| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch with inequalities or regions |
| Difficulty | Standard +0.3 This is a straightforward multi-part question testing standard techniques: factorising a cubic (with one factor given), sketching from factorised form, reading inequalities from the sketch, and applying a horizontal stretch transformation. All parts are routine A-level procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
6 The cubic polynomial $\mathrm { f } ( x )$ is defined by $\mathrm { f } ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } + 2 x + 3$.\\
(i) Given that ( $x - 3$ ) is a factor of $\mathrm { f } ( x )$, express $\mathrm { f } ( x )$ in a fully factorised form.\\
(ii) Sketch the graph of $y = \mathrm { f } ( x )$, indicating the coordinates of any points of intersection with the axes.\\
(iii) Solve the inequality $\mathrm { f } ( x ) < 0$, giving your answer in set notation.\\
(iv) The graph of $y = \mathrm { f } ( x )$ is transformed by a stretch parallel to the $x$-axis, scale factor $\frac { 1 } { 2 }$. Find the equation of the transformed graph.
\hfill \mbox{\textit{OCR H240/01 2018 Q6 [9]}}