| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find derivative after algebraic simplification (fractional/mixed powers) |
| Difficulty | Easy -1.3 This is a straightforward C1 question requiring basic index law manipulation to simplify algebraic fractions, followed by routine term-by-term differentiation of a polynomial. Both parts involve standard procedures with no problem-solving or conceptual challenges—simpler than average A-level questions. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(2x^{3/2}\) or \(p = \frac{3}{2}\) | B1 | Not \(2x\sqrt{x}\) |
| \(-x\) or \(-x^1\) or \(q = 1\) | B1 | (2 marks total) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{dy}{dx} = 20x^3 + 2 \times \frac{3}{2}x^{1/2} - 1\) | M1 | For attempt to differentiate \(x^n \to x^{n-1}\) for any of the 4 terms |
| \(= 20x^3 + 3x^{1/2} - 1\) | A1, A1ft, A1ft | 1st A1 for \(20x^3\); 2nd A1ft for \(3x^{1/2}\) or \(3\sqrt{x}\), follow through on \(p\) but must be differentiating \(2x^p\) where \(p\) is a fraction; 3rd A1ft for \(-1\) (not unsimplified \(-x^0\)) (4 marks total) |
# Question 6:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2x^{3/2}$ or $p = \frac{3}{2}$ | B1 | Not $2x\sqrt{x}$ |
| $-x$ or $-x^1$ or $q = 1$ | B1 | (2 marks total) |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{dy}{dx} = 20x^3 + 2 \times \frac{3}{2}x^{1/2} - 1$ | M1 | For attempt to differentiate $x^n \to x^{n-1}$ for any of the 4 terms |
| $= 20x^3 + 3x^{1/2} - 1$ | A1, A1ft, A1ft | 1st A1 for $20x^3$; 2nd A1ft for $3x^{1/2}$ or $3\sqrt{x}$, follow through on $p$ but must be differentiating $2x^p$ where $p$ is a fraction; 3rd A1ft for $-1$ (not unsimplified $-x^0$) (4 marks total) |
---\begin{enumerate}
\item Given that $\frac { 2 x ^ { 2 } - x ^ { \frac { 3 } { 2 } } } { \sqrt { } x }$ can be written in the form $2 x ^ { p } - x ^ { q }$,\\
(a) write down the value of $p$ and the value of $q$.
\end{enumerate}
Given that $y = 5 x ^ { 4 } - 3 + \frac { 2 x ^ { 2 } - x ^ { \frac { 3 } { 2 } } } { \sqrt { } x }$,\\
(b) find $\frac { \mathrm { d } y } { \mathrm {~d} x }$, simplifying the coefficient of each term.\\
\hfill \mbox{\textit{Edexcel C1 2009 Q6 [6]}}