| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Compound growth applications |
| Difficulty | Easy -1.2 This is a straightforward application of geometric sequences requiring only direct substitution into standard formulas (nth term and sum of GP). The 5% growth rate immediately gives r=1.05, and both parts involve routine calculations with no problem-solving insight needed—significantly easier than average A-level questions. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04k Modelling with sequences: compound interest, growth/decay |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(r = 1.05\) with GP, 2011 is 11 years. Uses \(ar^{n-1}\) → \(\\)8144\( (or 8140) | B1 M1 A1 | Anywhere in the question. This could be marked as \)2 + 3\(. Allow if correct formula with \)n = 10$ co. (allow 3 sf) |
| (ii) Use of \(S_n\) formula → \(\\)71034$ | M1 A1 | Allow if used correctly with 10 or 11. co. (or 71 000) |
**(i)** $r = 1.05$ with GP, 2011 is 11 years. Uses $ar^{n-1}$ → $\$8144$ (or 8140) | B1 M1 A1 | Anywhere in the question. This could be marked as $2 + 3$. Allow if correct formula with $n = 10$ co. (allow 3 sf)
**(ii)** Use of $S_n$ formula → $\$71034$ | M1 A1 | Allow if used correctly with 10 or 11. co. (or 71 000)
**Total: [3] [2]**
---3 Each year a company gives a grant to a charity. The amount given each year increases by $5 \%$ of its value in the preceding year. The grant in 2001 was $\$ 5000$. Find\\
(i) the grant given in 2011,\\
(ii) the total amount of money given to the charity during the years 2001 to 2011 inclusive.
\hfill \mbox{\textit{CAIE P1 2006 Q3 [5]}}