| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2019 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Express in terms of substitution |
| Difficulty | Easy -1.2 This is a straightforward indices manipulation question requiring only basic index law recall (power rules and base conversion). All three parts follow standard patterns with no problem-solving or novel insight needed—simpler than average A-level content. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.06a Exponential function: a^x and e^x graphs and properties |
| Answer | Marks | Guidance |
|---|---|---|
| \(y^2\) | B1 (1 mark) | Allow \((y)^2\). Note that \(y \times y\) is not sufficient. |
| Answer | Marks | Guidance |
|---|---|---|
| \(8y\) | B1 (1 mark) | Allow exact equivalents such as \(8 \times y\) or \(y \times 8\). Note \(2^3 y\) is B0. |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{64}{y^4}\) | M1 A1 (2 marks) | M1: correct attempt at finding either the coefficient or correct index of \(y\); must be a product/quotient not a sum/difference. Look for \(64y^n\), \(\frac{64}{y^n}\), \(Ay^{-4}\) or \(\frac{A}{y^4}\). Condone correct inverted expression \(\frac{y^4}{64}\) for M1 A0. A1: \(\frac{64}{y^4}\) or exact equivalent \(64 \times y^{-4}\) as FINAL answer. No isw. |
## Question 2:
### Part (a):
$y^2$ | B1 (1 mark) | Allow $(y)^2$. Note that $y \times y$ is not sufficient.
### Part (b):
$8y$ | B1 (1 mark) | Allow exact equivalents such as $8 \times y$ or $y \times 8$. Note $2^3 y$ is B0.
### Part (c):
$\frac{64}{y^4}$ | M1 A1 (2 marks) | M1: correct attempt at finding either the coefficient or correct index of $y$; must be a product/quotient not a sum/difference. Look for $64y^n$, $\frac{64}{y^n}$, $Ay^{-4}$ or $\frac{A}{y^4}$. Condone correct inverted expression $\frac{y^4}{64}$ for M1 A0. A1: $\frac{64}{y^4}$ or exact equivalent $64 \times y^{-4}$ as FINAL answer. No isw.
---2. Given $y = 2 ^ { x }$, express each of the following in terms of $y$. Write each expression in its simplest form.
\begin{enumerate}[label=(\alph*)]
\item $2 ^ { 2 x }$
\item $2 ^ { x + 3 }$
\item $\frac { 1 } { 4 ^ { 2 x - 3 } }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2019 Q2 [4]}}