Edexcel C2 — Question 3 6 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeQuadratic in exponential form
DifficultyModerate -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.
Spec1.06g Equations with exponentials: solve a^x = b

  1. 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]
  2. Hence solve the equation \(4^x - 2^{(x + 1)} - 15 = 0\), giving your answers to 2 d. p. [4]

\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]}}