| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Polynomial intersection with algebra |
| Difficulty | Moderate -0.3 This is a straightforward C1 curve sketching question requiring basic polynomial expansion, factorization to find roots, and solving a cubic equation. While part (b) involves solving x²(x-2) = x(6-x) leading to a cubic, it factors nicely and requires only standard algebraic manipulation. The sketching is routine (finding intercepts and basic shape). Slightly below average difficulty due to being multi-step but using only fundamental techniques. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02p Interpret algebraic solutions: graphically1.02q Use intersection points: of graphs to solve equations |
\begin{enumerate}[label=(\alph*)]
\item On the same axes sketch the graphs of the curves with equations
\begin{enumerate}[label=(\roman*)]
\item $y = x^2(x - 2)$, [3]
\item $y = x(6 - x)$, [3]
\end{enumerate}
and indicate on your sketches the coordinates of all the points where the curves cross the $x$-axis.
\item Use algebra to find the coordinates of the points where the graphs intersect. [7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q10 [13]}}