| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2015 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Curve intersection leads to quadratic |
| Difficulty | Challenging +1.8 Part (a) is trivial verification (1 mark). Part (b) requires careful algebraic manipulation of nested radicals, strategic squaring twice while tracking domain restrictions, solving the resulting cubic using part (a), and validating solutions—significantly harder than standard A-level quadratic problems and typical of AEA's demand for sustained algebraic reasoning without obvious pathways. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
(a) Show that $(x + 1)$ is a factor of $2x^3 + 3x^2 - 1$
[1]
(b) Solve the equation
$$\sqrt{x^2 + 2x + 5} = x + \sqrt{2x + 3}$$
[8]
\hfill \mbox{\textit{Edexcel AEA 2015 Q2 [9]}}