| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Expansion with algebraic manipulation then integrate |
| Difficulty | Moderate -0.8 Part (a) is a straightforward binomial expansion of a simple expression with only three terms to find, requiring basic application of the binomial theorem. Part (b) is a routine integration after algebraic manipulation (dividing through by x^4), involving standard power rule integration. Both parts are mechanical applications of standard techniques with no problem-solving insight required, making this easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n1.08b Integrate x^n: where n != -1 and sums |
\begin{enumerate}[label=(\alph*)]
\item The expression $(2 + x^2)^3$ can be written in the form
$$8 + px^2 + qx^4 + x^6$$
Demonstrate clearly, using the binomial expansion, that $p = 12$ and find the value of $q$. [3 marks]
\item Hence find $\int \frac{(2 + x^2)^3}{x^4} dx$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2022 Q1 [6]}}