| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2025 |
| Session | October |
| Marks | 7 |
| Topic | Laws of Logarithms |
| Type | Two unrelated log parts: both solve equations |
| Difficulty | Standard +0.3 Both parts are standard substitution problems: (a) uses u=y³ to get a quadratic, then cube roots; (b) uses u=3^x to get a quadratic in u. These are textbook exercises requiring straightforward algebraic manipulation with no novel insight, making them slightly easier than average A-level questions. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.06g Equations with exponentials: solve a^x = b |
In this question you must show detailed reasoning.
Solve the following equations.
\begin{enumerate}[label=(\alph*)]
\item $y^6 + 7y^3 - 8 = 0$ [3]
\item $9^{x+1} + 3^x = 8$ [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2025 Q7 [7]}}