| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Non-zero terms only |
| Difficulty | Standard +0.3 This is a straightforward binomial expansion question with standard integration application. Part (i) requires rewriting as (4-x²)^(-1/2) = 2^(-1)(1-x²/4)^(-1/2) and applying the binomial series with n=-1/2, which is routine C4 material. Parts (ii) and (iii) involve basic term-by-term integration and direct substitution into arcsin respectively. The question is slightly above average difficulty due to the algebraic manipulation needed and the multi-part structure, but all techniques are standard textbook exercises with no novel problem-solving required. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs1.08d Evaluate definite integrals: between limits |
\begin{enumerate}[label=(\roman*)]
\item Find the first three non-zero terms of the binomial expansion of $\frac{1}{\sqrt{4-x^2}}$ for $|x| < 2$. [4]
\item Use this result to find an approximation for $\int_0^1 \frac{1}{\sqrt{4-x^2}} dx$, rounding your answer to 4 significant figures. [2]
\item Given that $\int \frac{1}{\sqrt{4-x^2}} dx = \arcsin\left(\frac{1}{2}x\right) + c$, evaluate $\int_0^1 \frac{1}{\sqrt{4-x^2}} dx$, rounding your answer to 4 significant figures. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C4 Q5 [7]}}