| Exam Board | OCR MEI |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2023 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Easy -1.2 Part (a) is a direct application of the standard summation formula for r² (giving 55), requiring only recall and basic arithmetic. Part (b) involves verifying that Euler's approximation formula yields this exact value, which is straightforward substitution and algebraic verification. This is below-average difficulty as it tests routine knowledge of summation formulae with minimal problem-solving required. |
| Spec | 1.04g Sigma notation: for sums of series |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(55\) | B1 [1] | Method need not be shown. May be done BC |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\int_1^5 x^2\,dx + \frac{5^2+1^2}{2} + \frac{1^2-2^2}{12} - \frac{5^2-6^2}{12}\) | M1 | Correct substitution into formula. Condone \(r\) but not \(n\) instead of \(x\). Square numbers may be evaluated |
| \(\left[\frac{x^3}{3}\right]_1^5 + \frac{26}{2} - \frac{3}{12} + \frac{11}{12} = \frac{124}{3} + \frac{41}{3} = 55\) | A1 [2] | Correct completion. Integration may be done BC. At least one step to be shown |
## Question 11:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $55$ | B1 [1] | Method need not be shown. May be done BC |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\int_1^5 x^2\,dx + \frac{5^2+1^2}{2} + \frac{1^2-2^2}{12} - \frac{5^2-6^2}{12}$ | M1 | Correct substitution into formula. Condone $r$ but not $n$ instead of $x$. Square numbers may be evaluated |
| $\left[\frac{x^3}{3}\right]_1^5 + \frac{26}{2} - \frac{3}{12} + \frac{11}{12} = \frac{124}{3} + \frac{41}{3} = 55$ | A1 [2] | Correct completion. Integration may be done BC. At least one step to be shown |
---11
\begin{enumerate}[label=(\alph*)]
\item Evaluate $\sum _ { r = 1 } ^ { 5 } r ^ { 2 }$.
\item Show that Euler's approximate formula, as given in line 13, gives the exact value of $\sum _ { r = 1 } ^ { 5 } r ^ { 2 }$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 3 2023 Q11 [3]}}