| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Quadratic function range and roots analysis |
| Difficulty | Moderate -0.3 This is a straightforward quadratic function question requiring completion of the square (part i) and solving a simple equation (part ii). Both parts use standard techniques with no problem-solving insight needed, making it slightly easier than average for A-level. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02v Inverse and composite functions: graphs and conditions for existence |
9 The function f is defined for all real values of $x$ as $\mathrm { f } ( x ) = c + 8 x - x ^ { 2 }$, where $c$ is a constant.\\
(i) Given that the range of f is $\mathrm { f } ( x ) \leqslant 19$, find the value of $c$.\\
(ii) Given instead that $\mathrm { ff } ( 2 ) = 8$, find the possible values of $c$.
\hfill \mbox{\textit{OCR H240/01 2018 Q9 [7]}}