| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Evaluate numerical powers |
| Difficulty | Easy -1.5 This is a straightforward recall question testing basic index laws with no problem-solving required. Students simply need to apply the rules that x^(1/2) means square root and negative powers mean reciprocals—purely mechanical computation with no conceptual challenge. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(5\) (or \(\pm 5\)) | B1 | Give B1 for 5 or ±5. Anything else is B0 (including just −5) |
| (b) \(25^{3/2} = \frac{1}{25^{-3/2}}\) or \(25^3 = 125\) or better | M1 | Requires reciprocal OR \(25^3 = 125\). Accept \(\frac{5}{{\sqrt[3]{625}}} \cdot 25^{-5} \cdot 25\sqrt{3} \cdot \frac{25}{\sqrt{25}}\) for M1 |
| \(\frac{1}{125}\) or \(0.008\) (or \(\pm \frac{1}{125}\)) | A1 | Correct answer with no working (or notation errors in working) scores both marks i.e. M1 A1. M1A0 for \(-\frac{1}{125}\) without \(+\frac{1}{125}\) |
(a) $5$ (or $\pm 5$) | B1 | Give B1 for 5 or ±5. Anything else is B0 (including just −5)
(b) $25^{3/2} = \frac{1}{25^{-3/2}}$ or $25^3 = 125$ or better | M1 | Requires reciprocal OR $25^3 = 125$. Accept $\frac{5}{{\sqrt[3]{625}}} \cdot 25^{-5} \cdot 25\sqrt{3} \cdot \frac{25}{\sqrt{25}}$ for M1
$\frac{1}{125}$ or $0.008$ (or $\pm \frac{1}{125}$) | A1 | Correct answer with no working (or notation errors in working) scores both marks i.e. M1 A1. M1A0 for $-\frac{1}{125}$ without $+\frac{1}{125}$
---Find the value of
\begin{enumerate}[label=(\alph*)]
\item $25 ^ { \frac { 1 } { 2 } }$
\item $25 ^ { - \frac { 3 } { 2 } }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2011 Q1 [3]}}