| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Sketch quadratic curve |
| Difficulty | Moderate -0.3 This is a standard C1 completing the square question with routine sketching and solving. Part (a) is textbook completing the square, part (b) requires identifying vertex and y-intercept (straightforward), and part (c) involves solving a quadratic using the completed square form. While part (c) requires manipulating surds to reach the specified form, all techniques are standard C1 procedures with no novel problem-solving required. Slightly easier than average due to being highly procedural. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown |
Given that
$$f(x) = x^2 - 6x + 18, \quad x \geq 0,$$
\begin{enumerate}[label=(\alph*)]
\item express $f(x)$ in the form $(x - a)^2 + b$, where $a$ and $b$ are integers. [3]
\end{enumerate}
The curve $C$ with equation $y = f(x)$, $x \geq 0$, meets the $y$-axis at $P$ and has a minimum point at $Q$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Sketch the graph of $C$, showing the coordinates of $P$ and $Q$. [4]
\end{enumerate}
The line $y = 41$ meets $C$ at the point $R$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the $x$-coordinate of $R$, giving your answer in the form $p + q\sqrt{2}$, where $p$ and $q$ are integers. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q10 [12]}}