|
|
Exam-Style Questions on Sequences Exponential ModelsProblems on Sequences Exponential Models adapted from questions set in previous Mathematics exams. |
1. | IGCSE Extended |
The diagrams above show a growing fractal of triangles. The sides of the largest equilateral triangle in each diagram are of length 1 metre.
In the second diagram there are four triangles each with sides of length \(\frac{1}{2}\) metre.
In the third diagram there are 16 triangles each with sides of length \(\frac{1}{4}\) metre.
(a) Complete this table for more diagrams.
| Diagram 1 | Diagram 2 | Diagram 3 | Diagram 4 | Diagram 5 | Diagram 6 | Diagram \(n\) | ||
| Length of Side | 1 | \(\frac{1}{2}\) | \(\frac{1}{4}\) | |||||
| Power of 2 | 20 | 2-1 | 2-2 |
(b) Complete this table for the number of the smallest triangles in diagrams 4, 5 and 6.
| Diagram 1 | Diagram 2 | Diagram 3 | Diagram 4 | Diagram 5 | Diagram 6 | Diagram \(n\) | ||
| Number of smallest triangles | 1 | 4 | 16 | |||||
| Power of 2 | 20 | 22 | 24 |
(c) Calculate the number of the smallest triangles in the diagram where the smallest triangles have sides of length \(\frac{1}{256}\) metre.
If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.
The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
The solutions to the questions on this website are only available to those who have a Transum Subscription.
Exam-Style Questions Main Page
To search the entire Transum website use the search box in the grey area below.
