7) = 8/sin(5π/14) or BC² = 8² + 8² - 2(8)(8)cos(2π/7)
- [A1] BC = 6.94(2)
- [M1] arc CD = their 6.94 × 9π/14 Expect 14.02(0)
- [M1] arc CB = 8 × 2π/7 Expect 7.18(1)
- [A1] perimeter = 6.94 + 14.02 + 7.18 = 28.1
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