| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Compound growth applications |
| Difficulty | Moderate -0.3 This is a straightforward application of geometric sequences requiring identification of first term and common ratio (147/150 = 0.98), then using standard formulas for nth term and sum. Part (i) is routine calculation, part (ii) applies the sum formula directly, and part (iii) requires common-sense reasoning rather than mathematical sophistication. Slightly easier than average due to clear setup and standard techniques. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
7 Chris runs half marathons, and is following a training programme to improve his times. His time for his first half marathon is 150 minutes. His time for his second half marathon is 147 minutes. Chris believes that his times can be modelled by a geometric progression.\\
(i) Chris sets himself a target of completing a half marathon in less than 120 minutes. Show that this model predicts that Chris will achieve his target on his thirteenth half marathon.\\
(ii) After twelve months Chris has spent a total of 2974 minutes, to the nearest minute, running half marathons. Use this model to find how many half marathons he has run.\\
(iii) Give two reasons why this model may not be appropriate when predicting the time for a half marathon.
\hfill \mbox{\textit{OCR H240/01 2018 Q7 [9]}}