| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Evaluate numerical powers |
| Difficulty | Easy -1.8 This is a straightforward C1 question testing basic manipulation of surds and negative indices. Part (a) requires simple rationalization (dividing 21 by √7 = 3√7), and part (b) is direct recall that 8^{-1} = 1/8. Both are routine textbook exercises with no problem-solving element, making this easier than the typical A-level question. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\frac{21}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = 3\sqrt{7}\) | M1 A1 | |
| (b) \(\frac{1}{\sqrt[3]{8}} = \frac{1}{2}\) | M1 A1 | (4 marks) |
(a) $\frac{21}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = 3\sqrt{7}$ | M1 A1 |
(b) $\frac{1}{\sqrt[3]{8}} = \frac{1}{2}$ | M1 A1 | (4 marks)\begin{enumerate}[label=(\alph*)]
\item Express $\frac{21}{\sqrt{7}}$ in the form $k\sqrt{7}$. [2]
\item Express $8^{-1}$ as an exact fraction in its simplest form. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q1 [4]}}