| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Expand from factored form |
| Difficulty | Moderate -0.8 This is a straightforward C1 question requiring basic factorisation (taking out common factor x, then factorising a quadratic) and sketching a cubic curve using the roots. The techniques are routine and the question follows a standard template with no problem-solving insight required, making it easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(= x(4 - 3x - x^2) = x(1 - x)(4 + x)\) | M1, M1 A1 | |
| (b) Sketch showing: roots at \((-4, 0)\), \((0, 0)\), \((1, 0)\); correct shape of cubic | B3 | (6 marks) |
**(a)** $= x(4 - 3x - x^2) = x(1 - x)(4 + x)$ | M1, M1 A1 |
**(b)** Sketch showing: roots at $(-4, 0)$, $(0, 0)$, $(1, 0)$; correct shape of cubic | B3 | (6 marks)5.
$$f ( x ) = 4 x - 3 x ^ { 2 } - x ^ { 3 }$$
\begin{enumerate}[label=(\alph*)]
\item Fully factorise $4 x - 3 x ^ { 2 } - x ^ { 3 }$.
\item Sketch the curve $y = \mathrm { f } ( x )$, showing the coordinates of any points of intersection with the coordinate axes.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q5 [6]}}