| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Moderate -0.3 This is a straightforward application of standard arithmetic sequence formulas (sum of n terms, nth term) with clear setup and routine algebraic manipulation. Part (iv) requires minimal conceptual insight (recognizing negative sales are impossible). Slightly easier than average due to the structured multi-part scaffolding and direct formula application, though the algebraic manipulation in part (iii) provides some modest challenge. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks |
|---|---|
| \(S_6 = \frac{6}{2}[3000 + (5 \times -x)] = 8100\) | M1 A1 |
| \(3000 - 5x = 2700, \quad x = 60\) | M1 A1 |
| Answer | Marks |
|---|---|
| \(= 1500 - (7 \times 60) = 1500 - 420 = £1080\) | M1 A1 |
| Answer | Marks |
|---|---|
| \(S_n = \frac{n}{2}[3000 - 60(n-1)]\) | M1 |
| Answer | Marks |
|---|---|
| \(= 30n[50 - (n-1)] = 30n(51-n) \quad [k = 30]\) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| the value of sales in a month would become negative which is not possible | B1 | (10) |
# Question 8:
## Part (i):
$S_6 = \frac{6}{2}[3000 + (5 \times -x)] = 8100$ | M1 A1 |
$3000 - 5x = 2700, \quad x = 60$ | M1 A1 |
## Part (ii):
$= 1500 - (7 \times 60) = 1500 - 420 = £1080$ | M1 A1 |
## Part (iii):
$S_n = \frac{n}{2}[3000 - 60(n-1)]$ | M1 |
$= n[1500 - 30(n-1)]$
$= 30n[50 - (n-1)] = 30n(51-n) \quad [k = 30]$ | M1 A1 |
## Part (iv):
the value of sales in a month would become negative which is not possible | B1 | **(10)**
---8. A store begins to stock a new range of DVD players and achieves sales of $\pounds 1500$ of these products during the first month. In a model it is assumed that sales will decrease by $\pounds x$ in each subsequent month, forming an arithmetic sequence.
Given that sales total $\pounds 8100$ during the first six months, use the model to\\
(i) find the value of $x$,\\
(ii) find the expected value of sales in the eighth month,\\
(iii) show that the expected total of sales in pounds during the first $n$ months is given by $k n ( 51 - n )$, where $k$ is an integer to be found.\\
(iv) Explain why this model cannot be valid over a long period of time.\\
\hfill \mbox{\textit{OCR C2 Q8 [10]}}