| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2015 |
| Session | January |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Basic indefinite integration |
| Difficulty | Easy -1.8 This is a pure algebraic simplification question testing basic index laws and surds, not integration despite the topic label. Both parts require only direct application of power rules with no problem-solving. Part (a) is trivial (x²), and part (b) involves straightforward manipulation of indices and surds. This is significantly easier than average A-level content. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(x^2\) | B1 [1] | This answer only |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{4}x^4\) or \(\frac{1}{2^2}x^4\) or \(0.25x^4\) | B1, B1 [2] | First B1: for \(\frac{1}{4}x^k\) as final answer, \(k\) can be 0. Accept \(\frac{1}{2^2}\) for B1 but \(2^{-2}\) is not simplified and is B0. Second B1: for \(x\) to power 4 (independent mark) so \(kx^4\) with \(k\) a constant as final answer. Mark the final answer on this question. |
# Question 1:
## Part (a)
$x^2$ | B1 [1] | This answer only
## Part (b)
$\frac{1}{4}x^4$ or $\frac{1}{2^2}x^4$ or $0.25x^4$ | B1, B1 [2] | First B1: for $\frac{1}{4}x^k$ as final answer, $k$ can be 0. Accept $\frac{1}{2^2}$ for B1 but $2^{-2}$ is not simplified and is B0. Second B1: for $x$ to power 4 (independent mark) so $kx^4$ with $k$ a constant as final answer. Mark the final answer on this question.
---Simplify the following expressions fully.
\begin{enumerate}[label=(\alph*)]
\item $\left( x ^ { 6 } \right) ^ { \frac { 1 } { 3 } }$
\item $\sqrt { 2 } \left( x ^ { 3 } \right) \div \sqrt { \frac { 32 } { x ^ { 2 } } }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2015 Q1 [3]}}