0580 P43 - Jun 2016 - Q10 - 17 marks
14938
Each diagram uses equilateral triangle tiles and rhombus tiles, all with side length 1 unit.
| Diagram | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Triangle tiles | 2 | 3 | 4 | 5 | 6 |
| Rhombus tiles | 1 | 3 | 6 | ||
| Total tiles | 3 | 6 | 10 | ||
| Number of 1 unit lengths | 8 | 15 | 24 |
(a) Complete the table. [6]
The number of 1 unit lengths in Diagram \(n\) is \(n^2+4n+p\).
(b(i)) Find \(p\). [2]
(b(ii)) Find the number of 1 unit lengths in Diagram 10. [1]
(c) The total number of tiles in Diagram \(n\) is \(an^2+bn+1\). Find \(a\) and \(b\). [5]
A square-based glass pyramid at the Louvre has four triangular faces, each represented by Diagram 17.
(d(i)) Find the total tiles on one face. [2]
(d(ii)) 11 tiles are removed from one face for an entrance. Find the total tiles used for the pyramid. [1]
