| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 3 |
| 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 indices question requiring only direct application of basic index laws with no problem-solving. Part (a) is simple numerical evaluation, and part (b) applies the power rule mechanically to both coefficient and variable. Easier than the calibration example at -1.5 due to being even more routine, but not trivial enough for -2.0. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(2\) | B1 | |
| (b) \(x^9\) seen, or (answer to (a))\(^3\) seen, or \((2x^3)^3\) seen | M1 | Look for \(x^9\) first; if seen, this is M1. If not seen, look for (answer to (a))\(^3\), e.g. \(2^3\), which would score M1 even if it does not subsequently become 8. (Similarly for other answers to (a)). In \((2x^3)^3\), the \(2^3\) is implied, so this scores the M mark. |
| \(8x^9\) | A1 |
(a) $2$ | B1 |
(b) $x^9$ seen, or (answer to (a))$^3$ seen, or $(2x^3)^3$ seen | M1 | Look for $x^9$ first; if seen, this is M1. If not seen, look for (answer to (a))$^3$, e.g. $2^3$, which would score M1 even if it does not subsequently become 8. (Similarly for other answers to (a)). In $(2x^3)^3$, the $2^3$ is implied, so this scores the M mark.
$8x^9$ | A1 |
**Negative answers:**
- (a) Allow $-2$. Allow $\pm 2$. Allow '2 or $-2$'.
- (b) Allow $\pm 8x^9$. Allow '8$x^9$ or $-8x^9$'.
**Note:** If part (a) is wrong, it is possible to 'restart' in part (b) and to score full marks in part (b).
**Total: 3 marks**
---\begin{enumerate}[label=(\alph*)]
\item Write down the value of $16 ^ { \frac { 1 } { 4 } }$.
\item Simplify $\left( 16 x ^ { 12 } \right) ^ { \frac { 3 } { 4 } }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2008 Q2 [3]}}