| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Solve power equations |
| Difficulty | Easy -1.3 This is a straightforward C1 indices question requiring only direct application of index laws and fractional powers. Part (a) involves a single-step manipulation (raising both sides to the power 2/3), and part (b) is routine conversion and calculation with negative fractional indices. Both parts are standard textbook exercises with no problem-solving or conceptual challenge beyond basic recall. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(x = (\sqrt[3]{27})^2 = 3^2 = 9\) | M1 A1 | |
| (b) \(= (\frac{2}{3})^{-1} = \sqrt[4]{9} = \frac{2}{3}\) | M1 A1 | (4) |
**(a)** $x = (\sqrt[3]{27})^2 = 3^2 = 9$ | M1 A1 |
**(b)** $= (\frac{2}{3})^{-1} = \sqrt[4]{9} = \frac{2}{3}$ | M1 A1 | (4)\begin{enumerate}[label=(\alph*)]
\item Solve the equation
$$x^{\frac{3}{2}} = 27.$$ [2]
\item Express $(2\frac{1}{4})^{-\frac{3}{2}}$ as an exact fraction in its simplest form. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q3 [4]}}