| 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 -1.3 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 insightâidentifying the vertex, plotting intercepts, using the two-point formula, and finding midpoints are all standard textbook exercises. |
| 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 |
| Answer | Marks | Guidance |
|---|---|---|
| \(9\) | B1 | (1 mark) |
| Answer | Marks |
|---|---|
| Shape | B1 |
| Position of max | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(5\) on \(y\)-axis | B1 | |
| \(-1\) and \(5\) on \(x\)-axis | M1 A1 | (5 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Gradient: \(\frac{8-(-7)}{3-(-2)}\) | M1 A1 | |
| \(y - 8 =\) "gradient" \((x-3)\) leading to \(y = 3x - 1\) | M1 A1 | (4 marks) |
| Where \(y = 0\), \(x = \frac{1}{3}\) | M1 A1ft | (2 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Mid point: \(\left(\frac{-7+8}{2}, \frac{-2+3}{2}\right) = \left(\frac{1}{2}, \frac{1}{2}\right)\), \(k = 1\) | M1 A1 | (2 marks) (14 marks) |
## Question 8:
### Part (a)
$9$ | B1 | (1 mark)
### Part (b)
Shape | B1 |
Position of max | B1 |
### Part (c)
$5$ on $y$-axis | B1 |
$-1$ and $5$ on $x$-axis | M1 A1 | (5 marks)
### Part (d)
Gradient: $\frac{8-(-7)}{3-(-2)}$ | M1 A1 |
$y - 8 =$ "gradient" $(x-3)$ leading to $y = 3x - 1$ | M1 A1 | (4 marks)
Where $y = 0$, $x = \frac{1}{3}$ | M1 A1ft | (2 marks)
### Part (e)
Mid point: $\left(\frac{-7+8}{2}, \frac{-2+3}{2}\right) = \left(\frac{1}{2}, \frac{1}{2}\right)$, $k = 1$ | M1 A1 | (2 marks) **(14 marks)**8.
$$f ( x ) = 9 - ( x - 2 ) ^ { 2 }$$
\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 Q8 [14]}}