| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Quadratic in exponential form |
| Difficulty | Moderate -0.3 This is a standard C2 exponential equation using substitution to form a quadratic. Part (a) is straightforward algebraic manipulation (showing 4^x = u^2 and 2^(x+1) = 2u), and part (b) requires factorising the quadratic, then solving u = 2^x using logarithms. While it involves multiple techniques, these are all routine C2 skills with no novel insight required, making it slightly easier than average. |
| Spec | 1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}[label=(\alph*)]
\item Using the substitution $u = 2^x$, show that the equation $4^x - 2^{(x + 1)} - 15 = 0$ can be written in the form $u^2 - 2u - 15 = 0$. [2]
\item Hence solve the equation $4^x - 2^{(x + 1)} - 15 = 0$, giving your answers to 2 d. p. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q3 [6]}}