| Exam Board | AQA |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Solve exponential equations |
| Difficulty | Easy -1.3 This is a straightforward indices/powers question requiring only basic recall of index laws. Parts (a)(i) and (a)(ii) are direct applications of definitions (√3 = 3^(1/2) and 1/9 = 3^(-2)), while part (b) combines these results with simple algebraic manipulation. No problem-solving insight is needed—it's a routine drill exercise testing fundamental index notation, making it easier than the typical A-level question. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| 3(a)(i) | States correct value of p | AO1.2 |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(ii) | States correct value of q | AO1.2 |
| (b) | Uses valid method to find x , PI | AO1.1a |
| Answer | Marks | Guidance |
|---|---|---|
| Obtains correct x , ACF | AO1.1b | A1 |
| Total | 4 |
Question 3:
--- 3(a)(i) ---
3(a)(i) | States correct value of p | AO1.2 | B1 | 1
p
2
(a)(ii) | States correct value of q | AO1.2 | B1 | q 2
(b) | Uses valid method to find x , PI | AO1.1a | M1 | 1
x 2
2
x 2.5
Obtains correct x , ACF | AO1.1b | A1
Total | 4\begin{enumerate}[label=(\alph*)]
\item Write down the value of $p$ and the value of $q$ given that:
\begin{enumerate}[label=(\roman*)]
\item $\sqrt{3} = 3^p$ [1 mark]
\item $\frac{1}{9} = 3^q$ [1 mark]
\end{enumerate}
\item Find the value of $x$ for which $\sqrt{3} \times 3^x = \frac{1}{9}$ [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 1 Q3 [4]}}