| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch with inequalities or regions |
| Difficulty | Moderate -0.8 This is a straightforward C1 question requiring basic curve sketching of a translated parabola and a linear function, followed by solving a quadratic inequality using the graphical method. All techniques are routine: completing the square is already done, finding intercepts is mechanical, and reading off the inequality solution from the sketch requires no novel insight. Easier than average but not trivial due to the multi-step nature. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02m Graphs of functions: difference between plotting and sketching1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks | Guidance |
|---|---|---|
| (a) [Graph showing line \(y = 2x - 1\)] | B2 | |
| [Graph showing parabola \(y = (x - 2)^2\) with vertex at \((2, 0)\), point \((0, 4)\) marked] | B3 | |
| (b) \(x^2 - 4x + 4 \geq 2x - 1\) | M1 | |
| \(x^2 - 6x + 5 \geq 0\) | M1 | |
| \((x - 1)(x - 5) \geq 0\) | ||
| \(x \leq 1\) or \(x \geq 5\) | A1 | (8) |
**(a)** [Graph showing line $y = 2x - 1$] | B2 |
[Graph showing parabola $y = (x - 2)^2$ with vertex at $(2, 0)$, point $(0, 4)$ marked] | B3 |
**(b)** $x^2 - 4x + 4 \geq 2x - 1$ | M1 |
$x^2 - 6x + 5 \geq 0$ | M1 |
$(x - 1)(x - 5) \geq 0$ |
$x \leq 1$ or $x \geq 5$ | A1 | (8)\begin{enumerate}[label=(\alph*)]
\item Sketch on the same diagram the curve with equation $y = (x - 2)^2$ and the straight line with equation $y = 2x - 1$.
Label on your sketch the coordinates of any points where each graph meets the coordinate axes. [5]
\item Find the set of values of $x$ for which
$$(x - 2)^2 > 2x - 1.$$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q6 [8]}}