| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2017 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Simplify algebraic expressions with indices |
| Difficulty | Easy -1.3 This is a straightforward Core 1/2 indices and surds question requiring only direct application of standard rules (power of 0.5, negative powers, rationalizing). Part (a) and (b) are routine index law applications, while (c) involves basic surd manipulation. No problem-solving or insight needed—purely procedural recall. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{3}x^2\) | B1 | Accept exact alternatives like \(\frac{x^2}{3}\) and \(0.\dot{3}x^2\) but not \(0.33x^2\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\left(\frac{x}{\sqrt{2}}\right)^{-2} = \frac{2}{x^2}\) | B1 | Accept exact alternatives such as \(2 \times x^{-2}\) or \(2 \times \frac{1}{x^2}\) (all forms must have a '2') |
| Answer | Marks | Guidance |
|---|---|---|
| \(\sqrt{3}(x) \div \sqrt{\frac{48}{x^4}} = \frac{\sqrt{3}}{\sqrt{48}} \times x\sqrt{x^4} = \frac{1}{4}x^3\) | M1 | Either the correct coefficient (accept \(\frac{1}{4}\) or 0.25) or the correct power of \(x\) (accept \(x^3\) or \(\frac{1}{x^{-3}}\)) |
| \(\frac{1}{4}x^3\) | A1 | Only accept \(\frac{1}{4}x^3\) or simplified equivalents such as \(0.25 \times x^3\). Do NOT accept \(\frac{1}{4x^{-3}}\) |
## Question 2:
**(a)**
| $\frac{1}{3}x^2$ | B1 | Accept exact alternatives like $\frac{x^2}{3}$ and $0.\dot{3}x^2$ but not $0.33x^2$ |
**(b)**
| $\left(\frac{x}{\sqrt{2}}\right)^{-2} = \frac{2}{x^2}$ | B1 | Accept exact alternatives such as $2 \times x^{-2}$ or $2 \times \frac{1}{x^2}$ (all forms must have a '2') |
**(c)**
| $\sqrt{3}(x) \div \sqrt{\frac{48}{x^4}} = \frac{\sqrt{3}}{\sqrt{48}} \times x\sqrt{x^4} = \frac{1}{4}x^3$ | M1 | Either the correct coefficient (accept $\frac{1}{4}$ or 0.25) or the correct power of $x$ (accept $x^3$ or $\frac{1}{x^{-3}}$) |
| $\frac{1}{4}x^3$ | A1 | Only accept $\frac{1}{4}x^3$ or simplified equivalents such as $0.25 \times x^3$. Do NOT accept $\frac{1}{4x^{-3}}$ |
---\begin{enumerate}
\item Simplify the following expressions fully.\\
(a) $\left( \frac { 1 } { 9 } x ^ { 4 } \right) ^ { 0.5 }$\\
(b) $\left( \frac { x } { \sqrt { 2 } } \right) ^ { - 2 }$\\
(c) $x \sqrt { 3 } \div \sqrt { \frac { 48 } { x ^ { 4 } } }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2017 Q2 [4]}}