| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Simplify algebraic expressions with indices |
| Difficulty | Easy -1.3 This is a straightforward C1 indices question with two routine parts: (a) evaluating a fractional power of a perfect square (81^(3/2) = 729), and (b) applying basic index laws to simplify an algebraic expression. Both require only direct recall and application of standard rules with no problem-solving or insight needed. Slightly easier than the 25^(1/2) calibration example due to being completely mechanical. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(81^{\frac{3}{2}} = (81^{\frac{1}{2}})^3 = 9^3\) or \(81^{\frac{3}{2}}=(81^3)^{\frac{1}{2}}=(531441)^{\frac{1}{2}}\) | M1 | Dealing with either the 'cube' or 'square root' first. A correct answer implies this mark. Also accept \(81^{\frac{3}{2}} = 81^1 \times 81^{\frac{1}{2}} = 81\times9\) |
| \(= 729\) | A1 | cao 729. Accept \((\pm)729\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \((4x^{-\frac{1}{2}})^2 = 16x^{-2}\) or \(\frac{16}{x^2}\) or equivalent | M1 | For correct use of power 2 on both 4 and the \(x^{-\frac{1}{2}}\) term |
| \(x^2(4x^{-\frac{1}{2}})^2 = 16x\) | A1 | cao \(= 16x\) |
## Question 2:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $81^{\frac{3}{2}} = (81^{\frac{1}{2}})^3 = 9^3$ or $81^{\frac{3}{2}}=(81^3)^{\frac{1}{2}}=(531441)^{\frac{1}{2}}$ | M1 | Dealing with either the 'cube' or 'square root' first. A correct answer implies this mark. Also accept $81^{\frac{3}{2}} = 81^1 \times 81^{\frac{1}{2}} = 81\times9$ |
| $= 729$ | A1 | cao 729. Accept $(\pm)729$ |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $(4x^{-\frac{1}{2}})^2 = 16x^{-2}$ or $\frac{16}{x^2}$ or equivalent | M1 | For correct use of power 2 on both 4 and the $x^{-\frac{1}{2}}$ term |
| $x^2(4x^{-\frac{1}{2}})^2 = 16x$ | A1 | cao $= 16x$ |
---\begin{enumerate}[label=(\alph*)]
\item Evaluate $81 ^ { \frac { 3 } { 2 } }$
\item Simplify fully $x ^ { 2 } \left( 4 x ^ { - \frac { 1 } { 2 } } \right) ^ { 2 }$\\
\includegraphics[max width=\textwidth, alt={}, center]{6db8acbd-7f61-46ff-8fdc-f0f4a8363aa6-03_83_150_2675_1804}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2014 Q2 [4]}}