| Exam Board | OCR |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Range restriction with excluded interval (linear/mixed denominator) |
| Difficulty | Challenging +1.2 This is a Further Pure 2 question requiring polynomial division to find oblique asymptote, vertical asymptote identification, and range analysis via completing the square or calculus. While systematic, it demands multiple techniques and the range restriction proof requires algebraic manipulation beyond routine A-level, placing it moderately above average difficulty. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02n Sketch curves: simple equations including polynomials |
5 (i) Find the equations of the asymptotes of the curve with equation
$$y = \frac { x ^ { 2 } + 3 x + 3 } { x + 2 }$$
(ii) Show that $y$ cannot take values between - 3 and 1 .
\hfill \mbox{\textit{OCR FP2 Q5 [8]}}