| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Sum/difference of two binomials simplification |
| Difficulty | Standard +0.3 This is a straightforward binomial expansion question requiring students to expand two binomials, observe that odd powers cancel, collect coefficients, then solve a quadratic equation. While it involves multiple steps and a substitution, the techniques are standard C2 material with no novel insight required—slightly easier than average due to the symmetric structure that simplifies the algebra. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.04a Binomial expansion: (a+b)^n for positive integer n |
\begin{enumerate}[label=(\alph*)]
\item Given that
$$(2 + x)^5 + (2 - x)^5 = A + Bx^2 + Cx^4,$$
find the values of the constants $A$, $B$ and $C$. [6]
\item Using the substitution $y = x^2$ and your answers to part (a), solve,
$$(2 + x)^5 + (2 - x)^5 = 349.$$ [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q10 [11]}}