| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Arithmetic progression with parameters |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic progression question requiring basic manipulation of the standard AP formula (a, a+d, a+2d) to find k, then applying the sum formula. Part (a) involves solving a simple linear equation (6k - k = k + 6 - 6k), and part (b) is direct substitution into S_n = n/2(2a + (n-1)d). Both parts are routine applications of standard formulas with no problem-solving insight required, making this easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(2\times 6k = k + k + 6\) or \(6k - k = k + 6 - 6k\), or \(2d = 6\) leading to \(d = 3\), \(\therefore 6k - 3 = k\) | B1 | OE. A correct equation in \(k\) only. Can be implied by correct final answer |
| \(k = \frac{6}{10}\) or \(0.6\) | B1 | OE |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(d = 3\) | B1 | Correct value of \(d\) can be implied by a correct final answer. Working may be seen in part (a) but must be used in (b) |
| \(S_{30} = \frac{30}{2}(2\times\text{'their }k\text{'} + 29\times\text{'their }d\text{'})\) | M1 | It needs to be clear that the candidate is using a correct sum formula. There is no requirement to check the candidates working for \(d\) but it must be clearly identified |
| \(S_{30} = 1323\) | A1 | ISW if corrected to 1320 |
## Question 4(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2\times 6k = k + k + 6$ or $6k - k = k + 6 - 6k$, or $2d = 6$ leading to $d = 3$, $\therefore 6k - 3 = k$ | **B1** | OE. A correct equation in $k$ only. Can be implied by correct final answer |
| $k = \frac{6}{10}$ or $0.6$ | **B1** | OE |
---
## Question 4(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $d = 3$ | **B1** | Correct value of $d$ can be implied by a correct final answer. Working may be seen in part (a) but must be used in (b) |
| $S_{30} = \frac{30}{2}(2\times\text{'their }k\text{'} + 29\times\text{'their }d\text{'})$ | **M1** | It needs to be clear that the candidate is using a correct sum formula. There is no requirement to check the candidates working for $d$ but it must be clearly identified |
| $S_{30} = 1323$ | **A1** | ISW if corrected to 1320 |
---4 The first, second and third terms of an arithmetic progression are $k , 6 k$ and $k + 6$ respectively.
\begin{enumerate}[label=(\alph*)]
\item Find the value of the constant $k$.
\item Find the sum of the first 30 terms of the progression.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2022 Q4 [5]}}