| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Sketch quadratic curve |
| Difficulty | Moderate -0.8 This is a straightforward C1 completing-the-square question with routine sketching. Part (a) requires basic algebraic manipulation to complete the square, part (b) is direct application of the discriminant formula, and part (c) involves finding intercepts and sketching a downward parabola—all standard textbook exercises requiring no problem-solving insight. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points1.02n Sketch curves: simple equations including polynomials |
8.
$$4 x - 5 - x ^ { 2 } = q - ( x + p ) ^ { 2 }$$
where $p$ and $q$ are integers.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $p$ and the value of $q$.
\item Calculate the discriminant of $4 x - 5 - x ^ { 2 }$
\item On the axes on page 17, sketch the curve with equation $y = 4 x - 5 - x ^ { 2 }$ showing clearly the coordinates of any points where the curve crosses the coordinate axes.
\includegraphics[max width=\textwidth, alt={}, center]{089c3b5b-22ab-4fa2-8383-4f30cefa792a-11_1143_1143_260_388}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2012 Q8 [8]}}