| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Solve power equations |
| Difficulty | Moderate -0.3 This is a straightforward C1 question requiring basic manipulation of fractional indices and surds. Part (a) involves direct substitution and rationalizing a denominator (routine technique). Part (b) requires factoring out x^(-1/2) and solving a simple equation, leading to a standard surd form. While it tests multiple skills, all are standard C1 techniques with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators1.02f Solve quadratic equations: including in a function of unknown |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| (a) \(= 3\sqrt{3} - \frac{8}{\sqrt{3}} = 3\sqrt{3} - \frac{8}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\) | B1 M1 | |
| \(= 3\sqrt{3} - \frac{8}{3}\sqrt{3} = \frac{1}{3}\sqrt{3}\) | A1 | |
| (b) \(x^{\frac{3}{2}} = 8x^{-\frac{1}{2}}\) → \(x^2 = 8\) | M1 A1 | |
| \(x = \pm\sqrt{8} = \pm 2\sqrt{2}\) | M1 A1 | (7) |
## Question 6:
| Answer/Working | Marks | Notes |
|---|---|---|
| **(a)** $= 3\sqrt{3} - \frac{8}{\sqrt{3}} = 3\sqrt{3} - \frac{8}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$ | B1 M1 | |
| $= 3\sqrt{3} - \frac{8}{3}\sqrt{3} = \frac{1}{3}\sqrt{3}$ | A1 | |
| **(b)** $x^{\frac{3}{2}} = 8x^{-\frac{1}{2}}$ → $x^2 = 8$ | M1 A1 | |
| $x = \pm\sqrt{8} = \pm 2\sqrt{2}$ | M1 A1 | **(7)** |
---6.
$$f ( x ) = x ^ { \frac { 3 } { 2 } } - 8 x ^ { - \frac { 1 } { 2 } } .$$
\begin{enumerate}[label=(\alph*)]
\item Evaluate f(3), giving your answer in its simplest form with a rational denominator.
\item Solve the equation $\mathrm { f } ( x ) = 0$, giving your answers in the form $k \sqrt { 2 }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q6 [7]}}