| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sum of specific range of terms |
| Difficulty | Standard +0.3 Part (a) is a straightforward application of the arithmetic series formula requiring one algebraic step. Part (b) requires finding which terms fall in the given range and calculating a partial sum, involving multiple steps but using standard techniques with no novel insight required—slightly above average difficulty for AS-level. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(5(3 + 9d) = 127.5\) | B1 | OE |
| \(d = 2.5\) | B1 | |
| 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Attempt to find either the first term or the last term in the set by considering \(1.5 + 2.5(n-1) > 25\) or \(1.5 + 2.5(n-1) < 100\) or equivalent equations | M1 | Using their \(d\). May be implied by correct answers. |
| State or imply that 11th term or 26.5 is the first in the set | A1 | |
| State or imply that 40th term or 99 is the last in the set | A1 | |
| Either use \(S_{40} - S_{10}\); or use \(\frac{1}{2}n(a+l)\) with correct results for their \(d\); or use \(\frac{1}{2}n[2a + (n-1)d]\) with correct results for their \(d\) | DM1 | Their 40 and 10 from correct working with their \(d\). Correct values 30, 26.5 and 99 respectively. Correct values 30, 26.5 and 2.5 respectively. |
| Obtain 1882.5 | A1 | OE |
| 5 |
## Question 7(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5(3 + 9d) = 127.5$ | B1 | OE |
| $d = 2.5$ | B1 | |
| | **2** | |
## Question 7(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Attempt to find either the first term or the last term in the set by considering $1.5 + 2.5(n-1) > 25$ or $1.5 + 2.5(n-1) < 100$ or equivalent equations | M1 | Using their $d$. May be implied by correct answers. |
| State or imply that 11th term or 26.5 is the first in the set | A1 | |
| State or imply that 40th term or 99 is the last in the set | A1 | |
| Either use $S_{40} - S_{10}$; or use $\frac{1}{2}n(a+l)$ with correct results for their $d$; or use $\frac{1}{2}n[2a + (n-1)d]$ with correct results for their $d$ | DM1 | Their 40 and 10 from correct working with their $d$. Correct values 30, 26.5 and 99 respectively. Correct values 30, 26.5 and 2.5 respectively. |
| Obtain 1882.5 | A1 | OE |
| | **5** | |7 The first term of an arithmetic progression is 1.5 and the sum of the first ten terms is 127.5 .
\begin{enumerate}[label=(\alph*)]
\item Find the common difference.
\item Find the sum of all the terms of the arithmetic progression whose values are between 25 and 100 .
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2024 Q7 [7]}}