Higher November 2023 Paper 6 Q20
20 This shape is formed from a rectangle and two sectors of circles.
Not to scale
Points A, B and C lie on a straight line.
Angle CBD = 35°.
DE = \(5t\) and EF = \(2t\).
(a) Explain why BC = \(2t\).
Give a reason for each step of your explanation. [2]
Give a reason for each step of your explanation. [2]
(b) Show that the perimeter of the shape is \(\frac{23}{12}\pi t + 14t\). [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| BD = EF or BD = \(2t\) and [opposite sides of a] rectangle [are equal] | 1 | For two marks, \(2t\) must be seen in at least one statement as BD or on the diagram as BD | |
| BC = BD [= \(2t\)] and radii [of a sector/circle] | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| ABF = 55 and AB = \(5t\) | B1 | Stated or seen on diagram | |
| \(\dfrac{\textit{their}\ 55}{360} \times 2\pi \times \textit{their}\ 5t\) | M1 | All M marks may be seen within a summarising expression | |
| \(\dfrac{35}{360} \times 2\pi \times 2t\) | M1 | ||
| \(5t + 2t + 5t + 2t\) | M1 | Condone \(10t + 4t\), \(7t + 7t\) etc but not \(14t\) | |
| \(\frac{35}{360} \times 2\pi \times 2t + \frac{55}{360} \times 2\pi \times 5t + 5t + 2t + 5t + 2t\) \(= \frac{23}{12}\pi t + 14t\) | A1 | ||