| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Sketch quadratic curve |
| Difficulty | Moderate -0.8 This is a straightforward C1 quadratic question requiring factorization to find intercepts and sketching a parabola. The steps are routine: set x=0 for y-intercept, solve quadratic equation for x-intercepts, identify the parabola opens downward. No problem-solving insight needed, just standard technique application, making it easier than average. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks |
|---|---|
| \(y\)-intercept: \(f(0) = 15\), giving \((0, 15)\) | B1 |
| \(15 - 7x - 2x^2 = 0 \Rightarrow (5+2x)(3-x)=0\) | M1 |
| \(x = -\frac{5}{2}\) or \(x = 3\), giving \(\left(-\frac{5}{2}, 0\right)\) and \((3, 0)\) | A1 |
| Answer | Marks |
|---|---|
| Correct shape (inverted \(\cup\) shaped parabola) | B1 |
| Correct intercepts marked on axes | B1 |
# Question 6:
## Part (a):
| $y$-intercept: $f(0) = 15$, giving $(0, 15)$ | B1 | |
| $15 - 7x - 2x^2 = 0 \Rightarrow (5+2x)(3-x)=0$ | M1 | |
| $x = -\frac{5}{2}$ or $x = 3$, giving $\left(-\frac{5}{2}, 0\right)$ and $(3, 0)$ | A1 | |
## Part (b):
| Correct shape (inverted $\cup$ shaped parabola) | B1 | |
| Correct intercepts marked on axes | B1 | |
---6. Given that $\mathrm { f } ( x ) = 15 - 7 x - 2 x ^ { 2 }$,
\begin{enumerate}[label=(\alph*)]
\item find the coordinates of all points at which the graph of $y = \mathrm { f } ( x )$ crosses the coordinate axes.
\item Sketch the graph of $y = \mathrm { f } ( x )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q6 [5]}}