| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Simplify algebraic expressions with indices |
| Difficulty | Easy -1.2 This is a straightforward indices manipulation question requiring only mechanical application of power laws (negative and fractional indices) to algebraic expressions. It involves routine procedures with no problem-solving or conceptual insight needed—students simply apply rules systematically to reach the answer. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(y^{-\frac{1}{2}} = \left(\frac{64x^6}{25}\right)^{-\frac{1}{2}} = \frac{5}{8}x^{-3}\) | M1 A1 A1 [3] | M1: sight of 5 or 0.2, 8 or 0.125, \(x^3\) or \(x^{-3}\); do not award if the 5 is \(5^2\); A1: correct coefficient \(\frac{5}{8}x^p\); A1: \(\frac{5}{8}x^{-3}\) cao, accept \(0.625x^{-3}\); note \(\frac{0.625}{x^3}\) not correct form |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((25y)^{\frac{2}{3}} = 16x^4\) | B1, B1 [2] | B1: 16 or \(x^4\) correct in final answer; B1: \(16x^4\) cao; allow \(16 \times x^4\) |
# Question 4:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $y^{-\frac{1}{2}} = \left(\frac{64x^6}{25}\right)^{-\frac{1}{2}} = \frac{5}{8}x^{-3}$ | M1 A1 A1 [3] | M1: sight of 5 or 0.2, 8 or 0.125, $x^3$ or $x^{-3}$; do not award if the 5 is $5^2$; A1: correct coefficient $\frac{5}{8}x^p$; A1: $\frac{5}{8}x^{-3}$ cao, accept $0.625x^{-3}$; note $\frac{0.625}{x^3}$ not correct form |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(25y)^{\frac{2}{3}} = 16x^4$ | B1, B1 [2] | B1: 16 or $x^4$ correct in final answer; B1: $16x^4$ cao; allow $16 \times x^4$ |
---4. Given that
$$y = \frac { 64 x ^ { 6 } } { 25 } , x > 0$$
express each of the following in the form $k x ^ { n }$ where $k$ and $n$ are constants.
\begin{enumerate}[label=(\alph*)]
\item $y ^ { - \frac { 1 } { 2 } }$
\item $( 25 y ) ^ { \frac { 2 } { 3 } }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2018 Q4 [5]}}