| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Difficulty | Challenging +1.2 This is a Further Maths question requiring knowledge that sum of squares has a standard formula, then adapting it to odd integers only. Students must recognize that odd integers from 1 to 779 are the first 390 odd numbers, express them as (2r-1)², expand and use standard summation formulas. While it requires multiple steps and algebraic manipulation, the approach is methodical rather than requiring novel insight—harder than a routine C3 question but not exceptionally challenging for Further Maths students. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
\textbf{In this question you must show detailed reasoning.}
The series $S$ is defined as being the sum of the squares of all positive \textbf{odd} integers from $1^2$ to $779^2$.
Determine the value of $S$. [5]
\hfill \mbox{\textit{OCR Further Pure Core 2 2024 Q4 [5]}}