| 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 solve equation |
| Difficulty | Moderate -0.8 This is a straightforward C1 completing the square question with standard parts: complete the square (routine algebraic manipulation), state line of symmetry (direct read-off), and solve a quadratic equation using the completed square form. All parts follow textbook procedures with no problem-solving or novel insight required, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | \(f(x) = 2[x^2 - 2x] + 1\) | M1 |
| \(= 2[(x-1)^2 - 1] + 1\) | M1 | |
| \(= 2(x-1)^2 - 1,\) \(a = 2, b = -1, c = -1\) | A2 | |
| (b) | \(x = 1\) | B1 |
| (c) | \(2(x-1)^2 - 1 = 3\) | M1 |
| \((x-1)^2 = 2\) | M1 A1 | |
| \(x = 1 \pm \sqrt{2}\) | M1 A1 | (8) |
(a) | $f(x) = 2[x^2 - 2x] + 1$ | M1 |
| $= 2[(x-1)^2 - 1] + 1$ | M1 |
| $= 2(x-1)^2 - 1,$ $a = 2, b = -1, c = -1$ | A2 |
(b) | $x = 1$ | B1 |
(c) | $2(x-1)^2 - 1 = 3$ | M1 |
| $(x-1)^2 = 2$ | M1 A1 |
| $x = 1 \pm \sqrt{2}$ | M1 A1 | (8)$$\text{f}(x) = 2x^2 - 4x + 1.$$
\begin{enumerate}[label=(\alph*)]
\item Find the values of the constants $a$, $b$ and $c$ such that
$$\text{f}(x) = a(x + b)^2 + c.$$ [4]
\item State the equation of the line of symmetry of the curve $y = \text{f}(x)$. [1]
\item Solve the equation $\text{f}(x) = 3$, giving your answers in exact form. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q6 [8]}}