| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2019 |
| Session | March |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Find year when threshold exceeded |
| Difficulty | Moderate -0.3 Part (i) is a straightforward application of the GP sum formula requiring simple algebraic manipulation to reach the given result (2 marks). Part (ii) involves writing down standard AP formulas for nth term and sum, then solving simultaneous equations—routine bookwork with no conceptual challenges. Both parts are slightly easier than average A-level questions as they require only direct formula application without problem-solving insight. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks |
|---|---|
| 6(i) | ( ) |
| Answer | Marks |
|---|---|
| n 2−1 | M1 |
| Answer | Marks |
|---|---|
| p 2n −1 >1000p → 2n >1001 AG | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
| Answer | Marks | Guidance |
|---|---|---|
| 6(ii) | p+( n−1 ) p=336 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | B1 | Expect n( p+np )=7224 |
| Answer | Marks | Guidance |
|---|---|---|
| Eliminate n or p to an equation in one variable | M1 | Expect e.g. 168(1 + n) = 7224 or 1 + 336/p =43 etc |
| n = 42, p = 8 | A1A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 6:
--- 6(i) ---
6(i) | ( )
p 2n −1
S = soi
n 2−1 | M1
( )
p 2n −1 >1000p → 2n >1001 AG | A1
2
Question | Answer | Marks | Guidance
--- 6(ii) ---
6(ii) | p+( n−1 ) p=336 | B1 | Expect np = 336
n 2p+( n−1 ) p=7224
2 | B1 | Expect n( p+np )=7224
2
Eliminate n or p to an equation in one variable | M1 | Expect e.g. 168(1 + n) = 7224 or 1 + 336/p =43 etc
n = 42, p = 8 | A1A1
5
Question | Answer | Marks | Guidance\begin{enumerate}[label=(\roman*)]
\item The first and second terms of a geometric progression are $p$ and $2p$ respectively, where $p$ is a positive constant. The sum of the first $n$ terms is greater than $1000p$. Show that $2^n > 1001$. [2]
\item In another case, $p$ and $2p$ are the first and second terms respectively of an arithmetic progression. The $n$th term is $336$ and the sum of the first $n$ terms is $7224$. Write down two equations in $n$ and $p$ and hence find the values of $n$ and $p$. [5]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2019 Q6 [7]}}