| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Vertex form already given |
| Difficulty | Easy -1.2 This C1 question involves straightforward tasks: identifying the maximum of a parabola in completed square form (immediate from inspection), sketching a quadratic (routine), finding a line equation through two given points (standard formula application), finding x-intercept (simple substitution), and finding k from a midpoint condition (basic coordinate geometry). All parts are direct applications of standard techniques with no problem-solving or insight required, making it easier than average. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.03a Straight lines: equation forms y=mx+c, ax+by+c=0 |
$f(x) = 9 - (x - 2)^2$
\begin{enumerate}[label=(\alph*)]
\item Write down the maximum value of $f(x)$. [1]
\item Sketch the graph of $y = f(x)$, showing the coordinates of the points at which the graph meets the coordinate axes. [5]
\end{enumerate}
The points $A$ and $B$ on the graph of $y = f(x)$ have coordinates $(-2, -7)$ and $(3, 8)$ respectively.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find, in the form $y = mx + c$, an equation of the straight line through $A$ and $B$. [4]
\item Find the coordinates of the point at which the line $AB$ crosses the $x$-axis. [2]
\end{enumerate}
The mid-point of $AB$ lies on the line with equation $y = kx$, where $k$ is a constant.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{4}
\item Find the value of $k$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q19 [14]}}