| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete square then find vertex/turning point |
| Difficulty | Moderate -0.8 This is a straightforward completing the square question with standard transformations. Part (a) is routine algebraic manipulation, part (b) is direct reading from completed square form, and part (c) applies basic transformation rules that are commonly taught and practiced in C1. The multi-part structure adds length but not conceptual difficulty. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(f(x) = (x-5)^2 - 25 + 17\) | M1 | |
| \(f(x) = (x-5)^2 - 8\) | A2 | |
| (b) \((5, -8)\) | B1 | |
| (c) (i) \((5, -4)\) | B2 | |
| (ii) \(\left(\frac{3}{2}, -8\right)\) | B2 | (8) |
(a) $f(x) = (x-5)^2 - 25 + 17$ | M1 |
$f(x) = (x-5)^2 - 8$ | A2 |
(b) $(5, -8)$ | B1 |
(c) (i) $(5, -4)$ | B2 |
(ii) $\left(\frac{3}{2}, -8\right)$ | B2 | (8)6. $f ( x ) = x ^ { 2 } - 10 x + 17$.
\begin{enumerate}[label=(\alph*)]
\item Express $\mathrm { f } ( x )$ in the form $a ( x + b ) ^ { 2 } + c$.
\item State the coordinates of the minimum point of the curve $y = \mathrm { f } ( x )$.
\item Deduce the coordinates of the minimum point of each of the following curves:
\begin{enumerate}[label=(\roman*)]
\item $\quad y = \mathrm { f } ( x ) + 4$,
\item $y = \mathrm { f } ( 2 x )$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q6 [8]}}