| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and Series |
| Type | Finding Constants from Identity |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring expansion of the sum using standard formulas (∑r² = n(n+1)(2n+1)/6 and ∑1 = n), then equating coefficients. While it involves algebraic manipulation and knowledge of summation formulas, it's a routine textbook exercise with a clear method and no novel insight required. Slightly above average difficulty due to being Further Maths content, but still mechanical. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
2 Given that $\sum _ { r = 1 } ^ { n } \left( a r ^ { 2 } + b \right) \equiv n \left( 2 n ^ { 2 } + 3 n - 2 \right)$, find the values of the constants $a$ and $b$.
\hfill \mbox{\textit{OCR FP1 2008 Q2 [5]}}