| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Express result in specific form |
| Difficulty | Moderate -0.5 Part (a) is straightforward binomial expansion with n=4. Part (b)(i) is direct substitution. Part (b)(ii) requires recognizing that (1-√2)^8 = [(1-√2)^4]^2 and using conjugate properties, which adds modest problem-solving but remains a standard C2 exercise with clear structure and routine techniques. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.04a Binomial expansion: (a+b)^n for positive integer n |
\begin{enumerate}
\item (a) Expand $( 1 + x ) ^ { 4 }$ in ascending powers of $x$.\\
(b) Using your expansion, express each of the following in the form $a + b \sqrt { 2 }$, where $a$ and $b$ are integers.\\
(i) $( 1 + \sqrt { 2 } ) ^ { 4 }$\\
(ii) $( 1 - \sqrt { 2 } ) ^ { 8 }$
\item The second and fifth terms of an arithmetic sequence are 26 and 41 repectively.\\
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q6 [9]}}