| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Identify transformation from equations |
| Difficulty | Moderate -0.8 This is a straightforward C1 question requiring basic differentiation of a quadratic and identification of a horizontal translation. Part (a) involves differentiating (x-a)² and equating coefficients, while part (b) simply asks for the transformation description. Both parts are routine applications of standard techniques with no problem-solving required. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(y = x^2 - 2ax + a^2\) | B1 | |
| \(\frac{dy}{dx} = 2x - 2a = 2x - 6\) | M1 A1 | |
| Therefore \(a = 3\) | A1 | |
| (b) Translation by 3 units in the negative \(x\)-direction | B2 | (6) |
**(a)** $y = x^2 - 2ax + a^2$ | B1 |
$\frac{dy}{dx} = 2x - 2a = 2x - 6$ | M1 A1 |
Therefore $a = 3$ | A1 |
**(b)** Translation by 3 units in the negative $x$-direction | B2 | (6)\begin{enumerate}
\item The curve $C$ has the equation $y = ( x - a ) ^ { 2 }$ where $a$ is a constant.
\end{enumerate}
Given that
$$\frac { \mathrm { d } y } { \mathrm { dx } } = 2 x - 6 ,$$
(a) find the value of $a$,\\
(b) describe fully a single transformation that would map $C$ onto the graph of $y = x ^ { 2 }$.\\
\hfill \mbox{\textit{Edexcel C1 Q3 [6]}}