| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2018 |
| Session | January |
| 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 indices manipulation question requiring only direct application of basic index laws (power of a power, multiplication/division of powers, negative indices). Both parts are routine drill exercises with no problem-solving element, making it easier than average for A-level. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\left(3x^{\frac{1}{2}}\right)^4 = 81x^2\) | B1B1 | B1: Obtains \(ax^n\), \((a,n \neq 0)\) where \(a=81\) or \(n=2\); B1: \(81x^2\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\frac{2y^7 \times (4y)^{-2}}{3y} = \frac{y^4}{24}\) | B1B1 | B1: Obtains \(ay^n\), \((a,n\neq 0)\) where \(a=\frac{1}{24}\) or \(n=4\); B1: \(\frac{y^4}{24}\) |
## Question 3:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\left(3x^{\frac{1}{2}}\right)^4 = 81x^2$ | B1B1 | B1: Obtains $ax^n$, $(a,n \neq 0)$ where $a=81$ or $n=2$; B1: $81x^2$ |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{2y^7 \times (4y)^{-2}}{3y} = \frac{y^4}{24}$ | B1B1 | B1: Obtains $ay^n$, $(a,n\neq 0)$ where $a=\frac{1}{24}$ or $n=4$; B1: $\frac{y^4}{24}$ |
---3. Simplify fully
\begin{enumerate}[label=(\alph*)]
\item $\left( 3 x ^ { \frac { 1 } { 2 } } \right) ^ { 4 }$
\item $\frac { 2 y ^ { 7 } \times ( 4 y ) ^ { - 2 } } { 3 y }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2018 Q3 [4]}}