| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2009 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Moderate -0.8 This is a straightforward application of standard summation formulae (∑r³, ∑r², ∑r) that students memorize for FP1. While it requires algebraic manipulation and factorization, it's a routine textbook exercise with no problem-solving or insight required—just direct substitution and simplification. The factorization adds minimal difficulty. |
| Spec | 1.04g Sigma notation: for sums of series4.06a Summation formulae: sum of r, r^2, r^3 |
3 Find $\sum _ { r = 1 } ^ { n } \left( 4 r ^ { 3 } + 6 r ^ { 2 } + 2 r \right)$, expressing your answer in a fully factorised form.
\hfill \mbox{\textit{OCR FP1 2009 Q3 [6]}}