| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve |linear| = constant |
| Difficulty | Moderate -0.8 Part (a) requires solving |x-2|-3=1, which simplifies to |x-2|=4, a straightforward modulus equation with two cases yielding x=6 or x=-2. Parts (b) and (c) are routine: completing the square for the range and simple function composition. This is a standard textbook exercise testing basic modulus manipulation and function properties with no problem-solving insight required. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02l Modulus function: notation, relations, equations and inequalities1.02v Inverse and composite functions: graphs and conditions for existence |
\begin{enumerate}
\item The function f is defined by
\end{enumerate}
$$\mathrm { f } : x \mapsto | x - 2 | - 3 , x \in \mathbb { R }$$
(a) Solve the equation $\mathrm { f } ( x ) = 1$.
The function g is defined by
$$\mathrm { g } : x \mapsto x ^ { 2 } - 4 x + 11 , x \geq 0$$
(b) Find the range of g .\\
(c) Find $g f ( - 1 )$.\\
\hfill \mbox{\textit{Edexcel C3 Q1 [8]}}