| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Proof by induction |
| Type | Prove by exhaustion (cases) |
| Difficulty | Standard +0.3 This is a straightforward induction proof with a simple divisibility statement. The algebra is routine (expanding (n+1)³ + (n+2)³ + (n+3)³ and showing divisibility by 9), requiring only basic manipulation and factoring. While it's a Further Maths question, it's a standard template application of induction with no novel insight needed, making it slightly easier than average. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps |
5 Prove by induction that the sum of the cubes of three consecutive positive integers is divisible by 9 .
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q5 [5]}}