| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Express in form with given base |
| Difficulty | Easy -1.3 This is a straightforward indices question requiring only basic recall of index laws and simple algebraic manipulation. Part (a) involves recognizing standard powers (8=2³, 1/8=2⁻³, √2=2^(1/2)), while part (b) requires substituting these values and solving a simple linear equation. No problem-solving insight is needed, making it easier than average. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| (i) \(p = 3\) | B1 | |
| (ii) \(q = -3\) | B1 | |
| (iii) \(r = \frac{1}{2}\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(2^{1/2} \times 2^x = 2^{-3}\) | M1 | Converting to powers of 2 and adding indices |
| \(x + \frac{1}{2} = -3\), so \(x = -3\frac{1}{2}\) | A1 | cao |
# Question 2:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| (i) $p = 3$ | B1 | |
| (ii) $q = -3$ | B1 | |
| (iii) $r = \frac{1}{2}$ | B1 | |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| $2^{1/2} \times 2^x = 2^{-3}$ | M1 | Converting to powers of 2 and adding indices |
| $x + \frac{1}{2} = -3$, so $x = -3\frac{1}{2}$ | A1 | cao |
---2
\begin{enumerate}[label=(\alph*)]
\item Write down the values of $p , q$ and $r$ given that:
\begin{enumerate}[label=(\roman*)]
\item $8 = 2 ^ { p }$;
\item $\frac { 1 } { 8 } = 2 ^ { q }$;
\item $\sqrt { 2 } = 2 ^ { r }$.
\end{enumerate}\item Find the value of $x$ for which $\sqrt { 2 } \times 2 ^ { x } = \frac { 1 } { 8 }$.
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2011 Q2 [5]}}