SPS SPS SM Pure 2024 September — Question 4 4 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2024
SessionSeptember
Marks4
TopicExponential Equations & Modelling
TypeQuadratic in exponential form
DifficultyStandard +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.
Spec1.02a Indices: laws of indices for rational exponents1.06g Equations with exponentials: solve a^x = b

  1. In this question you must show all stages of your working.
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)

\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]}}