| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Polynomial with line intersection |
| Difficulty | Easy -1.2 This is a straightforward C1 question involving basic curve sketching of a quadratic in completed square form, finding a line equation from two points, and simple coordinate geometry. All parts require only routine procedures with no problem-solving insight—reading the maximum from completed square form, plotting intercepts, using the two-point formula for a line, and finding midpoints. Significantly easier than average A-level questions. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02n Sketch curves: simple equations including polynomials1.03a Straight lines: equation forms y=mx+c, ax+by+c=0 |
$f(x) = 9 – (x – 2)^2$
(a) Write down the maximum value of $f(x)$.
(1)
(b) Sketch the graph of $y = f(x)$, showing the coordinates of the points at which the graph meets the coordinate axes.
(5)
The points $A$ and $B$ on the graph of $y = f(x)$ have coordinates $(-2, -7)$ and $(3, 8)$ respectively.
(c) Find, in the form $y = mx + c$, an equation of the straight line through $A$ and $B$.
(4)
(d) Find the coordinates of the point at which the line $AB$ crosses the x-axis.
(2)
The mid-point of $AB$ lies on the line with equation $y = kx$, where $k$ is a constant.
(e) Find the value of $k$.
(2)6.
$$f ( x ) = 9 - ( x - 2 ) ^ { 2 }$$
\begin{enumerate}[label=(\alph*)]
\item Write down the maximum value of $\mathrm { f } ( x )$.
\item Sketch the graph of $y = \mathrm { f } ( x )$, showing the coordinates of the points at which the graph meets the coordinate axes.
The points $A$ and $B$ on the graph of $y = \mathrm { f } ( x )$ have coordinates $( - 2 , - 7 )$ and $( 3,8 )$ respectively.
\item Find, in the form $y = m x + c$, an equation of the straight line through $A$ and $B$.
\item Find the coordinates of the point at which the line $A B$ crosses the $x$-axis.
The mid-point of $A B$ lies on the line with equation $y = k x$, where $k$ is a constant.
\item Find the value of $k$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q6 [14]}}