| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Moderate -0.5 This is a straightforward algebraic manipulation question requiring only the application of standard summation formulas (∑r and ∑r²) and basic algebra to verify a given result. While it's from Further Maths FP1, it involves routine techniques with no problem-solving insight needed—students simply expand, substitute the formulas, and simplify to match the given answer. It's slightly easier than average due to being purely mechanical verification rather than derivation or proof requiring creativity. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
Use the standard results for $\sum_{r=1}^n r$ and $\sum_{r=1}^n r^2$ to show that, for all positive integers $n$,
$$\sum_{r=1}^n (6r^2 + 2r + 1) = n(2n^2 + 4n + 3).$$
[6]
\hfill \mbox{\textit{OCR FP1 Q1 [6]}}