| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2015 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Simplify algebraic expressions with indices |
| Difficulty | Easy -1.2 This is a straightforward indices manipulation question requiring only direct application of index laws (power of a power, negative indices, fractional indices). Each part involves 1-2 mechanical steps with no problem-solving or conceptual insight needed. Easier than average A-level material. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{1}{3}x\) | B1 | Accept equivalents such as \(\frac{x}{3}\), \(\frac{1}{3} \times x\), \(\frac{1}{3}x^1\), \(3^{-1}x\) etc. Do not award on incorrect index work e.g. \(\frac{1}{3}x = x^{-3}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(81x^{-3}\) | B1 | Accept exact equivalents such as \(81 \times x^{-3}\). Do not accept \(\frac{81}{x^3}\) as final answer unless preceded by \(81x^{-3}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(x^{\frac{3}{2}}\) | B1 | Accept exact equivalents such as \(1 \times x^{1.5}\). Do not accept \(x\,x^{\frac{1}{2}}\) or \(x\sqrt{x}\) as final answer unless preceded by \(x^{\frac{3}{2}}\) |
## Question 3:
**(a)**
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{1}{3}x$ | B1 | Accept equivalents such as $\frac{x}{3}$, $\frac{1}{3} \times x$, $\frac{1}{3}x^1$, $3^{-1}x$ etc. Do not award on incorrect index work e.g. $\frac{1}{3}x = x^{-3}$ |
**(b)**
| Answer | Mark | Guidance |
|--------|------|----------|
| $81x^{-3}$ | B1 | Accept exact equivalents such as $81 \times x^{-3}$. Do not accept $\frac{81}{x^3}$ as final answer unless preceded by $81x^{-3}$ |
**(c)**
| Answer | Mark | Guidance |
|--------|------|----------|
| $x^{\frac{3}{2}}$ | B1 | Accept exact equivalents such as $1 \times x^{1.5}$. Do not accept $x\,x^{\frac{1}{2}}$ or $x\sqrt{x}$ as final answer unless preceded by $x^{\frac{3}{2}}$ |3. Given that
$$y = \frac { 1 } { 27 } x ^ { 3 }$$
express each of the following in the form $k x ^ { n }$ where $k$ and $n$ are constants.
\begin{enumerate}[label=(\alph*)]
\item $y ^ { \frac { 1 } { 3 } }$
\item $3 y ^ { - 1 }$
\item $\sqrt { ( 27 y ) }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2015 Q3 [3]}}