| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2019 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Compound growth applications |
| Difficulty | Moderate -0.3 This is a straightforward application of geometric progression formulas with r=1.1. Part (i) requires using the nth term formula to find the first term, and part (ii) uses the sum formula. Both are direct substitutions into standard GP formulas with no conceptual challenges or problem-solving required beyond recognizing the GP structure. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04k Modelling with sequences: compound interest, growth/decay |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Identifies common ratio as \(1.1\) | B1 | |
| Use of \(x(1.1)^{20} = 20\) | M1 | SOI |
| \(x\left(= \frac{20}{(1.1)^{20}}\right) = 3.0\) | A1 | Accept 2.97 |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\text{their } 3.0 \times \left[\frac{(1.1)^{21}-1}{1.1-1}\right] \rightarrow 192\) | M1 A1 | Correct formula used for M mark; Allow 2.97 used from (i); Accept 190 from \(x = 2.97\ldots\) |
| Total: 2 |
**Question 4(i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Identifies common ratio as $1.1$ | B1 | |
| Use of $x(1.1)^{20} = 20$ | M1 | SOI |
| $x\left(= \frac{20}{(1.1)^{20}}\right) = 3.0$ | A1 | Accept 2.97 |
| **Total: 3** | | |
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**Question 4(ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\text{their } 3.0 \times \left[\frac{(1.1)^{21}-1}{1.1-1}\right] \rightarrow 192$ | M1 A1 | Correct formula used for M mark; Allow 2.97 used from (i); Accept 190 from $x = 2.97\ldots$ |
| **Total: 2** | | |4 A runner who is training for a long-distance race plans to run increasing distances each day for 21 days. She will run $x \mathrm {~km}$ on day 1 , and on each subsequent day she will increase the distance by $10 \%$ of the previous day's distance. On day 21 she will run 20 km .\\
(i) Find the distance she must run on day 1 in order to achieve this. Give your answer in km correct to 1 decimal place.\\
(ii) Find the total distance she runs over the 21 days.\\
\hfill \mbox{\textit{CAIE P1 2019 Q4 [5]}}