| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Easy -1.2 This is a straightforward application of standard arithmetic sequence formulas (nth term and sum) with clear real-world context. Part (i) requires direct substitution into the nth term formula, while part (ii) involves solving a quadratic inequality from the sum formula—both are routine textbook exercises requiring only recall and basic algebraic manipulation, making this easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| A.P.: \(5 + 8 + 11\ldots\) | M1 | |
| \(\Rightarrow a_8 = 5 + 7\times 3 = £26\) | A1 | [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| We require \(S_n > 200\) so solve \(S_n = 200\) | M1 | |
| \(S_n = \frac{n}{2}(2a + (n-1)d) = \frac{n}{2}(10 + (n-1)3) = 200\) | ||
| \(\Rightarrow 10n + 3n(n-1) = 400 \Rightarrow 3n^2 + 7n - 400 = 0\) | A1 | |
| \(\Rightarrow n = \frac{-7 \pm \sqrt{49 + 4800}}{6} = \frac{-7 \pm 69.6}{6} = 10.4\) | M1 | |
| So minimum time is 11 years. | A1 | [4] |
## Question 3:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| A.P.: $5 + 8 + 11\ldots$ | M1 | |
| $\Rightarrow a_8 = 5 + 7\times 3 = £26$ | A1 | **[2]** |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| We require $S_n > 200$ so solve $S_n = 200$ | M1 | |
| $S_n = \frac{n}{2}(2a + (n-1)d) = \frac{n}{2}(10 + (n-1)3) = 200$ | | |
| $\Rightarrow 10n + 3n(n-1) = 400 \Rightarrow 3n^2 + 7n - 400 = 0$ | A1 | |
| $\Rightarrow n = \frac{-7 \pm \sqrt{49 + 4800}}{6} = \frac{-7 \pm 69.6}{6} = 10.4$ | M1 | |
| So minimum time is 11 years. | A1 | **[4]** |
---3 On his $1 ^ { \text {st } }$ birthday, John was given $\pounds 5$ by his Uncle Fred. On each succeeding birthday, Uncle Fred gave a sum of money that was $\pounds 3$ more than the amount he gave on the last birthday.\\
(i) How much did Uncle Fred give John on his $8 { } ^ { \text {th } }$ birthday?\\
(ii) On what birthday did the gift from Uncle Fred result in the total sum given on all birthdays exceeding £200?
\hfill \mbox{\textit{OCR MEI C2 Q3 [6]}}