| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Shaded region between arcs |
| Difficulty | Standard +0.3 This is a standard C2 sector/segment question requiring area of sector formula (½r²θ), arc length (rθ), and chord length using cosine rule. All techniques are routine applications of circle theorems and radians with no novel problem-solving required. The multi-part structure and 10 marks make it slightly above average difficulty, but it's a textbook exercise type. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_1}
Figure 1 shows a gardener's design for the shape of a flower bed with perimeter ABCD.
AD is an arc of a circle with centre O and radius 5 m.
BC is an arc of a circle with centre O and radius 7 m.
OAB and ODC are straight lines and the size of ∠AOD is θ radians.
(a) Find, in terms of θ, an expression for the area of the flower bed. [3 marks]
Given that the area of the flower bed is 15 m²,
(b) show that θ = 1.25. [2 marks]
(c) calculate, in m, the perimeter of the flower bed. [3 marks]
The gardener now decides to replace arc AD with the straight line AD.
(d) Find, to the nearest cm, the reduction in the perimeter of the flower bed. [2 marks]
\hfill \mbox{\textit{Edexcel C2 Q5 [10]}}