| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2024 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Find n given sum condition |
| Difficulty | Moderate -0.8 Part (a) is direct application of the arithmetic series formula with given values. Part (b) requires setting up an equation S_{2k} = 10S_k and solving for k, which involves algebraic manipulation but follows a standard pattern for AS-level arithmetic progression questions. The question is straightforward with no conceptual challenges beyond formula application. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks |
|---|---|
| 2(a) | 20 20 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 2 | M1 | Correct use of either S formula with a = —20 and d = 5. |
| Answer | Marks |
|---|---|
| 550 | A1 |
| Answer | Marks |
|---|---|
| 2(b) | 2k k |
| Answer | Marks | Guidance |
|---|---|---|
| 2 2 | M1* | Correct use of S formula with a=−20, d=5 and either k or |
| Answer | Marks | Guidance |
|---|---|---|
| | DM1 | Equating their S to 10 × their S and reaching a 2-term |
| Answer | Marks | Guidance |
|---|---|---|
| k=12 | A1 | Condone extra solution k =0. |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 2:
--- 2(a) ---
2(a) | 20 20
( 2−20+(20−1)5 ) (−20+75)
or
2 2 | M1 | Correct use of either S formula with a = —20 and d = 5.
20
550 | A1
2
--- 2(b) ---
2(b) | 2k k
( −40+(2k−1)5 ) or ( −40+(k−1)5 )
2 2 | M1* | Correct use of S formula with a=−20, d=5 and either k or
n
2k.
n
(a+l)
This mark can be awarded for clear use of when
2
correct values of a and d are used.
−40k+10k2 −5k =−200k+25k2 −25k 1 5k2 −180k =0
| DM1 | Equating their S to 10 × their S and reaching a 2-term
2k k
quadratic or 2 term linear equation if k has been cancelled.
Condone errors in simplification.
k=12 | A1 | Condone extra solution k =0.
3
Question | Answer | Marks | GuidanceThe first term of an arithmetic progression is $-20$ and the common difference is $5$.
\begin{enumerate}[label=(\alph*)]
\item Find the sum of the first 20 terms of the progression. [2]
\end{enumerate}
It is given that the sum of the first $2k$ terms is 10 times the sum of the first $k$ terms.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the value of $k$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2024 Q2 [5]}}