| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2023 |
| Session | March |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Compare two growth models |
| Difficulty | Moderate -0.8 This is a straightforward application of standard AP and GP formulas with no conceptual challenges. Students simply substitute given values (a=5.00, d=0.02 for part a; a=5.00, r=1.004 for part b) into nth term formulas. The context is simple, calculations are routine, and no problem-solving insight is required—easier than a typical A-level question. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks | Guidance |
|---|---|---|
| \(5.00 + 20\times 0.02\) or \(5.02 + 19\times 0.02\) | M1 | Allow for \(a=5\), \(n=20\) with \(d=0.02\) only. \(a=5\), \(n=21\) (OE) with \(d=0.2\) gets M1 only |
| \(5.40\) | A1 | |
| 2 |
| Answer | Marks | Guidance |
|---|---|---|
| \(r = \frac{5.02}{5} = 1.004\) or \(\frac{251}{250}\) | B1 | |
| \(5.00\times(\text{their } 1.004)^{20}\) or \(5.02\times(\text{their } 1.004)^{19}\) | M1 | Allow \(a=5\), \(n=20\) |
| \(5.42\) | A1 | Any correct rounding of \(5.41557108\) |
| 3 |
## Question 4(a):
| $5.00 + 20\times 0.02$ or $5.02 + 19\times 0.02$ | M1 | Allow for $a=5$, $n=20$ with $d=0.02$ only. $a=5$, $n=21$ (OE) with $d=0.2$ gets M1 only |
|---|---|---|
| $5.40$ | A1 | |
| | **2** | |
## Question 4(b):
| $r = \frac{5.02}{5} = 1.004$ or $\frac{251}{250}$ | B1 | |
|---|---|---|
| $5.00\times(\text{their } 1.004)^{20}$ or $5.02\times(\text{their } 1.004)^{19}$ | M1 | Allow $a=5$, $n=20$ |
| $5.42$ | A1 | Any correct rounding of $5.41557108$ |
| | **3** | |
---4 The circumference round the trunk of a large tree is measured and found to be 5.00 m . After one year the circumference is measured again and found to be 5.02 m .
\begin{enumerate}[label=(\alph*)]
\item Given that the circumferences at yearly intervals form an arithmetic progression, find the circumference 20 years after the first measurement.
\item Given instead that the circumferences at yearly intervals form a geometric progression, find the circumference 20 years after the first measurement.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2023 Q4 [5]}}