| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Discriminant for real roots condition |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing routine completing the square (a=1, b=2), basic sketching, and discriminant application. Part (d) requires solving a quadratic inequality but follows directly from discriminant < 0. All techniques are standard textbook exercises with no novel problem-solving required, making it easier than average. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points |
$x^2 + 2x + 3 \equiv (x + a)^2 + b$.
\begin{enumerate}[label=(\alph*)]
\item Find the values of the constants $a$ and $b$. [2]
\item Sketch the graph of $y = x^2 + 2x + 3$, indicating clearly the coordinates of any intersections with the coordinate axes. [3]
\item Find the value of the discriminant of $x^2 + 2x + 3$. Explain how the sign of the discriminant relates to your sketch in part (b). [2]
\end{enumerate}
The equation $x^2 + kx + 3 = 0$, where $k$ is a constant, has no real roots.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find the set of possible values of $k$, giving your answer in surd form. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q10 [11]}}