| Exam Board | OCR MEI |
|---|---|
| Module | Further Pure Core AS (Further Pure Core AS) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Sum from n+1 to 2n or similar range |
| Difficulty | Standard +0.8 This is a Further Maths AS question requiring manipulation of summation formulas. Part (i) is routine verification, but part (ii) requires algebraic skill to express the sum using the standard formula for Σr², then simplify the difference of two sums into a fully factorised form—a multi-step algebraic challenge beyond typical A-level Core questions. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (i) | 62(cid:14)72(cid:14)82(cid:14)92(cid:14)102 |
| = 330 AG | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| [1] | M | |
| 1.1 | Must show method | Or 385-55 |
| 6 | (ii) | 2n n |
| Answer | Marks |
|---|---|
| 6 | C |
| Answer | Marks |
|---|---|
| [4] | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | For attempt at difference |
Question 6:
6 | (i) | 62(cid:14)72(cid:14)82(cid:14)92(cid:14)102
= 330 AG | B1
I
[1] | M
1.1 | Must show method | Or 385-55
6 | (ii) | 2n n
(cid:166)r2(cid:16)(cid:166)r2
E
r(cid:32)1 r(cid:32)1
1 1
(cid:32) (2n)(2n(cid:14)1)(4n(cid:14)1)(cid:16) (n)(n(cid:14)1)(2n(cid:14)1)
6 6
P
1
(cid:32) n(2n(cid:14)1)((8n(cid:14)2)(cid:16)(n(cid:14)1))
6
S
1
(cid:32) n(2n(cid:14)1)(7n(cid:14)1)
6 | C
M1
A1
M1
A1
[4] | 3.1a
1.1
1.1
1.1 | For attempt at difference
For successful substitution of
2n into formula
Factors n and 2n+1
oe, must be correct and
factorised\begin{enumerate}[label=(\roman*)]
\item Show that, when $n = 5$, $\sum_{r=n+1}^{2n} r^2 = 330$. [1]
\item Find, in terms of $n$, a fully factorised expression for $\sum_{r=n+1}^{2n} r^2$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Pure Core AS Q6 [5]}}