| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Evaluate numerical powers |
| Difficulty | Easy -1.3 Question 1 parts (a) and (b) are routine index law exercises requiring only direct recall and application of fractional/negative powers. These are standard C1 textbook exercises with minimal problem-solving required, making them easier than average A-level questions. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.07i Differentiate x^n: for rational n and sums1.08b Integrate x^n: where n != -1 and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\int(8x^3+4)\,dx = \frac{8x^4}{4}+4x\) | M1, A1 | M1: \(x^n \to x^{n+1}\), so \(x^3 \to x^4\) or \(4 \to 4x\). A1: Either term with coefficient unsimplified (power must be simplified) — so \(\frac{8}{4}x^4\) or \(4x\) (accept \(4x^1\)) |
| \(= 2x^4+4x+c\) | A1 | Fully correct simplified solution with \(c\). Allow \(2x^4+4x+cx^0\) |
## Question 1:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\int(8x^3+4)\,dx = \frac{8x^4}{4}+4x$ | M1, A1 | M1: $x^n \to x^{n+1}$, so $x^3 \to x^4$ or $4 \to 4x$. A1: Either term with coefficient unsimplified (power must be simplified) — so $\frac{8}{4}x^4$ or $4x$ (accept $4x^1$) |
| $= 2x^4+4x+c$ | A1 | Fully correct simplified solution with $c$. Allow $2x^4+4x+cx^0$ |
---\begin{enumerate}
\item (a) Write down the value of $8 ^ { \frac { 1 } { 3 } }$.\\
(b) Find the value of $8 ^ { - \frac { 2 } { 3 } }$.\\
\item Given that $y = 6 x - \frac { 4 } { x ^ { 2 } } , x \neq 0$,\\
(a) find $\frac { \mathrm { d } y } { \mathrm {~d} x }$,\\
(b) find $\int y \mathrm {~d} x$.\\
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q1}}