| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | January |
| 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 C1 indices question requiring only direct application of index laws with no problem-solving. Part (a) is basic numerical evaluation of a negative fractional power, and part (b) applies the power rule mechanically to simplify an expression. Both parts are routine drill exercises below average A-level difficulty. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(16^{\frac{1}{4}} = 2\) or \(\frac{1}{16^{\frac{1}{4}}}\) or better | M1 | For a correct statement dealing with the \(\frac{1}{4}\) or the \(-\) power. Award if 2 is seen or for reciprocal of their \(16^{\frac{1}{4}}\). s.c. \(\frac{1}{4}\) is M1A0, \(2^{-1}\) is M1A0 |
| \(16^{-\frac{1}{4}} = \frac{1}{2}\) or \(0.5\) (ignore \(\pm\)) | A1 | \(\pm\frac{1}{2}\) is not penalised so M1A1 |
| (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\left(2x^{-\frac{1}{4}}\right)^4 = 2^4 x^{-\frac{4}{4}}\) or \(\frac{2^4}{x^{\frac{4}{4}}}\) or equivalent | M1 | For correct use of the power 4 on both the 2 and the \(x\) terms |
| \(x\left(2x^{-\frac{1}{4}}\right)^4 = 2^4\) or \(16\) | A1 cao | For cancelling the \(x\) and simplifying to one of these two forms. Correct answers with no working get full marks |
| (2) |
## Question 1:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $16^{\frac{1}{4}} = 2$ or $\frac{1}{16^{\frac{1}{4}}}$ or better | M1 | For a correct statement dealing with the $\frac{1}{4}$ or the $-$ power. Award if 2 is seen or for reciprocal of their $16^{\frac{1}{4}}$. s.c. $\frac{1}{4}$ is M1A0, $2^{-1}$ is M1A0 |
| $16^{-\frac{1}{4}} = \frac{1}{2}$ or $0.5$ (ignore $\pm$) | A1 | $\pm\frac{1}{2}$ is not penalised so M1A1 |
| | **(2)** | |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\left(2x^{-\frac{1}{4}}\right)^4 = 2^4 x^{-\frac{4}{4}}$ or $\frac{2^4}{x^{\frac{4}{4}}}$ or equivalent | M1 | For **correct** use of the power 4 on both the 2 and the $x$ terms |
| $x\left(2x^{-\frac{1}{4}}\right)^4 = 2^4$ or $16$ | A1 cao | For cancelling the $x$ and simplifying to one of these two forms. Correct answers with no working get full marks |
| | **(2)** | |
---\begin{enumerate}[label=(\alph*)]
\item Find the value of $16 ^ { - \frac { 1 } { 4 } }$
\item Simplify $x \left( 2 x ^ { - \frac { 1 } { 4 } } \right) ^ { 4 }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2011 Q1 [4]}}