4MA0 Higher June 2012 Paper 3 Q13
13
Diagram NOT accurately drawn
The diagram shows two congruent regular pentagons and part of a regular \(n\)-sided polygon A.
Two sides of each of the regular pentagons and two sides of A meet at the point \(P\).
Calculate the value of \(n\).
Show your working clearly.
(5)
| Scheme | Marks |
|---|---|
finds int angle of pentagon \(\dfrac{(5-2) \times 180}{5}\) or finds ext angle of pentagon \(\dfrac{360}{5}\) | M1 |
| 108 or 72 | A1 |
| If there is clear evidence the candidate thinks the interior angle is 72° or the exterior angle is 108°, do not award the above two marks. | |
| int angle of polygon = 144 or ext angle of polygon = 36 | B1 |
| \(\dfrac{360}{36}\) or \(\dfrac{180(n-2)}{n} = 144\) oe | M1 |
| 10 | A1 |
| (Total 5 marks) |
Notes
M1: for \(\dfrac{(5-2) \times 180}{5}\) or \(\dfrac{360}{5}\)
A1: for 108 or 72
B1: for int angle of polygon = 144 or ext angle of polygon = 36
M1: for \(\dfrac{360}{36}\) or \(\dfrac{180(n-2)}{n} = 144\) oe
A1: for 10 cao
Award no marks for an answer of 10 with no working
Award 5 marks for an answer of 10 if at least the first M1A1 are awarded
Award M1A1 for int angle of pentagon shown as 108° or ext angle shown as 72° on printed diagram or on candidate’s own diagram
Award B1 for int angle of polygon shown as 144° or ext angle shown as 36° on printed diagram or candidate’s own diagram