4400 Higher June 2008 Paper 3 Q13
13
Diagram NOT accurately drawn
The diagram shows part of a tiling pattern.
The tiling pattern is made from three shapes.
Two of the shapes are squares and regular hexagons.
The third shape is a regular \(n\)-sided polygon A.
Work out the value of \(n\).
(5)
| Scheme | Marks |
|---|---|
finds int angle of hexagon \(\dfrac{(6 - 2) \times 180}{6}\) or finds ext angle of hexagon \(\dfrac{360}{6}\) | M1 |
| 120 or 60 | A1 |
| int angle of polygon = 150 or ext angle of polygon = 30 | B1 |
| \(\dfrac{360}{30}\) or \(\dfrac{180(n - 2)}{n} = 150\) oe | M1 |
| 12 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for \(\dfrac{(6 - 2) \times 180}{6}\) or \(\dfrac{360}{6}\)
A1: for 120 or 60
B1: int angle of polygon = 150 or ext angle of polygon = 30
M1: for \(\dfrac{360}{30}\) or \(\dfrac{180(n - 2)}{n} = 150\) oe
A1: for 12 cao
Award no marks for an answer of 12 with no working.
Award 5 marks for an answer of 12 if at least 2 of the previous 4 marks scored.
Award M1 A1 for int angle of hexagon shown as \(120^\circ\) or ext angle shown as \(60^\circ\) on printed diagram or on candidate’s own diagram
If there is clear evidence the candidate thinks the interior angle is \(60^\circ\) or the exterior angle is \(120^\circ\), do not award these two marks.
Award B1 for int angle of polygon shown as \(150^\circ\) or ext angle shown as \(30^\circ\) on printed diagram or on candidate’s own diagram