Higher June 2019 Paper 2 Q16
16. The diagram below shows a plan view of a stage, \(ABCD\).
\(ABC\) is a sector of a circle, with centre \(C\).
Diagram not drawn to scale
(a) The band Fredalive need a stage area of at least 11·5 m2 to set up equipment and perform.
Is this stage suitable for Fredalive to set up equipment and perform?
You must show all your working. [5]
Conclusion
The stage is suitable: Yes ☐ No ☐
Is this stage suitable for Fredalive to set up equipment and perform?
You must show all your working. [5]
Conclusion
The stage is suitable: Yes ☐ No ☐
(b) Fredalive want to place a banner around the perimeter of the stage.
Will a banner of length 14 m fit around this stage without leaving a gap?
You must show all your working. [6]
Conclusion
The banner will fit without leaving a gap: Yes ☐ No ☐
Will a banner of length 14 m fit around this stage without leaving a gap?
You must show all your working. [6]
Conclusion
The banner will fit without leaving a gap: Yes ☐ No ☐
| Scheme | Marks | Comments |
|---|---|---|
| Area of sector \(\dfrac{42}{360} \times \pi \times 3.6^2\) | M1 | |
| Answer in range 4.748 (m2) to 4.75... (m2) | A1 | May be implied later |
| (Area ACD) \(\frac12 \times 3.6 \times 4.1 \times \sin 67(^\circ)\) | M1 | |
| 6.79(...m2) | A1 | May be implied later |
| Total area 11.53(8..m2) to 11.54(...m2) AND Yes | B1 | FT provided at least M2 A1 previously awarded (with appropriate conclusion) |
| Scheme | Marks | Comments |
|---|---|---|
| (Arc length) \(2 \times \dfrac{42}{360} \times \pi \times 3.6\) | M1 | |
| 2.64 (m) | A1 | Accept 2.63(...m) |
| (Triangle ACD) \(AD^2 = 18.2(356\ldots)\) | M2 | M1 for \(AD^2 = 4.1^2 + 3.6^2 - 2\times4.1\times3.6\times\cos 67(^\circ)\) |
| \(AD = 4.27(\ldots\text{m})\) | A1 | Accept 4.3(m) |
| (Perimeter) \((4.1 + 3.6 + 2.64 + 4.27)\) 14.6(1 m) AND No | B1 | FT correct evaluation of ‘their arc’ + ‘their AD’ + 4.1 + 3.6 provided at least M2 and A1 previously awarded |
| (11) |