| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2005 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Evaluate numerical powers |
| Difficulty | Easy -1.8 This is a straightforward recall question testing basic index laws with a simple base (8 = 2³). Part (a) requires recognizing cube roots, part (b) combines negative and fractional indices. Both are routine calculations with no problem-solving element, making this easier than the -1.5 calibration example. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(2\) | B1 (1) | Penalise \(\pm\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(8^{-\frac{2}{3}} = \frac{1}{\sqrt[3]{64}}\) or \(\frac{1}{(a)^2}\) or \(\frac{1}{\sqrt[3]{8^2}}\) or \(\frac{1}{8^{\frac{2}{3}}}\) | M1 | Allow \(\pm\) |
| \(= \frac{1}{4}\) or \(0.25\) | A1 (2) |
## Question 1:
### Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| $2$ | B1 (1) | Penalise $\pm$ |
### Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| $8^{-\frac{2}{3}} = \frac{1}{\sqrt[3]{64}}$ or $\frac{1}{(a)^2}$ or $\frac{1}{\sqrt[3]{8^2}}$ or $\frac{1}{8^{\frac{2}{3}}}$ | M1 | Allow $\pm$ |
| $= \frac{1}{4}$ or $0.25$ | A1 (2) | |
**Notes:** M1 for understanding that "$-$" power means reciprocal. $8^{\frac{2}{3}} = 4$ is M0A0; $-\frac{1}{4}$ is M1A0.
---\begin{enumerate}[label=(\alph*)]
\item Write down the value of $8 ^ { \frac { 1 } { 3 } }$.
\item Find the value of $8 ^ { - \frac { 2 } { 3 } }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2005 Q1 [3]}}