| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2002 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Finding unknown power and constant |
| Difficulty | Challenging +1.8 This AEA question requires equating binomial coefficients to form an equation in p, then solving a quadratic. It demands careful algebraic manipulation of general binomial coefficient formulas and consideration of the sign constraint, going beyond routine expansion exercises. The multi-step reasoning and need to work with general p (not a specific integer) elevates it above standard A-level, though it's more algebraic than conceptually deep. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
In the binomial expansion of
$$(1 - 4x)^p, \quad |x| < \frac{1}{4},$$
the coefficient of $x^2$ is equal to the coefficient of $x^4$ and the coefficient of $x^3$ is positive.
Find the value of $p$.
[9]
\hfill \mbox{\textit{Edexcel AEA 2002 Q2 [9]}}