| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | September |
| Marks | 4 |
| Topic | Exponential Equations & Modelling |
| Type | Quadratic in exponential form |
| Difficulty | Standard +0.3 This is a standard quadratic-in-exponential problem requiring recognition that 4^x = (2^x)^2 and algebraic manipulation to form a quadratic equation. The substitution u = 2^x is routine, and solving the resulting quadratic is straightforward. Slightly easier than average due to being a well-practiced technique with clear structure. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}
\item In this question you must show all stages of your working.
\end{enumerate}
Solutions relying on calculator technology are not acceptable.
Solve
$$2 \times 4 ^ { x } - 2 ^ { x + 3 } = 17 \times 2 ^ { x - 1 } - 4$$
(Total for Question 4 is 4 marks)\\
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q4 [4]}}